JNTU B.Tech II METALLURGY AND MATERIAL SCIENCE Previous Question Paper (March - 2022 - R16)

To determine the Miller indices (hkl) of the given plane, follow these steps:

1. Identify the intercepts on the crystallographic axes: X = 1, Y = 2, Z = ∞ (since the plane is parallel to the Z-axis).
2. Take the reciprocals of the intercepts: 1/1 = 1, 1/2 = 0.5, 1/∞ = 0.
3. Reduce these to the smallest set of integers by multiplying by the least common multiple (which is 2 in this case): 1 × 2 = 2, 0.5 × 2 = 1, 0 × 2 = 0.

The Miller indices of the plane are (210).

Grain size significantly influences the mechanical behavior of polycrystalline materials, primarily described by the Hall-Petch relationship. The effect can be summarized as follows:

• Yield Strength: As the average grain size decreases, the number of grain boundaries increases. Grain boundaries act as barriers to dislocation motion. Consequently, finer-grained materials exhibit higher yield strength because more stress is required to force dislocations across these boundaries.
• Ductility and Toughness: Generally, refining the grain size improves both strength and toughness simultaneously, which is unique among strengthening mechanisms. Finer grains promote more uniform plastic deformation by distributing strain over a larger number of grains.
• Hardness: Hardness increases with decreasing grain size due to the increased resistance to plastic deformation.
• Creep Resistance: At high temperatures, grain boundaries can become sites for diffusion and grain boundary sliding. Therefore, coarse-grained materials often exhibit better creep resistance at elevated temperatures compared to fine-grained materials.

The relationship between yield stress (σ_y) and grain diameter (d) is given by the formula:

where σ₀ is the starting stress for dislocation movement and k_y is a material-specific constant.