Dislocations - Virginia Tech
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Transcript Dislocations - Virginia Tech
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:
2Eg 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:
KIc 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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