Using equations or plots show why developing a compressive r

Using equations or plots show why developing a compressive residual stresses on the surface of a part helps with its fatigue life?

Solution

A material having compressive residual stress helps to prevent brittle fracture because the initial crack is formed under compressive (negative tensile) stress. To cause brittle fracture by crack propagation of the initial crack, the external tensile stress must overcome the compressive residual stress before the crack tips experience sufficient tensile stress to propagate.