Abstract
This paper describes an analytical approach for analysing of longitudinal fracture in beam structures which exhibit smooth material inhomogeneity along the height and length. A solution to the strain energy release rate is derived for a general loading scheme assuming non-linear mechanical behaviour of the material. The Ramberg-Osgood stress-strain relation is used to model the material non-linearity. It is assumed that the three material properties which are involved in the Ramberg-Osgood stress-strain relation vary continuously along the height and length of the beam (exponential laws are applied for describing the distribution of these properties along the height and length of the beam). The solution derived is valid for a longitudinal crack located arbitrary along the beam height. It is shown that the approach developed can be applied for evaluating the effects of material inhomogeneity along the height and length of the beam, non-linear mechanical behaviour of the material, crack location along the beam height and the crack length on the longitudinal fracture.
Highlights
The properties of the inhomogeneous materials are functions of coordinates
It is assumed that the material has non-linear mechanical behaviour which is modelled by the Ramberg-Osgood stress-strain relation
It is assumed that the three material properties which are involved in the Ramberg-Osgood relation vary continuously in thickness and longitudinal directions of the beam
Summary
The properties of the inhomogeneous materials are functions of coordinates. This fact complicates significantly the fracture analysis of structural members and components made of inhomogeneous materials. Another characteristic feature which should be taken into account in longitudinal fracture analyses is the non-linear mechanical behaviour of inhomogeneous materials. Various analyses of longitudinal cracks in inhomogeneous (functionally graded) beam structures have been developed by the author assuming non-linear mechanical behaviour of the material [11,12,13,14]. The basic aim of the present paper is to peform an analytical investigation of longitudinal fracture of inhomogeneous beams under a genearl loading scheme by applying the RambergOsgood constitutive law for modelling non-linear elastic mechanical behaviour of the material assuming that the three material properties which are involved in the constitutive law vary smoothly along the thickness and longitudinal directions of the beam. The solution derived is used to investigate the effect of various geometrical and material parameters on the longitudinal fracture behaviour
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