Fracture Behavior of Bulk Crystalline MaterialsFundamentals of Fracture

Ductile Fracture Brittle Fracture Crack Initiation and Propagation

Fracture Mechanics Fracture Toughness Design

Fundamentals of FractureA separation of an object into two or more pieces in

response to active stresses far below the melting temperature of the material.

Atoms on the surface of a material give rise to a surface energy Stems from the open bonds on the outer atoms Grain boundary surface energy

link to grain boundary surface energy section (fract3.ppt)Two steps in the process of fracture:

Crack initiation Propagation

Fundamentals of FractureSimple fracture may occur by one of two

methods, ductile or brittle Dependent upon the plastic deformation of the

material Properties which influence the plastic deformation of a material

• Modulus of elasticity• Crystal structure

Related links: The Dislocation Process

Link to dislocation emission processes (Rice paper??) Ductile-to-Brittle Trasition

Link to ductile-brittle transition (fract2.ppt)

Fundamentals of Fracture (a) Highly ductile

fracture (b) Moderately ductile

fracture with necking Called a cup-and -

cone fracture Most common form of

ductile fracture (c) Brittle fracture

No plastic deformation occurring

Ductile FractureInvolves a substantial amount of plastic

deformation and energy absorption before failure. Crack propagation occurs very slowly as the

length the crack grows. Often termed a stable crack, in that it will not

grow further unless additional stress is appliedThe fracture process usually consists of

several stages:

Ductile Fracture (a) Initial necking (b) Cavity formation (c) Cavities form a crack (d) Crack propagation (e) Final shear

occurs at an angle of 45, where shear stress is at a maximum

Atomistic Simulation of Ductile FractureLink to Ductile fracture model /

movie

Mode Ifracture

Brittle FractureExhibits little or no plastic deformation and low

energy absorption before failure. Crack propagation spontaneous and rapid

Occurs perpendicular to the direction of the applied stress, forming an almost flat fracture surface

Deemed unstable as it will continue to grow without the aid of additional stresses

Crack propagation across grain boundaries is known as transgranular, while propagation along grain boundaries is termed intergranular

Brittle Fracture

Atomistic Simulation of Brittle FractureLink or movie of simulated brittle

fracture...Mode Ifracture

Crack Initiation and PropagationCracks usually initiate at some point of stress

concentration Common areas include scratches, fillets, threads, and

dents Propagation occurs in two stages:

Stage I propagates very slowly along crystallographic planes of high shear stress and may constitute either a large or small fraction of the fatigue life of a specimen

Stage II the crack growth rate increases and changes direction, moving perpendicular to the applied stress

Crack Initiation and Propagation

Crack Initiation and PropagationImage 1 [110](110) crackon student simulations fracture pagemode I fractureanimated gifhttp://www.mse.vt.edu/~farkas/

st_projects/home.htmlCrack propagation simulated in the V

T Cave

Crack Initiation and PropagationDouble-ended crack simulations

Fracture MechanicsUses fracture analysis to determine the critical

stress at which a crack will propagate and eventually fail

The stress at which fracture occurs in a material is termed fracture strength For a brittle elastic solid this strength is estimated to be

around E/10, E being the modulus of elasticity

This strength is a function of the cohesive forces between the atoms

Experimental values lie between 10 and 1000 times below this value

These values are a due to very small flaws occurring throughout the material referred to as stress raisers

Fracture MechanicsIf we assume that the crack is elliptical in shape

and it’s longer axis perpendicular to the applied stress, the maximum stress at the crack tip is:

o is the nominal applied tensile stress t is the radius of curvature of the crack tip a is the length of a surface crack (becomes a/2 for an internal

crack) Fracture will occur when the stress level exceeds this

maximum value m.

2/1

02

tm

a

Fracture MechanicsThe ratio m/0 is known as the stress

concentration factor, Kt :

It is the degree to which an external stress is amplified at the tip of a small crack

2/1

0

2

t

mt

aK

Griffith Theory of Brittle FractureThe critical stress required for crack

propagation in a brittle material is given by:

E = modulus of elasticity s= specific surface energy

• link to fract3.ppt on grain boundary surface energy a = half the length of an internal crack

Applies only in cases where there is no plastic deformation present.

2/12

aE s

c

Fracture ToughnessStresses near the crack tip of a material can

also be characterized by the stress intensity factor, K,

A critical value of K exists, similar to the value c, known as fracture toughness given by:

Y is a dimensionless parameter that depends on both the specimen and crack geometries.

Carries the unusual units of

aYKc

mMPainpsi

Plane Strain Fracture ToughnessKc depends on the thickness of plate in question up

to a certain point when it becomes constant This constant value is known as the plane strain fracture

toughness denoted by:

The I subscript corresponds to a mode I crack displacementKIc values are used most often because they represent the worst

case scenario • Brittle materials have low KIc values, giving to catastrophic failure• ductile materials usually have much larger KIc values

KIc depends on temperature, strain rate, and microstructure

• Increases as grain size decreases

aYK Ic

Fracture Toughness in DesignThere are three crucial factors which must be

considered in designing for fracture: The fracture toughness (Kc or plane strain Kic) the imposed stress () and the flaw size (a)

It must be determined first what the limits and constraints on the variables will be Once two of them are determined, the third will be fixed For example, if the stress level and plane strain fracture

toughness are fixed, then the maximum allowable flaw size must be:

21

aY

Ka Icc Next section