Fracture and Failure

Fracture and Failure

1. diff stress-strain curves

   • stiff vs flexible: gradient of stress strain curve in elastic region
   • ductile vs brittle: ductile has high deformation btw yield and fracture
   • strong / resilient vs weak: stress applied before material breaks

2. Types of fractures

   • A) Highly ductile with necking down to a point
     • "cup and cone": see combinations of shear direction and production of voids that join up
   • B)Medium level ductility with some necking
   • C) Brittle: amount of yield before fracture is important. No necking
   • Ductile VS Brittle
     • Ductile usually leads to single fracture surface as initiation of one fracture reduces stresses elsewhere
     • Ductile: energy used in propagating the crack and no in initiate more cracks
     • Brittle: once initiated crack runs quickly and get multiple fracture surfaces

3. FRACTURE

   • To produce fracture need to produce 2 fracture surfaces, which requires energy
     • energy balanced by the release in elastic energy stored in the material
   • Griffith's theory: draw
     • total energy required to make the crack surfaces (eq)
     • Critical crack length (grow and propagate) eq
     • stress needed to fracture a material containing cracks of length 2c or surface cracks of length c (eq)
       • more accurate relationship
     • stress intensity factor (K)
     • 2 measures of a material's properties
       • Toughness= critical strain energy release rate (Gc)
       • Fracture toughness= critical stress intensity factor (Kc)
       • For fracture K=Kc
   • Directions
     • Failure
       • 1) Opening
         • 2) Sliding
           • 3) Tearing
     • Load (altering fracture surface)
       • a) tension leads to dimples
       • b)Shear> elongated dimples
       • c) crack opening> elongated dimples
   • Evolution of ductlie fracture (draw)
   • failure in composites
     • causes
       • Filler: no important
         • Interface: common point of failure / can be reduced (chemically) coupling filler to matrix
           • Matrix: when there is excess filler
             • strong matrix relatively smooth fracture across fibres and resin
             • weak matrix:interface matrix debonds from fibres which pull out
       • around particles
         • get concentrations at the "poles" of the particles
         • get debonding at the pole or failure in matrix just above the poles where stress is highest
     • in fibre reinforced composites
       • type of failure controlled by strength and modulus of elasticity of matrix
       • failure depends on interaction of fibres and matrix
       • short fibre
         • stress at the end =0; middle is higher// can get above critical strength of the fibre and it fails
       • failure types (draw)
     • Fracture model
       • we assume uniform stress in material
       • fibres will break randomly and load is tranferred to the matrix
         • when a fiber fracture lead to stress concentration and crack propagates across adjacent fibres