Aula 0 - Análise de falhas

7/29/2019 Aula 0 - Análise de falhas

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Grupo de fadiga e materiais aeronáuticos

ANÁLISE MECÂNICA E METALÚRGICADE FALHAS NOS METAIS

Herman Jacobus Cornelis Voorwald

ABORDAGEM DE FADIGA E

MECÂNICA DA FRATURA




Definition:Definition:• Failure x Fracture:

– Fitness-for-Service (e.g. critical crack growth)

– Breaking-in-two

• Fracture : The stress at the atomic level

exceeds the cohesive strength of the material.

– Rupture

– Cleavage

• Fracture Mechanics: – Quantitative relations between the crack length, the

material’s inherent resistance to crack growth, and the stressat which the crack propagates at high speed to cause

structural failure.




Fratura Frágil: Aspectos MacroscópicosFratura Frágil: Aspectos Macroscópicos




Fratura Frágil: Aspectos MicroscópicosFratura Frágil: Aspectos Microscópicos




Fratura Frágil: Aspectos MicromecânicosFratura Frágil: Aspectos Micromecânicos




Fratura Frágil: Aspectos Macro / MicroscópicosFratura Frágil: Aspectos Macro / Microscópicos




Fratura Dúctil: Aspectos MacroscópicosFratura Dúctil: Aspectos Macroscópicos




Fratura Dúctil: Aspectos MicroscópicosFratura Dúctil: Aspectos Microscópicos




Fratura Dúctil: Aspectos Micro / MacroscópicosFratura Dúctil: Aspectos Micro / Macroscópicos




Fratura Dúctil: MicromecanismoFratura Dúctil: Micromecanismo




Fratura por Fadiga:Fratura por Fadiga:




Fracture MechanicsFracture Mechanics• Coast of Fracture:

– USA – 1982: $119 billion (4% PIB)

– Application of Fracture Mechanics: $28 billion

• Wh Structures Fail?

(1) Negligence during design, construction or operation of structure.(2) Application of new design or material, which produces an

unexpected and undesirable result (e.g. Liberty Ships).

• Generalized Failure Modes: – Cyclic load (fatigue fracture); Stress corrosion, Hydrogen-induced

cracks (fracture upon environment influence); Creep Fracture;Brittle Fracture (Cleavage); Ductile Fracture (Rupture).




Revolução Industrial (divisor de águas):Revolução Industrial (divisor de águas):

Antes: Depois:

compression tension




Histórico (PósHistórico (Pós--Revolução Industrial)Revolução Industrial)

• 3 grandes períodos de acidentes na história:

• : – 2000 mortes (Grã-Bretanha)

– descarrilamento de trem

– fratura em rodas, trilhos, eixos




• Fadiga dos Materiais:

– Concentradores de

Histórico (1860Histórico (1860--1870)1870)

Tensão – Carregamento cíclico:

• fratura com tensõesmenores que o limite

de escoamento domaterial

– Wöhler’s Curves (SxN)



Navio LibertyNavio LibertyDuring World War II

Built more than 2500 Liberty

Class Ships

About 700 experienced sever

structural failures

about 145 broke into two parts.

Reasons:- Flaws in welded joints

- High strength materials were

used (Low fracture

toughness)- Low temperature further reduced

the fracture toughness.



Iron

Stress-Strain Behavior versus Temperature

• Ductility is reduced with temperature reduction.

So, Ambient and Operating temperatures can affectfailure mode of materials.



Charpy Impact Data: Energy vs Temperature

Notched sample is hit and crack propagates.

• Temperature effect clear from these materials test.• A238 Steel has more dramatic dependence around ocean T.



Comet Firsts• First commercial airliner to use turbojet

engines.

• First commercial airliner to use totallyhydraulically actuated controls.

• First large commercial airliner to have gluedskin panels (Redux).

• First commercial airliner to have a highlyressurized cabin 8.25 si .

• Following the accidents to G-ALYP and G-ALYY a number of events took place which were alsounique:

• First commercial airliner to use high pressurerefueling.

• First use of underwater cameras in the collection of wreckage.

• First large scale reconstruction as part of an accident investigation.

• First use of a water tank to encase and test a whole aircraft.

• First use of medical forensics to solve an air accident (G-ALYY).



• After only eighteen months of service two aircraft

disappeared within threemonths of each other. TheSecretary of State for CivilAviation ordered a full

investigation into the causesof the disappearances. Thiswas carried out by the RoyalAircraft Establishment (RAE)at Farnborough and a court of enquiry was established.

