Computation of Mixed-Mode Stress Intensity Factors for Cracks in Three-Dimensional Functionally Graded Solids

Abstract

This work applies a two-state interaction integral to obtain stress intensity factors along cracks in three-dimensional functionally graded materials. The procedures are applicable to planar cracks with curved fronts under mechanical loading, including crack-face tractions. Interaction-integral terms necessary to capture the effects of material nonhomogeneity are identical in form to terms that arise due to crack-front curvature. A discussion reviews the origin and effects of these terms, and an approximate interaction-integral expression that omits terms arising due to curvature is used in this work to compute stress intensity factors. The selection of terms is driven by requirements imposed by material nonhomogeneity in conjunction with appropriate mesh discretization along the crack front. Aspects of the numerical implementation with ͑isoparametric͒ graded finite elements are addressed, and examples demonstrate the accuracy of the proposed method.

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

“…Using the displacement correlation technique, Yildirim et al (2005) studied the behavior of a semi-elliptical surface crack in an FGM coating bonded to a homogeneous substrate under mechanical or transient thermal loading conditions. Recently, Walters et al (2006) also reported mixed-mode stress intensity factors for threedimensional cracks in FGMs using a two-state interaction integral method.…”

Transient Stress Intensity Factors of Functionally Graded Hollow Cylinders with Internal Circumferential Cracks

“…In most of the published works on the analysis of cracked FG structures, analytical methods , energy methods combined with the standard FE analysis (Walters et al 2006;Zhang et al 2014), or the extended finite element method (XFEM) (Bayesteh & Mohammadi 2013) have been used for the calculation of SIFs. Analytical approaches are limited to specific (and often simple) geometries and loading conditions.…”

J resistance behavior in functionally graded materials using cohesive zone and modified boundary layer models

“…First, we perform elastic analysis for the specimen (stationary crack model without cohesive elements), considering only the elastic material properties (E and ν). The elastic analysis yields K I and T (calculated from interaction integral technique implemented in WARP3D -see Walters et al, 2005Walters et al, , 2006,which are used to determine the traction boundary conditions for the MBL model. The traction boundary conditions are determined from the elastic analysis of the MBL model (stationary crack model without cohesive elements) only considering E and ν (see Figure 15).…”

“…Fracture characteristics of FGMs have been investigated by many researchers during the past years, e.g. Eischen (1987), Erdogan (1995), Gu and Asaro (1997), Anlas et al (2000), Paulino (2002a, 2003), and Walters ( , 2005and Walters ( , 2006. In the present study, fracture behaviors of FGMs are investigated with special emphasis on the crack growth resistance using cohesive zone and modified boundary layer (MBL) models.…”