Question

The modulus of resilience is equal to:

• A. Area under elastic region only
• B. Area under entire stress-strain curve
• C. Maximum stress \(\times\) strain
• D. Plastic work

Hint:

Be clear on these area-under-curve energy terms:
- Area under Elastic Region \(\rightarrow\) Modulus of Resilience (\( \sigma_y^2 / 2E \)).
- Area under Entire Curve (Elastic + Plastic) \(\rightarrow\) Modulus of Toughness.
To maximize resilience (e.g., for springs), select materials with high yield strength and low elastic modulus.

Answer 1

The Correct Option is A

Think of a component being loaded only within its elastic range, the way a spring is loaded before it takes a permanent set. All the mechanical work put into deforming it elastically is stored as recoverable strain energy, and the moment the load is removed, this energy is released back and the part returns to its original shape. On a stress-strain plot, this stored energy per unit volume corresponds only to the triangular region bounded by the origin, the yield point, and the strain axis, since that is the portion of loading where the material is still behaving elastically. Once the material yields and begins to flow plastically, the extra energy absorbed goes into permanent deformation instead and no longer counts toward resilience, and if this plastic region is included all the way to fracture, what is measured instead is the modulus of toughness, not resilience. So the correct choice is option (A).