DELAMINATION IN MULTI-LAYERED FUNCTIONALLY GRADED BEAMS - AN ANALYTICAL STUDY BY USING THE RAMBERG-OSGOOD EQUATION

The paper is focused on analysing the delamination fracture in multi-layered functionally graded cantilever beam structures which exhibit nonlinear mechanical behaviour of the material by using the Ramberg-Osgood equation. It is assumed that in each layer of the material is functionally graded in both thickness and length directions. The beam under consideration is made of adhesively bonded horizontal layers which have different thicknesses and material properties. The number of layers is arbitrary. Besides, the delamination crack is located arbitrary between layers. Power laws are applied to describe the continuous variation of the modulus of elasticity in each layer. A nonlinear solution for the strain energy release rate is derived by analysing the energy balance. The solution is verified by obtaining the strain energy release rate also by considering the complementary strain energy. Effects of the material gradients in thickness and length directions, the crack location along the beam height, the material nonlinearity and the crack length on the delamination fracture behaviour are elucidated.