Lengthwise Fracture of Two-Dimensional Functionally Graded Non-Linear Elastic Beam

Abstract

Non-linear elastic analysis of lengthwise fracture in functionally graded single leg four-point bending beam configuration is performed. The material is functionally graded along the height as well as along the width of the beam. A lengthwise crack is located arbitrary along the beam height. The mechanical behaviour of beam is described by power-law stress-strain relation. The fracture is studied analytically in terms of the strain energy release rate. The solution derived is verfied by analysing the fracture with the help of the J-integral. The influences of crack location, material gradient along the height as well as along the width of beam and the nonlinear behaviour of material on the fracture are investigated. It is found that the material non-linearity has to be taken into account in fracture mechanics based safety design of functionally graded structural members and components. The analysis revealed also that the strain energy release rate can be regulated effectively by employing appropriate material gradients in functionally graded structures.