JNTU B.Tech III MECHANICAL METALLURGY Previous Question Paper (October - 2020 - R13)

Plastic deformation occurs primarily through two mechanisms: slip and twinning. Slip is the dominant mechanism, involving the movement of dislocations along specific crystallographic planes and directions, known as slip systems. When a shear stress is applied, dislocations move through the crystal lattice, causing atomic planes to slide over one another incrementally. This process is analogous to moving a rug by creating a ripple and pushing it to the other end. Twinning, conversely, involves a homogeneous shear of a portion of the crystal such that the new orientation is a mirror image of the parent lattice. While slip results in a permanent displacement of atoms, twinning typically occurs when slip is restricted, such as in low-symmetry or hexagonal close-packed structures.

In a perfect crystal, slip occurs through the simultaneous shearing of an entire atomic plane over another. This requires overcoming the periodic potential energy of the lattice. The theoretical shear stress, τ_max, can be estimated using the Frenkel model, which assumes a sinusoidal relationship between shear stress and atomic displacement:

For small displacements, the shear stress is related to shear strain γ by Hooke's Law, τ = Gγ, where G is the shear modulus. Since γ = x/d (where d is the interplanar spacing), we have:

Equating the slope at x=0, we find τ_max = Gb / 2πd. Given that b ≈ d, the theoretical shear stress is approximately G / 2π, which is roughly G/10. In reality, metals deform at stresses orders of magnitude lower (often G/10⁴ to G/10⁵) because actual crystals contain dislocations. These defects allow deformation to occur by the sequential movement of dislocations at much lower energy requirements than the simultaneous shearing of an entire plane.