rabIm;)ens

Single Point Incremental Forming

João Luís Padrão de Brito Câmara

Dissertação para obtenção do Grau de Mestre em

Engenharia Mecânica

Júri

Presidente: Prof. Rui Manuel dos Santos Oliveira Baptista

Orientador: Prof. Paulo António Firme Martins

Co-orientador: Profª. Maria Beatriz Cipriano de Jesus Silva

Vogal: Prof. Luís Manuel Mendonça Alves

Setembro de 2009

I

Resumo

Hoje em dia existe uma necessidade crescente de desenvolvimento de técnicas de

produção que se adaptem à introdução contínua de novos produtos no mercado. Para

suprir tais necessidades o processo de estampagem incremental tem sido

recentemente objecto de estudo e a sua aplicabilidade é agora consensual no que diz

respeito à produção de pequenas séries e de protótipos em componentes de chapa

metálica. O processo desenvolve-se à temperatura ambiente e requer um centro de

maquinagem CNC, uma ferramenta de ponta esférica e uma estrutura simples para

suporte e fixação da chapa a enformar.

Esta tese proporciona uma melhor compreensão da influência do raio da ferramenta

na aparecimento da fractura com ou sem ocorrência prévia de estricção, que é um

assunto actual e internacionalmente discutido no âmbito dos mecanismos de

enformabilidade do processo em causa. É também estudada a influência do raio de

canto nas peças realizadas por estampagem incremental e foi criado, neste âmbito, um

novo teste com o objectivo de se obterem valores de tensão num larga área do

primeiro quadrante do espaço das tensões principais e consequentemente reduzir o

número final de testes. Foram confirmados os anteriores resultados de Skjøedt [1] que

mostram que se deve utilizar a FFL para analisar os limites formabilidade de um

determinado material sujeito a uma estratégia de multi-passagem em estampagem

incremental. Foi também confirmada a diferença entre o AA1050-H111 e o mesmo

material tratado termicamente, no que diz respeito à enformabilidade.

Finalmente, como uma continuação lógica do trabalho experimental realizado, esta

tese abordou estratégias multi-passagem em estampagem incremental com o

objectivo de substituir os processos tradicionais. Assim sendo, a principal contribuição

desta tese foi o fabrico com sucesso de uma geometria rectangular de paredes planas

e a produção de um protótipo para uma aplicação doméstica.

Keywords: Estampagem incremental, Protótipo, Enformabilidade, Multi-passagem.

II

Abstract

Nowadays there is an increasingly demanding need for the development of agile

manufacturing techniques that can easily be adaptable to a constant introduction of

new products in the market. Single point incremental forming (SPIF) is a new

innovative and feasible solution for the rapid prototyping and the manufacturing of

small batch sheet parts. The process is carried out at room temperature (cold forming)

and requires a CNC machining centre, a spherical tip tool and a simple support to fix

the sheet being formed.

This thesis provides a better understanding of the influence of the tool radius in the

occurrence of fracture without previous necking or fracture following previous necking

as in case of conventional stamping, which is a matter of ongoing international

discussion around the formability mechanism of SPIF. It is also analyzed the influence

of the corner radius in SPIF made parts and a new pyramid test was created in order to

get strain measurements in a large area of the first quadrant of the principal strain

space and as consequence to reduce the overall number of tests. The previous results

of Skjøedt [1] showing that the fracture forming limit determined under simple

(monotonic) strain paths can be applied to check formability limits in multi-stage SPIF

were confirmed and the difference in formability between the AA1050-H111 and the

same material annealed was checked.

Finally, as a logical continuation of the experimental work previously performed, the

thesis was extended to multi-stage SPIF with the objective of replacing conventional

fabrication procedures by new manufacturing routes based on single point

incremental forming. The main contribution of this thesis to multi-stage SPIF was the

successful manufacturing of a pyramid with vertical walls and the production of a

prototype part for a home appliance application.

Keywords: Single Point Incremental Forming, Prototype, Formability, Multi-Stage.

III

Acknowledgements

First, I would like to express my thankfulness to my supervisor, Professor Paulo Martins

for his invaluable scientific advice, discussions and suggestions that provided a

stimulating guidance throughout this work and also for the opportunity that was given

to me to develop my research work at the Danmarks Tekniske Universitet (DTU).

I am also grateful to my co-supervisor, Professor Beatriz Silva, for her close guidance

and comments on my thesis.

Concerning the experimental work performed at the DTU, I am truly grateful to

Professor Niels Bay for his hospitality, for the opportunity to use the experimental

facilities and for his valuable comments on my thesis and his influence to my work. I

wish to thank MSc. Peter Søe Nielsen for his continuous help and assistance during my

research work.

I would like to acknowledge MSc. Valentino Cristino for his help in the experimental

work at the Instituto Superior Técnico (IST).

I also would like to thank Tomas Ladecky for his friendship, company and stimulating

discussions about SPIF.

I want to express my special gratitude Susana for her encouragement and support.

Finally, I would like to address my appreciation to my parents Fernando Brito Câmara

and Teresa Brito Câmara and to my sister for the love and unfailing support during all

my studies. I cannot forget to acknowledge the rest of my family for the unconditional

support and to all my friends, in special Marco Jorge and Luís Barreira for the

continuous help and friendship.

Deep in my heart, I dedicated this thesis to my parents, my sister and Susana.

IV

Contents

Resumo .……………………………………………………………………………………………………………………. I

Abstract ……………………………………………………………………………………………….……………….….. II

Acknowledgements ……………………………………………………………………………………………….….III

Contents ……………………………………………………………………………………………………………………IV

List of Tables ………………………………………………………………………………………………………….…VII

List of Figures………………………………………………………………………………………………………..….VIII

List of Symbols…………………………………………………………………………………………………………….XI

1 Introduction ........................................................................................................... 1

1.1 Organization of the dissertation ............................................................................ 1

1.2 References ............................................................................................................. 2

2 State-of-the-Art ..................................................................................................... 3

2.1 Sheet Metal Forming Processes with Incremental Approach ............................... 3

2.1.1 Hamering .................................................................................................... 3

2.1.2 Multi-point forming ................................................................................... 3

2.1.3 Shot Peen Forming ..................................................................................... 4

2.1.4 Laser Forming Process ................................................................................ 4

2.1.5 Water Jet Forming ...................................................................................... 5

2.1.6 Spinning ...................................................................................................... 5

2.1.7 Incremental Sheet Forming Process .......................................................... 6

2.2 Single Point Incremental Forming ......................................................................... 7

2.3 Incremental Forming with Counter Tool ............................................................... 8

2.4 Two Point Incremental Forming ............................................................................ 9

2.4.1 Two Point Incremental Forming (partial die) ............................................. 9

2.4.2 Two Point Incremental Forming (full die)................................................... 9

2.5 Multistage Forming ............................................................................................. 10

2.6 Applications of Incremental Sheet Forming Process ........................................... 11

2.7 Others materials .................................................................................................. 12

2.8 New Incremental Forming Process Configurations ............................................. 13

2.9 References ........................................................................................................... 14

V

3 Theoretical background ....................................................................................... 17

3.1 State of stress and strain ..................................................................................... 19

3.2 Friction at the tool–sheet contact interface ....................................................... 20

3.3 The inclined wall adjacent to the forming tool ................................................... 21

3.4 Thinning at the corner radius .............................................................................. 22

3.5 Crack propagation in rotational symmetric SPIF parts ........................................ 22

3.6 Forming limits ...................................................................................................... 23

3.7 References ........................................................................................................... 25

4 Experimental work............................................................................................... 26

4.1 Material characterization .................................................................................... 26

4.2 Forming limits ...................................................................................................... 29

4.3 Experimental Setup ............................................................................................. 30

4.3.1 CNC Machine ............................................................................................ 30

4.3.2 Forming tools ............................................................................................ 31

4.3.3 SPIF clamping system ............................................................................... 32

4.3.4 Lubrication Conditions .............................................................................. 32

4.4 Plan of experiments ............................................................................................. 33

4.5 CAD/CAM design development ........................................................................... 35

4.6 References ........................................................................................................... 39

5 Results and Discussion ......................................................................................... 40

5.1 Influence of tool diameter in Formability ........................................................... 40

5.1.1 Conical Shape............................................................................................ 40

5.1.2 Pyramidal Shape ....................................................................................... 43

5.2 Influence of Heat Treatment in Formability ........................................................ 47

5.3 Influence of different corner radius in the formability . ..................................... 48

6 Multi-stage SPIF ................................................................................................... 51

6.1 Conical shape ......................................................................................................... 53

6.1.1 Improvement of the cone with vertical walls .......................................... 55

6.2 Pyramid with vertical walls .................................................................................. 59

6.3 Conclusion ........................................................................................................... 63

6.4 References ........................................................................................................... 63

7 Prototype Development ...................................................................................... 64

VI

7.1 Thermoforming mould of sanitary bathtub for a shower ................................... 64

7.2 Experimental setup .............................................................................................. 65

7.3 Investigated strategies ........................................................................................ 65

7.3.1 Stripes and hollow .................................................................................... 66

7.3.2 Top area .................................................................................................... 66

7.3.3 Wall ........................................................................................................... 69

7.4 Formability analysis ............................................................................................. 70

7.5 Conclusion ........................................................................................................... 73

7.6 References ........................................................................................................... 73

8 Conclusions and future work ............................................................................... 74

VII

List of Tables

Table 3.1 - States of stress and strain in SPIF and conventional stamping ................................ 20

Table 4.1 - Tensile tests result for material AA 1050-H111 ........................................................ 28

Table 4.2 - Machine Technical Specifications.............................................................................. 30

Table 4.3 - Plan of experiments ................................................................................................... 34

Table 4.4 - Process conditions ..................................................................................................... 37

Table 5.1 - Influence of the 4 Different Corner Radius in the Fracture Depth of the Pyramidal

parts. ........................................................................................................................................... 49

Table 6.1 - Plan of experiment .................................................................................................... 56

Table 7.1 - Top area and walls strategies. ................................................................................... 67

Table 7.2 - Global prototype strategy. ........................................................................................ 70

VIII

List of Figures

Figure 2.1 - Incremental hamering process. ................................................................................. 3

Figure 2.2 - Tool for Multi-point Forming. .................................................................................... 4

Figure 2.3 - Laser Forming. ............................................................................................................ 5

Figure 2.4 - spinning variants. ....................................................................................................... 5

Figure 2.5 - Deformation of element in shear formed cone. ........................................................ 6

Figure 2.6 - Schematic representation of the Incremental Backward Bulge process. .................. 6

Figure 2.7 - Incremental Stretch Expanding process scheme. ...................................................... 7

Figure 2.8 - Schematic representation of a cross section view of SPIF process. The tool rotates

and could perform a round or helical path. .................................................................................. 7

Figure 2.9 - Schematic representation of Incremental Forming with Counter Tool. .................... 8

Figure 2.10 - TPIF (partial die) ....................................................................................................... 9

Figure 2.11 - TPIF (full die) ............................................................................................................ 9

Figure 2.12 - SPIF Multistage strategy. ........................................................................................ 10

Figure 2.14 - Non-rotational part. ............................................................................................... 11

Figure 2.13 - Five stage forming. ................................................................................................. 11

Figure 2.15 - Reflexive surface for headlights. ............................................................................ 11

Figure 2.16 - Automotive heat/vibration shield. ......................................................................... 12

Figure 2. 17 - Silencer housing for trucks. ................................................................................... 12

Figure 2.18 - Medical applications of ISMF. ................................................................................ 12

Figure 2.19 - PVC part made by SPIF process. ............................................................................. 13

Figure 2.20 - Incremental forming using cylindrical rollers......................................................... 13

Figure 3.1 - Schematic representation of local contact area between the tool and the sheet and

identification of the basic modes of deformation of SPIF. ......................................................... 18

Figure 3.2 - Membrane analysis of SPIF. Schematic representation of shell element and details

showing the acting stresses in the meridional, circumferential and thickness directions. ........ 19

Figure 3. 3 - Schematic representation of the stress field in a radial slice through the

instantaneous, small plastic zone. .............................................................................................. 21

Figure 3.4 - Crack propagation in SPIF ........................................................................................ 23

Figure 3.5 - Schematic representation of the forming limits of SPIF against those of ............... 24

Figure 4.2 - Plastic rulers ............................................................................................................. 26

Figure 4.1 - Grid of initial circles .................................................................................................. 26

Figure 4.3 - Thickness measurements of SPIF made part. .......................................................... 27

Figure 4.4 - Fracture depth measurements. ............................................................................... 27

Figure 4.5 - Testing machine ....................................................................................................... 28

Figure 4.6 - Tensile and Biaxial bulge test specimens. ................................................................ 28

Figure 4.7 - Experimental measurement of fracture thickness in tensile and bulge specimens. 29

Figure 4.8 - Experimental measurement of fracture width in tensile and bulge specimens. ..... 29

Figure 4.9 - Fracture Forming Limit Diagram containing the FLC and the FFL. ........................... 30

Figure 4.10 – CNC machine center. ............................................................................................. 30

Figure 4.11 – Utilized forming tools. ........................................................................................... 31

Figure 4.12 - Polishing device Rotwerk EDM 300 DS. ................................................................. 31

Figure 4.13 - SPIF clamping tools. ............................................................................................... 32

Figure 4.14 - Wear on a part made from AA1050-O. .................................................................. 32

IX

Figure 4.15 - Lubrication wear test. ............................................................................................ 33

Figure 4.16 - Parts manufactured by one-step method with varying drawing angle. ................ 35

Figure 4.17 - Wall profile. ............................................................................................................ 36

Figure 4.18 – Process conditions. ................................................................................................ 36

Figure 4.19 - Angular speed. ....................................................................................................... 37

Figure 4.20 - Surface scaring as a result of step down tool path. ............................................... 38

Figure 4.21 - Helical tool path removed surface scaring. ............................................................ 38

Figure 5.1 - Influence of the Tool Diameter in the Fracture Depth obtained for the Conical

shape. .......................................................................................................................................... 41

Figure 5.2 - Fracture Forming Limit Diagram containing the FLC and the FFL for two conical SPIF

parts made with 8mm and with 12mm diameter tools. ............................................................. 41

Figure 5.3 - Fracture Forming Limit Diagram containing the FLC and the FFL for three conical

