FRACTURE Brittle Fracture Ductile to Brittle transition Fracture Mechanics T.L. Anderson CRC Press, Boca Raton, USA (1995)

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

Ductile Fracture Brittle Temperature Factors affecting fracture Strain rate State of stress

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

Tension Torsion Fatigue Conditions of fracture Creep Low temperature Brittle fracture Temper embrittlement Hydrogen embrittlement

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

Slip plane Shear fracture of ductile single crystals Not observed in polycrystals

Completely ductile fracture of polycrystals → rupture Very ductile metals like gold and lead behave like this

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)

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

= Characterization of Cracks 2a a Surface or interior Crack length Crack orientation with respect to geometry and loading Crack tip radius

Crack growth and failure Brittle fracture Griffith Global ~Thermodynamic Energy based Crack growth criteria Local ~Kinetic Stress based Inglis

It should be energetically favorable For growth of crack Sufficient stress concentration should exist at crack tip to break bonds

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

Griffith’s criterion for brittle crack propagation When crack grows U → c →

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

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

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

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

Griffith versus Inglis

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

Safety regions applying Griffith’s criterion alone Unsafe c* Safe  → a0

Safety regions applying Inglis’s criterion alone Unsafe  → a0

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

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

Griffith y Inglis f f , y → T → DBTT Ductile Brittle Brittle  fractures before yield Ductile  yields before fracture

f f , y → y (BCC) y (FCC) T → DBTT No DBTT

Griffith versus Hall-Petch

> 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

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

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

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)

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

Orowan’s modification to the Griffith’s equation to include “plastic energy”