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