Hybrid semi-analytical calculation of the stress intensity factor for heterogeneous and functionally graded plates

Abstract

One of the significant successes in the Linear Elastic Fracture Mechanics field is the groundwork of stress intensity factor computation. By considering a linear elastic model of 2-D and 3-D finite width rectangular plates, the present work shows a new semi-analytical procedure to compute the stress intensity factor of the crack opening mode. Plates are made of homogeneous and graded heterogeneous media, characterized by different crack lengths and elastic moduli. The stress intensity factor was evaluated using the proposed procedure combined with a numerical one without the knowledge of the material properties in the crack tip to overcome the limitations related to the errors affecting the traditional solutions in the case of spatial variation of the constitutive properties within the structure. The obtained results have been compared with the well-established theoretical literature for homogeneous cases. Moreover, a mesh sensitivity analysis has been performed by varying the elements’ number along the crack length showing the effectiveness and feasibility of the proposed procedure, even in the case of coarse discretization, with consistent advantage in terms of computational costs. Furthermore, by keeping the crack length constant, parametric analyses have been carried out to investigate the effects of material graded heterogeneities on the stress distribution. The limitation of this study concerns the assumption that the delamination front is supposed to be straight, and the proposed strategy cannot be implemented in the case of an arbitrarily shaped front. Finally, the application of this research is in the field of production engineering and, Without setting a priori-specific discretization of the domain near the tip, the present approach paves the way to further implementation in crack propagation procedures.