Which of the following theories is suitable for ductile material?
- AMaximum principal stress theory
- BMaximum Principal strain theory
- CMaximum Shear stress theory
- DDistortion energy theoryCorrect
Solution
Concept
Failure theories for ductile materials
Formula
NONE
Step-by-step solution
1. Distortion energy theory (Von Mises theory) considers failure based on energy associated with shape change rather than volume change. 2. Experimental evidence shows that distortion energy theory gives the most accurate results for yield failure in ductile materials under combined loading. 3. Therefore, distortion energy theory is the most suitable theory of failure for ductile materials. Answer: D
Explanation
The Distortion Energy Theory, also known as von Mises theory, provides the most accurate failure prediction for ductile materials under complex static loading. It accounts for distortion energy while ignoring hydrostatic pressure, which does not cause plastic yield in ductile metals.
Why the other options are wrong
A) Maximum principal stress theory is suitable for brittle materials. B) Maximum principal strain theory is generally inaccurate for ductile materials. C) Maximum shear stress theory is conservative for ductile materials, whereas distortion energy theory is most accurate.
Shortcut
Ductile materials are best evaluated by Maximum Shear Stress Theory (Tresca) and Distortion Energy Theory (Von Mises).
Common mistake
Confusing Maximum Principal Stress theory (suitable for brittle materials) with Distortion Energy theory.
Correct answer: D) Distortion energy theory