Fracture Mechanics Lecture Slides.pptx

8/10/2019 Fracture Mechanics Lecture Slides.pptx

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DR MARK BINGLEY

PEMBROKE 237

[email protected]


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MECH 1064

APPLIED ENGINEERING MECHANICS

3 SUBJECT AREAS

MECHANICS OF MATERIALS Mark BingleyMECHANICS ` Michael OkerekeENGINEERING DYNAMICS Kaushika Hettiartachi


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MECHANICS OF MATERIALS IN CONTEXT

Engineering Mechanics is concerned with analysing stresses in abody or component subject to external loading

Stress analysis deals with:

Tension/Compression LoadsTorsionBending

MECHANICS OF MATERIALS assesses whether theresultant stresses in a body are large enough to causefailure


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FAILUREFAILURE is said to occur if the stresses causes changes in thecomponent that mean it is no longer fit for use(it does not necessarily mean catastrophic fracture - separation of abody into 2 or more parts although it could)

TYPES OF FAILURE - EXAMPLES

Yielding and Plastic DeformationDuctile FractureBrittle Fracture

FatigueCreep Deformation and FailureComposite FailureWear

Corrosion


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FRACTURE MECHANICSFast, Unstable, Catastrophic

BRITTLE FRACTURE


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This is an exampleof brittle fracturecaused by usingcold water for ahydrostaticpressure test andthen pressurizingvessel. Thetemperature of the

water caused themetal to becomebrittle.


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Jan. 15, 1919: Morass of Molasses Mucks Up Boston

21 dead - 150 injuredImage below shows elevated train structure destroyed in incident


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AIMS AND OBJECTIVES OF LECTURE To appreciate which materials are susceptible

to Brittle Fracture

To understand the role of cracks in BrittleFracture

To understand the concepts of FractureMechanics through a stress analysis approach

To be able to analyse simple problems inFracture Mechanics and carry out thecalculations necessary to solve problems


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TENSILE BEHAVIOUR OF CERAMICS(TYPICAL BRITTLE MATERIALS)


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WHY CONCRETE IS BRITTLE

http://www.bbc.co.uk/learningzone/clips/13763.flv
http://www.bbc.co.uk/learningzone/clips/13763.flvhttp://www.bbc.co.uk/learningzone/clips/13763.flvhttp://www.bbc.co.uk/learningzone/clips/13763.flvhttp://www.bbc.co.uk/learningzone/clips/13763.flv


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TENSILE BEHAVIOUR OF HIGH STRENGTHMETALS

NORMAL DUCTILE BEHAVIOUR BRITTLE BEHAVIOUR


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WHICH MATERIALS ARE SUSCEPTIBLE TOBRITTLE FRACTURE

HIGH STRENGTHLOW-DUCTILITY MATERIALS:

CERAMICS AND GLASSES

HIGH STRENGTH METALS Low C Steels (at low

temps) Medium-High C Steels

Q and T Steels Aerospace/Automotive

Al Alloys Titanium Alloys


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TOUGHNESSTHE RESISTANCE TO FRACTURE

TOUGH MATERIALS

Require large amounts of (Deformation) Energyto cause Fracture

BRITTLE MATERIALSFail with low Energy input


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IMPACT TESTING

final height initial height

Impact loading:

-- severe testing case-- makes material more brittle-- decreases toughness

Adapted from Fig. 8.12(b),Callister 7e. (Fig. 8.12(b) isadapted from H.W. Hayden,W.G. Moffatt, and J. Wulff, TheStructure and Properties ofMaterials , Vol. III, MechanicalBehavior , John Wiley and Sons,Inc. (1965) p. 13.)

(Charpy)


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16

Increasing temperature...

--increases % EL and K c Ductile-to-Brittle Transition Temperature (DBTT) ...

TEMPERATURE

BCC metals (e.g., iron at T < 914 C)

I m p a c

t E n e r g y

Temperature

High strength materials ( y > E /150)

polymers

More DuctileBrittle

Ductile-to-brittletransition temperature

FCC metals (e.g., Cu, Ni)

Adapted from Fig. 8.15,Callister 7e.


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IMPORTANCE OF CRACKSCRACKS OR FLAWS MUST BE PRESENT FOR BRITTLE FRACTURE TO

OCCUR

In inherently brittle materials such as ceramics the cracks may besub-microscopic

However Larger Cracks Form Easily in Metals During Casting

During Forming During Heat-Treatment During Grinding During Joining (WELDING) During Service (Corrosion, Wear, Mishandling, Fatigue)

QUESTION WE NEED TO ASK:UNDER WHAT CIRCUMSTANCES (LOAD CONDITIONS) DO CRACKSPROPAGATE?

