Transcript Slide 1

FRACTURE
• Fracture is the separation, or fragmentation,
of a solid body into two or more parts under
the action of stress.
• Process of fracture- with two componentsCRACK INITIATION CRACK PROPAGATION
FRACTURE
DUCTILE
BRITTLE
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 boundaries also contain a surface energy due to
the large number of open bonds
• 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
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
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
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(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
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
Ductile fracture
A pure and inclusion
free metal can
elongate under
tension to give
approx. 100% RA and
a point fracture.
The central fracture
surface consists of
numerous cup-like
depressions generally
called dimples.
Dimple size depends
largely on the number
of inclusion sites.
(a) Stages in ductile fracture from inclusions
(b) Fracture toughness v/s thickness
Dimples in a ductile fracture
of mild steel (x5000)
Intergranular fracture in low
alloy steel (x1500)
Cleavage patterns in HS steel
fracture (x12000)
Fatigue striations in Nimonic
80A (x7000)(A.Strang)
(a) Yield and cohesive stress curves
(b) Slow notch bend test
(c) Effect of temperature on the Izod value of mild steel
Cohesive stress-strain curves, B, N, and F.
If the two curves intersect at Y, brittle fracture occurs
preceded by plastic deformation, which decreases
as the cohesive strength curve becomes lower with
respect to the yield stress-strain curve.
Orowan has shown that if the yield stress is denoted
by Y, the strength for brittle fracture by B (both Y and
B depend on the plastic strain), and the initial value
of Y (for strain = 0) by Y0
The following are the relationships:
• The material is brittle if B < Y0;
• The material is ductile but notch-brittle if Y0
< B < 3Y0
• The material is not notch-brittle if 3Y < B.
Brittle fracture
• Brittle fracture is characterised by the very small
amount of work absorbed and by a crystalline
appearance of the surfaces of fracture, often
with a chevron pattern pointing to the origin of
fracture, due to the formation of discontinuous
cleavage cracks which join up
It can occur at a low stress of 75-120
MPa with great suddenness; the
velocity of crack propagation is
probably not far from that of sound in
the material in this type of fracture
plastic deformation is very small, and
the crack need not open up
considerably in order to propagate, as
is necessary with a ductile failure.
The work required to propagate a crack is given by
Griffith`s formula:
σ = tensile stress required to propagate
a crack of length c
γ = surface energy of fracture faces
E = Young`s modulus
Orowan modified the Griffith theory to include
a plastic strain energy factor, p
Initiation and propagation portions of fatigue life
Location of local stresses near a crack tip
in cylindrical coordinates
Mode 1:
Opening or tensile mode (the crack faces are pulled
apart)
Mode 2:
Sliding or in-plane shear (the crack surfaces slide over
each other)
Mode 3:
Tearing or anti-plane shear (the crack surfaces move
parallel to the leading edge of the crack and relative to
each other)
• Most alloys contain second phases which lose
cohesion with the matrix or fracture and the voids so
formed grow as dislocations flow into them.
• Coalescence of the voids forms a continuous
fracture surface followed by failure of the remaining
annulus of material usually on plane at 45° to the
tension axis.
• The central fracture surface consists of numerous
cup-like depressions generally called dimples.
• The shape of the dimples is strongly influenced by
the direction of major stresses-circular in pure
tension and parabolic under shear
Behaviour described
Terms used
Crystallographic mode
Shear
Cleavage
Appearance of Fracture
Fibrous
Granular
Strain to Fracture
Ductile
Brittle
Ref: M.Gensamer
Stress intensity factor
for
(a) Center-cracked
plate loaded in
tension,
(b) Edge-cracked
plate loaded in
tension,
(c) Double-edgecracked plate
loaded in tension
(d) Cracked beam in
pure bending
Plane stress and plane strain conditions
Plane stress
plane strain
Monotonic plastic zone size
plane stress
plane strain
Reversed plastic zone size
TYPICAL FATIGUE STRESS CYCLES
(a) REVERSED (b) REPEATED
(c ) IRREGULAR OR RANDOM
Atomistic Simulation of Brittle Fracture
• Image 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
• 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:
•
• Fracture will occur when the stress level exceeds
this maximum value .
Fracture Mechanics
• The ratio σm/ σ0 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
Griffith Theory of Brittle Fracture
• The critical stress required for crack
propagation in a brittle material is given by:
•
– E = modulus of elasticity
– gs= specific 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:
– Y is a dimensionless parameter that depends
on both the specimen and crack geometries.
– Carries the unusual units of
•
FRACTURE TOUGHNESS
Yielding near crack tip.
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
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 must be:
•
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
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:
•
• Fracture will occur when the stress level
exceeds this maximum value .