Stress–strain curve interpretation: For the portion from O to A on the typical mild-steel stress–strain diagram (straight-line region), does Hooke's law hold good?

Introduction / Context:Hooke's law states that within the elastic limit, stress is directly proportional to strain. On a standard tensile test for mild steel, the initial linear segment of the stress–strain curve reflects this proportionality.

Given Data / Assumptions:

• Standard tensile test specimen of mild steel.
• Segment O–A on the stress–strain diagram denotes the linear, proportional region.
• Small strains; engineering stress and strain definitions.

Concept / Approach:Hooke’s law: sigma = E * epsilon in the proportional (elastic) region. Point A is typically the proportional limit (very close to the elastic limit for many steels), beyond which linearity is lost and yielding commences.

Step-by-Step Solution:

Verification / Alternative check:Experimental plots show a linear stress–strain relation up to the proportional limit for ductile metals; unloading within this range shows recoverable (elastic) strain.

Why Other Options Are Wrong:Statements restricting validity to beyond yield or the plastic region are incorrect; Hooke’s law fails after proportionality is lost.Confusing elastic limit and proportional limit does not change the validity on O–A.

Common Pitfalls:Assuming Hooke’s law persists into plasticity; misreading diagram labels; mixing true and engineering stress–strain curves.

Final Answer:

Agree