This is the area of FRACTURE MECHANICS


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STRESS ANALYSIS OF CRACKS(LOADING MODES)


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STRESS ANALYSIS OF CRACKS(MODE 1 LOADING)

CRACKS ARE DANGEROUSBECAUSE:

THEY ACT AS STRESSRAISERS


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Linesrepresentareas of equalstress

Where linesare closetogether is anarea of stress

concentration

STRESS CONCENTRATION IN PERSPEX UNDER LOADING

All specimens are ofequal width at theircentre abruptchanges in cross-section give rise tolarger stressconcentrations


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HOW DANGEROUS (HOW LIKELY TOCAUSE FAILURE) A CRACK IS,

IS DETERMINED BY SOMETHINGCALLED THESTRESS INTENSITY FACTOR

THE SIZE OF THE STRESS INTENSITYFACTOR IS RELATED TO:

THE STRESS ON THE CRACKEDCOMPONENT THE SIZE OF THE CRACK


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STRESS INTENSITY FACTOR (K)

K = APPLIED Stress Intensity Factor

Magnitude of K depends upon:Applied Stress( )Crack Length (a)Crack Shape Factor (Y)

Y depends uponCrack shapeSpecimen size, shapeGeometry and type of loading

aY K s


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STRESS INTENSITY FACTORK

This is a measure of the intensity of the localstress at the crack rootAs will be seen on the following slides it varies withthe geometry of the part

Figs (a), (b), (i), (j) represent infinite (large) plates plate dimension >>> crack length

Figs (c), (d), (f), (g) represent finite platesplate dimension crack length

STRESS INTENSITY


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STRESS INTENSITYFACTOR SOLUTIONS

(a), (b)Infinite (large) Plates)

a K b

a K a

s

s

1.1)(

)(

(c)Finite Plates

Y varies with 2 a /W ratioAccording to graphical solutions

1.1 = edge factor


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STRESS INTENSITY FACTOR SOLUTIONS CONT`D

(d), (e)Finite Plates Y varies according to graphs


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STRESS INTENSITY FACTOR SOLUTIONS

Y value indicated for a/W = 0.4

(f), (g)Finite Plates Y varies according to graphs


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STRESS INTENSITY FACTOR SOLUTIONS CONT`D

Solutions for

(i) Circular cracks(j) Elliptical cracksembedded in

infinite (large)plates

NOTE:For Semi-circularand Semi-ellipticalcracks at thesurface/edge of aplateThe equationsgiven are multipliedby the edge-factor(1.1)


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STRESS INTENSITY FACTORS CONT`DTo be used with the Elliptical Crack Solution (j)


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FRACTURE

FAST BRITTLE - FRACTURE WILL OCCUR WHEN:

K = K IC

KIC is the CRITICAL STRESS INTENSITY FACTORorPLANE STRAIN FRACTURE TOUGHNESS

KIC is a MATERIAL PROPERTY

IC K aY s


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FRACTURE TOUGHNESS VALUES OF A RANGE OFMATERIALS


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FRACTURE STRESSAt Fracture:

Applied Stress ( ) = Fracture Stress ( f )

IMPORTANTFracture Stress of a material is not ConstantIt depends on the crack length present

Large Crack Length gives Low Fracture StressSmall Crack Length gives High Fracture Stress

aY K f IC s


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UNITS OF K AND KICK = Y a

K = (MPa)(m) = MPam

K = (MN/m 2)(m 1/2 ) = MNm -3/2


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CLASS EXAMPLES1. A plate is to be loaded in service to a stress of 400 MPa.

Examination of the plate reveals a centre crack 10 mm long.If the plane strain fracture toughness (K 1C) is 70 MPam , isthe plate safe to be put into service?

2. A plate was found to contain a circular shaped crack 15 mmin diameter. The plate fractured at a stress of 650 MPa.What is the K 1C value of the material ?

3. An aerospace aluminium alloy has a yield stress of 500 MPaand a plane strain fracture toughness value (K 1C) of

25 MPam . The design stress is half the yield stress. What isthe critical crack size (that would result in fracture). Assumethat the crack is in the form of an edge crack.


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Q1 ANSWER

For centre-crack in infinite plate refer to fig 8.7(a)

2a = 10 mm

a = 5 mm

K = 50.13 MPam

K IC = 70 MPam K < K ICNO FRACTURE

a K s

3105400 K


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Q2 ANSWER

Circular crack in infinite plate refer to fig 8.7(i)

2a = 15 mm

a = 7.5 mm

K IC = 63.5 MPam

a K s

2

3105.76502

IC K

a K f IC s

2


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Q3 ANSWER

Edge crack in infinite plate refer to fig 8.7 (b)

Assume design stress = fracture stress = f = ( y / 2)Where y = yield stress

Critical crack size ( a ) = 0.0026 m = 2.6 mm

a K s 1.1

a K f IC s 1.1

a 2

5001.125

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Fracture Mechanics Lecture Slides.pptx