Stress–strain diagram for a ductile metal: over which labeled portion does stress remain directly proportional to strain (Hooke’s law region)?

Introduction / Context:
A typical engineering stress–strain curve for mild steel begins with a linear segment where stress is proportional to strain. Correctly identifying this proportional (elastic) region is fundamental to applying Young’s modulus in design.

Given Data / Assumptions:

• Standard tensile test specimen (ductile metal).
• Diagram points: O (origin), A (proportional limit), followed by yield/ultimate points.
• Engineering stress and strain used.

Concept / Approach:
Hooke’s law states sigma = E * epsilon within the proportional limit. On the graph, the straight-line region O–A indicates constant slope equal to E, beyond which nonlinearity and yielding begin.

Step-by-Step Solution:

Verification / Alternative check:
Unload anywhere within O–A: the material returns to original length (primarily elastic behavior). Beyond A, permanent set appears.

Why Other Options Are Wrong:
Segments including A–C, A–D, D–E include yielding, strain hardening, necking, or plastic flow, where proportionality does not hold.

Common Pitfalls:
Confusing proportional limit with elastic limit; assuming linearity persists beyond A; mixing true vs engineering curves.

Final Answer:

from O to A