Theoretical analysis of fracture in non-linear elastic functionally graded beam of linearly changing thickness with three longitudinal cracks

Abstract

The present paper is focussed on fracture analysis of a functionally graded nonlinear elastic cantilever beam structure with three longitudinal cracks. The cross-section of the beam is a rectangle. The beam height increases linearly towards the clamped end. The material is functionally graded along the thickness of the beam. The J-integral approach is applied in the fracture analysis. The solutions to the J-integral for the three cracks are verified by deriving of the strain energy release rate. For this purpose, the complementary strain energy cumulated in the beam is differentiated with respect to the areas of the three cracks. A parametric investigation of the longitudinal fracture behaviour of the beam is carried-out by applying the solutions to the J-integral. The effects of the beam geometry, the crack length and the material gradient along the beam thickness on the longitudinal fracture behaviour are evaluated and discussed.