Question

When cracks propagate in a brittle material, the following option(s) is/are correct

• A. elastic strain energy decreases
• B. surface energy increases
• C. surface energy decreases
• D. elastic strain energy increases

Hint:

Think of brittle fracture like this: the material {pays} an energy cost (increase in surface energy) to get a bigger energy {refund} (decrease in elastic strain energy). The crack grows if the refund is bigger than the cost.

Answer 1

The Correct Option is A, B

Step 1: Understanding the Concept:
This question relates to the energy balance criteria for fracture in brittle materials, as first proposed by A.A. Griffith. The propagation of a crack involves a trade-off between two types of energy within the material.
Step 2: Key Principles of Brittle Fracture:
According to Griffith's theory, a crack will propagate if the energy released by the crack growth is greater than or equal to the energy required to create the new crack surfaces.
Elastic Strain Energy: A stressed material stores potential energy, known as elastic strain energy. When a crack forms and grows, it allows the material around the crack to relax, thereby releasing some of this stored energy. Thus, as a crack propagates, the overall elastic strain energy of the component decreases. This decrease is the driving force for fracture.
Surface Energy: To create a new crack, atomic bonds at the crack plane must be broken. This requires energy. The energy required per unit area of new surface is called the surface energy. As a crack propagates, its surface area increases, and therefore, the total surface energy of the system increases. This increase is the resistance to fracture.
Step 3: Evaluating the Options:
- (A) elastic strain energy decreases: Correct. The propagation of the crack releases stored strain energy from the surrounding material.
- (B) surface energy increases: Correct. New surfaces are created as the crack grows, which requires an input of energy, thus increasing the total surface energy.
- (C) surface energy decreases: Incorrect. Creating surfaces always requires energy.
- (D) elastic strain energy increases: Incorrect. The system moves to a lower energy state by releasing strain energy.
Step 4: Why This is Correct:
The propagation of a crack is an energetically favorable process only when the decrease in elastic strain energy is sufficient to supply the increase in surface energy needed to form the new crack faces. Therefore, options (A) and (B) correctly describe the energy changes during brittle crack propagation.