Stress–strain behavior near the elastic limit As a ductile material approaches its elastic limit during a tensile test, how does the tensile strain respond to further increases in applied stress?

Introduction / Context:
This question checks your understanding of the stress–strain curve for engineering materials, especially the transition from the linear elastic region to the nonlinear region near the elastic (or proportional) limit. Knowing how strain responds as you approach this limit is vital for selecting safe working stresses and avoiding permanent deformation.

Given Data / Assumptions:

• Tensile loading of a typical ductile metal specimen (mild steel–type behavior).
• Quasi-static loading; temperature effects ignored.
• Elastic limit is close to but not necessarily identical to the proportional limit.

Concept / Approach:
In the elastic range, Hooke’s law holds and strain is proportional to stress. As the material approaches the elastic limit, the curve deviates from linearity. The tangent modulus reduces and a given increment of stress produces a larger increment of strain compared to the linear region. This manifests as strain increasing more rapidly with stress.

Step-by-Step Solution:

Verification / Alternative check:
Many test curves show a clear knee near yield. The secant modulus beyond the knee is lower than E, confirming faster strain growth.

Why Other Options Are Wrong:

• Proportional increase (option c) applies only strictly within the proportional limit, not as the limit is reached.
• Decrease in strain with increasing stress (options b and d) contradicts material behavior.
• Constant strain (option e) cannot occur while stress is still rising.

Common Pitfalls:
Confusing elastic limit with yield point or assuming perfect linearity up to yield for all materials; many alloys deviate slightly before yield.

Final Answer:
Increases more rapidly (nonlinear rise begins)