Question

The area under the linear curve of stress-strain diagram with in the elastic limit is known as

• A. Strain energy
• B. Kinetic energy
• C. Potential energy
• D. Gravitational energy

Hint:

Area under the $\sigma$-$\varepsilon$ curve within the elastic limit = Resilience (or elastic strain energy per unit volume). If the area is calculated across the entire curve up to the point of fracture, it represents the material's Toughness.

Answer 1

The Correct Option is A

Concept: When a solid material undergoes mechanical deformation due to an external load, the work performed by that force is transferred into the material and stored internally as potential energy associated with the displacement of atomic bonds. This stored internal energy is called Strain Energy (or elastic strain energy). On a standard engineering stress-strain ($\sigma$-$\varepsilon$) diagram, the area under the curve represents the mechanical work done per unit volume ($U_v$) of the material: \[ U_v = \int \sigma \, d\varepsilon \] If the loading remains strictly within the linear elastic limit (Hooke's Law region, where $\sigma = E \cdot \varepsilon$), the curve is a straight line starting from the origin. The area under this linear portion forms a right triangle. The area of this triangle represents the elastic strain energy stored per unit volume, a property known as the Modulus of Resilience: \[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \cdot \varepsilon \cdot \sigma = \frac{\sigma^2}{2E} \]

Step 1: Evaluate the physical definitions of the choices.
Let's analyze each type of energy listed to identify the correct classification:
• Strain Energy: The internal mechanical energy stored within a deformed body within its elastic limit, which can be fully recovered upon unloading.
• Kinetic Energy: The energy an object possesses due to its macroscopic translational or rotational motion ($E_k = \frac{1}{2}mv^2$). It is not related to internal material deformation.
• Potential Energy: A broad category of stored energy based on position or configuration (e.g., electrostatic, chemical). While strain energy is technically a form of elastic potential energy, "Strain Energy" is the specific engineering term used for deforming bodies.
• Gravitational Energy: The potential energy an object possesses due to its position within a gravitational field ($E_g = mgh$).

Step 2: Match the geometric representation to the correct engineering term.
The area under a stress-strain diagram represents work converted into internal deformation energy. Within the elastic limit, this is precisely defined as Strain Energy, matching Option (A).