Question

The stress at which the stress-strain curve deviates from linearity is:

• A. Endurance limit
• B. Proportionality limit
• C. Elastic limit
• D. No limit

Hint:

Proportionality limit is always lower than elastic limit in ductile materials.

Answer 1

The Correct Option is B

Concept: In material stress–strain behavior, the relationship between stress ($\sigma$) and strain ($\epsilon$) is initially linear, obeying Hooke’s law: \[ \sigma \propto \epsilon \quad \Rightarrow \quad \sigma = E\epsilon \] where $E$ is Young’s modulus. However, this linearity holds only up to a certain point called the proportionality limit.

Step 1: Understand stress-strain curve behavior.
The stress-strain curve consists of:
• Linear elastic region (Hooke’s law valid)
• Non-linear elastic region
• Plastic deformation region The first deviation from linearity occurs even before permanent deformation begins.

Step 2: Definition of proportionality limit.
The proportionality limit is defined as: \[ \text{The maximum stress up to which stress is directly proportional to strain.} \] Beyond this point: \[ \sigma \not\propto \epsilon \] but material may still return to original shape.

Step 3: Distinguish from elastic limit.

• Proportionality limit → deviation from linearity begins
• Elastic limit → permanent deformation begins Thus proportionality limit comes first. Final Answer: \[ \boxed{\text{Proportionality limit}} \]