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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 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 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 I
fracture
Brittle Fracture
Exhibits 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 Fracture
Link or movie of simulated brittle
fracture...
Mode I
fracture
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) crack
on student simulations fracture page
mode I fracture
animated gif
http://www.mse.vt.edu/~farkas/st_projec
ts/home.html
Crack propagation simulated in the VT
Cave
Crack Initiation and
Propagation
Double-ended crack simulations
Fracture Mechanics
Uses 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:
 a
s m  2s 0 
 rt
1/ 2



so is the nominal applied tensile stress
 rt 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 sm.
Fracture Mechanics
The ratio sm/s0 is known as the stress
concentration factor, Kt :
1/ 2
 a 
sm
Kt 
 2 
s0
 rt 
It is the degree to which an external stress is
amplified at the tip of a small crack
Griffith Theory of Brittle
Fracture
The critical stress required for crack propagation
in a brittle material is given by:
 2 Eg s 
sc  

 a 
1/ 2
 E = modulus of elasticity
 gs= 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.
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
sc, known as fracture toughness given by:
K  Ys a
c
 Y is a dimensionless
parameter that depends on both the
specimen and crack geometries.
Carries the unusual units of

psi in MPa m

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:
K Ic  Ys a
The I subscript corresponds to a mode I crack displacement
KIc 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
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 (s)
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
2
must be:
1  K Ic 
ac 


  Y a 
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