Question

Modulus of elasticity is a measure of

• A. True stress
• B. Toughness
• C. Stiffness
• D. Resilience

Hint:

Associate these key concepts:

• Modulus of Elasticity \(\rightarrow\) Stiffness (Resistance to elastic deformation)

• Area under elastic curve \(\rightarrow\) Resilience (Elastic energy storage)

• Area under total curve \(\rightarrow\) Toughness (Energy absorption before fracture)

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Modulus of Elasticity, also known as Young's Modulus (\(E\)), is a fundamental material property that describes its response to elastic loading. It is the slope of the linear portion of the stress-strain curve.

Step 2: Key Formula or Approach:
Within the elastic limit, Hooke's Law states: \[ \sigma = E \epsilon \] or \[ E = \frac{\sigma}{\epsilon} = \frac{\text{Stress}}{\text{Strain}} \]

Step 3: Detailed Explanation:
Let's define the terms in the options:

• (A) True stress: This is the applied load divided by the instantaneous cross-sectional area. It's a way of calculating stress, not a property measured by the modulus.

• (B) Toughness: This is a material's ability to absorb energy and plastically deform before fracturing. It is represented by the total area under the stress-strain curve.

• (C) Stiffness: This is a qualitative measure of a material's resistance to elastic deformation. A material that requires a high stress to produce a small amount of elastic strain is considered stiff. Since \(E = \sigma/\epsilon\), a high value of \(E\) means high stiffness. Therefore, the Modulus of Elasticity is the quantitative measure of a material's stiffness.

• (D) Resilience: This is a material's ability to store elastic energy. It is represented by the area under the elastic portion of the stress-strain curve.
The Modulus of Elasticity directly quantifies how much a material stretches elastically under a given stress, which is the definition of stiffness.

Step 4: Final Answer:
The Modulus of Elasticity is a quantitative measure of a material's stiffness.