(a) How does the Griffith criterion help to explain the fracture of brittle materials?(b) Describe how it can be extended to semi-brittle materials.

(a) The Griffith criterion, proposed by A.A. Griffith in 1921, is a theory that helps explain the fracture of brittle materials. It is based on the concept of energy balance and the presence of flaws or cracks in materials. According to this theory, a material will fracture when the energy released by the growth of a crack is greater than the energy required to create new surfaces.

Here are the steps to explain this:

1. Griffith assumed that a material contains a small crack or flaw.
2. When a stress is applied, the crack will tend to open, increasing the surface area of the material.
3. This increase in surface area requires energy, known as the surface energy.
4. At the same time, the opening of the crack releases elastic strain energy stored in the material.
5. If the released strain energy is greater than the surface energy required to create the new surfaces, the crack will grow and may lead to fracture.

(b) The Griffith criterion can be extended to semi-brittle materials by considering the plastic deformation around the crack tip. In semi-brittle materials, the region near the crack tip undergoes some amount of plastic deformation before the crack propagates. This plastic deformation absorbs some of the strain energy released by the crack growth, thus raising the energy barrier for crack propagation.

Here are the steps to explain this:

1. In semi-brittle materials, the area around the crack tip undergoes plastic deformation.
2. This plastic deformation absorbs some of the strain energy released by the crack growth.
3. This means that more energy is required for the crack to propagate in semi-brittle materials compared to brittle materials.
4. Therefore, semi-brittle materials are tougher and more resistant to fracture than brittle materials.