Delamination of Two-Dimensional Functionally Graded Multilayered Non-Linear Elastic Beam - an Analytical Approach

Delamination fracture of a two-dimensional functionally graded multilayered four-point bending beam that exhibits non-linear behaviour of the material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under consideration has an arbitrary number of layers. Each layer has individual thickness and material properties. A delamination crack is located arbitrary between layers. The material is two-dimensional functionally graded in the cross-section of each layer. The beam mechanical behaviour is described by a power-law stress-strain relation. The fracture is analyzed also by applying the J-integral approach in order to verify the solution derived for the strain energy release rate. The effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture are evaluated. It is found that the material non-linearity leads to increase of the strain energy release rate. Therefore, the material non-linearity should be taken into account in fracture mechanics based safety design of two-dimensional functionally graded multilayered structural members. It is found also that the delamination behaviour can be effectively regulated by using appropriate material gradients in the design stage of functionally graded multilayered structural members and components.