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FRACTURE Brittle Fracture Ductile to Brittle transition
Fracture Mechanics T.L. Anderson CRC Press, Boca Raton, USA (1995)
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Breaking of Liberty Ships
Continuity of the structure Welding instead of riveting Residual stress Breaking of Liberty Ships Microcracks Cold waters High sulphur in steel
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Ductile Fracture Brittle Temperature Factors affecting fracture Strain rate State of stress
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Crystallographic mode Shear Cleavage Appearance of Fracture surface
Behaviour described Terms Used Crystallographic mode Shear Cleavage Appearance of Fracture surface Fibrous Granular / bright Strain to fracture Ductile Brittle Path Transgranular Intergranular
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Tension Torsion Fatigue Conditions of fracture Creep Low temperature Brittle fracture Temper embrittlement Hydrogen embrittlement
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Types of failure Low Temperature Promoted by High Strain rate Triaxial state of State of stress Brittle fracture Little or no deformation Observed in single crystals and polycrystals Have been observed in BCC and HCP metals but not in FCC metals
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Slip plane Shear fracture of ductile single crystals Not observed in polycrystals
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Completely ductile fracture of polycrystals → rupture
Very ductile metals like gold and lead behave like this
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Ductile fracture of usual polycrystals
Cup and cone fracture Necking leads to triaxial state of stress Cracks nucleate at brittle particles (void formation at the matrix-particle interface)
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Theoretical shear strength and cracks
The theoretical shear strength (to break bonds and cause fracture) of perfect crystals ~ (E / 6) Strength of real materials ~ (E / 100 to E /1000) Tiny cracks are responsible for this Cracks play the same role in fracture (of weakening) as dislocations play for deformation Cohesive force Applied Force (F) → r → a0
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= Characterization of Cracks 2a a Surface or interior Crack length
Crack orientation with respect to geometry and loading Crack tip radius
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Crack growth and failure
Brittle fracture Griffith Global ~Thermodynamic Energy based Crack growth criteria Local ~Kinetic Stress based Inglis
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It should be energetically favorable
For growth of crack Sufficient stress concentration should exist at crack tip to break bonds
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Brittle fracture →. ► cracks are sharp & no crack tip blunting
Brittle fracture → ► cracks are sharp & no crack tip blunting ► No energy spent in plastic deformation at the crack tip
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Griffith’s criterion for brittle crack propagation
When crack grows U → c →
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Increasing stress U → c → Griffith By some abracadabra At constant stress when c > c* by instantaneous nucleation then specimen fails At constant c (= c* → crack length) when exceeds f then specimen fails
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On increasing stress the critical crack size decreases
To derive c* we differentiated w.r.t c keeping constant c → Fracture stable 0 0 → If a crack of length c* nucleates “instantaneously” then it can grow with decreasing energy → sees a energy downhill On increasing stress the critical crack size decreases
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Stress criterion for crack propagation
Cracks have a sharp tip and lead to stress concentration 0 0 → applied stress max → stress at crack tip → crack tip radius For a circular hole = c
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After lot of approximations
Work done by crack tip stresses to create a crack (/grow an existing crack) = Energy of surfaces formed After lot of approximations Inglis a0 → Interatomic spacing
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Griffith versus Inglis
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Rajesh Prasad’s Diagrams
Validity domains for brittle fracture criteria Validity region for Stress criterion Inglis Blunt cracks = c Validity region for Energy criterion Griffith c → Sharp cracks > c a0 3a0 → Approximate border for changeover of criterion Sharpest possible crack
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Safety regions applying Griffith’s criterion alone
Unsafe c* Safe → a0
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Safety regions applying Inglis’s criterion alone
Unsafe → a0
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c → c* → a0 3a0 Griffith unsafe Inglis unsafe unsafe
Griffith unsafe Inglis safe safe c → c* Griffith safe Inglis unsafe unsafe Griffith safe Inglis unsafe safe Griffith safe Inglis safe safe → a0 3a0
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Ductile – brittle transition
Deformation should be continuous across grain boundary in polycrystals for their ductile behaviour ► 5 independent slip systems required (absent in HCP and ionic materials) FCC crystals remain ductile upto 0 K Common BCC metals become brittle at low temperatures or at v.high strain rates Ductile y < f yields before fracture Brittle y > f fractures before yielding
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Griffith y Inglis f f , y → T → DBTT Ductile Brittle
Brittle fractures before yield Ductile yields before fracture
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f f , y → y (BCC) y (FCC) T → DBTT No DBTT
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Griffith versus Hall-Petch
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> d-½ → Grain size dependence of DBTT T2 T1 T1 f T2 T1 y T2
f , y → Large size Finer size d-½ → DBT Finer grain size has higher DBTT better
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Grain size dependence of DBTT- simplified version - f f(T)
> T1 T1 f T1 y T2 f , y → Finer size d-½ → DBT Finer grain size has lower DBTT better
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Protection against brittle fracture
↓ f ↓ done by chemical adsorbtion of molecules on the crack surfaces Removal of surface cracks etching of glass (followed by resin cover) Introducing compressive stresses on the surface Surface of molten glass solidified by cold air followed by solidification of the bulk (tempered glass) → fracture strength can be increased 2-3 times Ion exchange method → smaller cations like Na+ in sodium silicate glass are replaced by larger cations like K+ on the surface of glass → higher compressive stresses than tempering Shot peening Carburizing and Nitriding Pre-stressed concrete
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Cracks developed during grinding of ceramics extend upto one grain
Cracks developed during grinding of ceramics extend upto one grain use fine grained ceramics (grain size ~ 0.1 m) Avoid brittle continuous phase along the grain boundaries → path for intergranular fracture (e.g. iron sulphide film along grain boundaries in steels → Mn added to steel to form spherical manganese sulphide)
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r → distance from the crack tip
Ductile fracture Ductile fracture → ► Crack tip blunting by plastic deformation at tip ► Energy spent in plastic deformation at the crack tip → y r → y Schematic → r → Sharp crack Blunted crack r → distance from the crack tip
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Orowan’s modification to the Griffith’s equation to include “plastic energy”
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