The diagram below shows the stress-strain curves of two materials, Material A and Material B. Material A has a finer grain structure, while Material B has a coarser grain structure. Based on the diagram, which of the following statements is correct regarding their toughness?

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RRB JE CBT 2 (Mechanical Engineering) ReExam Official Paper (Held On: 04 Jun, 2025)

Material A (finer grain size) has higher toughness than Material B (coarser grain size).
Both materials have the same toughness, as indicated by their identical total strain values.
Toughness can be determined directly by comparing the slopes of the stress-strain curves
Material A (finer grain size) has lower toughness than Material B (coarser grain size).

Answer 1

Explanation:

Toughness and Stress-Strain Curves:

Toughness is a measure of a material's ability to absorb energy up to fracture. It is represented by the area under the stress-strain curve of a material. The greater the area under the curve, the tougher the material. Toughness is influenced by several factors, including the material's strength, ductility, and grain size.
In this scenario, we are comparing two materials, Material A (with finer grain structure) and Material B (with coarser grain structure), based on their stress-strain curves. The finer grain structure of Material A typically leads to enhanced strength and ductility due to the Hall-Petch effect, which states that finer grains increase a material's resistance to deformation.

Material A (finer grain size) has higher toughness than Material B (coarser grain size).

This option is correct because finer grain structures, as in Material A, generally result in higher toughness. Finer grains improve both the strength and ductility of the material, contributing to a larger area under the stress-strain curve. This increased area directly correlates to higher toughness. In contrast, Material B, with its coarser grain structure, is likely to have lower strength and ductility, leading to a smaller area under its stress-strain curve and, hence, lower toughness.

Grain Structure and Mechanical Properties:

Finer Grain Structure: Finer grains increase the number of grain boundaries, which act as obstacles to dislocation movement. This enhances strength (as per the Hall-Petch relationship) and can also improve ductility, resulting in higher toughness.
Coarser Grain Structure: Coarser grains have fewer grain boundaries, making it easier for dislocations to move. This typically leads to lower strength and ductility, reducing the material's toughness.