3 – Fracture of Materials

Mechanical & Aerospace Engineering

West Virginia University

3 – Fracture of Materials



Part of the top of an Aloha Airlines jet peeled of during the flight



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.





Fracture of MaterialsTypes of Fracture

Brittle FractureDuctile Fracture

Brittle to Ductile Transition

Fracture MechanicsStress ConcentrationLEFMK & GKc

Appendix - Griffith Theory

Outline



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



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



Brittle vs. Ductile FractureDuctile materials - extensive plastic deformation andenergy absorption (“toughness”) before fractureBrittle materials - little plastic deformation and lowenergy absorption before fracture



Brittle vs. Ductile Fracture

(a)Brittle fracture; (b) Shearing fracture in single crystal (c) Completely ductile (d) Ductile fracture



Ductile Fracture

(a)Necking, (b) Cavity Formation, (c) Cavity coalescence to form a crack,



Ductile Fracture

(d) Crack propagation, (e) Fracture



Ductile Fracture(Cap-and-cone fracture in Al)



Ductile Fracture

Scanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation.



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)



Brittle Fracture

Brittle fracture in a mild steel



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.)



Brittle Fracture



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.



Ductile-to-Brittle Transition

DBTT: Ductile-Brittle Transition Temperature



Fracture Mechanics & Fracture Toughness

• Stress Concentration

• Energy Release Rate

• Crack Tip Plasticity

• Fracture Toughness



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)



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




The stress distribution at the crack tip in a thin plate for an elastic solid is given by:

(2)




K: Stress Intensity Factor

Unit of K: psiin, MN/(m3/2), or MPam

(3)K f a




Substitute K into Equation (3):

(4)




Fracture Modes

Opening In-plane Shear Out-of-Plane Shear



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



Energy Release Rate

Griffith Approach:

G = 2a/E

Where is the nominal stress, a is half-length of crack, E is Young’s Modulus



Relationship between K and G

Plain Stress:

G = KI2/E

Plain Strain:

G = KI2(1-2)/E

Mode I



Plain Stress vs. Plain Strain



Crack Tip Plasticity

Irwin Approach



Crack Tip Plasticity

Irwin Approach



Crack Tip Plastic Zone Shape



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.



Fracture Toughness Measurement

MEASURE STRENGTH WITH A CRACK OF KNOWN LENGTH

SHARP CRACK

LINEAR ELASTIC?

SMALL PROCESS ZONE RULES

ASTM STANDARDS: E-399



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



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



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



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



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

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3 – Fracture of Materials