Calculation of KII in crack face contacts using X-FEM. Application to fretting fatigue

Abstract In this work, the modeling of LEFM problems that imply crack face closure and contact using the extended finite element method (X-FEM) is presented aiming at its application to fretting fatigue problems. An assessment of the accuracy in the calculation of KII is performed for two different techniques to model crack face contacts in X-FEM: one is based on the use of additional elements to establish the contact and the other on a segment-to-segment (or mortar) approach. It is concluded that only the segment-to-segment approach can lead to optimal convergence rates of the error in KII. The crack face contact modeling has also been applied to a fretting fatigue problem, where the estimation of KII under crack closure conditions plays an important role in the stage I of fatigue crack propagation. The effect of the crack face friction coefficient has been studied and its influence on the range of KII has been ascertained during loading and unloading cycles.

[1]  Eugenio Giner,et al.  An improvement of the EDI method in linear elastic fracture mechanics by means of an a posteriori error estimator in G , 2004 .

[2]  C. Navarro,et al.  On the use of multiaxial fatigue criteria for fretting fatigue life assessment , 2008 .

[3]  Giorgio Donzella,et al.  Stress intensity factor range and propagation mode of surface cracks under rolling–sliding contact , 2003 .

[4]  S. Bogdański,et al.  A dimensionless multi-size finite element model of a rolling contact fatigue crack , 2005 .

[5]  A finite element analysis of fretting fatigue crack growth behavior in Ti–6Al–4V , 2008 .

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

[7]  J. Rice,et al.  The growth of slip surfaces in the progressive failure of over-consolidated clay , 1973, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Nicolas Moës,et al.  Robust implementation of contact under friction and large sliding with the eXtended finite element method , 2010 .

[9]  Eugenio Giner,et al.  An Abaqus implementation of the extended finite element method , 2009 .

[10]  Anthony Gravouil,et al.  A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method , 2007 .

[11]  Eugenio Giner,et al.  Crack face contact in X‐FEM using a segment‐to‐segment approach , 2010 .

[12]  M Truchon,et al.  Fatigue Crack Path Behavior Under Polymodal Fatigue , 1985 .

[13]  Tae-Yeon Kim,et al.  A mortared finite element method for frictional contact on arbitrary interfaces , 2006 .

[14]  C. Qian,et al.  Fatigue crack growth under mode II loading , 1995 .

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

[16]  Samuel Geniaut,et al.  An X‐FEM approach for large sliding contact along discontinuities , 2009 .

[17]  David Nowell,et al.  The effect of rapidly varying contact stress fields on fretting fatigue , 2002 .

[18]  A. Dorogoy,et al.  Shear loaded interface crack under the influence of friction: a finite difference solution , 2004 .

[19]  R. Plank,et al.  Fatigue crack propagation under non-proportional mixed mode loading , 1999 .

[20]  S. Leen,et al.  A combined wear and crack nucleation–propagation methodology for fretting fatigue prediction , 2008 .

[21]  Mario Guagliano,et al.  Experimental and numerical analysis of sub-surface cracks in railway wheels , 2005 .

[22]  M. W. Brown,et al.  A REVIEW OF FATIGUE CRACK GROWTH IN STEELS UNDER MIXED MODE I AND II LOADING , 1992 .

[23]  Peter Wriggers,et al.  Computational Contact Mechanics , 2002 .

[24]  M. C. Dubourg,et al.  A Predictive Rolling Contact Fatigue Crack Growth Model: Onset of Branching, Direction, and Growth—Role of Dry and Lubricated Conditions on Crack Patterns , 2002 .

[25]  P. Forsyth.  Fatigue damage and crack growth in aluminium alloys , 1963 .

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

[27]  Eugenio Giner,et al.  Extended Finite Element Method for Fretting Fatigue Crack Propagation , 2008 .

[28]  Yoshiharu Mutoh,et al.  Fracture mechanics approach to fretting fatigue and problems to be solved , 2003 .

[29]  Samuel Geniaut,et al.  A stable 3D contact formulation using X-FEM , 2007 .

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

[31]  H. Bui,et al.  The sliding interface crack with friction between elastic and rigid bodies , 2005 .

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

[33]  Guillermo E. Morales-Espejel,et al.  3D two scale X-FEM crack model with interfacial frictional contact: Application to fretting fatigue , 2010 .

[34]  Amir R. Khoei,et al.  An enriched finite element algorithm for numerical computation of contact friction problems , 2007 .

[35]  Takashi Miyata,et al.  The condition of fatigue crack growth in mixed mode condition , 1975 .

[36]  Liming Liu,et al.  Analysis of subsurface crack propagation under rolling contact loading in railroad wheels using FEM , 2007 .

[37]  Eugenio Giner,et al.  Error estimation for the finite element evaluation of G I and G II in mixed-mode linear elastic fracture mechanics , 2005 .

[38]  G. Gladwell,et al.  Solid mechanics and its applications , 1990 .

[39]  Marie-Christine Baietto,et al.  A multi-model X-FEM strategy dedicated to frictional crack growth under cyclic fretting fatigue loadings , 2010 .

[40]  Brian Moran,et al.  Energy release rate along a three-dimensional crack front in a thermally stressed body , 1986, International Journal of Fracture.

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

[42]  Ted Belytschko,et al.  An extended finite element method for modeling crack growth with frictional contact , 2001 .

[43]  Deng Xiaomin.  An asymptotic analysis of stationary and moving cracks with frictional contact along bimaterial interfaces and in homogeneous solids , 1994 .

[44]  D. Pecknold,et al.  Modeling of fatigue crack closure in inclined and deflected cracks , 2004 .

[45]  Nicolas Moës,et al.  A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method , 2009 .

[46]  Nicolas Moës,et al.  Imposing Dirichlet boundary conditions in the extended finite element method , 2006 .

[47]  A. Combescure,et al.  A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact , 2007 .

[48]  T. Laursen.  Computational Contact and Impact Mechanics , 2003 .

[49]  B. Audoly.  Asymptotic study of the interfacial crack with friction , 2000 .

[50]  Ronaldo I. Borja,et al.  A contact algorithm for frictional crack propagation with the extended finite element method , 2008 .