Multilayered Functionally Graded Non-linear Elastic Beams with Logarithmic Material Gradient

A Delamination Analysis

Abstract

The delamination fracture in a multilayered functionally graded cantilever beam configuration that exhibits material non-linearity is analyzed in terms of the strain energy release rate. The beam under consideration has an arbitrary number of adhesively bonded horizontal layers of different thicknesses and material properties. The delamination crack is located arbitrary along the beam height. The material non-linearity is described by a stress-strain relation that involves two material properties. It is assumed that the two material properties are functionally graded in both width and thickness directions in each layer. Logarithmic laws are used to describe the variation of the material properties in the cross-sections of the layers (the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section). The balance of the energy is analyzed in order to derive the strain energy release rate. The J-integral approach is applied for verification. Parametric investigations are carried-out in order to evaluate the influence of the gradients of the two material properties in both width and thickness directions of the layers on the delamintion fracture behaviour. The results obtained show that the strain energy release rate can be controlled by using appropriate material gradients in the design stage of multilayered functionally graded structural members exhibiting material non-linearity.