Refer to the schematic shown. Two dog-bone samples, labelled 1 and 2, of a Cu-alloy are tested under tension at room temperature to points “E” and “P”, respectively. Subsequently, they are unloaded completely and metallographically polished. Brinell hardness testing was performed in the gauge section of the samples. Which one of the following can be inferred about the measured Brinell hardness number (BHN)?
Show Hint
Hardness increases with the amount of plastic deformation because strain hardening raises dislocation density and resistance to indentation.
A conclusion about BHN of samples 1 and 2 cannot be made, with the provided information
Hide Solution
Verified By Collegedunia
The Correct Option isC
Solution and Explanation
The stress–strain curve shows two marked points:
- Sample 1 is loaded only up to point “E”, which lies near the elastic–plastic transition.
- Sample 2 is loaded to point “P”, which is much deeper into the plastic region.
When a metal is plastically deformed, it undergoes work-hardening due to increased dislocation density. The more the plastic deformation, the greater the strain hardening, and therefore the higher the hardness after unloading.
Sample 1 experiences very little plastic strain, while sample 2 undergoes significant plastic deformation. Thus, sample 2 becomes more strain-hardened than sample 1.
Therefore, the Brinell hardness number satisfies:
\[
\text{BHN}_1 \(<) \text{BHN}_2
\]
So, option (C) is correct.
