Tensile testing – Breaking stress versus ultimate tensile stress\n\nIn a standard tensile test on a ductile material, the engineering breaking (fracture) stress is how related to the ultimate tensile stress?

Introduction / Context:
The engineering stress–strain curve for ductile metals shows a peak (ultimate tensile stress) followed by necking until fracture. Understanding the difference between ultimate and breaking stress is vital for safe design and correct interpretation of material data.

Given Data / Assumptions:

• Engineering stress is calculated using original area.
• After UTS, localized necking reduces actual area.
• Material is ductile so necking occurs prior to fracture.

Concept / Approach:
Ultimate tensile stress (UTS) is the maximum engineering stress attained. After necking starts, load typically drops while the original area is still used to compute engineering stress, so the engineering stress value at fracture (breaking stress) is lower than the UTS.

Step-by-Step Solution:
Before necking: load rises → stress increases.UTS reached at maximum load divided by original area.Necking: load decreases, original area constant for engineering stress → stress value drops.Breaking stress (at fracture) < UTS for ductile materials.

Verification / Alternative check:
True stress (based on instantaneous area) may increase during necking, but engineering stress (based on original area) decreases; testing standards and typical curves confirm breaking stress lower than UTS.

Why Other Options Are Wrong:
(a) equal to is false for ductile materials; (c) greater than contradicts the curve; (d) it can be compared using definitions; (e) is an unnecessary conditional—necking generally occurs in ductile materials.

Common Pitfalls:
Mixing true stress with engineering stress; misreading the stress–strain curve endpoints.

Final Answer:
less than