Crack Theory

Question 1

Strain energy

Answer 1

Strain energy is a close relative of potential energy and is measure of the amount of energy stored in a material that has undergone strain, whether it be compressive, tensile, shear, bending or torsion. The strain energy per unit volume of a material can be determined using the formula:

SE = (1/2)σε

Where SE = strain energy/unit volume (J/m^3)
σ = stress (Pa)
ε = strain

Question 2

Crack formation - why do cracks form and grow?

Answer 2

Theoretically, materials with perfect linking of the atomic planes would be strong in compression and tension, however, small imperfections (for example air bubbles in ceramics) cause this not to be the case, and allow for the propagation and formation of larger cracks. When a crack forms, the strain energy held in the entire object is retained by now concentrated at the bottom of the crack, thus increasing the strain energy energy at the tip so cracks get bigger faster.

Question 3

Critical crack length

Answer 3

There is a critical length that a crack must get to before it proceeds through a material. While determining the critical crack length is beyond the scope of our course, some important things to note are that critical crack length is directly proportional to the Young’s Modulus of a material, and inversely proportional to the applied stress.