SPIF parts made with 20mm, 30mm and with 50mm diameter tools. ....................................... 42

Figure 5.4 - Fracture Forming Limit Diagram containing the FLC and the FFL for a conical SPIF

parts made with 50 mm diameter tools. .................................................................................... 43

Figure 5.5 - Influence of the Tool Diameter in the Fracture Depth obtained for the Pyramidal

shape. .......................................................................................................................................... 44

Figure 5.6 - Influence of the Tool Diameter in the Thickness Evolution of the wall in a Pyramidal

shape SPIF part – Measurement made in a wall Parallel to the Rolling Direction. ..................... 44

Figure 5.7 - Influence of the Tool Diameter in the Thickness Evolution of the wall in a Pyramidal

shape SPIF part – Measurement made in a wall Parallel to the Rolling Direction. ..................... 45

Figure 5.8 - Fracture Forming Limit Diagram containing the FLC and the FFL for two pyramidal

SPIF parts made with 8mm and with 12mm diameter tools. ..................................................... 45

Figure 5.9 - Fracture Forming Limit Diagram containing the FLC and the FFL for two pyramidal

SPIF parts made with 20 mm, 30 mm and 50 mm diameter tools. ............................................ 46

Figure 5.10 - Fracture Forming Limit Diagram containing the FLC and the FFL for a pyramidal

SPIF part made with 50 mm diameter tool. ................................................................................ 46

Figure 5.11 - Influence of the Heat Treatment in the Fracture Depth. ....................................... 47

Figure 5.12 - Fracture Forming Limit Diagram containing the FLC, the FFL and the fracture

points obtained from a pyramidal SPIF part made of AA1050-H111 and from a pyramidal SPIF

part made of the same material but annealed. Both were made with 12mm diameter tool. ... 48

Figure 5.13 - Fracture Forming Limit Diagram containing the FLC and the FFL obtained for a

pyramidal SPIF part in which the 4 corners have different diameters; made with 8mm diameter

tool. ............................................................................................................................................. 50

Figure 6.1 - Schematic representation of the sine law. .............................................................. 51

Figure 6.3 - Five stage forming . .................................................................................................. 51

Figure 6.2 - Cylinder with vertical walls . .................................................................................... 51

Figure 6.4 - Thickness distribution (Legend displays thickness in mm) . .................................... 52

Figure 6.5 - Schematic representation of vertical wall created by the whole side of the tool [4].

..................................................................................................................................................... 52

Figure 6.6 - Tool paths of the four stages utilized to produce a cone with vertical walls. ......... 53

Figure 6.7 - Status of residual cone during the manufacturing of the cone with vertical walls. 53

Figure 6.8 - FFLD for final stage of cone with residual cone ....................................................... 54

Figure 6.9 - Cone with vertical walls and without residual cone . .............................................. 55

Figure 6.10 - Scheme of the tool paths for cone with vertical walls and with flat bottom. ....... 55

X

Figure 6.11 - CAM tool paths for the cone with vertical walls and without residual cone (stage

by stage). ..................................................................................................................................... 55

Figure 6.12 - Four stages of cone with vertical walls and flat bottom. ....................................... 56

Figure 6.13 - FFLD for 1st stage of cone with vertical walls without residual cone. .................... 57

Figure 6.14 - FFLD for 2nd stage of cone with vertical walls without residual cone. ................. 58

Figure 6.15 - FFLD for 3rd stage of cone with vertical walls without residual cone. .................. 58

Figure 6.16 - FFLD for 4th stage of cone with vertical walls without residual cone. ................... 59

Figure 6.17 - First and second tool path of pyramid with vertical walls. .................................... 60

Figure 6.18 - Helical tool path for the third forming step of the pyramid with vertical walls. ... 60

Figure 6.19 - Tool paths for 4th (a), 5th (b) and 6th (c) forming step. ............................................ 61

Figure 6.20 - Scheme of utilized tool paths (in black for D tool movement, in red for U tool

movement and in yellow for H tool movement) for the pyramid with vertical walls. ............... 61

Figure 6.21 - Pyramid with 22mm long vertical walls. ................................................................ 61

Figure 6.22 - Springback .............................................................................................................. 62

Figure 6.23 - FFLD with experimental strains. ............................................................................. 62

Figure 7.1 - Thermoforming process scheme. ............................................................................ 64

Figure 7.2 - Moulds for thermoforming of a shower baths manufactured by casting technology.

..................................................................................................................................................... 65

Figure 7.3 - Geometric characteristics shown as tool paths of the prototype part. ................... 65

Figure 7.4 - Stripes and hollow manufacturing. .......................................................................... 66

Figure 7.5 - Backing plate for prototype part. ............................................................................. 66

Figure 7.6 - Strategy #1 and #2 for shaped corner and wall. ...................................................... 67

Figure 7.7 - Strategy #3 showing the fracture. ............................................................................ 68

Figure 7.8 - Gradually increased corner made according to the strategy # 4. ............................ 68

Figure 7.9 - Final shape of the top area and wall. ....................................................................... 68

Figure 7.10 - DDHU tool paths strategy for the wall. .................................................................. 69

Figure 7.11 - Tool paths outlines ................................................................................................. 69

Figure 7.12 - Final prototype part. .............................................................................................. 70

Figure 7.13 - Prototype of aluminum mould with different corners signed (corner B is identical

with the opposite corner). .......................................................................................................... 71

Figure 7.14 - FFLD containing the FLC and the FFL for corner A of the prototype of aluminum

mould. ......................................................................................................................................... 71

Figure 7.15 - FFLD containing the FLC and the FFL for corner B of the prototype of aluminum

mould. ......................................................................................................................................... 72

Figure 7.16 - FFLD containing the FLC and the FFL for corner C of the prototype of aluminum

mould. ......................................................................................................................................... 72

XI

List of Symbols

Latin Symbols

A elongation at break C integration constant DC critical value of damage D0 base diameter of a truncated cone E Young Modulus f feed Rate F bend test maximum load FLD0 limiting major strain at fracture when the minor strain is equal to

zero FLD0 incre FLD0 point for incremental forming H height of a truncated cone UT toughness Z depth of a part emajor major engineering strain eminor minor engineering strain h height of a part K strength coefficient n strain hardening coefficient r radial coordinate r1 radius of curvature of meridian at the element (radius of the SPIF

tool) r2 radius of the element rpunch punch radius rtool radius of the tool t thickness of the sheet t0 initial thickness of the sheet tf final thickness of the sheet

Greek Symbols

� drawing angle (sine law) β y-intercept of the linear relationship between the initial thickness and the

maximum drawing angle ε strain ε� effective strain ε� circumferential strain ε� meridional strain ε� thickness strain μ friction coefficient μ� meridional component of the friction coefficient μ� circumferential component of the friction coefficient θ circumferential direction σ stress [MPa] σ effective stress σ� circumferential stress

XII

σ� meridional stress σ� thickness stress σ� yield stress σ� hydrostatic stress σ �� ultimate Strength ϕ meridional direction ψ drawing angle between the inclined wall and the initial flat configuration of the sheet ψ� designed drawing angle ψ��� maximum drawing angle

Abbreviations (Acronyms)

2D – Two Dimensional

3D – Three Dimensional

3DP – Three Dimensional Printing

CAD – Computer Assisted Design

CAM – Computer Assisted Manufacturing

CGA - Circle Grid Analysis

CNC – Computer Numerical Control

DIN – Deutshes Institut für Normung (German Institute for Standardization)

DTU – Danmarks Tekniske Universitet

EN - European Standard

FE – Finite Element

FEM – Finite Element Method

FFL – Fracture Forming Limit Line

FFLD - Fracture Forming Limit Diagram

FLA – “Fracture Line of Attack”

FLC – Forming Limit Curve

FLD - Forming Limit Diagram

HRc – Rockwell C Hardeness

HSS – High Strength Steel

IFWCT – Incremental Forming With Counter Tool

ISMF – Incremental Sheet Metal Forming

ISO – International Organization for Standardization

IST – Instituto Superior Técnico

MPF – Multi-point Forming

MSc - Master of Science

NP – Norma Portuguesa (Portuguese Standard)

PP – Polypropylene PVC – Polyvinyl Chloride

RP – Rapid Prototyping

SPIF – Single Point Incremental Forming

TPIF – Two Point Incremental Forming

1

1 Introduction

Conventional sheet metal forming processes require large batch sizes (mass

production) because these processes require large energy costs and very high

investment in equipment and tooling (i.e. machine-tools, moulds, dies, jigs and

fixtures). Single Point Incremental Forming (SPIF) is a new metal forming process with

a high potential economic payoff for rapid prototyping applications suitable for flexible

and small quantity production fulfilling this gap in metal forming processes.

This thesis is aimed to get a better understanding of the influence of the tool radius in

the occurrence of fracture without previous necking or fracture following previous

necking as in case of conventional stamping, which is a matter of ongoing international

discussion around the formability mechanism of SPIF.

Other important objectives of this thesis are: to analyze the influence of the corner

radius in the overall formability of SPIF parts and to enhance the conventional pyramid

test in order to get strain measurements in a large area of the first quadrant of the

principal strain space. The later leads to a reduction of the overall number of tests and

to further confirm the results of Skjøedt [1] and Silva [2] claiming that the fracture

forming limit determined under simple (monotonic) strain paths can be applied to

analyze the formability limits in multi-stage SPIF. The thesis also studies the differences

in formability arising from the utilization of the same material in two different

conditions AA1050-H111 and AA1050-O (annealed).

In order to apply the knowledge acquired during the experimental work, as it is

referred above and to extend the applicability of multi-stage SPIF besides the

manufacturing of pyramids and cones with vertical walls, an application for a house

holding appliance was done.

1.1 Organization of the dissertation

This thesis is organized in 8 different chapters including this introduction and a

conclusion summarizing the major contributions and outcomes of the research work.

Chapter 2 begins with a short state-of-the-art review of incremental forming

processes, proceeds with the presentation of SPIF and the identification of practical

applications.

Chapter 3 starts with an overview of the new theoretical framework for SPIF that is

developed under membrane analysis with bi-directional in-plane contact friction

forces.

Chapter 4 gives a comprehensive description of the experimental techniques utilized

for material characterization and formability limits determination, an overview of the

SPIF experimental set-up and finally a short description of the CAD/CAM design

development.

2

Chapter 5 draws from the observation and analysis of the major process parameters

which influence the formability limits of the SPIF to validation against the theoretical

framework.

Chapter 6 deals with multi-stage SPIF and presents a strategy for manufacturing parts, with vertical walls. The strategy is applied to manufacture a pyramid with vertical walls. A SPIF made prototype part, its design and development are presented in chapter 7 with the aim of applying the overall knowledge that was acquired in the previous sections of the thesis. Finally, overall conclusions and future work are given in chapter 8. It is hoped that the

present work contributes towards a better understanding of the mechanics of SPIF.

1.2 References

[1] Silva MB, Skjoedt M, Atkins AG, Bay N, Martins PAF (2008) Single Point Incremental

Forming & Formability/Failure Diagrams. Journal of Strain Analysis for Engineering

Design 43(1):15–36.

[2] Silva M., Single Point Incremental Forming, PhD Thesis, Instituto Superior Técnico

(2008)

3

2 State-of-the-Art

The present chapter starts with a state of the art review of the Incremental Sheet

Metal Forming Process (SPIF) in terms of description, variations, formability and recent

applications with other materials and other configurations.

2.1 Sheet Metal Forming Processes with Incremental Approach

There are many different processes in metal forming that use an incremental

approach. With this approach, the deformation of the material is carried out

incrementally and as a consequence, less forming loads are required comparing with

the conventional processes. Some of these processes worked as the basis of SPIF. With

this in mind, it follows a short overview of sheet incremental forming technologies.

2.1.1 Hamering

One of the oldest processes in sheet incremental forming is Hammering. This process

was initially done manually but with the technological developments it can be done in

a modern CNC. Nowadays, Hammering takes advantage of the robotic technology and

it uses a robotic arm that controls the movement of the tool and punches the sheet,

which is clamped in a support frame, in circular trajectories descending step by step in

each round. See Figure 2.1.

2.1.2 Multi-point forming (MPF)

The production of a panel by Multi-point Forming (MPF) technology is very similar to

the forming process with solid dies. Where the latter uses two opposite solid dies that

are pressed on a sheet metal blank to shape it into a particular geometry, the MPF

technology replaces the solid die by a matrix of several punches with specific geometry

that are adjustable in height by means of linear actuators [3, 4], in order to be able to

change to diverse kind of shapes in a relative short period of time, see Figure 2.2.

Figure 2.1 - Incremental Hammering process.

(a) Incremental Hammering scheme[1];

(b) Industrial robot[2].

(a)

(b)

4

Figure 2.2 - Tool for multi-point forming [3].

2.1.3 Shot Peen Forming

Shot Peen Forming is a dieless process performed at room temperature, whereby

small round steel shot impact the surface of the work piece. Every piece of shot acts as

a tiny peening hammer, producing elastic stretching of the upper surface and local

plastic deformation that manifests itself as a residual compressive stress. The

combination of elastic stretching and compressive stress generation causes the

material to develop a compound, convex curvature on the peened side [5].

The shot impacts are statically distributed and they are usually made of steel balls

which are accelerated using compressed air though a nozzle. The shot peen forming

process is ideal for forming large panel shapes where the bend radii are reasonably

large and without abrupt changes in contour so it is widely used in aircraft industry. In

order to improve productivity, formability and applicability, Kopp and Schulz [6] have

been doing research in Double-Sided Simultaneous shot peen forming.

All the Sheet Metal Forming processes described so far are more flexible than the

conventional ones. To perform even better in what concerns to flexibility and

consequently cut development costs and lead time some processes without tool were

developed. It will be presented next a brief description of three Sheet Metal Forming

Processes with this last characteristic.

2.1.4 Laser Forming Process

Laser Forming Process, see Figure 2.3, is based in thermal stresses that are induced on

the blank (clamped in a structure) by laser irradiation on the sheet metal [7, 8].

5

Figure 2.3 - Laser forming [7].

The thermal stresses induce plastic strains resulting in bending or buckling of the

material. This process can also be used to make repairs or modifications in sheet metal

components [9, 10]. The costs of the forming stand, the need of qualified personnel,

the high energy consuming, the need of personal safety protection equipments and

the need (sometimes) of pre-coating of the metal sheet in order to enhance the

absorptive coupling are the main disadvantages of this process. Some of these

problems were successfully solved by replacing the laser by plasma arc [11].

