Question

Total recoverable strain energy stored within the elastic limit in the stress-strain curve is called-

• A. Ductility
• B. Hardness
• C. Resilience
• D. Tensile strength

Hint:

Materials designed for springs must have high resilience.
To achieve this, they need a high yield strength ($\sigma_y$) and a low elastic modulus ($E$).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the mechanical term used to describe the total elastic strain energy that a material can absorb and subsequently release upon unloading.

Step 2: Key Formula or Approach:
The maximum elastic strain energy per unit volume that can be stored is called the Modulus of Resilience ($U_r$), which is the area under the elastic portion of the stress-strain curve:
\[ U_r = \int_0^{\epsilon_y} \sigma d\epsilon = \frac{\sigma_y^2}{2E} \]
where:
$\sigma_y$ is the yield strength.
$E$ is Young's Modulus.

Step 3: Detailed Explanation:

• When a material is loaded within its elastic limit, the work done on the material is stored as elastic strain energy by stretching atomic bonds.

• Because the deformation is entirely elastic, this energy is fully recoverable when the load is removed.

• This property of absorbing and recovering energy within the elastic limit is called resilience.

• For comparison:
- Toughness: Represents the total energy absorbed up to fracture (elastic + plastic energy).
- Ductility: Is the measure of a material's ability to undergo plastic deformation before fracture.
- Hardness: Is the resistance of a material to localized plastic deformation (scratching or indentation).

Step 4: Final Answer:
The recoverable strain energy stored within the elastic limit is called resilience.