Yield phenomenon – stress to start yielding vs. to continue yielding In a ductile metal showing upper and lower yield points, how does the stress required to initiate yielding compare with the stress required to continue yielding?

Introduction / Context:Many low-carbon steels display a yield point phenomenon: an upper yield point where yielding initiates and a lower yield point where plastic flow continues at a reduced stress. Understanding this behavior is important for interpreting tensile tests and designing against plastic deformation.

Given Data / Assumptions:

• Ductile metal with a Lüders-type yield point (upper and lower yield).
• Monotonic tension test.

Concept / Approach:At the onset of yielding, dislocation sources activate and break away from Cottrell atmospheres, causing a temporary peak (upper yield). Once plastic flow starts, fewer obstacles oppose dislocation motion, so a lower stress (lower yield) sustains continued yielding.

Step-by-Step Solution:Observation: σ_upper > σ_lower for materials showing a yield point plateau.Therefore, stress to initiate yielding (at the upper yield point) exceeds the stress to continue plastic flow (lower yield point).

Verification / Alternative check:Tensile test curves of mild steel typically show a drop from the upper yield to a lower, nearly constant stress as Lüders bands propagate.

Why Other Options Are Wrong:

• (b) contradicts test evidence.
• (c) and (d) refer to “stop yielding,” which is not a standard descriptor in this context.
• (e) confuses yield with ultimate strength.

Common Pitfalls:Equating 0.2% proof stress behavior (smooth curve alloys) with discrete yield point materials; they are not identical phenomena.

Final Answer:It is more than that necessary to continue yielding