2.1.5 Water Jet Forming

The Water Jet Forming is similar to the laser forming, replacing the laser by a water jet.

As advantages we have: more flexibility, better surface integrity, less tooling

requirements, lower equipment costs and less environmental impact. In the other

hand, Water Jet Forming is less accurate, consumes more energy and takes more time

than the other incremental metal forming processes [12].

2.1.6 Spinning

Spinning can be divided in two different types of technology (see Figure 2.4):

• Conventional Spinning

• Shear Spinning

Figure 2.4 - Spinning variants [13].

a) Conventional Spinning of a cone using multiple.

b) Shear Forming of a cone using a single pass.

(a) (b)

6

In Conventional Spinning (see Figure 2.4 a) axisymmetric parts are gradually formed

over a mandrel using a rounded tool or roller. The equipment needed is similar to a

lathe to clamp the blank sheet metal on the center in a mandrel, and this set is

revolved. The tool applies a localized pressure to deform the blank by axial and radial

motions over the surface of the part. The tool can be manual or mechanically actuated

and the tool production costs are low being suitable for producing small series because

usually involves a sequence of steps.

Shear Spinning (see Figure 2.4 b) is quite similar to Conventional Spinning and the

difference is the action which is stretching instead of bending. This fact has a major

influence on the variation of thickness along the wall which follows the commonly

known sine law (Figure 2.1) [13].

�� = �� sin � (2.1)

Figure 2.5 - Deformation of an element in a shear formed cone [13].

2.1.7 Incremental Sheet Forming Process (ISFP)

In 1994 Matsubara [14] developed the Incremental Backward Bulge Process, where the

blank is clamped in a rig that allows downward movement, the blank center is

supported by a support post and the forming tool controlled by CNC with a rotation

movement that describes the trajectories needed to obtain the desired part, see

Figure 2.6. This process allows the production of symmetrical and non symmetrical

shapes.

Figure 2.6 - Schematic representation of the Incremental Backward Bulge process [13].

In Stretch Expanding, as in

formed, although in this case the deformation is done through the relative rotation of

the blank (along with the rotational head) and the tool without using a mandrel, as

shown in Figure 2.7.

Figure 2.7 -

The ISMF processes can be divided into three different classifications .

Incremental Forming (SPIF

Point Incremental Forming (TPIF). The following section will provide details of each

technology.

2.2 Single Point Incremental Forming

Single Point Incremental

incremental forming processes like

capability of produce non-axisymmetric parts.

The blank sheet is clamped in a universal stationary blank holder and the form

describes the contour of the desired geometry controlled by a regular CNC machine

(see Figure 2.8).

Figure 2.8 - Schematic representation of a cross section view of

7

xpanding, as in Spinning, only rotational symmetrical shapes can be

formed, although in this case the deformation is done through the relative rotation of

the blank (along with the rotational head) and the tool without using a mandrel, as

Incremental Stretch Expanding Process scheme [14].

The ISMF processes can be divided into three different classifications .

SPIF), the Incremental Forming with Counter Tool and the Two

Point Incremental Forming (TPIF). The following section will provide details of each

Single Point Incremental Forming

Forming (SPIF) gives a new important contribute to

incremental forming processes like Spinning and stretch expanding which is the

axisymmetric parts.

The blank sheet is clamped in a universal stationary blank holder and the form

describes the contour of the desired geometry controlled by a regular CNC machine

Schematic representation of a cross section view of SPIF process [15]. The

could perform a round or helical path.

, only rotational symmetrical shapes can be

formed, although in this case the deformation is done through the relative rotation of

the blank (along with the rotational head) and the tool without using a mandrel, as

The ISMF processes can be divided into three different classifications . The Single Point

), the Incremental Forming with Counter Tool and the Two

Point Incremental Forming (TPIF). The following section will provide details of each

) gives a new important contribute to

and stretch expanding which is the

The blank sheet is clamped in a universal stationary blank holder and the forming tool

describes the contour of the desired geometry controlled by a regular CNC machine

]. The tool rotates and

8

The main advantages of the SPIF Process are [16]:

• Production of parts directly from the CAD file;

• Inexistence of positive or negative die;

• Design changes can be easily and quickly performed;

• Increase of material formability;

• Can be performed in a conventional CNC machine;

• Due to the incremental nature of the process, forces are small;

• Dimension of parts are only limited by the machine tool;

• Good surface finish quality can be achieved.

The main disadvantages of the SPIF Process are:

• Longer forming time compared with conventional Deep Drawing

Process;

• Limited to small size production batches;

• The forming of right angles must be achieved by multi-stage strategies;

• Springback occurs, although it can be minimized using some correction

algorithms;

• Less geometry accuracy, particularly in convex radii and bending edges

areas [17].

2.3 Incremental Forming with Counter Tool

The Incremental Forming with Counter Tool (IFWCT) is a variation of SPIF that does not

use backing plate, and instead a counter tool is utilized that makes the same trajectory

of the main tool, see Figure 2.9.

Figure 2.9 - Schematic representation of Incremental Forming with Counter Tool [18].

9

2.4 Two Point Incremental Forming

In Two Point Incremental Forming (TPIF) the blank is clamped in the blankholder which

can be adjusted in the Z axis. The forming tool is similar to the tool in SPIF and

performs a trajectory of the outer surface of the part, from top to bottom of the

geometry. TPIF can be separated in two categories: with partial die, see Figure 2.10

and with full die, see Figure 2.11.

2.4.1 Two Point Incremental Forming (partial die)

Figure 2.10 - TPIF (partial die) [19].

The partial die here has the same function as the backing plate in SPIF, supporting only

the essential areas of the blank and also, enhancing the geometry accuracy. With

unspecific geometry, the same partial die can be used to make different parts with

similar geometry [18, 20].

2.4.2 Two Point Incremental Forming (full die)

TPIF with full die is not considered as a dieless approach and has the advantage of

good geometry accuracy of parts [17, 18, 21, 22], because the blank during forming is

constrained by the tool and the die (see Figure 2.11).

Figure 2.11 - TPIF (full die) [19].

As disadvantages, the costs of this process are higher due to the costs associated with

the die material (steel, aluminium, plastic, wood or foam [23]) and fabrication. Poor

10

flexibility it is also important to refer because it is needed a specific die for each

specific part.

2.5 Multistage Forming

For every material with a specific thickness, a maximum forming angle can be

determined by means of a simple cone forming test in were parameters like

incremental step size and tool diameter are kept constant. Using conventional

toolpaths, when a sufficiently portion of a workpiece has a wall angle that exceeds this

maximum angle, the part will fail during processing.

This maximum wall angle limits the process and it is easy to see that is impossible to

make parts with right angle walls (i.e. at a drawing angle of 90 degree), because the

wall thickness in this conditions would be zero according to the sine law (equation 2.1).

It has been experimentally verified that the process follows this law with a tendency to

overform slightly.

To increase the maximum wall angle, the initial thickness of the sheet can be increased

but obviously this strategy has limitations on the maximum machine load and overall

part thickness specifications. The diameters of the tool and the selected stepdown also

have an influence on the maximum forming angle [25].

Another strategy to obtain large wall angles is to aim for material redistribution by

shifting material from other zones in the part to the inclined wall areas.

Finally, several authors have already adopted multistage strategies. Consecutive

toolpaths, corresponding to virtual parts with increasing wall angles, are being

executed in a multi-step procedure. Typically a large offset from the backing plate is

favored for the first passes since this allows for more bending, avoiding extreme

strains near the top of the part.

Also in order to overcoming this limitation some researchers [24] applied multiple

stages strategies with success (using pre-forms).

Figure 2.12 - SPIF Multistage strategy [25].

11

Recently Skjoedt et al. [26] proposed a solution to obtain cones with vertical walls, for

SPIF without support through a forming strategy shown in the Figure 2.13.

Also Douflou et al [27] used multistage strategies to achieve non-rotation parts, see

Figure 2.14.

Figure 2.14 - Non-rotational part [27].

Multistage SPIF will be deeply analyzed in a forecoming chapter of this thesis.

2.6 Applications of Incremental Sheet Forming Process

The ISFP applications can be separated in two different main areas:

• Rapid prototyping for automotive industry, for example: reflexive surfaces for

headlights, see Figure 2.15; a heat/vibration shield see Figure 2.16; and a

silencer housing for trucks, see Figure 2.17; etc.

Figure 2.15 - Reflexive surface for headlights [29, 30].

Figure 2.13 - Five stage forming [28].

12

Figure 2.16 - Automotive heat/vibration shield [30].

Figure 2. 17 - Silencer housing for trucks [26].

• Non-automotive applications, for example: motorbike seats, motorbike gas

tank, solar oven, production dies, moulds surfaces and some medical

applications, see Figure 2.18.

Figure 2.18 - Medical applications of ISMF.

a) Cranial plate[32].

b) Dental plate[31].

Some other possible fields of application for ISMF are architecture, home appliances

industry, aerospace and marine industry.

2.7 Others materials

Aerospace and biomedical applications are being more and more utilized in the past

years. Tanaka et al. [31] proved the viability of the SPIF process of pure titanium in a

denture plate application, see Figure 2.18 (b), where the main difficulties in the

production of this part were the surface quality, needing to find optimal combination

between feed rate and lubrication. Hussain et al. [33] proved that SPIF can also be

(a) (b)

13

applied in commercially pure titanium if a proper tool, good lubricant and lubrication

method are adopted.

Jackson et al. [34] verified the viability of producing parts with sandwich panels. This

kind of panels are largely applied in aircraft interiors, car body panels and in

architecture panels saving weight, absorbing sound, vibrations and impact, and

isolating thermically.

In what concerns to polymers, Franzen et al. [35] characterized and evaluated the

formability limits of the process for commercial PVC (Polyvinyl Chloride), and

concluded that SPIF of commercial PVC sheets at room temperature seems promising

for the manufacture of complex polymer sheet components with very high depths, see

Figure 2.19. The application of polypropylene (PP) in SPIF was performed by Le et al.

[36] and several different geometries were studied.

Figure 2.19 - PVC part made by SPIF process [35].

Finally, Ji and Kim [37] verified the viability of producing by Multistage SPIF Magnesium

AZ31 parts at warm temperatures, and concluded that the formability increased with

the increase of the forming temperature. This material is only formable at warm

temperatures due to its brittleness. It is also a very promising material for structural

applications due to its high strength-to-weight ratio.

2.8 New Incremental Forming Process Configurations

In order to obtain a rectangular shell, forming vertical wall and improve finishing of the

bottom of parts, Iseki and Naganawa [38] proposed a special tool, see Figure 2.20 to be

used after a part is pre-formed.

Figure 2.20 - Incremental forming using cylindrical rollers [39].

a) Horizontal wall surface forming.

b) Vertical wall surface forming.

(a) (b)

14

Shankar et al. [19] investigated the use in ISMF of preformed sheet by Simple Bending,

Deep Drawing, spinning, etc in order to enhance geometrical accuracy and thickness

distribution. As conclusion, the parts had higher thickness and lower springback.

Another configuration called Sliding Sheet Incremental Forming, was proposed by

Ambrogio et al. [39] in order to increase formability without excessive thinning. In this

case, instead of clamping the sheet, the blankholder has a controlled force that allows

radial flow of the flange material. This characteristic increases the formability and

decreases the sheet thinning. In the other hand, ISMF flexibility is compromised due to

more complex equipment.

2.9 References

[1] Schäfer T., Schraft R.D., Incremental sheet metal forming by industrial robots using

a hammering tool, 10èmes Assises Européennes de Prototypage Rapide, Paris, France

(2004).

[2] Schäfer T., Verfahren zur hämmernden Blechumformung mit Industrieroboter,

Institut für Industrielle Fertigung und Fabrikbetrieb der Universität Stuttgart, (2007).

(in German)

[3] Li M., Liu Y., Su S., Li G., Multi-point forming: a flexible manufacturing method for a

3-d surface sheet, Journal of Materials Processing Technology 87 (1999) 277-280.

[4] Li M.Z., Cai Z.Y., Sui Z., Yan Q.G., Multi-point forming technology for sheet metal,

Journal of Materials Processing Technology 129 (2002) 333-338.

[5] Retrieved from: www.metalimprovement.com/shot_peen_forming.php

[6] Kopp R., Schulz J., Flexible Sheet Forming Technology by Double-sided

Simultaneous shot peen forming, Annals of CIRP, 51-1 (2002) 195-198.

[7] Duflou J.R., Callebaut B., Verbert J., De Baerdemaeker H., Laser Assisted

Incremental Forming: Formability and Accuracy Improvement, Annals of CIRP, 56-1

(2007) 273-276.

[8] Duflou J.R., Callebaut B., Verbert J., De Baerdemaeker H., Improved SPIF

performance through dynamic local heating, Journal of Materials Processing

Technology, 48-5 (2008) 543-549.

[9] Geiger M., Vollertsen F., The Mechanisms of Laser Forming, Annals of CIRP, 42-1

(1993) 301-304. (in German)

[10] Geiger M., Synergy of Laser Material Processing and Metal Forming, Annals of

CIRP, 43 (1994) 563-570.

[11] Male A.T., Li P.J., Chen Y.W., Zhang Y.M., Flexible forming of sheet metal using

plasma arc, Journal of Materials Processing Technology 115 (2001) 61-64.

[12] Jurisevic B., Kuzman K., Junkar M., Water jetting technology: an alternative in

incremental sheet metal forming, International Journal of Advanced Manufacturing

Technology 31 (2006) 18-23.

15

[13] Hagan E. and Jeswiet J., “A review of conventional and modern single point sheet

metal forming methods”. Journal of Engineering Manufacture, 217 (2003) 213–225.

[14] Matsubara S., Incremental backward bulge forming of a sheet metal with a

hemispherical tool, Journal of the Japan Society for Technology of Plasticity, 35 (1994)

1311-1316.

[15] Franzen V., Kwiatkowski L., Neves J., Martins P.A.F. and Tekkaya: “On the

capability of single point incremental forming for manufacturing polymer sheet parts”,

9th International Conference on Theory of Plasticity, (2008).

