Consider the following statements, choose the correct option Assertion (A): A mild steel tension specimen has a cup and cone fracture at failure. Reason (R): Mild steel is weak in shear and failure of the specimen in shear takes place at 45° to the direction of the applied tensile force.
- ABoth A and R are correct and R is the correct explanation for ACorrect
- BBoth A and R are correct but R is not the correct explanation for A
- CA is correct but R is false
- DA is false but R is correct
Solution
Concept
Cup and Cone Fracture
Formula
τmax = σ / 2
Step-by-step solution
- Identify that mild steel is a ductile material and is weaker in shear than in tension - Apply τ\_max = σ / 2 to find that maximum shear stress occurs at 45° to the tensile force - Conclude that shear failure along 45° forms the cup and cone fracture, making both Assertion and Reason correct
Explanation
Mild steel is a ductile material, making it weaker in shear than in tension. Under a tensile load, the maximum shear stress occurs along planes inclined at 45° to the applied force. Because of this weakness in shear, the material slips and fractures along these 45° planes, forming a characteristic cup and cone shape at failure. Therefore, Assertion (A) is correct, and Reason (R) correctly explains why this type of failure occurs.
Shortcut
Shortcut: Remember "Ductile = Shear = 45° = Cup & Cone". Mild steel is ductile, making it weakest in shear, which occurs at 45° to the tensile force to form the cup and cone shape. Since the shear weakness directly causes the 45° cup and cone fracture, both A and R are true, and R correctly explains A.
Common mistake
A common mistake students make is selecting Option B, incorrectly believing that Reason (R) is merely a true independent statement rather than the direct explanation for Assertion (A), because they fail to link the 45° shear slip plane directly to the formation of the cup-and-cone surface profile.
Correct answer: A) Both A and R are correct and R is the correct explanation for A