FRACTURE

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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 components-
• CRACK INITIATION CRACK PROPAGATION
• FRACTURE
• DUCTILE BRITTLE

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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
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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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

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• 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
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Cleavage patterns in HS steel fracture (x12000)
Dimples in a ductile fracture of mild steel
(x5000)
Intergranular fracture in low alloy steel
(x1500)
Fatigue striations in Nimonic 80A
(x7000)(A.Strang)
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(a) Yield and cohesive stress curves
(b) Slow notch bend test
(c) Effect of temperature on the Izod value of mild steel
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• 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 lt Y0
• The material is ductile but notch-brittle if Y0 lt
  B lt 3Y0
• The material is not notch-brittle if 3Y lt B.

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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

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• 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.

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The work required to propagate a crack is given
by Griffiths formula
s tensile stress required to propagate
a crack of length c?
surface energy of fracture facesE Youngs
modulus
Orowan modified the Griffith theory to include a
plastic strain energy factor, p
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Initiation and propagation portions of fatigue
life
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Location of local stresses near a crack tip in
cylindrical coordinates
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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)
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• 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

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Behaviour described Terms used Behaviour described Terms used Behaviour described Terms used
Crystallographic mode Appearance of Fracture Strain to Fracture Shear Fibrous Ductile Cleavage Granular Brittle
Ref M.Gensamer
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Stress intensity factor for
(a) Center-cracked plate loaded in tension,
(b) Edge-cracked plate loaded in tension,
(c) Double-edge-cracked plate loaded in tension
(d) Cracked beam in pure bending
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Plane stress and plane strain conditions
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Plane stress
plane strain
Monotonic plastic zone size
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plane stress
plane strain
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Reversed plastic zone size
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TYPICAL FATIGUE STRESS CYCLES (a) REVERSED (b)
REPEATED (c ) IRREGULAR OR RANDOM
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• Atomistic Simulation of Brittle Fracture
• Image of simulated brittle fracture
• Mode I fracture

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• 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

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Crack Initiation and Propagation
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• Crack Initiation and Propagation
• Double-ended crack simulations

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• 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

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• Fracture Mechanics
• If we assume that the crack is elliptical in
  shape and its 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 .

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• Fracture Mechanics
• The ratio sm/ s0 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

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• 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.

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• 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

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FRACTURE TOUGHNESS
Yielding near crack tip.
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• 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

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• 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

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• 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

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• Fracture Mechanics
• If we assume that the crack is elliptical in
  shape and its 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 .

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