Explain the difference between elastic strain and plastic strain.

Elastic strain is a type of strain that occurs when a material is subjected to stress, and the material deforms in a way that is reversible upon removal of the stress. In other words, when the stress is removed, the material returns to its original shape and size. This behavior is usually exhibited within the material's elastic limit, which is the maximum stress a material can sustain without any permanent deformation. \( Hooke's \) law relates the stress and strain within the elastic limit for a material, with the constant of proportionality being the material's elastic modulus, or Young's modulus.

Plastic strain, on the other hand, is a type of strain that occurs when the stress applied on the material is beyond its elastic limit. The deformation in this case is permanent and irreversible even after removal of the stress. This behavior is often associated with materials that can undergo significant deformation before breakage, such as ductile metals. In this region, the stress-strain curve is generally nonlinear, and the relationship between stress and strain is driven by the material's plasticity.

The main differences between elastic and plastic strain can be summarized as follows: 1. Reversibility: Elastic strain is reversible, and the material returns to its original shape and size after the stress is removed. In contrast, plastic strain results in permanent deformation. 2. Elastic Limit: Elastic strain occurs within the material's elastic limit, while plastic strain occurs beyond it. 3. Stress-strain relationship: The stress-strain relationship in elastic strain is linear and follows \( Hooke's \) law with the elastic modulus as the constant of proportionality. In plastic strain, the relationship is nonlinear and depends on the material's plastic properties. 4. Energy storage: Materials under elastic strain store the energy as potential energy, which is released when the stress is removed. In plastic strain, a considerable amount of energy is dissipated as heat, and only a small portion is stored as potential energy. 5. Structural consequences: Elastic strain, being reversible, has limited structural consequences. However, plastic strain can lead to a permanent change in the shape or size of the structural or machine components, which may affect functionality or cause failure.