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).