Analyses of delaminations in non-linear elastic multilayered inhomogeneous beam configurations

This paper presents investigation of delamination fracture behavior of multilayered non-linear elastic beam configurations by using the Ramberg-Osgood stress-strain relation. It is assumed that each layer exhibits continuous material inhomogeneity along the width as well as along thickness of the layer. An approach for determination of the strain energy release rate is developed for a delamination crack located arbitrary along the multilayered beam height. The approach can be applied for multilayered beams of arbitrary cross-section under combination of axial force and bending moments. The layers may have different thickness and material properties. The number of layers is arbitrary. The approach is applied for analyzing the delamination fracture behavior of a multilayered beam configuration subjected to four-point bending. The beam has a rectangular cross-section. The delamination crack is located symmetrically with respect to the beam midspan. The strain energy release rate is derived assuming that the modulus of elasticity varies continuously in the cross-section of each layer according to a hyperbolic law. In order to verify the solution to the strain energy release rate, the delamination fracture behavior of the multilayered non-linear elastic four-point bending beam configuration is studied also by applying the method of the J-integral. The solution to the strain energy release rate derived in the present paper is used in order to perform a parametric study of delamination.