[16] Jadhav S., Goebel R., Homberg W., Kleiner M., Process optimization and control

for incremental forming sheet metal forming, Proceedings of the International Deep

Drawing Research Group Conference, IDDRG, Bled, Slovenia (2003) 165-171.

[17] Hirt G., Ames J., Bambach M., Basic Investigation into the Characteristics of dies

and suppot tools used in CNC-Incremental Sheet Forming, Proceedings of the

International Deep Drawing Research Group Conference, IDDRG, Porto, Portugal

(2006) 341-348.

[18] Jadhav S., Basic Investigations of the Incremental Sheet Metal Forming Process on

a CNC Milling Machine, Institut für Umformtechnik und Leichtbau, Germany (2004).

[19] Shankar R., Jadhav S., Goebel R., Homberg W., Kleiner M., Incremental Sheet

Metal Forming of Preformed Sheets, Proceeding of the 8th International Conference

on Technology of Plasticity, Verona, Italy (2005).

[20] Jeswiet J., Incremental single point forming, Proceedings of NSF Design and

Manufacturing Research Conference (2000).

[21] Matsubara S., A computer numerically controlled dieless incremental forming of a

sheet metal, Proceedings Institution of Mechanical Engineers, Vol 215 Part B, IMechE

(2001) 959-966.

[22] Tiburi F., Schaeffer L., Aspectos Técnicos e Económicos da Estampagem

Incremental, XXVII Senafor, X Conferencia Nacional de Conformação de Chapas, Brazil

(2007) 255-275. (in Portuguese)

[23] Jeswiet J., Micari F., Hirt G., Bramley A., Duflou J. and Allwood J., Asymmetric

single point incremental forming of sheet metal, Annals of CIRP, 54 (2005) 623-650.

[24] Cavallini B. and Puigpinos L.: “Incremental sheet forming: new technology for the

manufacture of sheet metal parts directly from CAD files”, Rapid Product Development

RPD2006, (2006).

[25] Bambach M., Hirt G., Ames J., Modeling of Optimization Strategies in the

Incremental CNC Sheet Metal Forming Process, Numiform 2004 – Proceedings of the

8th International Conference on Numerical Methods in Industrial Forming Processes,

Columbus, Ohio (2004) 1969-1974.

[26] Skjoedt M., Bay N., Endelt B. and Ingarrao G.: “Multi-stage strategies for single

point incremental forming of a cup”, 11th ESAFORM conference on metal forming –

ESAFORM2008, (2008).

16

[27] Douflou J. R., Verbert J., Belkassem B., Gu J., Sol H., Henrard C., Habraken A.M.

Process window enhancement for single point incremental forming through multi-step

toolpaths, CIRP Annals - Manufacturing Technology 57 (2008) 253–256

[28] Skjoedt M., Silva M.B., Martins P.A.F., Bay N., Strategies and Limits in Multistage

Single Point Incremental Forming (in press).

[29] Jeswiet J., Hagan E., Rapid proto-typing of a headlight with sheet metal,

Proceedings of Shelmet (2001) 165-170.

[30] Jeswiet J., Recent results for SPIF. Seminar on Incremental Forming, Cambridge

University (2004) CdRom.

[31] Tanaka S., Nakamura T., Hayakawa K., Nakamura H., Motomura K., Incremental

Sheet Metal Forming Process for Pure Titanium Denture Plate, Proceedings of the 8th

International Conference on Technology of Plasticity – ICTP (2005) 135-136.

[32] Duflou J., Production Processes - Cranial plate,

http://www.mech.kuleuven.be/pp/research/SPIF_cranial.en.html (2006).

[33] Hussain G., Gao L., Hayat N., Cui Z., Pang Y.C., Dar N.U., Tool and lubrication for

negative incremental forming of a commercially pure titanium sheet, Journal of

Materials Processing Technology 203 (2008) 193-201.

[34] Jackson K.P., Allwood J.M., Landert M., Incremental forming of sandwich panels,

Journal of Materials Processing Technology, 204 (2008) 290-303.

[35] Franzen V., Kwiatkowski L., Martins P.A.F., Tekkaya A.E., Single point incremental

forming of PVC, Journal of Materials Processing Technology 209 (2009) 462-469.

[36] Le V.S., Ghiotti A., Lucchetta G., Preliminary Studies on Single Point Incremental

Forming for Thermoplastic Materials, 11th ESAFORM 2008 Conference on Material

Forming, Lyon, France (2008).

[37] Ji Y.H., Park J.J., Formability of magnesium AZ31 sheet in the incremental forming

at warm temperature, Journal of Materials Processing Technology 201 (2008) 254-358.

[38] Iseki H., Naganawa T., Vertical wall surface forming of rectangular shell using

multistage incremental forming with spherical and cylindrical rollers, Journal of

Materials Processing Technology 130-131 (2002) 675-679.

[39] Ambrogio G., Filice L., Gagliardi F., Micari F., Sheet Incremental Forming: A New

Process Configuration allowing a Sheet Material controlled flow under the Blank-

holder, Proceedings of the 8th ICTP – International Conference on Technology of

Plasticity, Verona, Italy (2005).

17

3 Theoretical background

The mode of deformation that occurs in SPIF has been subject of controversy in the

metal forming community with some authors [1] claiming that the deformation takes

place by stretching instead of shearing and others [2], claiming the opposite. Although

assertions are mainly based on similarities to the well-known processes of stamping

and shear-spinning rather than experience evidence concerning SPIF.

Examination of the likely mode of material failure at the transition zone between the

corner radius and the inclined wall of the sheet is consistent with stretching, the

governing mode of deformation in SPIF. Allwood et al. [3] identified the mechanics of

SPIF as a combination of stretching and bending deformation modes in opposition to

vertical shear which was claimed initially by others authors.

As regards the forming limits of SPIF there are three different views:

• Formability is limited by necking;

• The Forming Limit Curve (FLC) in SPIF is significantly raised compared with

conventional FLCs being utilized in the analysis of sheet metal forming

processes (e.g. stamping, deep drawing, etc.) [4].

• The rise in formability is due to a large amount of through-thickness shear [3, 5]

or, instead, due to serrated strain paths arising from cyclic, local plastic

deformation [6].

This last approach (which hereafter is referred to as the ‘necking line of attack’ or NLA)

is adopted in most of the numerical and experimental contributions to the

understanding of formability in SPIF that have been published in the last few years.

The alternative, and non-traditional, view of formability in SPIF recently proposed by

Silva et al. [1], and supported by Cao et al. [7] and Emmens and Van Den Boogaard [8],

considers that:

(a) formability is limited by fracture without experimental evidence of previous

necking;

(b) the suppression of necking in conjunction with the low growth rate of

accumulated damage is the key mechanism for ensuring the high levels of

formability in SPIF;

(c) FLCs, which give the loci of necking strains, are not relevant and should be

replaced by the Fracture Forming Limits (FFLs). This approach will be hereafter

referred to as the ‘fracture line of attack’ (FLA), see figure 3.5.

As conclusion, plane stretching is the principal mode of deformation in SPIF, and it is

the start point for the theoretical framework that will be presented in the following

sections.

The smear-mark interferences between the tool and the surface of the she

circle-grid analysis lead us to the classification of all tool paths that we can find in

as a combination of the three basic modes of deformation

Figure 3.1 - Schematic representation of local contact area between the tool and the sheet and

identification of the basic modes of deformation of

A- Flat surfaces under plane

B- Rotational symmetric surfaces under plane strain stretching conditions

C-

It’s important to notice that stretching and equal bi-axial stretching can be founded in analytical model to be derived in this thesiof deformation founded in

18

mark interferences between the tool and the surface of the she

grid analysis lead us to the classification of all tool paths that we can find in

as a combination of the three basic modes of deformation shown in Figure

Schematic representation of local contact area between the tool and the sheet and

identification of the basic modes of deformation of SPIF.

Flat surfaces under plane strain stretching conditions

Rotational symmetric surfaces under plane strain stretching conditions

Corners under equal bi-axial stretching conditions

It’s important to notice that other modes of deformation between plane strain axial stretching can be founded in SPIF parts, however the

odel to be derived in this thesis will only be focused on the extreme modes of deformation founded in SPIF.

mark interferences between the tool and the surface of the sheet and the

grid analysis lead us to the classification of all tool paths that we can find in SPIF

Figure 3.1.

Schematic representation of local contact area between the tool and the sheet and

Rotational symmetric surfaces under plane strain stretching conditions

other modes of deformation between plane strain parts, however the

s will only be focused on the extreme modes

19

3.1 State of stress and strain

The shell element CDEF shown in Figure 3.2 is subjected to normal and shear forces

and also to bending moments in conformation with the hemispherical tip of the tool

and forming a contact area between the tool and the part of the tool immediately

ahead of the moving tool, see Figure 3.1.

Figure 3.2 - Membrane analysis of SPIF. Schematic representation of shell element and details showing

the acting stresses in the meridional, circumferential and thickness directions.

Applying the membrane equilibrium condition, neglecting the bending moments and

assuming meridional and thickness stresses to be principal stresses we can achieve the

state of strain in SPIF. Other assumptions are made: the material is assumed to be

rigid, perfectly plastic and isotropic. Also, the resultant friction stress acting in the tool

(sheet contact interface) is assumed to consist of two different in-plane components: a

meridional component - μ�σ� caused by the downward movement of the tool and a

circumferential component - μ�σ� caused by circumferential feed and the rotation of

the tool. This last assumption implies the coefficient of friction: μ = �μ�� + μ�� .

The force equilibrium along the thickness, circumferential and meridional directions,

results in:

20

� " #$ "% #� + �& " #$ � sin #$2 + (�& + #�&)*" + #"+#$*� + #�+ sin #$2+ �, "% #� � sin #$2 cos � + *�, + #�,+ "% #� � sin #$2 cos � = 0

σ� r% dα 3t + ��� 5 − μ� σ� r% dα 3 r + �7� 5 dθ − *σ� + dσ�+ r% dα 3t + ��� 5 = 0 (1)

*�, + #�,+ *" + #"+ #$ *� + #�+ − �& " #$ � + 8& � " #$ "% #�− �, #$2 "% #� � sin � − *�, + #�,+ #$2 "% #� � sin � = 0

The distribution of stresses in the three typical deformation zones (A, B and C) can be

easily obtained from equation 1 neglecting the higher order terms, performing some

geometrical simplifications considering the Tresca yield criterion and assuming that

single point incremental forming of flat and rotationally symmetric surfaces is

performed under plane strain conditions, d9: = 0 ,[1].

Obtained by membrane analysis, the stresses and strains along the principal directions

are shown in Table 3.1.

Table 3.1 - States of stress and strain in SPIF and conventional stamping

3.2 Friction at the tool–sheet contact interface

Frictional effects along the circumferential direction can be neglected and the only

friction forces that should be taken in account are the forces exerted in the meridional

direction [2]. Based on this and starting from the membrane equilibrium condition

along the meridional direction (equation 1) and neglecting the variation of thickness

Assumption State of strain State of stress Hydrostatic stress

SPIF

(fl

at a

nd

rota

tio

nal

sy

mm

etri

c su

rfac

es)

Plane strain conditions (A)

and (B)

dε� = −dε� > 0 dε� = 0 dε� < 0

σ� = σ% = σ�31 + tr�>>?5 > 0

σ� = σ� = 12 *σ% + σ@+

σ� = σ@ = −σ� t*r�>>? + t+ < 0

σ� = σ�2 Ar�>>? − tr�>>? + tB

SPIF

(co

rner

s)

Equal bi-axial stretching (C)

dε� = dε� > 0 dε� < 0

σ� = σ� = σ% = σ�31 + 2tr�>>?5> 0

σ� = σ@ = −2σ� t*r�>>? + 2t+ < 0

σ� = 2σ�3 A r�>>? − tr�>>? + 2tB

Co

nve

nti

on

al

stam

pin

g (r

ota

tio

nal

sym

met

ric

surf

aces

)[1

]

Equal bi-axial stretching

dε� = dε� > 0 dε� < 0

σ� = σ� = σ% = σ�D1 + 2trEFGHIJ > 0

σ� = σ@ = −σ� t(rEFGHI + t) < 0

σ� = 2σ�3 KrEFGHI − t2rEFGHI + tL

21

M MN ≅ 0, it is possible to reach to the following relationship for the meridional stress

distribution �& along the curvature from the bottom to the top (from B to C) of the

plastic zone (Figure 3.3):

σ� = σ�PexpTμU (2)

Figure 3. 3 - Schematic representation of the stress field in a radial slice through the instantaneous, small

plastic zone.

In equation 2, k takes the value 1 for plane strain or 2 for equal bi-axial and V is

defined in detail of deformed part included in Figure 3.3.

Analyzing the equation 2, it is possible to conclude that the meridional stress increases

with r because of the friction at the tool-sheet contact interface. It is also possible to

say that the increasing rate is higher in the corners (k=2) of SPIF parts than in the flat

rotationally symmetric surfaces (k=1).

3.3 The inclined wall adjacent to the forming tool

Using the membrane in equilibrium equation 1 in the thickness direction that " = ∞ as

well as the contact pressure � = 0 on the surface of the CD element, one obtains �, = 0 along the wall adjacent to the forming tool. Since the meridional stresses �&

are the only stresses acting in this region, we achieve the following condition based on

the stretching force that is supported by the inclined wall of the sheet:

σ�W = σ�X 7X7W (3)

22

Analyzing the previous equation, the meridional stress σ�decreases from point C to D.

Because the meridional stress at point C must be kept below the yield stress for a

perfectly-plastic material, it follows that the inclined wall surface of the sheet adjacent

to the tool is elastic.

This result together with the stress analysis performed before in the previous sections

allows plotting the schematic representation of the stress field in a radial slice of the

SPIF component that contains the small localized plastic zone (Figure 3.3), for the case

of plane strain.

3.4 Thinning at the corner radius

Having as starting point the membrane equilibrium condition in the meridional

direction (in equation 1) and neglecting friction and introducing the following

boundary conditions r = rY, σ� = σ�P and t = tZ it’s possible to reach:

σ� = σ�P �[� (4)

Physically, equation 4 illustrates that the reduction in thickness t tends to balance the

rise in the meridional stresses �& so that �&� is constant in the small localized zone

being plastically deformed. It is also important to notice that although the variation in

the wall thickness of inclined surface can be estimated by � = �Z sin \ , thinning

occurrence has to do with meridional tensile stresses �& rather than shear acting in

the small localized zone being plastically deformed.

