Plastic region behavior in tensile testing:\nBeyond the elastic limit on a stress–strain curve, how does tensile strain vary compared to applied stress?

Introduction / Context:
The stress–strain curve of ductile materials shows an elastic region (linear, Hookean) followed by a plastic region. Understanding how strain evolves relative to stress beyond the elastic limit is crucial for safe design and for predicting permanent deformations.

Given Data / Assumptions:

• Standard uniaxial tensile test on a ductile metal specimen.
• Observation focuses on the region beyond the elastic limit (onset of plasticity).
• Monotonic loading; room temperature; engineering stress–strain definition.

Concept / Approach:
In the elastic region, stress is proportional to strain (σ = E ε). Once the elastic limit is exceeded, plastic deformation begins. Additional strain accrues at a faster rate for comparatively small increases in stress, especially near yield where the curve flattens (yield plateau in some steels).

Step-by-Step Solution:

Verification / Alternative check:
Typical stress–strain plots for steels show a yield plateau or gradual hardening: significant strain develops with little to moderate stress increase, confirming the qualitative relationship.

Why Other Options Are Wrong:

• Decreasing strain with increasing stress contradicts physical behavior.
• “Remains proportional” is only valid in the elastic region, not beyond.

Common Pitfalls:
Confusing engineering and true stress–strain beyond necking; misreading the yield plateau as constant strain; assuming linearity throughout loading.

Final Answer:
increases more quickly