3 – Fracture of Materials
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Transcript of 3 – Fracture of Materials
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Mechanical & Aerospace Engineering
West Virginia University
3 – Fracture of Materials
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Part of the top of an Aloha Airlines jet peeled of during the flight
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Liberty Ship failures involved both brittle fractures and fatigue fractures.Of 2700 ships built, 400 suffered hull and deck fractures. 90 were considered serious and in 20 ships fracture was essentially total with 10 ships breaking in half without warning.
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Fracture of MaterialsTypes of Fracture
Brittle FractureDuctile Fracture
Brittle to Ductile Transition
Fracture MechanicsStress ConcentrationLEFMK & GKc
Appendix - Griffith Theory
Outline
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Fracture: separation of a body into pieces due to stress, at temperatures below the melting point.
Steps in fracture:Crack formationCrack propagation
Depending on the ability of material to undergo plasticdeformation before the fracture two fracture modes can be defined - ductile or brittle
Fracture
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Ductile fracture - most metals (not too cold):Extensive plastic deformation ahead of crackCrack is “stable”: resists further extension unless
applied stress is increased
Brittle fracture - ceramics, ice, cold metals:Relatively little plastic deformationCrack is “unstable”: propagates rapidly without increase in applied stress
Ductile fracture is preferred in most applications
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Brittle vs. Ductile FractureDuctile materials - extensive plastic deformation andenergy absorption (“toughness”) before fractureBrittle materials - little plastic deformation and lowenergy absorption before fracture
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Brittle vs. Ductile Fracture
(a)Brittle fracture; (b) Shearing fracture in single crystal (c) Completely ductile (d) Ductile fracture
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Ductile Fracture
(a)Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack,
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Ductile Fracture
(d) Crack propagation, (e) Fracture
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Ductile Fracture(Cap-and-cone fracture in Al)
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Ductile Fracture
Scanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation.
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Brittle Fracture
No appreciable plastic deformationCrack propagation is very fastCrack propagates nearly perpendicular to
the direction of the applied stressCrack often propagates by cleavage – breaking of atomic bonds along specific crystallographic planes (cleavage planes)
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Brittle Fracture
Brittle fracture in a mild steel
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Brittle Fracture
A.Transgranular fracture: Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.
B. Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)
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Brittle Fracture
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Ductile-to-Brittle Transition
Ductile-to-Brittle Transition: As temperature decreases a ductile material can become brittle
Alloying usually increases the ductile-to-brittle transition temperature.
FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals.
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Ductile-to-Brittle Transition
DBTT: Ductile-Brittle Transition Temperature
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Fracture Mechanics & Fracture Toughness
• Stress Concentration
• Energy Release Rate
• Crack Tip Plasticity
• Fracture Toughness
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Stress Concentration
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Stress Concentration
For a long crack oriented perpendicular to the applied stress the maximum stress near the crack is:
m 2 (a/)1/2
where σ is the applied external stress, a is the half-length of the crack, and ρ the radius of curvature of the crack tip. (note that a is half-length of the internal flaw, but the full length for a surface flaw).
(1)
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Stress Concentration Factor
The ratio of the maximum stress and the nominal applied tensile stress is denoted as the stress concentration factor, Kt, where Kt can be calculated by Equation 1. The stress concentration factor is a simple measure of the degree to which an external stress is amplified at the tip of a small crack.
1/ 22( )mt
aK
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Stress Concentration
The stress distribution at the crack tip in a thin plate for an elastic solid is given by:
(2)
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Stress Concentration
K: Stress Intensity Factor
Unit of K: psiin, MN/(m3/2), or MPam
(3)K f a
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Stress Concentration
Substitute K into Equation (3):
(4)
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Stress Concentration
Fracture Modes
Opening In-plane Shear Out-of-Plane Shear
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Energy Release Rate
Energy Release Rate: In 1956, Irwin defined an energy release rate, G, which is a measure of the energy available for an increment of crack extension:
G = - dU/dA
Since G is obtained from the derivative of a potential, it is also called the crack extension force or crack driving force
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Energy Release Rate
Griffith Approach:
G = 2a/E
Where is the nominal stress, a is half-length of crack, E is Young’s Modulus
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Relationship between K and G
Plain Stress:
G = KI2/E
Plain Strain:
G = KI2(1-2)/E
Mode I
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Plain Stress vs. Plain Strain
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Crack Tip Plasticity
Irwin Approach
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Crack Tip Plasticity
Irwin Approach
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Crack Tip Plastic Zone Shape
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Fracture Toughness
Kc: If we assume a material fails locally at some combination of stresses and strains, then crack extension must occur at a critical K value. This Kc value, which is a measure of fracture toughness, is a material constant that is independent of the size and geometry of the cracked body.
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Fracture Toughness Measurement
MEASURE STRENGTH WITH A CRACK OF KNOWN LENGTH
SHARP CRACK
LINEAR ELASTIC?
SMALL PROCESS ZONE RULES
ASTM STANDARDS: E-399
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SUMMARY
Types of Fracture: Brittle FractureDuctile Fracture
Ductile Fracture: Crack initiation, crack growth, fracture, fractography
Brittle Fracture: Intergranular & Transgranular (Cleavage)Brittle to Ductile Transition: DBTT
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SUMMARY – Cont’d
Stress ConcentrationStress distribution in front of the crack tipStress concentration factor
Linear Elastic Fracture MechanicsK: Stress Intensity FactorG: Energy Release RateRelationship between K & GCrack tip plasticity
Fracture Toughness
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Appendix - Griffith Theory for Brittle Fracture
For defect-free material:
0
2aE
th
Where E – Young’s modulus
– specific surface energy
a0 – lattice parameter
th – theoretical strength of the material
th ~ E/10 is orders of magnitude higher than usually observed
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Energy criterion for brittle fracture (Griffith Theory)Energy criterion: when rate of
change of the release of elastic energy with respect to crack size rate at which energy is consumed to create new surfaces, fracture occurs
adad
Ea
dad
s 42
2
Onset:
Where – Griffith’s stress (the critical stress)
s – surface energy/per unit area
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Griffith Equation
• Griffith equation is only for glasses & ceramics – brittle fracture, no plastic deformation occurs prior to fracture
• Metals and polymers plastic deformation occurs before fracture modified Griffith equation (Orowan equation)
aE s
G 2