ANALYSIS OF APPROXIMATED CURVED CRACKS IN HOMOGENEOUS AND GRADED MATERIALS
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Abstract
In this paper two stages of analysis are studied. In stage I, the influence of crack shape on the
crack-tip stresses, critical loads and subsequent propagation direction is investigated via a simple
analytical model for cracks in homogeneous materials. This model is verified through finite element
simulations using ANSYS. It is demonstrated that accurate predictions of mechanical energy release
rate and crack deflection angle may be obtained from a smaller number of crack shape parameters.
In stage II, this concept is extended to curved cracks in functionally graded materials (FGMs).It is
common that analytical and computational models of fracture in FGMs have focused almost
extensively on straight cracks. If it can be demonstrated that straight cracks give an adequate
approximation of curved cracks in graded materials, then the existing solutions for straight cracks
provide a sufficient foundation for fracture analysis of FGMs. On the other hand, if straight cracks
do not adequately approximate curved cracks in FGMs, then the development of solutions for non
straight cracks in graded materials is priority. Three cracks shapes approximations are performed to
compare with the actual crack in isotropic and graded materials. The crack propagation and the SIFs
were simulated using finite element method. It was concluded that piecewise linear crack shapes
provide a significantly better approximation than straight crack shapes. Accordingly, analytical
solutions for piecewise linear cracks in graded materials would be very useful, and should be a
focus of future work in this area.
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