CRACK GROWTH MODELING USING XIGA

Abstract

In the design and analysis of any component fracture analysis is one of the prime concern of every design engineer. Study of stationary crack as well as crack growth, both plays major role in fracture mechanics analysis. High stresses are generated in the components subjected to different loading and boundary conditions, which if exceeds the material strength results in progressive or catastrophic failure. State of stress becomes more severe in the presence of flaws (cracks, holes and inclusions), results in reduced strength of the component due to stress singularity existing near the tip of the crack. In order to determine the life of the component, stress values in the close vicinity of crack tip should be evaluated. The key parameter to be investigated accurately for fracture analysis is stress intensity factor (SIF). If the discontinuities are present in the component than analysis using classical finite element method (FEM) becomes difficult. Use of extended finite element method (XFEM) can solve the problem up to some extent but approximation of complex geometries is not exact which results in more approximation error compared to isogeometric analysis (IGA). However, exact modelling of the geometry can be achieved by using IGA also the solution fields can be approximated by using same higher order non uniform rational B-splines (NURBS) basis functions used for approximating the geometry. Amalgamation of IGA with partition of unity (PU) concept of XFEM results in a versatile numerical tool extended isogeometric analysis (XIGA). Analysis of fracture mechanics problems using XIGA enhances the accuracy and efficiency by manifolds because of reducing geometric approximation error and significantly accurate approximation of solution field using higher order NURBS basis function. In the present work, the modelling and simulation of few fracture mechanics problems would be carried out using the XIGA method. To analyse the problems with discontinuity i.e. crack, XIGA is used for different loading and boundary conditions. Superiority of XIGA over XFEM is shown, also by using XIGA the convergence towards the analytical solution is shown for relatively coarse mesh than XFEM. Variation of mode-I SIF with different crack lengths, Jdomain dimensions, J-domain positions is shown. Quasi-static or stable crack growth is shown in a crack with circular shape.