• One part of the investigation examined cabin pressurization. This used water to produce cabin loading and hydraulic rams to generate wing loading. BOACComet, Yoke Uncle, was placed inside a water tank with the wings protrudingthrough seals in the walls of the tank. The loads which were applied simulateda three hour flight in ten minutes.




Contribution of the Aeronautic Sector:Contribution of the Aeronautic Sector:

NOVAS FILOSOFIAS DE PROJETO

• VIDA SEGURA (“SAFE-LIFE”)

• FALHA SEGURA (“FAIL-SAFE”)

• TOLERÂNCIA AO DANO (“DAMAGE TOLERANCE”)





FILOSOFIAS DE PROJETO VIDA SEGURA (SAFE-LIFE)

• A nucleação de uma trinca implica em falha iminente.

•

A vida segura de um componente consiste da etapa de iniciação da trinca, desconsiderando a etapa de propagação,resultando na inutilização deste, antes que sua vida útil tenha sido alcançada.

• Aplicada em materiais de alta resistência mecânica, os quais

apresentam tamanho de trinca crítica muito pequeno e,portanto, de difícil inspeção.• É representada pela curva σ σσ σ - N, a qual identifica, para

qualquer nível de tensão, uma vida correspondente em fadiga.





FILOSOFIAS DE PROJETO FALHA SEGURA (FAIL-SAFE)

•

trinca de comprimento não crítico; • Deverá propiciar um extenso período de propagação da

trinca sem que haja redução na resistência residual estática;

• Estima-se uma vida média para a propagação da trinca (Mecânica da Fratura) cujo tamanho não comprometa a resistência estática do componente.





FILOSOFIAS DE PROJETO TOLERÂNCIA A DANO (DAMAGE TOLERANCE)

• Com onente ue a ós determinada “vida se ura”

deveria ser substituído, mas apresenta sobremetal suficiente para propagação estável da trinca.• Necessita-se de inspeções periódicas, reparos

oportunos e eficientes programas de prevenção à

corrosão.• Programas suplementares de inspeções com o

objetivo de detectar trincas por fadiga em aeronaves projetadas pelo princípio de “vida segura”.

Comet 1 Boeing 777 200 Boeing 747 400



Comet 1 Boeing 777-200 Boeing 747-400

28.3 m (93'0") 63.73 m (209'1")

35.1 m 60.93 m 64.92 m

(115'0") (199'11") (213')

89 kN 925 kN 1080 kN

(20,000 lbst) (208,000 lbst) (242,696 lbst)

764 km/h 987 km/h 940 km/h

Length 70.66 m (231'10")

Wingspan

Engines 4 de Havilland

Ghost

2 Rolls-Royce

Trent 800

4 Rolls-Royce

RB211-524 GT

Total Thrust

Cruising

Speed

(475 mph) (557 mph) (584 mph)

10.7 km 10.7 km 10.7 km

(40,000 feet) (40,000 feet) (40,000 feet)

2815 km 7505 km 13,278 km

(1750 miles) (4660 miles) (8245 miles)

5450 kg 109,116 kg 215,374 kg

(12,000 lb) (240,600 lb) (474,900 lb)

31,750 kg 135,580 kg 181,985 kg

(70,000 lb) (298,900 lb) (399,000 lb)

52,000 kg 229,520 kg 391,500 kg

(115,000 lb) (506,000 lb) (870,000 lb)Passengers 36 - 44 305 - 328 421

Flight Crew 4 2 2

Payload

Weight Empty

Max Take Off

Weight

CruiseAltitude

Range











Failure: Fracture and Fatiguetemperature, stress and cyclic loading effect

It is important to understand the

mechanisms for failure,especially to prevent in-servicefailures via design.

Ship-cyclic loading - waves and cargo.

This can be accomplished via:Materials selection;Processing (strengthening);Design Safety (combination).

Objective:• describe crack propagation for ductile and brittle materials.• explain why brittle materials are much less strong than possible theoretically.• define and use Fracture Toughness.

• define fatigue and creep and specify conditions in which they are operative.• what is steady-state creep and fatigue lifetime? Identify from a plot.

From Callister, photo Neal Noenzi (NYTimes)




Introduction to Fracture MechanicsIntroduction to Fracture Mechanics

• Conventional design philosophy

• Strength (• Strength (σσσσσσσσYsYs))

• Changes:• Improved NDE• Defect is not the end of life

• Cost of Replacement & Repair

• Possibility of continued service

• Buckling• Buckling• Deflection• Deflection

•• vo ress oncen ra onvo ress oncen ra on

Fracture MechanicsFracture MechanicsStudy of mechanical behavior of cracked materials subjected to anapplied load.




