Question

In a tensile test, a ductile material exhibits necking after reaching its ultimate tensile strength. If the ultimate tensile strength is 500 MPa, what happens to the stress in the necked region?

• A. It decreases.
• B. It remains the same.
• C. It increases.
• D. It fluctuates.

Hint:

Tensile Test: Necking. After UTS, ductile materials neck. Engineering stress (Load/Original Area) decreases. True stress (Load/Instantaneous Area) increases in the necked region until fracture.

Answer 1

The Correct Option is C

In a tensile test represented on an engineering stress-strain diagram: - Engineering Stress (\(\sigma_e\)) = Load (P) / Original Area (\(A_0\)).
- Engineering Strain (\(\epsilon_e\)) = Change in Length / Original Length.
The Ultimate Tensile Strength (UTS) corresponds to the maximum load the specimen can withstand (\(P_{max}\)), so UTS = \(P_{max}/A_0\).
After reaching the UTS, ductile materials start to neck, meaning the cross-sectional area (\(A\)) begins to decrease significantly in a localized region.
Although the load (P) being applied may decrease after the UTS is reached (leading to a decrease in *engineering* stress), the *true* stress (\(\sigma_t\)) within the necked region increases dramatically because the decreasing area concentrates the load.
$$ \sigma_t = \frac{P}{A_{instantaneous}} $$ Since \(A_{instantaneous}\) decreases rapidly during necking while P decreases more slowly (or remains high initially), the true stress \(\sigma_t\) in the necked region continues to increase until fracture occurs.
The question asks what happens to the stress *in the necked region*, which usually implies the true stress.
Therefore, the stress increases.