Tensile test on a ductile material – compare true and nominal (engineering) stresses at fracture During a standard tension test on a ductile metal specimen, which statement is correct regarding stresses computed at the instant of fracture?

Introduction / Context:In tensile testing, two stress definitions are common: engineering (nominal) stress based on original area and true stress based on instantaneous area. After necking, these values diverge significantly.

Given Data / Assumptions:

• Ductile material showing clear yield, strain hardening, necking, and final fracture.
• Ultimate stress (engineering) occurs at maximum load P_max divided by original area A_0.
• True stress at fracture uses the instantaneous minimum area A_f at fracture.

Concept / Approach:Once necking begins, the load may drop, but area reduces faster; consequently, true stress σ_true = P/A_inst can continue to rise even as P decreases. Engineering stress σ_eng = P/A_0 ignores area reduction and therefore underestimates the final local stress state.

Step-by-Step Solution:Before necking: σ_true ≈ σ_eng (areas similar).At maximum load: σ_ult = P_max/A_0 (engineering definition).At fracture: A has shrunk to A_f ≪ A_0; therefore σ_true,fracture = P_fracture/A_f is typically higher than σ_ult, while σ_eng,fracture = P_fracture/A_0 is lower.Hence, the correct comparison is: σ_true at fracture > σ_ult (engineering).

Verification / Alternative check:Consistent with Considère criterion and necking behavior; true-stress–true-strain curves show continued hardening up to fracture in many ductile metals.

Why Other Options Are Wrong:

• (a) Engineering stress at fracture is usually less than the ultimate (since load has dropped).
• (c) and (e) contradict the different areas used.
• (d) is invalid because (b) is correct.

Common Pitfalls:Comparing loads instead of stresses; forgetting the strong reduction in area after necking.

Final Answer:True stress at fracture is higher than the ultimate engineering stress