The Fracture Mechanics Approach:The Fracture Mechanics Approach:Fracture Mechanics vs. Strength of Materials




The Fracture Mechanics Approach:The Fracture Mechanics Approach:Fracture Mechanics vs. Strength of Materials




Effect of Crack in a StructureEffect of Crack in a Structure

Static loading Residual Strength Diag

Design Strength

highest service

load

Normal serviceload

Failure

Residual

Strength

Crack Size

Time

The central difficulty in designing against fracture in high-strength materials is thatthe presence of cracks can modify the local stresses to such an extent that theelastic stress analyses are insufficient.




Objective of Fracture Mechanics TechnologyObjective of Fracture Mechanics TechnologyDevelop prediction methods and calculate of how fast cracks will grow and how

fast the residual strength will decrease.

Specifically:1. What is the residual strength as a function of crack size?

2. What size of a crack can be tolerated at the service load (Critical crack size)?

.

4. What size of preexisting flaw (crack) can be permitted at the moment structure starts its life?5. How often should the structure be inspected?

Includes 4 disciplines:Engineering – Load 7 Stress Analysis

Applied Mechanics – Crack tip stress field & Driving Force

Testing – Quantify Critical parameters & Verify Analytical Parameters

Material Science – failure process at the atomic scale. Includes dislocations & impurities

Fracture Mechanics DisciplineFracture Mechanics Discipline




Coverage of Fracture MechanicsCoverage of Fracture Mechanics

Fracture Fracture processand criteria

plasticity testing applications

materials scienceengineering

applied mechanics

10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2

fracture mechanics




The Fracture Mechanics Approach:The Fracture Mechanics Approach:Simplified Family Tree of Simplified Family Tree of Fracture Mechanics




The Fracture Mechanics Approach:The Fracture Mechanics Approach:Effect of Fracture Toughness on the governing Failure MechanismEffect of Fracture Toughness on the governing Failure Mechanism




MAJOR HISTORICAL DEVELOPMENT IN FRACTURE MECHANICSMAJOR HISTORICAL DEVELOPMENT IN FRACTURE MECHANICS

• In 1898, a German Engineer by the name of Kirsch showed that astress concentration factor of 3 was found to exist around a circular hole in an infinite plate subjected to uniform tensile stresses;

• While investigating the unexpected failure of naval ships in 1913, Inglisex en e e so u on or s resses aroun a c rcu ar o e n an n n e

plate to the more general case of an ellipse. It should be noted that thisproblem was solved 3 years earlier by Kolosoff (who was the mentor of Muschelisvili) in St Petersbourg, however history remembers only Ingliswho showed that a stress concentration factor prevails around the

ellipse (where a is the half length of the major axis, and ρ is theradiusof curvature).





• Inglis’s early work was followed by the classical studies of Griffith, who

was not orginally interested in the strength of cracked structures(fracture mechanics was not yet a discipline), but rather in the tensilestrength of crystalline solids and its relation to the theory based on their

,

Young’s Modulus. With his assistant Lockspeiser, Griffith was thenworking at the Royal Aircraft Establishment (RAE) at Farnborough,England and was testing the strength of glass rods of differentdiameters at different temperatures. They found that the strengthincreased rapidly as the size decreased. Asymptotic values of 1,600and 25 Ksi were found for infinitesimally small and bulk size specimens,respectively.





• On the basis of those two observations, Griffith’s first major contribution

to fracture mechanics was to suggest that internal minute flaws acted asstress raisers in solids, thus strongly affecting their tensile strengths.Thus, in reviewing Inglis’s early work, Griffith determined that the

reducing the glass strength from the theoretical value to the actuallymeasured value.

• The second major contribution made by Griffith was in deriving athermodynamical criterion for fracture by considering the total change inenergy taking place during cracking. During crack extension, potentialenergy (both external work and internal strain energy) is released and“transferred” to form surface energy.





• After Griffith’s work, the subject of fracture mechanics was relativelydormant for about 20 years until 1939 when Westergaard (Westergaard1939a) derived an expression for the stress field near a sharp crack tip.

