Question

According to Griffith's theory, the critical condition for crack propagation in a brittle material is when the energy release rate \( G \) equals:

• A. The strain energy density at the crack tip.
• B. The total strain energy in the material.
• C. The surface energy per unit area of the crack.
• D. The elastic modulus of the material.

Hint:

In Griffith's theory, a crack propagates when the energy released from extending the crack equals the surface energy needed to form new crack surfaces.

Answer 1

The Correct Option is C

According to Griffith’s theory of brittle fracture, a crack will propagate in a brittle material when the energy available for crack extension, known as the energy release rate \( G \), is equal to or exceeds the surface energy required to create new crack surfaces.
In other words, crack growth becomes energetically favorable when: \[ G = 2\gamma \] where \( \gamma \) is the surface energy per unit area of one crack face (and thus \( 2\gamma \) accounts for both crack surfaces).
This theory applies to linear elastic, brittle materials and provides the foundational understanding for fracture mechanics. It relates material toughness to the balance between strain energy release and surface energy.