Mixed mode crack growth in elasto-plastic-creeping solids using XFEM

Abstract In this work, an extended finite element based fully implicit algorithm is proposed to predict the creep deformation and creep crack growth in elasto-plastic-creeping solids. The effect of stress relaxation and redistribution due to creep strain is captured through elasto-plastic-creep analysis. In creep crack growth analysis, mostly C ∗ is used to compute the creep crack growth which includes only extensive creep whereas C ( t ) -integral includes small-scale creep, transition creep and extensive creep. Thus, in the present study, creep crack characterization parameter C ( t ) -integral is evaluated using XFEM to compute creep crack growth rate. The mixed mode stress intensity factors are evaluated using domain based interaction integral approach to estimate the crack growth direction. Various numerical issues related to history dependency of plasticity and creep are properly addressed. To validate the present approach, various numerical problems are solved and the predicted creep deformation and creep crack growth results are compared with the experimental observations.

[1]  Noel P. O’Dowd,et al.  Creep crack growth prediction using a damage based approach , 2003 .

[2]  A. Needleman,et al.  Creep crack growth by grain boundary cavitation under monotonic and cyclic loading , 2017 .

[3]  Sohichi Hirose,et al.  An extended consecutive-interpolation quadrilateral element (XCQ4) applied to linear elastic fracture mechanics , 2015 .

[4]  David L. McDowell,et al.  Inclusion of primary creep in the estimation of the Ct parameter , 1990 .

[5]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[6]  Consideration of primary creep at a stationary crack tip: Implications for the Ct parameter , 1988 .

[7]  S. B. Biner,et al.  On the stress and strain fields ahead of a stationary crack in creeping solids , 1985 .

[8]  Timon Rabczuk,et al.  Dual‐horizon peridynamics , 2015, 1506.05146.

[9]  Timon Rabczuk,et al.  Element-wise fracture algorithm based on rotation of edges , 2013 .

[10]  C. Schweizer.  Evolution equations for the C(t)-integral and the crack-tip opening displacement CTOD for elastic–viscoplastic material behavior and temperature dependent material properties , 2016 .

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

[12]  Mcdowell,et al.  CRACK TIP PARAMETERS FOR CREEP-BRITTLE CRACK GROWTH , 2002 .

[13]  S. Ahmad,et al.  Creep crack simulations using continuum damage mechanics and extended finite element method , 2019 .

[14]  A. S. Shedbale,et al.  Elasto-plastic fatigue crack growth analysis of plane problems in the presence of flaws using XFEM , 2015 .

[15]  Bijay K. Mishra,et al.  Evaluation of mixed mode stress intensity factors for interface cracks using EFGM , 2011 .

[16]  S. Dushman,et al.  Creep of Metals , 1944 .

[17]  Michael A. Sutton,et al.  Experimental investigation of near crack tip creep deformation in alloy 800 at 650^C , 1998 .

[18]  Ted Belytschko,et al.  Numerical Solutions of Mixed Mode Dynamic Fracture in Concrete using Element-Free Galerkin Methods , 1995 .

[19]  A. S. Shedbale,et al.  A coupled FE–EFG approach for modelling crack growth in ductile materials , 2016 .

[20]  N. Petrinic,et al.  Introduction to computational plasticity , 2005 .

[21]  Andreas Klenk,et al.  A new method of strength calculation and lifetime prediction of pipe bends operating in the creep range , 2005 .

[22]  Wei Sun,et al.  Testing and modelling of creep crack growth in compact tension specimens from a P91 weld at 650 °C , 2010 .

[23]  Liguo Zhao,et al.  A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature , 2008 .

[24]  F. Xuan,et al.  The influence of stress-regime dependent creep model and ductility in the prediction of creep crack growth rate in Cr–Mo–V steel , 2015 .

[25]  Yuebao Lei,et al.  Validation of contour integral functions (J and C(t)) in ABAQUS v6.11-v6.14 for combined mechanical and residual stresses , 2016 .

[26]  Kamran Nikbin,et al.  Probabilistic analysis of creep crack initiation and growth in pipe components , 2003 .

[27]  Yun‐Jae Kim,et al.  Creep failure simulations of 316H at 550 °C: Part I – A method and validation , 2011 .

[28]  A. Khoei.  Extended Finite Element Method: Theory and Applications , 2015 .

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

[30]  Chuanzeng Zhang,et al.  Analysis of generalized dynamic intensity factors of cracked magnetoelectroelastic solids by X-FEM , 2013 .

