Question

A metal has Young's modulus of 220 GPa and yielding strength 365 MPa. The metal is strained to 0.1% strain, then the stress is:

• A. 220 GPa
• B. 220 MPa
• C. 365 MPa
• D. 600 MPa

Hint:

Always convert units to a common base (like MPa) before calculating. Remember: \( 1~GPa = 1000~MPa \). Also, always verify if the calculated stress is below the yield point; if it were higher, the answer would likely be the yield strength or require a plastic deformation model.

Answer 1

The Correct Option is B

Concept: According to Hooke's Law, within the elastic limit, stress (\( \sigma \)) is directly proportional to strain (\( \epsilon \)). The constant of proportionality is Young's Modulus (\( E \)). \[ \sigma = E \times \epsilon \]

Step 1: Check if the strain is within the elastic region.
We must first determine if the resulting stress exceeds the yield strength. If it does, Hooke's Law no longer applies directly. Given:
• \( E = 220~GPa = 220,000~MPa \)
• \( \epsilon = 0.1% = 0.001 \)

Step 2: Calculate the stress using Hooke's Law.
\[ \sigma = 220,000~MPa \times 0.001 = 220~MPa \]

Step 3: Verify against Yield Strength.
The calculated stress (220 MPa) is less than the yield strength (365 MPa). This confirms the metal is still in the elastic region, and our calculation using Hooke's Law is valid.