3.5 Crack propagation in rotational symmetric SPIF parts

It is important to analyze the origin of the two modes of crack propagation on SPIF parts [3] (Figure 3.4):

• The circumferential straight crack propagation path

• The circumferential “zigzag” crack propagation path The circumferential straight propagation path (Figure 3.4 c) is similar to that found in

conventional stamping or deep drawing operations (Figure 3.4 d) and as known, the

crack opening is triggered by stretching mechanisms due to σ�.

The “zigzag” crack propagation path (Figure 3.4 b) is also triggered by σ� but its

morphology, doing zigzag around the circumferential direction is probably caused by

friction towards the rotation of the forming tool. The tip of the crack in “a” will be

under a much lower level of meridional stresses than at the onset point “o”.

Consequently, the propagation of the crack stops and the rotation of the tool will drag

it to point “b” which is similar to the initial point “o” restarting the crack propagation.

This cyclic mechanism gives the typical “zigzag” morphology to the crack.

23

Figure 3.4 - Crack propagation in SPIF.

a) Scheme of typical propagation path in SPIF.

b) Circumferential “zigzag” crack propagation path.

c) Circumferential straight crack propagation path.

d) Circumferential straight crack propagation path (part obtained by conventional deep-drawing.

3.6 Forming limits

The study based on observation of the morphology of the cracks and the

measurements of thickness along the cross-section of SPIF parts revealed that plastic

deformation occurs by uniform thinning until fracture without experimental evidence

of localized necking taking place before reaching the onset of fracture [4]. The

inexistence of necking can be explained by the inability of the necks to grow because it

would have to grow around the circumferential bend path that circumvents the tool

which is difficult to occurs and creates problems of neck development; even if all the

conditions could be met at the small plastic deformation zone in contact with the tool,

growth will be inhibited by the surrounding material which experiments much lower

stresses. As consequence of this, the FLCs of conventional sheet metal forming are

inapplicable to describe SPIF failure. FFLs curves showing the fracture strains placed

well above the FLCs should be used in SPIF.

(a)

(b)

(c)

(d)

24

Figure 3.5 - Schematic representation of the forming limits of SPIF against those of

stamping and deep drawing.

The FFLD in SPIF (Figure 3.5) can be characterized by means of ductile damage

mechanics based on void growth models,[5]. Assuming the Tresca yield criterion, linear

loading paths, and that f(σ� σ^ ) takes the simple form σ� σ^ , the total amount of

accumulated damage for plane strain and equal bi-axial stretching SPIF conditions

results in the following critical damage values:

DH = ` aba9�cZ dε� = %� d7effgh�7effgi�j ε%E?�Gk l�7�mG (5)

DH = ` aba9�cZ dε� = �@ d 7effgh�7effgi��j 2ε%nmh��m�? (6)

If the critical value of damage Dc at the onset of cracking is assumed to be path-

independent, by solving Equation 5 and 6 for o% it is possible to set up the following

identity:

9pqrsturtgh9pvgtwx yeztrw9{qrsturtghZ = 3|}5~*7effgi��+/*7effgh�+]h�~*7effgi�+/*7effgh�+]

3|}5~ zeffg�{ezeffgse ] = − �3zeffge 5i�@3zeffge 5i� (7)

Equation 7 gives the slope of the fracture forming line (FFLD) in the principal strain-

space (ε%, ε�) (Figure 3.5). For typical experimental values of r�>>? t⁄ in the range 2–10

the slope derived from Equation 7 will vary between -1.0 and -1.4. This supports the

assumption that the fracture forming limit in SPIF can be approximately expressed as ε% + ε� = q, where ε� = -q is the thickness strain at the onset of fracture in plane strain

conditions. This result is in close agreement with the typical loci of failure strains in

conventional sheet forming processes, where the slope of the FFLD is often about -1

[6].

ε

ε

0-n/2

1

1-1

11

-1/2

pure shear

2

1

biaxial stretching

local necking

simple tension

1ε + ε =

2n

FLC

plane strain

n

fracture

1ε + ε =

2q

q

FFL

25

The principal strain space and the forming limit curve will be very much utilized in the

fore coming sections of the thesis.

3.7 References

[1] Rodrigues J.M.C., Martins P.A.F., Tecnologia da Deformação Plástica: Aplicações Industriais, Escolar Editora (2005). (in Portuguese) [2]Silva MB, Skjoedt M, Atkins AG, Bay N, Martins PAF (2008) Single Point Incremental Forming & Formability/Failure Diagrams. Journal of Strain Analysis for Engineering Design 43(1):15–36. [3] Silva MB, Skjoedt M, Atkins AG, Bay N, Martins PAF (2008) Revisiting the fundamentals of single point incremental forming by means of membrane analysis. International Journal of Machine Tools & Manufacture 48 (2008): 73-83 [4] Allwood J.M., Shouler D.R., Tekkaya A.E., The increased forming limits of incremental sheet forming processes, Key Engineering Materials 344 (2007) 621-628. [5] P.A.F. Martins, N. Bay, M. Skjoedt, M.B. Silva Theory of single point incremental forming. CIRP Annals – Manufacturing Technology 57 (2008) 247-252 [6] Silva M.B, Single Point Incremental Forming, PhD Thesis, Instituto Superior Técnico

Portugal (2008)

26

4 Experimental work

This section starts by describing the experimental techniques that were utilized for the

material characterization and follows by introducing the technique utilized for

determining the material forming limits, the experimental SPIF setup utilized, the plan

of experiments and the CAD/CAM design development performed.

4.1 Material characterization

In sheet metal forming processes, the forming limit curve (FLC) is usually employed to

evaluate the limits of proportional straining before necking or the onset of a visible

strain concentration. The FLC describes the necking limit, but does not indicate if the

failure is due to local necking or fracture. The experimental results in ISMF do not fit

the conventional FLC, and the existence of necking in ISMF is a subject of controversy.

Under these circumstances there is a need to perform the evaluation of the material

forming limits in the principal strain space, namely the fracture forming limit (FFL).

The Circle Grid Analysis (CGA) utilized for obtaining the material forming limits

involved electrochemical etching a grid with pattern of 2mm diameter circles (before

deformation), shown in Figure 4.1. Then each circle's deformation is measured using

special purpose rulers as those shown in Figure 4.2.

In order to look for signs of necking in the aluminium parts made by SPIF there was a

need to measure the thickness variation along the walls of the parts. It was used a

measuring system specially designed. This measurement technique can ensure a

resolution of 0,01mm and works according to Figure 4.3.

Figure 4.1 - Grid of initial circles Figure 4.2 - Plastic rulers

27

Figure 4.3 - Thickness measurements of SPIF made part.

The fracture depth measurements were utilized in the analysis of formability that is

comprehensively described in chapter 5, where the specimens produced with different

process conditions were compared by taking the fracture depths as shown in Figure

4.4.

Figure 4.4 - Fracture depth measurements.

The tensile tests were performed in a Universal Materials Testing Machine, Instron

4507, see Figure 4.5 (a), in accordance with the standard for tensile tests NP EN 10

002-1 [1]. The load of the test was measured by means of a load cell of 200 kN and the

strains by means of an axial and transverse extensometer of high resolution. The

software used to control the machine and data acquisition was the Instron Series IX

software.

The bi-axial circular and elliptical hydraulic bulge tests were performed in a Universal

Sheet Metal Testing Machine, Erichsen 145/60, see Figure 4.5 (b). The capability of the

machine is 600 kN of drawing force, 300 kN of blank holder force, and a drawing speed

range from 0 - 600 mm/min. The measurement software utilized was Catman 2.0 from

HBM.

28

Figure 4.5 - Testing machines.

(a) Instron 4507, Universal Materials Testing Machine [2]

(b) Erichsen 145/60, Universal Sheet Metal Testing Machine [3]

The forming limits of the metal blanks were evaluated by means of circular (Ø100mm)

and elliptical (100/80 and 100/63mm) hydraulic bulge tests shown on 6 and by mean

of the tensile tests in order to investigate anisotropy of the blank sheets, which were

cut at 0, 45 and 90 degrees to the rolling direction, see Figure 4.6.

Figure 4.6 - Tensile and Biaxial bulge test specimens [3].

The main results for the tensile tests are presented in Table 4.1. Where σY is the Yield

Strength, σUTS is the Ultimate Strength, A the Elongation at Break, UT the Toughness

and E is the Young Module.

Material �� ~���] ���� ~���] � ~%] �� ~���] � ~���]

AA1050-H111

119,9 120,9 10 9,33 70943

AA1050-O 29,03 79,10 44,23 24,00 67063

Table 4.1 - Tensile tests result for both materials. [3]

(a) (b)

29

4.2 Forming limits

The circle grid analysis mentioned before was utilized for FLC determination by taking

the strains ε% and ε� from the area localized just outside the neck since they represent

the condition of the uniformly-thinned sheet just before necking occurs [3].

In what concerns the construction of Fracture Forming Limit (FFL) there was a need to

determine the ‘gauge length’ strains by thickness measurement executed directly on

the fracture as is shown in following Figure 4.7.

Figure 4.7 - Experimental measurement of fracture thickness in tensile and bulge specimens [3].

The experimental procedure for defining the in plane strains requires measuring the

width of the sample before and after the fracture, as is shown in Figure 4.8.

Figure 4.8 - Experimental measurement of fracture width in tensile and bulge specimens [3].

The experimental FFL is plotted in following Figure 4.7 can be approximated by a

straight line ε% + 0.79ε� = 1.37 for the AA1050-H111 and by a straight line ε% +1.08ε� = 1.77 for the AA1050-O [3].

30

Figure 4.9 - Fracture Forming Limit Diagram containing the FLC and the FFL for both materials [3].

4.3 Experimental Setup

A description of the experimental setup is described in the following subsections.

4.3.1 CNC Machine

The manufacturing of the experimental parts was performed at DTU (Danish Technical

University) facilities at Department of Mechanical Engineering in a 3 axes Cincinati

Milacron CNC machine centre shown in Figure 4.10 .

Figure 4.10 – CNC machine center.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

2,20

-0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

ε1

Minor True Strain ε2

FLC Exp.

FFL Exp. AA-1050-O

FFL Exp. AA-1050-H111

CNC Operating Sistem GE Fanuc Series O-M

Number of Axis 3

Machining Capacity (mm) 762/381/508

Max. Tool Diameter (mm) 100

Table 4.2 - Machine Technical Specifications.

31

The parameters of the CNC vertical machine are listed in Table 4.2, and the utilized

special equipment is described in the following section.

4.3.2 Forming tools

The tools were made from HSS (High strength steel) hardened to 64 HRC with

hemispherical tips and different diameters (8, 12, 20, 30, 50 mm) were utilized, see

Figure 4.12.

The idea of using tools from small to large diameters was necessary to understand if

the limits of formability change from fracture to necking as the size of the tool

increases approaching that to conventional stamping punches.

Figure 4.12 – Utilized forming tools.

To ensure a fine tool surface quality in order to minimize friction between the forming

tool and the metal sheet, the tool needed to be polished according to the following

procedure. First using the polishing device, see Figure 4.11, with an abrasive paper of

20μm; the major imperfections were removed from the tool surface. After this, the

tool was cleaned and a polishing diamond paste with 9μm abrasive grains was applied.

After a new clean, the surface was finished using again a polishing diamond paste but

this time with 6μm abrasive grains.

Figure 4.11 - Polishing device

Rotwerk EDM 300 DS.

32

4.3.3 SPIF clamping system

The CNC machine to perform SPIF made use of a dedicated clamping system, see

Figure 4.13.

Figure 4.13 - SPIF clamping tools.

The complete clamping system displayed in Figure 4.13 (d) is composed by the static

frame (a) fixed on the machine working table, the backing plate (b) to support the

formed sheet and to minimize springback and the blank holder (c) to hold the sheet

over the backing plate. The whole apparatus is clamped to the bottom corners of the

working table of the CNC by four screws.

4.3.4 Lubrication Conditions

The application of lubricant in ISMF is important to obtain a smooth surface and to

reduce the wear of the tool.

Bramley [4] observed that the type of lubricant is not a principal factor. Later, Carrino

et al [5] concluded that friction differences in SPIF are only obvious in comparison

between the process with and without lubrication.

The surface wear, see Figure 4.14, appeared during forming of the annealed plates

made from material AA1050-H111 performed with diluted Motorex cutting fluid 7755

AERO [6].

Figure 4.14 - Wear on a part made from AA1050-O.

(a) (b) (c)

(d)

33

Therefore to avoid this and to reduce the impact of friction between the forming tool

and the sheet, two different lubricants were tested under the same process conditions

on the material AA1050-H111 (which was used for tests due to the lack of annealed

plates AA1050-O). The results are presented on Figure 4.15.

Figure 4.15 - Lubrication wear test.

a)Castrol IloformTDN 81 [7]

b) Motorex cutting fluid 7755 AERO [6]

The parts lubricated by Castrol IloformTDN 81 forming fluid [7], shown in Figure 4.15

(a), reached substantially better surface quality roughness, when compared with the

Motorex cutting fluid diluted, shown in Figure 4.15 b). Also the tool wear was reduced

mainly because Castrol IloformTDN 81 [7] provides better lubrication due to its

excellent boundary lubrication properties.

Afterwards, Castrol Illoform TDN 81 [7] was applied in the AA1050-O and results in a

good finishing quality solving the wear problem.

The boundary (film) lubrication is based on the bonding arranged between the forming

tool and the blank sheet by fine close-fitting lubrication. The forming tools were

heated approximately to 100° C, because at the elevated temperature chemically

reactive constituents of the lubricant react with the contact surface forming a highly

resistant tenacious layer, or film on the moving solid surfaces (boundary film) which is

capable of supporting the load, the major wear and avoiding the breakdown.

4.4 Plan of experiments

The experimental work was designed in order to investigate the influence of the tool

diameter, heat treatment of the material and different corner part radius in

formability. The details of the experiments are listed below in Table 4.3.

(a) (b)

Test Geometry

Influence of

the tool

diameter.

Influence of

the Heat

treatment.

Influence of

the different

corner radius

in the same

part.

34

Geometry Tool path

Tool

diameter

(mm)

Amount of pieces

AA-1050

H111

8 2

12 2

20 2

30 2

50 2

8 2

12 2

20 2

30 2

50 2

12 2

12 2

8 2

Table 4.3 - Plan of experiments.