[31]  Yun‐Jae Kim,et al.  Creep failure simulations of 316H at 550 °C: Part II – Effects of specimen geometry and loading mode , 2013 .

[32]  Timon Rabczuk,et al.  Dual-horizon peridynamics: A stable solution to varying horizons , 2017, 1703.05910.

[33]  T. Belytschko,et al.  X‐FEM in isogeometric analysis for linear fracture mechanics , 2011 .

[34]  Timon Rabczuk,et al.  Finite strain fracture of 2D problems with injected anisotropic softening elements , 2014 .

[35]  Costas P. Providakis,et al.  Time-dependent creep fracture using singular boundary elements , 2002 .

[36]  Luiz Fernando Martha,et al.  Fatigue life and crack path predictions in generic 2D structural components , 2003 .

[37]  Timon Rabczuk,et al.  Damage and fracture algorithm using the screened Poisson equation and local remeshing , 2016 .

[38]  B. K. Mishra,et al.  A Modified Theta Projection Model for Creep Behavior of Metals and Alloys , 2016, Journal of Materials Engineering and Performance.

[39]  Sohichi Hirose,et al.  Dynamic stationary crack analysis of isotropic solids and anisotropic composites by enhanced local enriched consecutive-interpolation elements , 2017 .

[40]  B. K. Mishra,et al.  A new multiscale XFEM for the elastic properties evaluation of heterogeneous materials , 2017 .

[41]  Bijay K. Mishra,et al.  New enrichments in XFEM to model dynamic crack response of 2-D elastic solids , 2016 .

[42]  T. Belytschko,et al.  A three dimensional large deformation meshfree method for arbitrary evolving cracks , 2007 .

[43]  Frank A. McClintock,et al.  Creep relaxation of stress around a crack tip , 1981 .

[44]  Timon Rabczuk,et al.  Steiner-point free edge cutting of tetrahedral meshes with applications in fracture , 2017 .

[45]  Bijay K. Mishra,et al.  The numerical simulation of fatigue crack growth using extended finite element method , 2012 .

[46]  H. Lai,et al.  Estimation of C(t) and the creep crack tip stress field of functionally graded materials and verification via finite element analysis , 2016 .

[47]  E. A. de Souza Neto,et al.  Computational methods for plasticity , 2008 .

[48]  F. H. Norton,et al.  The Creep of Steel at High Temperatures , 2017 .

[49]  D. L. Marriott,et al.  Design for creep , 1972 .

[50]  T. Q. Bui,et al.  Analysis of a subinterface crack in piezoelectric bimaterials with the extended finite element method , 2013 .

[51]  G. Eggeler,et al.  Creep crack growth and cavitation damage in a 12% CrMoV steel , 1989 .

[52]  H. Nguyen-Xuan,et al.  A simple and robust three-dimensional cracking-particle method without enrichment , 2010 .

[53]  Sharif Rahman,et al.  An interaction integral method for analysis of cracks in orthotropic functionally graded materials , 2003 .

[54]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[55]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[56]  E. Busso,et al.  On the effects of loading conditions and geometry on time-dependent singular crack tip fields , 1995 .

[57]  B. K. Mishra,et al.  A simple, efficient and accurate Bézier extraction based T-spline XIGA for crack simulations , 2017 .

[58]  R. Durand,et al.  A local extrapolation method for finite elements , 2014, Adv. Eng. Softw..

[59]  Liguo Zhao,et al.  Finite element simulation of creep-crack growth in a nickel base superalloy , 2001 .

[60]  Wen-Xue Wang,et al.  A unified loading parameter for creep-crack growth , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[61]  Zhenqing Wang,et al.  Extended finite element method for power-law creep crack growth , 2014 .

[62]  Wei Sun,et al.  Creep crack growth data and prediction for a P91 weld at 650 °C , 2010 .

[63]  Tinh Quoc Bui,et al.  Simulation of dynamic and static thermoelastic fracture problems by extended nodal gradient finite elements , 2017 .

[64]  M. Saber.  Experimental and finite element studies of creep and creep crack growth in P91 and P92 weldments , 2011 .

[65]  T. Q. Bui,et al.  Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading , 2012 .

[66]  A. S. Shedbale,et al.  Ductile failure modeling and simulations using coupled FE–EFG approach , 2016, International Journal of Fracture.

[67]  Xiangqiao Yan,et al.  A boundary element modeling of fatigue crack growth in a plane elastic plate , 2006 .