Fatigue Crack Curvature Equation Derived using Finite Element Theory

Abstract

In this paper, finite element theory which is a mechanical engineering tool, is used as mathematical bridge between crack mechanics & stress - displacement equations. In this theory, the surface of a mechanical component is divided into a finite no. of Finite elements having finite dimensions and finite degrees of freedom. For this finite element, when load is applied we perform the discretisation of the domain, and from it calculate the displacement, stress, strain and curvature. From the equations, we calculate the radius of curvature of the crack for that finite element respectively which on addition of residual weights and summation we can derived the exact curve of the crack.