Strength terminology in materials: The stress beyond which a material shows permanent set is the yield stress; the highest stress that can be applied without any permanent set is called the __________.

Introduction:
Accurate terminology in mechanics of materials prevents design mistakes. Elastic limit, yield stress, ultimate stress, proof stress, and breaking stress describe different points on a stress–strain response. This question focuses on the highest stress that does not cause any permanent deformation (no “set”).

Given Data / Assumptions:

• Conventional tensile testing on metals.
• Small-strain elastic behavior followed by plasticity at higher stress.
• “Permanent set” means nonzero plastic strain after unloading.

Concept / Approach:
The elastic limit is the greatest stress that a material can withstand and still completely recover its original dimensions upon unloading. The yield stress corresponds to the onset of plastic deformation (observable offset). In some metals without a clear yield point, proof stress (e.g., 0.2% offset) is used as a practical substitute.

Step-by-Step Solution:
Identify the definition requested: no permanent set → purely elastic response.Match the term: “elastic limit.”Recognize that “yield stress” is the boundary where permanent set begins, so it is not the answer.

Verification / Alternative check:
Unloading–reloading hysteresis in tensile tests shows zero residual strain only below the elastic limit.

Why Other Options Are Wrong:

• Ultimate/breaking stress: occur well into plasticity.
• Yield stress/proof stress: relate to onset of plasticity, not the safe elastic maximum.

Common Pitfalls:
Using yield and elastic limit interchangeably. Some materials have a small interval between them; in design, safety factors ensure operation well below yield.

Final Answer:
elastic limit