Question

Hooke's law holds good up to

• A. Yield point
• B. Elastic limit
• C. Plastic limit
• D. Breaking point

Hint:

Stress-Strain Boundaries: HOOKE'S LAW holds good up to the ELASTIC LIMIT (or Limit of Proportionality). Beyond this, plastic deformation begins.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Constitutive linear elasticity: Hooke's law ($\sigma = E \cdot \epsilon$) strictly applies within the elastic limit limit of proportionality where stress is linearly proportional to strain.
Key Formula or Approach:
\[ \text{Hooke's Law: } \mathbf{\sigma = E \cdot \epsilon} \quad \implies \quad \text{Valid strictly up to } \mathbf{Elastic \text{ } Limit \text{ (Limit of Proportionality)}} \]

Step 2: Detailed Explanation:
In solid mechanics, material testing, and tensile stress-strain behavior:
- Hooke's Law (Robert Hooke, 1676) states that within the elastic range of a material, the applied stress ($\sigma$) is directly proportional to the resulting strain ($\epsilon$):
\[ \sigma \propto \epsilon \implies \sigma = E \cdot \epsilon \]
- On a tensile stress-strain curve:
1. Limit of Proportionality Elastic Limit (B): The upper boundary of the initial linear portion of the curve. Up to the Elastic limit, the material behaves elastically, Hooke's law holds strictly valid, and the material returns to its original dimensions upon unloading.
2. Beyond the elastic limit (Yield point, Plastic limit, Breaking point), plastic deformation occurs, stress-strain relationship becomes non-linear, and Hooke's law ceases to apply.

Step 3: Final Answer:
Therefore, Hooke's law holds good up to Elastic limit, corresponding to option (B).