• The large number of sudden and catastrophic fractures that occurred in

ships during and following World War II gave the impetus for thedevelopment of fracture mechanics. After the war, George Irwin, whowas at the U.S. Naval Research Laboratory, made use of Griffith’s idea,and thus set the foundations of fracture mechanics. He made three major contributions:

yielding at the crack tip;

introduced the concept of the stress intensity factor (SIF);

introduced the concept of energy release rate G.





• Subcritical crack growth (fatigue crack growth) was subsequentlystudied. Paris in 1961 proposed the first empirical equation relating therange of the stress intensity factor to the rate of crack growth;

• Non-linear considerations were further addressed by Wells, who around1963 utilized the crack opening displacement (COD) as the parameter tocharacterize the strength of a crack in an elasto-plastic solid, and byRice, who introduce his J integral in 1968 in probably the second most

referenced paper in the field (after Griffith); it introduced a pathindependent contour line integral that is the rate of change of thepotential energy for an elastic non-linear solid during a unit crackextension.




THEORETICAL STRENGTHTHEORETICAL STRENGTH




THEORETICAL STRENGTHTHEORETICAL STRENGTH




STRESS CONCENTRATION FACTOR (SCT)STRESS CONCENTRATION FACTOR (SCT)

The ratio between local stress and nominal stress isThe ratio between local stress and nominal stress iscalled the theoretical stress concentration factor(kt)called the theoretical stress concentration factor(kt)





KIRSCH (1898) – Kt = 3

INGLIS (1913)

GRIFFITH (1921)




GRIFFITH CRACK THEORYGRIFFITH CRACK THEORY –– STRAINSTRAIN--ENERGY RELEASE RATEENERGY RELEASE RATE

SEM TRINCA

COM TRINCA





THE FRACTURE ENERGY BALANCETHE GRIFFITH ENERGETIC BALANCE








4. 1948 George Irwin (US Naval Research Laboratory)Linear Elastic Fracture Mechanics

- Extended Griffith's theory to metals

- Developed mathematical methods to calculate fracture parameter and

measurement of critical fracture parameters (toughness)

, γ p = Plastic energy at the crack tip( )

a

p E f

π

γ γ σ

+=

Since the numerator is a material property, we can define as

Where K = Stress intensity factor at the crack tip

σ = remote stress

We can relate K to G, rate of change of total potential energy w.r.t. crack length a.

G = K2/E*

E* = effective elastic modulus

This theory is called: Griffith-Irwin-Orowan Theory of Fracture

a

K

π σ =




IRWINIRWIN –– OROWAN THEORYOROWAN THEORY –– STRAINSTRAIN--ENERGY RELEASE RATEENERGY RELEASE RATE




IRWINIRWIN –– OROWAN THEORYOROWAN THEORY –– STRAINSTRAIN--ENERGY RELEASE RATEENERGY RELEASE RATE




MECÂNICA DA FRATURA LINEARMECÂNICA DA FRATURA LINEAR--ELÁSTICAELÁSTICA -- MFLEMFLE




MECÂNICA DA FRATURA LINEARMECÂNICA DA FRATURA LINEAR--ELÁSTICAELÁSTICA -- MFLEMFLE

FALHA OCORRE QUANDO KI=KIc. NESTE

CASO, KI É A FORÇA MOTORA PARA FRATURAE KIc É A MEDIDA DE RESISTÊNCIA DOMATERIAL. COMO Gc, A PROPRIEDADE DESIMILITUDE DEVERIA SER APLICADA PARAKic. ISTO É, Kic É ASSUMIDO SER UMAPROPRIEDADE DO MATERIAL INDEPENDENTE

DE TAMANHO.




MECÂNICA DA FRATURA LINEARMECÂNICA DA FRATURA LINEAR--ELÁSTICAELÁSTICA –– MFLEMFLE -- SIMILITUDESIMILITUDE




Mathematical Definition of crackMathematical Definition of crack1. Definition

Crack is an elliptical notch with a semi-major axis length a (crack length) and semi-

minor length, b, is zero. In other words, radius of curvature at the crack tip is zero.




2. Stress Flow Around a Notch & Crack2. Stress Flow Around a Notch & Crack

(a) Loading transverse to the major axisNotchStress concentration (Kt):

Rmin is the radius of curvature at the tip of the major axis.

CrackStress intensity factor (K):

(b) Loading parallel to the major axisNotchStress concentration (Kt):

Rmax is the radius of curvature at the tip of the major axis.CrackStress intensity factor (K) = 0

ak nom π σ =

nomσ σ =

max21 Ranom +=σ σ

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Aula 0 - Análise de falhas