Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length

Abstract

Analyses of longitudinal fracture behavior of inhomogeneous beams which have continuously varying sizes of the cross-section along the beam length are carried-out. Beams of a rectangular cross-section are studied. It is assumed that beams exhibit continuous (smooth) material inhomogeneity along the width and height of the cross-section. A longitudinal crack located arbitrary along the beam height is analyzed. First, a cantilever beam with linearly varying width and height along the beam length is considered. The material of the beam has non-linear elastic mechanical behavior. The external loading consists of one bending moment applied at the free end of the lower crack arm. The fracture behavior is analyzed in terms of the strain energy release rate assuming that the modulus of elasticity is distributed continuously in the beam cross-section. The balance of the energy is considered in order to derive the strain energy release rate. A solution to the strain energy release rate is obtained also by considering the complementary strain energy for verification. The longitudinal fracture behavior of the inhomogeneous nonlinear elastic cantilever beam configuration is studied also for the cases when the variation of the width and height of the cross-section is described by sine and power laws.

Indeterminate Continuously Inhomogeneous Beam under End Rotation: A Longitudinal Fracture Study

“…As a result of this, one of the factors which have significant influence on the deformability, load-carrying capacity and safety of engineering structures made of such materials is the longitudinal fracture. Thus, various analyses of longitudinal fracture in continuously inhomogeneous (functionally graded) structural members have been performed recently (Carpinteri & Pugno, 2006;Rizov & Altenbach, 2020;Tilbrook et al, 2005). These analyses usually are concerned with structures subjected to external mechanical loading.…”