Stress intensity factors for three-dimensional cracks in functionally graded materials using enriched finite elements

Abstract

A three-dimensional enriched finite-element methodology is presented to compute stress intensity factors for threedimensional cracks contained in functionally graded materials (FGMs). A general-purpose 3D finite-element based fracture analysis program, FRAC3D, is enhanced to include this capability. First, using available solutions from the literature, comparisons have been made in terms of stresses under different loading conditions, such as uniform tensile, bending and thermal loads. Mesh refinement studies are also performed. The fracture solutions are obtained for edge cracks in an FGM strip and surface cracks in a finite-thickness FGM plate and compared with existing solutions in the literature. Further analyses are performed to study the behavior of stress intensity factor near the free surface where crack front terminates. It is shown that three-dimensional enriched finite elements provide accurate and efficient fracture solutions for threedimensional cracks contained in functionally graded materials.

Experimental and numerical investigation of a cracked transversely graded plate subjected to in plane bending

“…Similar reduction in the SIF near the intersection of the crack front and the free surface has been reported for surface cracks in graded plates by Ayhan (2007). This behavior of SIF is attributed to the existence of the corner singular stress field near the intersection of the crack front and the free surface (Benthem, 1977) and will be discussed in detail in the next section.…”

“…Such a situation also exists for semi-elliptical surface cracks in plates graded along the thickness and this problem has been studied in detail by Ayhan (2007Ayhan ( , 2008, Walters et al (2004) and Yildirim et al (2005) using finite element method. Walters et al (2006) have thoroughly explained the application of two-state interaction integral method to calculate mixed-mode stress intensity factor for three dimensional cracks in graded materials.…”

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

“…The thermal conductivity and the specific heat at constant pressure of FGMs vary gradually along the x direction. The variations of them have an exponential form [20][21][22], namely,…”

An improved numerical method for computation of stress intensity factors along 3D curved non-planar cracks in FGMs

“…Recently Shaghaghi et al (submitted for publication) successfully extended the procedure proposed by Gosz and Moran (2002) to 3D non-planar cracks in graded solids. Note that this topic was fairly unexplored because earlier works focused on 3D planar cracks only (Yu et al, 2010;Walters et al, 2004Walters et al, , 2006Yildirim et al, 2005;Ayhan, 2009Ayhan, , 2007. However, it was observed in Gosz and Moran (2002) that by imposing auxiliary fields in curvilinear coordinate system the auxiliary strain field is not symmetric gradient of auxiliary displacement field and auxiliary stress field is not in equilibrium.…”