XFEM fracture analysis of orthotropic functionally graded materials

Abstract In the present study, the extended finite element method (XFEM) has been used for fracture analysis of orthotropic functionally graded materials. Orthotropic crack tip enrichments have been used to reproduce the singular stress field near a crack tip. Moreover, the incompatible interaction integral method has been employed to extract the stress intensity factor components. Accuracy and convergence of the proposed method have been evaluated by numerical examples and quality results have been obtained by far fewer DOFs. Also, crack propagation in isotropic and orthotropic FGMs in the presence of crack tip enrichments has been investigated and various propagation criteria have been compared, and verified, if available, by experimental and numerical data in the literature. Application of XFEM in combination of the maximum circumferential tensile stress criterion for investigation of crack propagation in orthotropic FGM problems is performed for the first time.

[1]  Glaucio H. Paulino,et al.  Mixed-mode J-integral formulation and implementation using graded elements for fracture analysis of nonhomogeneous orthotropic materials , 2003 .

[2]  Stéphane Bordas,et al.  Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals , 2010 .

[3]  D. Chopp,et al.  Extended finite element method and fast marching method for three-dimensional fatigue crack propagation , 2003 .

[4]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[5]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[6]  John E. Dolbow,et al.  Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks , 1998 .

[7]  Mohamed L. Ayari,et al.  Maximum strain theory for mixed mode crack propagation in anisotropic solids , 1995 .

[8]  Glaucio H. Paulino,et al.  Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method , 2002 .

[9]  Glaucio H. Paulino,et al.  T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms , 2004 .

[10]  J. Dolbow,et al.  On the computation of mixed-mode stress intensity factors in functionally graded materials , 2002 .

[11]  Shuodao Wang,et al.  A Mixed-Mode Crack Analysis of Isotropic Solids Using Conservation Laws of Elasticity , 1980 .

[12]  A. Ayhan Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements , 2009 .

[13]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[14]  G. Sih Strain-energy-density factor applied to mixed mode crack problems , 1974 .

[15]  T. Belytschko,et al.  Non‐linear analysis of shells with arbitrary evolving cracks using XFEM , 2005 .

[16]  Ted Belytschko,et al.  Modeling fracture in Mindlin–Reissner plates with the extended finite element method , 2000 .

[17]  T. Belytschko,et al.  A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM , 2010 .

[18]  Martin H. Sadd,et al.  Elasticity: Theory, Applications, and Numerics , 2004 .

[19]  G. Paulino,et al.  Finite element evaluation of mixed mode stress intensity factors in functionally graded materials , 2002 .

[20]  Alireza Asadpoure,et al.  Crack analysis in orthotropic media using the extended finite element method , 2006 .

[21]  Soheil Mohammadi,et al.  Dynamic crack propagation analysis of orthotropic media by the extended finite element method , 2009 .

[22]  F. Erdogan,et al.  On the Crack Extension in Plates Under Plane Loading and Transverse Shear , 1963 .

[23]  S. Atluri,et al.  A finite-element program for fracture mechanics analysis of composite material , 1975 .

[24]  Alireza Asadpoure,et al.  Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method , 2007 .

[25]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[26]  Masayuki Niino,et al.  Recent development status of functionally gradient materials. , 1990 .

[27]  Murat Ozturk,et al.  The Mixed Mode Crack Problem in an Inhomogeneous Orthotropic Medium , 1999 .

[28]  G. Paulino,et al.  ISOPARAMETRIC GRADED FINITE ELEMENTS FOR NONHOMOGENEOUS ISOTROPIC AND ORTHOTROPIC MATERIALS , 2002 .

[29]  J. W. Eischen,et al.  Fracture of nonhomogeneous materials , 1987, International Journal of Fracture.

[30]  M. Haack Part B , 1942 .

[31]  Soheil Mohammadi,et al.  Delamination analysis of composites by new orthotropic bimaterial extended finite element method , 2011 .

[32]  Hareesh V. Tippur,et al.  COMPOSITIONALLY GRADED MATERIALS WITH CRACKS NORMAL TO THE ELASTIC GRADIENT , 2000 .

[33]  Eugenio Giner,et al.  Enhanced blending elements for XFEM applied to linear elastic fracture mechanics , 2009 .

[34]  Soheil Mohammadi,et al.  Dynamic analysis of fixed cracks in composites by the extended finite element method , 2010 .

