Mathematical modelling and the study of the influence of initial stresses on the SIF and ERR at the crack tips in a plate-strip of orthotropic material

Abstract

a b s t r a c tA plate-strip fabricated from the orthotropic material and containing a crack whose edges are parallel to the face planes of the plate is considered. It is assumed that the strip is stretched (or compressed) initially along the crack edges by uniformly distributed external normal forces acting on the simply supported ends of the plate-strip. After this initial stretching (or compression) the crack edges are loaded by additional uniformly distributed normal (opening) forces. As a result of the action of these additional forces the stress concentration characterized by the stress intensity factor (SIF) of mode I or by the energy release rate (ERR) of mixed mode arises at the crack tips. In this paper, the influence of the initial stresses on the SIF or ERR is modelled mathematically by the use of the threedimensional linearized theory of elasticity. The aim of the present investigations is to study the effect of the mechanical-orthotropic properties of the plate-strip material on this influence by the use of the finite element method (FEM) modelling of the corresponding boundary-value problem.Crown

A mixed boundary value problem in orthotropic strip containing a crack

“…Akbarov and Turan [5] examined an orthotropic plate strip containing a crack whose edges are parallel to the face planes of the plate. In this paper, the influence of the initial stresses on the SIF or the energy release rate was modeled mathematically by the use of the three-dimensional linearized theory of elasticity.…”

The Effect of the Shear Modulus on Planes which is Perpendicular to the Crack’s Edge-planes and Parallel to the Crack’s Front on the ERR in an Orthotropic Rectangular Prism with a Band Crack

“…Moreover, various methods of evaluating the SIF and ERR have been developed so far by Cherepanov (1967), Rice (1968), Shivakumar (1988), Fan et al (2007), Knowles and Sternberg (1972), Maiti (1992), Gosz et al (1998) etc. Based on the analyses of the above-mentioned investigations, there are many studies on the effects of the orthotropic and mechanical parameters on the SIF or on the ERR (Akbarov and Turan, 2009, Oneida et al, 2015, Ding and Li, 2014and Yusufoğlu and Turhan, 2012. However, these studies were discussed within the framework of the two-dimensional (2D) problem formulation.…”

“…Based on the analyses of the above-mentioned investigations, there are many studies on the effects of the orthotropic and mechanical parameters on the SIF or on the ERR (Akbarov and Turan, 2009, Oneida et al, 2015, Ding and Li, 2014and Yusufoğlu and Turhan, 2012. However, these studies were discussed within the framework of the two-dimensional (2D) problem formulation.…”