Amount of pieces

1050

H111

AA-1050

O

2 0

2 0

2 0

2 0

2 0

2 0

2 0

2 0

2 0

2 0

2 2

2 2

2 0

35

4.5 CAD/CAM design development

The three experimental shapes, shown in Figure 4.16 (a) the truncated pyramid shape,

(b) the truncated conical shape and (c) the truncated pyramid shape with different

corner radii, were designed and drawn in one operation in order to investigate the SPIF

process.

Figure 4.16 - Parts manufactured by one-step method with varying drawing angle.

To ensure compatibly between the performed tests, the geometries with the same

wall profile were created for all five tools diameters as well as for all parts

manufactured by one-step method. The drawing angle vary gradationally 5° every

15mm of depth, starting from 55° and reaching 80°, as it is shown in Figure 4.17.

(a) (b)

(c)

36

Figure 4.17 - Wall profile.

Ham and Jeswiet [8] clearly showed that the formability may not be significantly

affected by the step down size, however the increase of the step down increases also

the surface roughness.

The step down or tool pitch (ΔZ), quantified in Table 4.4, is an offset of the tool path in

the Z-axis per revolution along the tool path, see Figure 4.18.

The values of the step down for the different tools diameters were acquired from

defined values by Silva [3] and Skjøedt [9] for a tool with 12mm diameter by utilization

of direct proportion between tool diameter and step down.

The spindle speed for each tool diameter was determined with purpose to minimize

friction and to ensure equivalent process condition for all tools diameters.

As a initial values for calculation were used again the defined conditions for 12mm

diameter by Silva [3] and Skjøedt [9].

The following Figure 4.19 represents the cross section of the forming tool and

describes the kinetic circumstances involved in the SPIF process.

Figure 4.18 – Process conditions.

37

Figure 4.19 - Angular speed [10].

The angular speed was achieved considering subsequent relation:r

v

=ω , where v is

the tangential velocity of a point about the axis of rotation and was set as a constant

and r is the radius of rotation equal to the half of the tool diameter.

The friction between forming tool and specimen can be also eliminated by freely

rotations of forming tool.

The feed rate (f) has a main impact on the producing time. Jeswiet et al. [11] showed

that the feed rate influence formability (reducing the forming speed increases

formability). Also the friction conditions are affected by the feed rate.

The process conditions for the different tools diameters are listed in Table 4.4.

Tool Diameter – Ø (mm) 8 12 20 30 50

Step Down – ΔZ (mm) 0,35 0,5 0,83 1,25 2,1

Spindle Speed – ω (rpm) 53 35 21 14 8

Feed – f (mm/min) 1000 1000 1000 1000 1000

Table 4.4 - Process conditions.

The definition of the tool path is essential for the good surface quality. Likewise the

definition of tool path is important for the final accuracy of the desired part since, the

springback occurs in SPIF.

The most usual tool path has a constant step down for each revolution of the forming

tool along the specimen contour, what results into a surface with scar, see Figure 4.20.

38

Figure 4.20 - Surface scaring as a result of step down tool path [9].

The ideal tool path involve constant spindle feed in all three axes, unfortunately

utilized CAD/CAM program proEngineer Wildfire 4 does not offer sufficient functions

to execute this idea. Therefore the program called HeToPac [9] was utilized, which

provides continuous feed in all the tree directions.

HeToPac transfers the step down tool path into the helical tool path with constant Z

value for the first and for the last layer. This means that the tool path begins and is

finished with the one constant horizontal passage along the specimen’s contour as is

shown in Figure 4.21.

Figure 4.21 - Helical tool path removed surface scaring [9].

Skjøedt [9] demonstrated by visual comparison that the HeToPac works and also that

scaring could be removed from the manufactured surface, see Figure 4.21.

39

4.6 References

[1] NP EN 10 002-1 – Norma Portuguesa. Metallic materials: Tensile testing. Part 1:

Method of test (at ambient temperature) (1990). (in Portuguese)

[2] Neves J., Single Point Incremental Forming, MSc Thesis, Instituto Superior Técnico

Portugal (2008)

[3] Silva M.B, Single Point Incremental Forming, PhD Thesis, Instituto Superior Técnico

Portugal (2008)

[4] Bramley A.N., Incremental Sheet Forming Process for small batch and prototype

parts, in Idee-Vision-Innovation Edited by F. Vollersten and M. Kleiner, Verlag

Meisenbach (2001) ISBN 3-87525-149-0.

[5] Carrino L., Di Meo N., Sorrentino L., Strano M., The influence of friction in negative

dieless incremental forming, 9th ESAFORM International Conference on Materials

Forming, Glasgow, UK (2006) 203-206.

[6] Retrieved from: http://www.belmag.com/7755aero.htm

[7] Retrieved from:

http://www.castrol.com/castrol/productdetailmin.do?categoryId=9025617

&contentId=7047197

[8] Ham M., Jeswiet J., Single Point Incremental Forming and the Forming Criteria for

AA3003, Annals of CIRP vol. 55/1 (2006) 241-244.

[9] Skjøedt M., Rapid Prototyping by Single Point Incremental Forming of Sheet Metal,

PhD Thesis, Technical University of Denmark (2008)

[10] Retrieved from: http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html

[11] Jeswiet J., Micari F., Hirt G., Bramley A., Duflou J. and Allwood J., Asymmetric

single point incremental forming of sheet metal, Annals of CIRP, 54 (2005) 623-650.

40

5 Results and Discussion

Chapter 3 presented an analytical framework based on membrane analysis that is

capable of modeling the fundamentals of SPIF of metal sheets. Based on the

aforementioned model, it was concluded that the mode of failure at the transition

zone between the inclined wall and the corner radius of the sheet is consistent with

stretching, rather than shearing, being the governing mode of deformation in SPIF.

Also, the analysis of the morphology of the cracks combined with the experimentally

observed suppression of neck formation enabled to conclude that traditional FLC are

not applicable to describe failure. Instead, FFL should be employed to evaluate the

overall formability of the process.

This chapter presents an analysis of the influence of the tool diameter in the

formability of SPIF parts with the objective of understanding if there is a relation

between the diameter of the tool and the limits of formability for a specific material.

After this, the difference between the formability limits in parts with the same

geometry and toolpaths but made of AA1050-H111 and AA1050-O will be in

investigated. Finally, the influence of different corner radius in a pyramidal SPIF part

will be discussed in detail.

5.1 Influence of tool diameter in Formability

Two basic geometries are investigated: the truncated conical shape and the pyramidal

shape with identical wall profile, see Figure 4.17. Both geometries were made from

Aluminium AA-1050 H111.

The idea of using tools with different diameters is fundamental to understand if the

limits of formability change from fracture to necking with the increasing size of the

tool.

5.1.1 Conical Shape

The conical shape parts were performed with 8, 12, 20, 30 and 50 mm tool diameters

and were designed with the wall profile shown in previous chapter 4 (see Figure 4.17).

In the graphic of Figure 5.1, it can be seen that decreasing the tool diameter, increases

the fracture depth. It is also important to point out, in what concerns fracture depth,

that there is a transition zone between the 8 and 30mm diameter tool and finally that

there is no significant difference between parts made with 30 or 50mm diameter tool.

41

Figure 5.1 - Influence of the Tool Diameter in the Fracture Depth obtained for the Conical shape.

The formability of the 8 and 12 mm diameter tools is approximately identical. This fact

can be confirmed by the FFLD, Figure 5.2, where the strain reaches nearly the same

values for both tools. According to the Figure 5.2 it can be also verified that both parts

are under plain strain conditions.

Figure 5.2 - Fracture Forming Limit Diagram containing the FLC and the FFL for two conical SPIF parts

made with 8mm and with 12mm diameter tools.

0,00

10,00

20,00

30,00

40,00

50,00

60,00

70,00

0,00 10,00 20,00 30,00 40,00 50,00 60,00

Fra

ctu

re D

ep

th (

mm

)

Tool Diameter (mm)

cone

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 8mmTool diameter 12mmFFL Experimental

42

Analyzing Figure 5.3, it is verified that the formability increases with the decreasing of

the tool diameter and this fact is in accordance to the interpretation of the Figure 5.1.

The plain strain conditions remain the same as for the 8 mm and 12 mm diameter

tools.

Figure 5.3 - Fracture Forming Limit Diagram containing the FLC and the FFL for three conical SPIF parts

made with 20mm, 30mm and with 50mm diameter tools.

Analyzing the point measured just above and below the fracture for the 50mm tool,

Figure 5.4, it can be seen that it has much more higher extension than the points

around it. With this was concluded that there is necking before the fracture in this part

and also that there is no necking in the parts made with smaller diameter tools.

The SPIF process using bigger tool radius is more similar with conventional stamping.

The forces are distributed over a much bigger area than in case of smaller tool radius

which is the reason why the formability with bigger radius is much lower.

Due to the impossibility to measure the point exactly in the fracture, a point was

measured just above and below the fracture by summarization of the two separated

half (point is separated by the fracture line), see Figure 5.4. The rest of the fracture

points were measured in the places that can be also seen in the Figure 5.4(in blue).

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 20mm

Tool diameter 20mm fracture

Tool diameter 30mm

Tool diameter 30mm fracture

Tool diameter 50mm

Tool diameter 50 mm fracture

FFL Experimental

43

Figure 5.4 - Fracture Forming Limit Diagram containing the FLC and the FFL for a conical SPIF parts made

with 50 mm diameter tools.

After a systematic analysis of the parts performed with different tool diameters which

results are presented before (see Figure 5.1 to Figure 5.4), the main conclusions that

should be pointed out is that decreasing tool diameter, increases formability and that

necking occurs in the parts made with higher tool diameters which can be clearly seen

in the FFLD for the 50mm diameter tool in Figure 5.4. It is also important to refer that

the points in all the graphics of FFLDs for the conical shape are distributed close to the

major true strain axis as typical of plane strain conditions.

5.1.2 Pyramidal Shape

The pyramidal shape parts were performed with 8, 12, 20, 30 and 50mm tool

diameters and were designed with the same wall profile as the truncated cones.

The analysis of the graphic of Figure 5.5 is similar to the analysis of the graphic of

Figure 5.1. Again, it can be seen that decreasing the tool diameter, increases the

fracture depth and that exists a transition zone between the 8 and 30mm diameter

tool. Similarly to the results of the conical shapes, there is no difference in the fracture

depth between parts made with 30 or 50mm diameter tool.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 50 mm

Tool diameter 50 mm fracture

FFL Experimental

44

Figure 5.5 - Influence of the Tool Diameter in the Fracture Depth obtained for the Pyramidal shape.

In Figure 5.6 and Figure 5.7, where the variation of the thickness was plotted as a

function of the depth. It can be seen that the evolution of the thickness is different

when a small or a big diameter tool is used to SPIF the part. This fact worked as a clue

that understands the presence of necking before fracture in the case of the bigger

diameter tools.

Figure 5.6 - Influence of the Tool Diameter in the Thickness Evolution of the wall in a Pyramidal shape

SPIF part – Measurement made in a wall Parallel to the Rolling Direction.

0,00

10,00

20,00

30,00

40,00

50,00

60,00

70,00

0,00 10,00 20,00 30,00 40,00 50,00 60,00

Fra

ctu

re D

ep

th (

mm

)

Tool Diameter (mm)

pyramid

45

Figure 5.7 - Influence of the Tool Diameter in the Thickness Evolution of the wall in a Pyramidal shape

SPIF part – Measurement made in a wall Parallel to the Rolling Direction.

In the FFLD of the Figure 5.8, where the strain reaches nearly the same values for both

tools, the formability of the 8 and 12 mm diameter tools are approximately the same.

Figure 5.8 - Fracture Forming Limit Diagram containing the FLC and the FFL for two pyramidal SPIF parts

made with 8mm and with 12mm diameter tools.

In what concerns Figure 5.9, it is noticed that the formability increases with the

decreasing of the tool diameter and this fact is in accordance to the interpretation of

the Figure 5.5.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 8mmTool diameter 8mm fractureTool diameter 12mmTool diameter 12mm fractureFFL Experimental

46

Figure 5.9 - Fracture Forming Limit Diagram containing the FLC and the FFL for two pyramidal SPIF parts

made with 20 mm, 30 mm and 50 mm diameter tools.

In Figure 5.10 it can be easily seen that the corner is in equal bi-axial strain conditions.

In the inclined wall we know that we should expect plane strain conditions. These two

facts explain that, the points measured in a transition zone between the exact corner

and the wall, are placed in an area between the major true strain axis (plane strain)

and the equal bi-axial axis of the FFLD.

Figure 5.10 - Fracture Forming Limit Diagram containing the FLC and the FFL for a pyramidal SPIF part

made with 50 mm diameter tool.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 20mmTool diameter 20mm fractureTool diameter 30mmTool diameter 30mm fractureTool diameter 50mmTool diameter 50 mm fractureFFL Experimental

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Tool diameter 50 mmTool diameter 50 mm fractureFFL Experimental

47

According to the graphics described above higher formability is obtained for the 8mm tool,

almost the same formability for the 12 and 20mm tools, and formability decreasing with

the increase of tool diameter. This relation between the 12 and 20mm diameter tools can

be a result of the fact that the grid used is not enough refined to ensure the measurement

of some points exactly in the corners (bi-axial strain). It is also remarkable the tendency to

get points in the equal-biaxial strain with the increasing of tool diameter.

Some points that are on the equal-biaxial line can be founded exactly in the corners of

the parts. One example is shown in Figure 5.10.

5.2 Influence of Heat Treatment in Formability

In order to investigate the influence of the heat treatment on the formability of the

metal sheet, tests with 12 mm tool diameter were performed on AA1050-H111 and on

AA1050-O (1hour @ 243ºC, cooled in woven).

In Figure 5.11 it can be seen that the annealed material performs better in what

concerns to formability in both shapes, conical and pyramidal. It is also interesting to

see that the pyramidal shape allows achieving higher depths before fracture than the

conical shape, for both materials.

Figure 5.11 - Influence of the Heat Treatment in the Fracture Depth.

It is important to say that the tests were performed in both geometries (conical and

pyramidal) but due to difficulties in the measurements of the circle grids in the conical

parts made with the annealed material, the FFLD is made only from the measurements

made in the pyramidal parts.