[35]  F. Erdogan,et al.  Mode I Crack Problem in an Inhomogeneous Orthotropic Medium , 1997 .

[36]  Glaucio H. Paulino,et al.  Consistent Formulations of the Interaction Integral Method for Fracture of Functionally Graded Materials , 2005 .

[37]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[38]  J. Rice A path-independent integral and the approximate analysis of strain , 1968 .

[39]  T. Belytschko,et al.  Extended finite element method for three-dimensional crack modelling , 2000 .

[40]  Glaucio H. Paulino,et al.  The interaction integral for fracture of orthotropic functionally graded materials: Evaluation of stress intensity factors , 2003 .

[41]  Toshio Nakamura,et al.  Three-Dimensional Stress Fields of Elastic Interface Cracks , 1991 .

[42]  H. T. Corten,et al.  A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity , 1980 .

[43]  Jean-François Remacle,et al.  A substructured FE‐shell/XFE‐3D method for crack analysis in thin‐walled structures , 2007 .

[44]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[45]  Glaucio H. Paulino,et al.  On Fracture Criteria for Mixed-Mode Crack Propagation in Functionally Graded Materials , 2007 .

[46]  Soheil Mohammadi,et al.  XFEM fracture analysis of shells: The effect of crack tip enrichments , 2011 .

[47]  N. J. Pagano,et al.  Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension , 1970 .

[48]  N. J. Pagano,et al.  Interlaminar Stresses in Composite Laminates—An Approximate Elasticity Solution , 1974 .

[49]  D. Chopp,et al.  Modelling crack growth by level sets , 2013 .

[50]  Duygu Sarikaya,et al.  Mixed-Mode Fracture Analysis Of Orthotropic Functionally Graded Materials Under Mechanical And Thermal Loads , 2007 .

[51]  F. Erdogan,et al.  The crack problem for a nonhomogeneous plane , 1983 .

[52]  Michael H. Santare,et al.  Numerical Calculation of Stress Intensity Factors in Functionally Graded Materials , 2000 .

[53]  F. Erdogan,et al.  The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate , 1996 .

[54]  N. J. Pagano,et al.  On the Calculation of Interlaminar Normal Stress in Composite Laminate , 1974 .

[55]  Victor E. Saouma,et al.  Mixed mode crack propagation in homogeneous anisotropic solids , 1987 .

[56]  Patrick Laborde,et al.  A Reduced Basis Enrichment for the eXtended Finite Element Method , 2009 .

[57]  Ye Zhiming,et al.  Prediction of crack propagation in anisotropic solids , 1994 .

[58]  Noboru Konda,et al.  The mixed mode crack problem in a nonhomogeneous elastic medium. , 1990 .

[59]  Hussain,et al.  Strain Energy Release Rate for a Crack Under Combined Mode I and Mode II , 1974 .

[60]  T. Belytschko,et al.  MODELING HOLES AND INCLUSIONS BY LEVEL SETS IN THE EXTENDED FINITE-ELEMENT METHOD , 2001 .

[61]  A. Kawasaki,et al.  Functionally graded materials : design, processing and applications , 1999 .

[62]  Ted Belytschko,et al.  Parametric enrichment adaptivity by the extended finite element method , 2008 .

[63]  Alireza Asadpoure,et al.  Modeling crack in orthotropic media using a coupled finite element and partition of unity methods , 2006 .

[64]  Vladimir Sladek,et al.  3D crack analysis in functionally graded materials , 2011 .

[65]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[66]  Ali Shaghaghi Moghaddam,et al.  Finite element evaluation of stress intensity factors in curved non-planar cracks in FGMs , 2011 .

[67]  C. Comi,et al.  Extended finite element simulation of quasi-brittle fracture in functionally graded materials , 2007 .

[68]  P Kerfriden,et al.  Natural frequencies of cracked functionally graded material plates by the extended finite element method , 2011 .

[69]  Robert J. Asaro,et al.  Cracks in functionally graded materials , 1997 .

[70]  Robert J. Asaro,et al.  A Simplified Method for Calculating the Crack-Tip Field of Functionally Graded Materials Using the Domain Integral , 1999 .

[71]  P. C. Paris,et al.  On cracks in rectilinearly anisotropic bodies , 1965 .