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8/10/2019 Fracture Mechanics Lecture Slides.pptx
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DR MARK BINGLEY
PEMBROKE 237
m.s.bingley@gre.ac.uk
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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.flv8/10/2019 Fracture Mechanics Lecture Slides.pptx
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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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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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