Combining the analysis of the graphics of Figure 5.11 and Figure 5.12 concerning the

influence of heat treatment in the formability of SPIF made parts and, as expected,

higher formability was reached with the annealed material AA1050-O. In both cases

we can find some points near the fracture point which can mean that there is no

necking, leading the results to deformation till fracture.

50

52

54

56

58

60

62

64

66

68

Fra

ctu

re D

ep

th (

mm

)

cone AA1050-H111

cone AA1050-O

pyramid AA1050-H111

pyramid AA1050-O

48

Figure 5.12 - Fracture Forming Limit Diagram containing the FLC, the FFL and the fracture points

obtained from a pyramidal SPIF part made of AA1050-H111 and from a pyramidal SPIF part made of the

same material but annealed. Both were made with 12mm diameter tool.

One last remark for the fracture point for the material AA1050-H111 (in red, Figure

5.12) that is quite above the other points for the same material (in red, also). This can

be explained by the fact that this point is not exactly in the fracture but near the

fracture. The fracture points in the annealed material were not measured due to grid

damage.

5.3 Influence of different corner radius in the formability (pyramidal shape

with 4 different corner radius).

The relation between different corner radius and formability was investigated on the

pyramid shape with four different corners radii (4, 6, 10, 15mm).

Another objective of this new designed part was to gain strain measurements in a

large area of the first quadrant of the principal strain space reducing the overall

number of tests.

The smallest 8 mm diameter tool was applied in order to increase formability and to be

able to create smaller as well as bigger corner radii.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60 -0,40 -0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

SPIF Cone & Pyramid (max. depth)Simple Tension

FLC Experimental

Tool diameter 12mm

Tool diameter 12mm fracture

Tool diameter 12mm_annealedTool diameter 12mm_annealed fractureFFL Exp. AA1050-H111

49

First, it is very important to say that in this new design, the fracture occurred in the

smallest radius corner. Now, according to the Table 5.1 it can be seen that there is no

significant difference in the fracture depth between the pyramid with four different

corners and the cones or pyramid made of the same material and with the same tool.

This can tell us that there is no influence in the fracture depth and consequently in the

overall formability of this new designed shape.

Pyramidal Shape 4 Different Corners Pyramidal Shape

Part 1 Part 2 Part 1 Part 2 Part 3

Depth of each part

(mm) 55,6 57,7 63,4 64,5 63,9

Average of the

depth (mm) 56,65 63,93

Deviation (%) ------------- 12,85

Table 5.1 - Influence of the 4 Different Corner Radius in the Fracture Depth of the Pyramidal

parts.

Analyzing and comparing the results expressed in the graphics of the Figure 5.13, a

higher strain can be reached in the 8mm diameter corner compared with all the other

corners. Between the 12, 20 and 30mm corners there is not so big difference in

formability. Also with the decreasing of the corner’s diameter, the deformation

became more biaxial.

Finally the point displayed above the FFL (corner diameter 8mm fracture) should be

below it, and its position can only be explained by difficulties in measuring due to the

bad shape of the grid in the fracture that can lead us to a less accurate result.

50

Figure 5.13 - Fracture Forming Limit Diagram containing the FLC and the FFL obtained for a pyramidal

SPIF part in which the 4 corners have different diameters; made with 8mm diameter tool.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

Corner diameter 8mm

Corner diameter 8 mm fracture

Corner diameter 12mm

Corner diameter 20mm

Corner diameter 30mm

FFL Experimental

51

6 Multi-stage SPIF

Although SPIF enables higher deformation than the classical sheet forming processes,

it is limited by the drawing angle, α. The final sheet thickness tf in SPIF is determined by

a relation between the drawing angle and the initial thickness of sheet ti (Equation 2.1)

called Sine law, see Figure 6.1.

Figure 6.1 - Schematic representation of the sine law.

According to the Sine law it is very complicated to obtain parts with big drawing angles

(70-90°) without fracture because with the increase of the drawing angle, the final

thickness would be zero. To solve this problem, multi-stage forming method was

presented in order to increase maximum drawing angle, first in 1997 by Kitazawa et al.

[1] using two stages to produce hemi ellipsoidal shapes.

Later Skjøedt [2] went further on multi-stage and utilized a five stage strategy to

produce a cone with vertical walls, see Figure 6.3.

The idea of the five stage strategy, presented in Figure 6.2, was to extend the available

material (indicated by the dashed line) towards the corner (B). All the stages were

gradually stretched after the cone with 45° that was obtained in the first stage.

Skjøedt et al. [4] compared two multistage strategies, i.e. Down-Down (DD) and Down-

Up (DU) and proved that the distribution of strains depends mainly on the tool path

geometry and also on the forming direction (downwards or upwards). The results are

presented on the Figure 6.4.

Figure 6.3 - Cylinder with

vertical walls [2].

Figure 6.2 - Five stage forming [3].

α � �

� �

52

Figure 6.4 - Thickness distribution (Legend displays thickness in mm) [4].

As is shown in Figure 6.4 after the two stage DD strategy the area with higher material

thickness is localized just below the residual cone (60mm depth). Instead, in the DU

strategy and in the same area (60mm depth) the material thickness is the lowest one.

Hald et al. [5] presented a different multi-stage strategy for obtaining vertical walls. In

this strategy the steps are formed by the constant horizontal tool movement outwards

into the sides, see Figure 6.5.

The idea is to thin out the plate in the bottom. As nomenclature, when the movement

of the tool is performed by the horizontal movement with constant Z coordinate the

stage is represented by the capital letter H.

Figure 6.5 - Schematic representation of vertical wall created by the whole side of the tool [5].

The aim of the following section is to achieve complex shapes with vertical walls. For

this purpose was designed a cone with vertical walls based on the already presented

strategy of Skjøedt [2]. This strategy was improved in order to remove the obtained

residual cone. Subsequently and based on the experience gained, it was designed and

manufactured a part with a higher level of difficulty, a pyramid with vertical walls.

53

Besides the objective of producing parts with vertical walls there is also the aim of

checking if the FFL’s commonly utilized in single stage SPIF are also applicable in multi-

stage SPIF.

6.1 Conical shape

The following four tool paths, displayed in Figure 6.6, were designed in CAD/CAM

software ProEngineer Wildfire 4 in accordance to the previous work by Skjøedt [2].

The following cylindrical shape with vertical walls was manufactured and subsequently

analyzed in order to understand the deformation processes in multi-stage forming

process.

Figure 6.6 - Tool paths of the four stages utilized to produce a cone with vertical walls.

The first stage could be performed only by downwards movement like a regular cone

with 45 degrees drawing angle.

In second stage, the material was repeatedly extended by downwards movement

according to the designed tool path displayed in Figure 6.6(b).

In case of multistage SPIF with a DD strategy, a residual cone appears at the bottom of

the part, see Figure 6.7(a). The residual cone is formed even thought the tool paths

depths of the first and of the second stage are equal, because the geometry created in

the first stage was prolonged by the downwards movement of the wider second stage.

Figure 6.7 - Status of residual cone during the manufacturing of the cone with vertical walls.

(a) Residual cone presented after 2nd

stage,

(b) Residual cone presented after 3rd

stage,

(c) Final reduced residual cone after 4th

stage.

The third stage was manufactured by downwards movement with the objective to

extend material in the X-Y cross section, see Figure 6.6(c), which resulted in another

additional residual cone with a bigger diameter, see Figure 6.7(b).

(a) (b) (c) (d)

(a) (b) (c)

54

The final fourth stage, see Figure 6.6(d), was manufactured by upwards movement

starting at the bottom of the part in order to obtain the vertical walls and to eliminate

the additional residual cone obtained in the 3rd stage, see Figure 6.7(c).

The FFLD included in the Figure 6.8, which describes the strains distribution for the

final stage of the cone with vertical walls, was obtained using the techniques that were

mentioned mentioned in chapter 4.

Figure 6.8 - FFLD for final stage of cone with residual cone

All of the points are plotted under the FFL, what confirms that fracture did not occur in

this part. Also according to the FFLD the lowest strains are localized on the area where

the backing plate supports the part, followed by the evenly distributed strains that are

localized on the residual cone. A possible explanation for this can be that the residual

cone surface was formed just in the first step according to a cone geometry with 45

degrees wall angle.

In the other hand, the highest strains values correspond to the vertical walls and

horizontal bottom as it is shown on Figure 6.8, because the distribution of strains in

these areas is a result of the strain applied to the part in each step and because these

areas were those where the material was more deformed, see Figure 6.2.

It is also interesting to point out that the strain values for radius, connecting vertical

walls with flat bottom, are more close to equal-biaxial stretching, see Figure 6.8.

55

6.1.1 Improvement of the cone with vertical walls

The main drawback of the presented part is the formation of a residual cone. Silva [6]

improved the previous strategy making a cone with vertical walls and flat bottom, see

Figure 6.9.

Figure 6.9 - Cone with vertical walls and without residual cone [6].

The improvement was based on the idea to realize the tool paths according DDDU

strategy mentioned before, but with different depths for each stage in order to acquire

the flat bottom and the vertical walls in the final stage.

The following section is focused on the investigation and improvement of the strategy

by Silva [6].

The tool paths trajectories printed in Figure 6.10 were obtained by trial and error

method and they were designed and utilized to achieve geometry with vertical walls

and flat bottom. The red line represents the upwards movement of the last stage.

Figure 6.10 - Scheme of the tool paths for cone with vertical walls and with flat bottom.

The tool paths were designed in ProEngineer Wildfire 4 and presented in Figure 6.11.

Figure 6.11 - CAM tool paths for the cone with vertical walls and without residual cone (stage by stage).

1

2 3

4

56

In order to investigate the deformation circumstances were produced for each stage,

one experimental specimen, see Table 6.1.

Geometry Tool Diameter

(mm)

Amount of specimens

1st

step 2nd

step 3rd

step 4th

step

12 1 1 1 1

Table 6.1 - Plan of experiment

The residual cones appeared as a result of DD strategy after the second and after the

third stage, see Figure 6.12, but these residual cones were subsequently removed on

the last stage, which was designed especially for this purpose.

Figure 6.12 - Four stages of cone with vertical walls and flat bottom.

The FFLD showed on Figure 6.13 denotes the strains of the first stage formed by 45

degrees angle. For this reason the strains are evenly distributed with similar values

near the vertical line, (plane strain region).

57

Figure 6.13 - FFLD for 1st

stage of cone with vertical walls without residual cone.

For the subsequent second stage, it was shown that the biggest deformation takes

place around the area localized approximately 20mm below the backing plate, see

Figure 6.14. Again this stage is characterized by the plane strain conditions but with

higher values, when compared to the first stage.

58

Figure 6.14 - FFLD for 2nd stage of cone with vertical walls without residual cone.

In the third stage, shown on Figure 6.15 the strains with the lower values are placed

just below the residual cone, this is probably because during the DDD the material in

this area is less deformed than the material of the almost vertical walls.

Figure 6.15 - FFLD for 3rd stage of cone with vertical walls without residual cone.

59

In the final stage performed by upward movement of the tool, the residual cone was

removed. The position of the strains is just under the FFL, see Figure 6.16, shows that

the material was deformed to the maximum limit just before fracture.

Figure 6.16 - FFLD for 4th

stage of cone with vertical walls without residual cone.

The points in the transition area between the walls and the bottom are more closed to

equal-biaxial strain.

6.2 Pyramid with vertical walls

After the successful experiments described earlier, it was chosen to produce a pyramid

with vertical walls made from material AA1050-O. The 8mm diameter tool was chosen

because the tools with smaller diameters usually provide higher formality as it is

shown in chapter 5. The process conditions for 8mm tool diameter are presented in

Table 4.4.

The attempt was supported by previous expertise with multi-stage strategy and by trial

and error method.

The strategy was based on the idea that a pyramid with vertical walls could be

obtained by stretching a conical shape towards the four corners of a pyramid, see

Figure 6.17.

60

Figure 6.17 - First and second tool path of pyramid with vertical walls.

According to this idea the first tool path was designed with nearly circular cross section

in the X-Y plane and under the 45° angle, similarly as the already presented cone with

vertical walls. The first tool path is shown in Figure 6.17(a) as well as in Figure 6.20

with dimensions.

The second step starts with the stretching of the cone towards the corners in order to

obtain a square shape with 50mm corner radius, see Figure 6.17(b). It is performed by

downwards tool movement with a similar wall profile, see in Figure 6.20, as the second

stage of the cone with vertical walls i.e. arc with tangent under 60° angle.

It was noticed that the thickness distribution of DU strategy, shown in Figure 6.4, is

almost a mirror of the DD strategy. Therefore, it was predicted that after the DD stages

a third U stage could improve the material distribution.

With this in mind, an upwards tool path was created, see Figure 6.18.

Figure 6.18 - Helical tool path for the third forming step of the pyramid with vertical walls.

The design of the third step has been focused on the following objectives:

• relocate the material from the thicker areas to the thinnest ones;

• ensure constant thickness distribution for subsequent stretching;

• remove residual pyramid created after the second stage as a consequence of DD strategy;

• decrease the corner radius of the part.

The fourth downwards tool path, see Figure 6.19 (a), decreased bottom radius in the X-

Z plane and shaped 15 mm deep vertical walls shown in Figure 6.20 below.

(a) (b)

61

Figure 6.19 - Tool paths for 4th

(a), 5th

(b) and 6th

(c) forming step.

The fifth tool path was designed and produced with the constant depth value of Z =

52mm by H tool movement as it is shown in Figure 6.19(b). The aim was to thin out the

plate in the bottom and not on the sides, see Figure 6.5.

Figure 6.20 - Scheme of utilized tool paths (in black for D tool movement, in red for U tool movement and

in yellow for H tool movement) for the pyramid with vertical walls.

The final passage was performed once again by U movement (otherwise the residual

cone would occur) as a continuation of the previous H passage. The final shape is

shown in Figure 6.21.

Figure 6.21 - Pyramid with 22mm long vertical walls.

(a) (b) (c)

62

Even though the vertical walls were obtained after the fourth stage, see Figure 6.20,

the forming continued in order to decrease the corner radii. Probably as a

consequence of this additional forming a defect occurred in the final geometry, see

Figure 6.22.

Figure 6.22 – Close view of the defect occurred.

The forming limits were determined in accordance to the methods described in the

previous chapter 4. The experimental strains were only measured for the sixth (final)

stage.

