Elastic failure criteria: under the maximum tensile strain theory, failure is predicted to occur when the maximum tensile strain equals what value? (Here, σ = yield strength in simple tension, and E = Young's modulus of elasticity.)

Introduction / Context:
This question tests the classical elastic failure criteria used in strength of materials and machine design. Specifically, it focuses on the maximum tensile strain theory, sometimes associated with Saint-Venant’s hypothesis, and asks which threshold indicates the onset of elastic failure when multiaxial stresses act on a ductile member.

Given Data / Assumptions:

• σ denotes the yield strength obtained from a uniaxial tensile test.
• E denotes Young's modulus (modulus of elasticity) of the material.
• Material behavior is linearly elastic up to yield, and small-strain theory applies.

Concept / Approach:
In the maximum tensile strain theory, failure is predicted when the largest principal strain under a complex state equals the uniaxial yield strain. The uniaxial yield strain from a tensile test is simply σ/E, because Hooke’s law gives strain = stress / E in the elastic region.

Step-by-Step Solution:

Verification / Alternative check:
Under simple tension, the multiaxial case reduces to the test condition. The criterion must reproduce the same yield point as the test: σ/E, confirming consistency.

Why Other Options Are Wrong:

• E: This has units of stress; not a strain threshold.
• σ: Stress value, not a strain; theory uses strain equality.
• E/σ: Inverse of the correct ratio; wrong dimensionally.
• None of these: Incorrect because σ/E is present.

Common Pitfalls:
Confusing stress-based (e.g., maximum principal stress) and strain-based criteria; mixing units; forgetting that Hooke’s law links stress and strain by E in the elastic regime.

Final Answer:
σ/E