Question

Which of the following is known as the Griffith equation?

• A. \( \sigma = \left( \frac{2\gamma E}{\pi C} \right)^{1/2} \)
• B. \( \sigma = \left( \frac{\gamma E}{\pi C} \right)^{1/2} \)
• C. \( \sigma = \left( \frac{\gamma E}{2\pi C} \right)^{1/2} \)
• D. \( \sigma = \left( \frac{\pi C}{\gamma E} \right)^{1/2} \)

Hint:

Griffith’s theory explains why \textbf{brittle materials} fail at much lower stresses than predicted by classical strength theories, due to the presence of \textbf{microcracks}.

Answer 1

The Correct Option is B

The Griffith equation describes the stress required for the propagation of cracks in brittle materials and is derived from Griffith's theory of brittle fracture. Step 1: Understanding Griffith's Theory - Griffith's equation relates the fracture stress (\( \sigma \)) of a brittle material to its crack length (\( C \)), the surface energy (\( \gamma \)), and Young's modulus (\( E \)). The equation is given by: \[ \sigma = \left( \frac{\gamma E}{\pi C} \right)^{1/2} \] This relationship shows that larger cracks require less stress to propagate, which explains why materials with defects fail at lower stresses than perfect materials.


Step 2: Evaluating the Options - Option (A) - Incorrect: The numerator contains an extra factor of 2, which is not part of the Griffith equation. - Option (B) - Correct: This is the correct Griffith equation relating stress, surface energy, Young's modulus, and crack length. - Option (C) - Incorrect: The denominator has an extra factor of 2, which makes this option incorrect. - Option (D) - Incorrect: The equation is incorrectly inverted, making this option invalid.


Step 3: Conclusion The correct Griffith equation is \( \sigma = \left( \frac{\gamma E}{\pi C} \right)^{1/2} \), making option (B) the correct answer.