Fatigue crack growth simulations of 3-D problems using XFEM

Abstract In this work, a simple and efficient approach based on extended finite element method (XFEM) has been presented to simulate three-dimensional fatigue crack growth simulations. In XFEM, standard displacement based approximation is enriched by additional functions using partition of unity concept. These enrichment functions are derived from the theoretical background of the problem under consideration. In the proposed approach, a crack front has been divided into many piecewise curve crack segments to avoid an iterative solution. Three-dimensional triangulation scheme is adopted for the calculation of level set functions on the crack surface. At the crack front, the level set functions are approximated using the concept of hanging nodes using quadratic finite element shape functions. These level sets are used to accurately define the crack geometry. The fatigue crack growth simulations have been performed using Paris law of fatigue crack growth. Various 3-D planar, non-planar and arbitrary shape crack growth problems are solved to reveal the sturdiness and versatility of the proposed XFEM approach.

[1]  G. Irwin.  Crack-Extension Force for a Part-Through Crack in a Plate , 1962 .

[2]  Mark A Fleming,et al.  ENRICHED ELEMENT-FREE GALERKIN METHODS FOR CRACK TIP FIELDS , 1997 .

[3]  C. Shih,et al.  Elastic-Plastic Analysis of Cracks on Bimaterial Interfaces: Part I—Small Scale Yielding , 1988 .

[4]  Marc Duflot,et al.  Fatigue crack growth analysis by an enriched meshless method , 2004 .

[5]  J. Akin.  The generation of elements with singularities , 1976 .

[6]  R. D. Henshell,et al.  CRACK TIP FINITE ELEMENTS ARE UNNECESSARY , 1975 .

[7]  T. Belytschko,et al.  Vector level sets for description of propagating cracks in finite elements , 2003 .

[8]  D. Chopp,et al.  Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method , 2003 .

[9]  S. Atluri,et al.  CALCULATION OF FRACTURE MECHANICS PARAMETERS FOR AN ARBITRARY THREE-DIMENSIONAL CRACK, BY THE ‘EQUIVALENT DOMAIN INTEGRAL’ METHOD , 1987 .

[10]  Ted Belytschko,et al.  Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions , 2010 .

[11]  T. Fries.  A corrected XFEM approximation without problems in blending elements , 2008 .

[12]  Stéphane Roux,et al.  Three dimensional experimental and numerical multiscale analysis of a fatigue crack , 2010 .

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

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

[15]  M. Duflot.  A study of the representation of cracks with level sets , 2007 .

[16]  I. N. Sneddon,et al.  The distribution of stress in the neighbourhood of a flat elliptical crack in an elastic solid , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  T. Belytschko,et al.  New crack‐tip elements for XFEM and applications to cohesive cracks , 2003 .

[18]  Glaucio H. Paulino,et al.  Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems , 2009 .

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

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

[21]  Johann Rannou,et al.  A local multigrid X‐FEM strategy for 3‐D crack propagation , 2009 .

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

[23]  Carlos Armando Duarte,et al.  Extraction of stress intensity factors from generalized finite element solutions , 2005 .

[24]  M. Duflot.  A meshless method with enriched weight functions for three‐dimensional crack propagation , 2006 .

[25]  Julien Réthoré,et al.  Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver , 2013 .

[26]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[27]  A. Ayhan.  Mixed mode stress intensity factors for deflected and inclined corner cracks in finite-thickness plates , 2007 .

[28]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update , 2002 .

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

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

[31]  B. Moran,et al.  An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions , 2002 .

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

[33]  Marie-Christine Baietto,et al.  A two-scale extended finite element method for modelling 3D crack growth with interfacial contact , 2010 .

[34]  Benoit Prabel,et al.  Level set X‐FEM non‐matching meshes: application to dynamic crack propagation in elastic–plastic media , 2007 .

[35]  Glaucio H. Paulino,et al.  Interaction integral procedures for 3-D curved cracks including surface tractions , 2005 .

[36]  Michel Salaün,et al.  High‐order extended finite element method for cracked domains , 2005 .

[37]  Julien Réthoré,et al.  Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM , 2011 .

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

[39]  Anthony Gravouil,et al.  Fatigue crack propagation: In situ visualization using X-ray microtomography and 3D simulation using the extended finite element method , 2006 .

[40]  R. Barsoum.  Triangular quarter‐point elements as elastic and perfectly‐plastic crack tip elements , 1977 .

[41]  Paul A. Wawrzynek,et al.  Automated 3‐D crack growth simulation , 2000 .

[42]  Soheil Mohammadi,et al.  Extended Finite Element Method: for Fracture Analysis of Structures , 2008 .

[43]  N. Moës,et al.  Improved implementation and robustness study of the X‐FEM for stress analysis around cracks , 2005 .

[44]  Mamdouh M. Salama,et al.  Mixed-mode stress intensity factor solutions of a warped surface flaw by three-dimensional finite element analysis , 1987 .

[45]  Bhushan Lal Karihaloo,et al.  XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi‐materials , 2004 .

[46]  Guido Dhondt,et al.  AUTOMATIC 3-D MODE I CRACK PROPAGATION CALCULATIONS WITH FINITE ELEMENTS , 1998 .

[47]  B. Moran,et al.  A general treatment of crack tip contour integrals , 1987 .

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

[49]  Stéphane Roux,et al.  Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids , 2010 .