L1: Ductile vs brittle behaviour

Key Mechanisms

A. Crack Nucleation (Stroh Model)

Stress distribution around a crack in an infinite plate under uniaxial tensile loading \(\sigma_0\). The normal stress \(\sigma_n\) acts along the crack surface, with the coordinate system \((r, \theta)\) used to describe the stress field around the crack tip.

  • Dislocations pile up at obstacles (e.g., grain boundaries).

  • Shear stress builds up → nucleates microcrack.

  • Shear stress:

    (l = slip band length, r = distance ahead of pile-up)

B. Griffith Theory (Brittle Fracture)

  • Crack grows when:

    Strain energy released ≥ Energy to create new surfaces

  • Critical crack size (ac​) and fracture stress (σf):

    ​​

    (γs = surface energy, E = Young's/elastic modulus)

3. Factors Affecting Fracture

Factor

Effect on Fracture

Grain Size

Finer grains → higher toughness, ↓ DBTT

Temperature

Low temps → brittle (↑ DBTT)

Strain Rate

Higher rates → brittle behaviour

Stress Triaxiality

Hydrostatic stress → brittleness

4. Fractography Clues

  • Ductile: Dimples (cup-and-cone morphology).

  • Brittle:

    • Cleavage: Flat facets, river lines.

    • Intergranular: Crack along grain boundaries.

    • Transgranular: Crack through grains.

5. Practical Implications

  • Charpy Impact Test: Measures energy absorbed to determine DBTT.

  • Design Tips:

    • Reduce grain size (↑ strength + toughness).

    • Avoid stress concentrators (e.g., sharp notches).