Question

Which theory is commonly used to predict the failure of ductile materials under multiaxial stress states?

• A. Coulomb's theory
• B. Rankine's theory
• C. Maximum distortion energy theory
• D. Tresca's theory

Hint:

Remember:
- Ductile materials $\to$ von Mises (Distortion Energy) or Tresca (Max Shear Stress). von Mises is the most accurate.
- Brittle materials $\to$ Rankine (Max Principal Stress).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the preferred theory of failure used to predict yielding (failure) of ductile materials under multiaxial loading conditions.

Step 2: Key Formula or Approach:
The main theories of failure include:
- Maximum Principal Stress Theory (Rankine)
- Maximum Shear Stress Theory (Tresca)
- Maximum Distortion Energy Theory (von Mises)

Step 3: Detailed Explanation:

• Ductile materials fail primarily by yielding (slip along shear planes).

• The Maximum Distortion Energy Theory (von Mises theory) states that yielding begins when the distortion energy per unit volume equals that at the yield point in a simple tension test.

• Experimentally, the von Mises theory provides the most accurate and consistent predictions for the failure of ductile materials under multiaxial stress states compared to other theories.

• Rankine's theory is used for brittle materials, while Coulomb's theory is often applied to soils and concrete.

Step 4: Final Answer:
The Maximum distortion energy theory is commonly used for ductile materials under multiaxial stress states.