Fracture Behavior of Bulk Crystalline Materials

Fundamentals of Fracture Ductile Fracture Brittle Fracture Crack Initiation and Propagation

Fracture Mechanics Fracture Toughness Design

Fundamentals of Fracture

A 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 Fracture

Simple 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 TrasitionLink 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 Fracture

Involves 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 applied

The 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 Fracture

Link to Ductile fracture model / movie

Mode Ifracture

Brittle Fracture

Exhibits little or no plastic deformation and low energy absorption before failure.

Crack propagation spontaneous and rapidOccurs 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 Fracture

Link or movie of simulated brittle fracture...

Mode Ifracture

Crack Initiation and Propagation

Cracks 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 Propagation

Image 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 Propagation

Double-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 Mechanics

If 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 Mechanics

The 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 Fracture

The 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

a

E sc

Fracture Toughness

Stresses 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 Toughness

Kc 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 Design

There 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: 2

1

aY

Ka Icc Next section