The highest strains values correspond to the corners near the bottom as it is shown on

Figure 6.23. Similarly to previous studies focused on the cone with vertical walls, the

distribution of strains during forming is not uniform and these areas were much more

extended than the others.

Figure 6.23 - FFLD with experimental strains.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,200,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

pyramid

FFL Experimental

63

As seen, the values distributed close to plane strain are located on the vertical walls

while those close to equal bi-axial stretching are located at the corners,see Figure 6.23.

6.3 Conclusion

Results show that formability limits characterized by means of the FFL also apply in

multi-stage SPIF.

Similar shapes, with different tool paths, to those previously done by Skjøedt [2] and

Silva [6] were successfully obtained. Forming strategies were evaluated by circle grid

analysis and the results were plotted into the FFLD.

The main conclusion derived from the investigation is that the distribution of the

strains depends mainly on the tool path geometry and also on the forming direction.

The tool paths in the up direction imply more biaxial strains than the tool paths in the

opposite direction. This conclusion confirms the proposal that was initially formulated

by Skjøedt et al. [4].

6.4 References

[1] Kitazawa, K., and Nakane, M., Hemi-ellipsoidal stretch-expanding of aluminum

sheet by CNC incremental forming process with two path method, Keikinzoku/Journal

of Japan Institute of Light Metals, 47, (1997), 440-445, (in Japanese).

[2] Skjøedt M., Rapid Prototyping by Single Point Incremental Forming of Sheet Metal,

PhD Thesis, Technical University of Denmark (2008)

[3] Skjoedt M., Silva M.B., Martins P.A.F., Bay N., Strategies and Limits in Multistage

Single Point Incremental Forming (in press).

[4] Skjoedt M., Silva M.B., Martins P.A.F., Bay N., Strain Paths and Fracture in Multi-stage Single Point Incremental Forming, ICTP-2008, 9th International Conference on Technology of Plasticity, Gyeongju, Korea, 2008. [5] Hald B., and Soe Nielsen P., Multi Pass Strategies for Single Point Incremental

Forming, Dept. of Mechanical Engineering, Technical Report, Technical University of

Denmark (2007)

[6] Silva M.B Single Point Incremental Forming, PhD Thesis, Instituto Superior Técnico

Portugal (2008)

64

7 Prototype Development

7.1 Thermoforming mould of sanitary bathtub for a shower

Following the success of the previous experiments it was decided to apply the

expertise in multi-stage SPIF to the production of a mould for thermoforming of

sanitary pools, which should represent a good example to apply the multi-stage

strategy in a practical application.

The sanitary pools made from polymers are commonly produced by thermoforming

where a plastic sheet is heated and then draped over a mould where vacuum is

applied. The product is then allowed to cool down before being ejected from the

mould using a reverse pressure facility, see Figure 7.1.

Figure 7.1 - Thermoforming process scheme [2].

The selection of the best suited mould material depends largely on the severity and

length of the service required.

In general, the moulds for thermoforming are manufactured by conventional

machining or by techniques that requires a pattern (core) for mould generation. These

patterns are produced by hand when low accuracy is required or by machining when

higher accuracy is necessary.

The moulds shown in Figure 7.2 have been produced by the Lokas Ltd. [3] company

and are made by casting of aluminum. Since this technology requires pattern, which

involves more labor, it is believed that SPIF can provide a better option.

SPIF can be classified as a rapid prototyping manufacturing process even though the

tool path must be created in CAD/CAM software [4]. The production time can be

reduced if the client provides the CAD file of the part.

Also, SPIF is more suitable for the parts with complicated rounded geometries, which

fabrication otherwise requires difficult handmade patterns.

The main objective of our work was to produce a part with a similar geometry with the

part in Figure 7.2 by SPIF.

65

Figure 7.2 - Moulds for thermoforming of a shower baths manufactured by casting technology [3].

7.2 Experimental setup

Similarly to the multi-stage SPIF of pyramid with vertical, the material AA1050-O was

shaped with a 8mm diameter tool. The process conditions for the 8mm tool diameter

are presented in Table 4.4.

Because of the complexity of the prototype part, several strategies were investigated

in order to produce a sound final part without any fracture and with the correct

geometry.

7.3 Investigated strategies

The final geometry of the prototype part has four geometrical characteristics, shown

as tool paths in Figure 7.3.

Figure 7.3 - Geometric characteristics shown as tool paths of the prototype part.

a) Top Area.

b) Wall.

c) Stripes.

d) Hollow.

For the stripes, hollow and for the wall, the final shape was achieved at the first

attempt. The most challenging geometry to make was the top area for the reasons that

are described in the following section.

(a) (b) (c) (d)

66

7.3.1 Stripes and hollow

It was decided to manufacture the stripes and the hollow first. The reason for this

strategy is to avoid the need of a complicated support the in following operations.

The backing plate for this 1st stage is shown in Figure 7.4 and it was utilized first to

make the stripes and after turning the sheet over, to make the hollow shown in Figure

7.4.

Figure 7.4 - Stripes and hollow manufacturing.

7.3.2 Top area

Manufacturing continued in the top area with a shaped corner, where several

strategies were examined before choosing the most adequate. The metal sheet was

for this purpose supported by the tailored backing plate shown in Figure 7.5.

Figure 7.5 - Backing plate for prototype part.

The first investigated design, see #1 in Table 7.1, used the two stage DD strategy to

form a top area into the 15 mm depth with shaped corner. This strategy reached a

good final shape although a residual protrusion was obtained as a consequence of the

DD strategy. Although performing the subsequent D stage, where the walls are

shaped, an undesired geometry appeared as a consequence of insufficient backing

plate support, so this first strategy was abandoned. The obtained result is shown in

Figure 7.6(a).

Strategies

Top area

Top área depth

(mm)

Wall

Result - Figure

Table

In order to eliminate the previous problem

performed in three stages, DDU. The last U movement was designed in order to

remove the residual protrusion, which occurred

fracture during the forming of

was also not adequate, see

Figure 7.6

The first two strategies showed

support was considered in order to support the specimen during the wall forming. The

idea was to hold up the obtained top area by a support

corner.

The support was found very difficult and time consuming to manufacture and to clamp

in the SPIF rig. Therefore in the next strategies

in order to support the subsequent wall forming forces by itself. For this purpose the

depth of the top area was reduced from 15 mm to 7

In the strategy #3, see Table

Probably the reason for this was the small corner radius in the bottom of the top area

and the large drawing angle, see

67

, so this first strategy was abandoned. The obtained result is shown in

1 2 3

DD DDU D

15 15 7,5 7,5

D D -

7.6 (a) 7.6(b) 7.7 7.9

Table 7.1 - Top area and walls strategies.

In order to eliminate the previous problem, a second strategy, see #2 in

performed in three stages, DDU. The last U movement was designed in order to

remove the residual protrusion, which occurred before. However, these lead to

fracture during the forming of the walls using a D movement. Therefore,

, see Figure 7.6(b).

6 - Strategy #1 and #2 for shaped corner and wall.

The first two strategies showed lack of support by the backing plate. So, a special

support was considered in order to support the specimen during the wall forming. The

the obtained top area by a support located under the shaped

very difficult and time consuming to manufacture and to clamp

. Therefore in the next strategies, a new top area geometry was designed

in order to support the subsequent wall forming forces by itself. For this purpose the

depth of the top area was reduced from 15 mm to 7,5 mm.

Table 7.1, during the manufacture, a fracture occurred.

Probably the reason for this was the small corner radius in the bottom of the top area

and the large drawing angle, see Figure 7.7.

(a)

, so this first strategy was abandoned. The obtained result is shown in

4

D

7,5

D

7.9

a second strategy, see #2 in Figure 7.1, was

performed in three stages, DDU. The last U movement was designed in order to

However, these lead to

. Therefore, this strategy

lack of support by the backing plate. So, a special

support was considered in order to support the specimen during the wall forming. The

d under the shaped

very difficult and time consuming to manufacture and to clamp

a new top area geometry was designed

in order to support the subsequent wall forming forces by itself. For this purpose the

fracture occurred.

Probably the reason for this was the small corner radius in the bottom of the top area

(b)

68

Figure 7.7 - Strategy #3 showing the fracture.

Finally, in the fourth strategy, see #4 in Table 7.1, a gradually increased corner radius

was designed in the top area, see Figure 7.8.

Figure 7.8 - Gradually increased corner made according to the strategy # 4.

With this last strategy it was possible to produce a successful final part, see Figure 7.9.

Figure 7.9 - Final shape of the top area and wall.

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7.3.3 Wall

The wall was manufactured by multi-stage method after the stripes, the hollow and

the top area and includes four tool paths geometries, shown in Figure 7.10.

Figure 7.10 - DDHU tool paths strategy for the wall.

The first two tool paths, see Figure 7.10(a) and (b), were executed by D movement.

The third tool path, see Figure 7.10 (c), was designed in X-Y plane and had similar

purposes as the vertical tool path for the pyramid with vertical walls, that was

mentioned in the previous section. The part was finished by one last passage shown in

Figure 7.10 (d), that is by means of an upward movement.

Figure 7.11 - Tool paths outlines.

The tool paths have been executed into the depths described in Figure 7.11 and the

prototype of an aluminum mould for thermoforming of shower bath is shown in Figure

7.12 according to the global strategy presented in Table 7.2.

(a) (b) (c) (d)

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Geometry Strategy CAM Geometry

Stripes D

Hollow D

Top Area D

Walls DDHU

Table 7.2 - Global prototype strategy.

Figure 7.12 - Final prototype part.

7.4 Formability analysis

The forming limits have been investigated by the circle grid analysis executed

identically as in previous test cases. The three different corners of the part, see Figure

71

7.13, were measured and the results are displayed in FFLDs, see Figure 7.14, Figure

7.15 and Figure 7.16.

Figure 7.13 - Prototype of aluminum mould with different corners signed (corner B is identical with the

opposite corner).

The corner marked as A has the smallest radius so it was predicted that the strains

reached the highest values among the all tested corners.

Figure 7.14 - FFLD containing the FLC and the FFL for corner A of the prototype of aluminum mould.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,200,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

corner_A

FFL Experimental

72

Figure 7.15 - FFLD containing the FLC and the FFL for corner B of the prototype of aluminum mould.

The lowest values of strain are located in the transition area between the corner and

the shell.

Figure 7.16 - FFLD containing the FLC and the FFL for corner C of the prototype of aluminum mould.

Values for the smallest corner A reached the highest values of stain.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,200,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

corner_B

FFL Experimental

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

2,00

-0,60-0,40-0,200,00 0,20 0,40 0,60 0,80 1,00 1,20 1,40

Majo

r T

rue S

train

Minor True Strain

Biaxial Stretching

Simple Tension

FLC Experimental

corner_C

FFL Experimental

73

7.5 Conclusion

The prototype development was based on the previous experience and on a trial and

error method.

In what concerns the integration of the manufactured prototype into the

thermoforming process, there are still some improvements to be done. A

heating/cooling system and a suction system are necessary to ensure the correct

performance of the mould.

The new backing plates that were made to support the prototype part during

manufacturing were designed and produced by the CAD/CAM technologies. This fact

should be taken into account for the final cost estimation. Even so, a part with

rounded geometry and without high accuracy requirements can be produced by SPIF

with lower costs then by casting.

Finally the aim to put in practice our knowledge gained during the experiences

performed before was fulfilled by producing successfully a prototype part.

7.6 References

[1] Micari F., Ambrogio G., Filice L., Shape and dimensional accuracy in Single Point

Incremental Forming: State of the art and future trends, Journal of Materials

Processing Technology 191 (2007) 390-395.

[2] Retrieved from: http://www.lokas.cz/formy_do_termoforowania_wyrobow_

sanitarnych.php#

[3] Thrales, Lane, A vacuum forming guide, Formech International Ltd. Harpenden,

United Kingdom

[4] Skjøedt M., Rapid Prototyping by Single Point Incremental Forming of Sheet Metal,

PhD Thesis, Technical University of Denmark (2008)

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8 Conclusions and future work

The research work developed in this MSc research project was aimed to analyze the

formability limits and mechanisms of aluminium metal sheets during conventional and

multi-stage SPIF. For that some tests were performed changing the diameters of the

tools and the material conditions that were utilized for producing parts by the SPIF

process.

In what concerns the influence of the tool diameter, the experimental work performed

in this thesis allowed to conclude that formability increases with the decrease of the

diameter of the tool. The experiments performed in this thesis, allowed to observe the

existence or absence of necking in the parts made by SPIF and to conclude that necking

exists only in the parts made with bigger diameter tools, because the process is more

similar to that of conventional stamping.

The level of formability reached by the annealed material was much higher than

expected against AA1050-H111. Because the work was only based on pyramidal parts

it would be interesting, as a future work, to perform conical parts in order to make the

strain analyses also in these parts

The new pyramidal testing procedure that made possible to analyze the influence of

the corner radius in SPIF parts also fulfilled the objective of getting strain

measurements in a large area of the first quadrant of the principal strain space and

therefore reducing the overall number of tests. As a conclusion, a higher strain can be

reached in the 8mm diameter corner compared with all the other corners. Between

the 12, 20 and 30mm corner radius there is not such a big difference in formability.

Also by decreasing the diameter of the corners, deformation becomes more equal bi-

axial.

It was also confirmed that forming limit diagrams that give the loci of necking strains

are not therefore relevant to limits in SPIF. It is the fracture forming limit that needs to

be employed in the evaluation of formability in conventional SPIF.

A multi-stage SPIF strategy capable of enhancing the formability of the process was

presented and results confirm that SPIF is limited by fracture and not by necking.

According to this, some parts already made before were successfully manufactured

and studied again and served as a basis to the design and manufacture of a new

specimen that had never been attempted before; a pyramidal shape with vertical

walls. As future work it would be interesting to produce this part again in order to

make the strain analyses in all the steps of the manufacturing process and to get the

corresponding evolution of the strains paths.

In the last part of the thesis a prototype part is presented with the objective of

applying all the knowledge that was obtained during the MSc research project. The

part was chosen taking in account the possibility of making SPIF in both sides of the

metal sheet, the existence of different diameter corners and the presence of vertical

walls. The successful manufacture of the part was quite challenging and required

75

combination of the aforementioned expertise with trial-and-error systematic

procedures.