AH

2: Fracture Toughness

  • Brittle Fracture Mechanics Continuation

    • Focus on fracture toughness and its significance.

  • Critical Stress and Fracture Mechanics

    • The relationship for critical stress causing fracture is influenced by the strain energy release rate ($g_c$), Young's modulus ($E$), and Poisson's ratio.
    • Definition of a new property: critical stress intensity factor ($K_c$).
    • Includes the above properties at the point of crack propagation.

  • Stress Intensity Factors

    • General stress intensity factor ($K$) applies at any stress; at fracture point, it becomes the critical stress intensity factor or fracture toughness ($K_c$).
    • Fracture toughness ($K_c$) is affected by:
    • Strain energy release rate ($g_c$).
    • Young's modulus ($E$).
    • Poisson's ratio.

  • Fracture Modes

    • Different modes of fracture toughness:
    • Mode I (K1c): Tensile opening mode (e.g., splitting wood with a wedge).
    • Mode II: Shear mode normal to the crack leading edge (e.g., cutting a rotating cylinder).
    • Mode III: Tearing mode (e.g., tearing a phone book).
    • Focus will be on Mode I (K1c).

  • Comparative Fracture Toughness

    • Chart showing relative $K_{1c}$ values for materials:
    • Metals have the highest toughness.
    • Brittle metals (e.g., beryllium) can have toughness similar to tough ceramics.
    • Polymers do not absorb as much energy compared to metals.

  • Typical Values of K1c

    • All listed metals significantly outclass engineering ceramics in toughness.
    • Example values:
    • Metals: 24 MPa√m to tens of MPa√m.
    • Ceramics like partially stabilized zirconia below 10 MPa√m.

  • Charts of Material Properties

    • Fracture Toughness vs. Young's Modulus: Measures the relationship between toughness and modulus values.
    • Fracture Toughness vs. Elastic Limit: Metals occupy the upper right corner showing high yield stresses and fracture toughness.
    • Toughness generally decreases with increasing yield stress among metal alloys.

  • Plane Stress vs. Plane Strain Conditions

    • Plane strain conditions yield lower $K_{1c}$ values compared to plane stress.
    • Testing under plane strain gives more consistent $K_{1c}$ values and is considered a valid material property.

  • Specimen Geometry for Testing

    • Common specimen geometries:
    • Compact tension (for metals).
    • Three-point bend (for ceramics).
    • Notched round specimens.
    • Equation to determine minimum thickness for valid plane strain condition involving $K_{1c}$ and yield stress.

  • Stress Intensity Relation

    • General relation:
    • $K = rac{ ext{stress} imes ext{constant}}{ ext{geometry factors}}$
    • Includes geometry factors $Y$ (location of flaw) and $Q$ (shape of crack).
    • Geometry factors are listed in fracture mechanics handbooks (e.g., ASM Handbook).