An enhanced Lemaitre model formulation for materials processing damage computation

The Lemaitre damage model is now widely used to deal with coupled damage analyses for various mechanical applications. In this article, different extensions of the model are presented and discussed to deal with complex multiaxial configurations—such as multi-stages bulk forming processes. A specific treatment is done to account for compressive damage growth, and a stress triaxiality cut-off value is considered to avoid any damage evolution below a critical negative triaxiality. The damage potential is also modified to deal with highly ductile materials, and the plastic strain is split into a negative part and a positive part to differentiate damage growth for compressive states of stress and for tensile states of stress. Finally, an anisotropic damage approach based on the comparison between grain flow orientation and principal loading directions is defined. A combination of these extensions is achieved within a single Lemaitre formulation. Application on different examples show the robustness and accuracy of the model defined in this paper.

[1]  David R. Owen,et al.  Aspects of ductile fracture and adaptive mesh refinement in damaged elasto‐plastic materials , 2001 .

[2]  F. A. McClintock,et al.  A Criterion for Ductile Fracture by the Growth of Holes , 1968 .

[3]  Tomasz Wierzbicki,et al.  On the cut-off value of negative triaxiality for fracture , 2005 .

[4]  L. Xue.  Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading , 2007 .

[5]  R. M. Natal Jorge,et al.  Numerical modelling of ductile plastic damage in bulk metal forming , 2003 .

[6]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[7]  Pierre-Olivier Bouchard,et al.  Plastic instabilities analysis during T-shaped tubes hydro-forming process , 2009 .

[8]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[9]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[10]  Thierry Coupez,et al.  Toward large scale F.E. computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms , 2001 .

[11]  Wei Hua Tai,et al.  A new microvoid-damage model for ductile fracture , 1986 .

[12]  Stéphane Roux,et al.  Identification of a Damage Law by Using Full-field Displacement Measurements , 2005, physics/0511121.

[13]  Percy Williams Bridgman,et al.  Studies in large plastic flow and fracture , 1964 .

[14]  P. Steinmann.  FORMULATION AND COMPUTATION OF GEOMETRICALLY NON-LINEAR GRADIENT DAMAGE , 1999 .

[15]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1989 .

[16]  T. Coupez,et al.  Finite element solution of the 3D mold filling problem for viscous incompressible fluid , 1998 .

[17]  Jean-Louis Chaboche,et al.  Continuous damage mechanics — A tool to describe phenomena before crack initiation☆ , 1981 .

[18]  Thierry Coupez,et al.  Parallel meshing and remeshing , 2000 .

[19]  Pierre-Olivier Bouchard,et al.  On the influence of particle distribution and reverse loading on damage mechanisms of ductile steels , 2008 .

[20]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[21]  Milan Jirásek,et al.  Nonlocal models for damage and fracture: Comparison of approaches , 1998 .

[22]  Nicola Bonora,et al.  Modeling ductile damage under fully reversed cycling , 2003 .

[23]  S. Shima,et al.  Criteria for ductile fracture and their applications , 1980 .

[24]  Pc Pandey,et al.  An isotropic damage model for ductile material , 1995 .

[25]  Yingbin Bao,et al.  Ductile crack formation on notched Al2024-T351 bars under compression–tension loading , 2004 .

[26]  P. Bouchard,et al.  Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm , 2009 .

[27]  J. Lewandowski,et al.  The effects of superimposed hydrostatic pressure on deformation and fracture: Part I. Monolithic 6061 aluminum , 1993 .

[28]  K. Saanouni.  On the numerical prediction of the ductile fracture in metal forming , 2008 .

[29]  J. Lewandowski,et al.  The influence of hydrostatic pressure on fracture of single-crystal and polycrystalline NiAl , 1994 .

[30]  Jean-Loup Chenot,et al.  Finite element modelling and control of new metal forming processes , 2006 .

[31]  Jean-Loup Chenot,et al.  Numerical treatment of contact and friction in FE simulation of forming processes , 2002 .

[32]  Pierre-Olivier Bouchard,et al.  Finite Element Modeling of Tube Piercing and Creation of a Crack , 2008 .

[33]  T. Wierzbicki,et al.  A new model of metal plasticity and fracture with pressure and Lode dependence , 2008 .

[34]  P. W. Bridgman.  Studies in large plastic flow and fracture : with special emphasis on the effects of hydrostatic pressure , 1964 .

[35]  Nicola Bonora,et al.  A nonlinear CDM model for ductile failure , 1997 .

[36]  Jean Lemaitre,et al.  Local approach of fracture , 1986 .

[37]  Mgd Marc Geers,et al.  A critical comparison of nonlocal and gradient-enhanced softening continua , 2001 .

[38]  J. M. A. César de Sá,et al.  Damage modelling in metal forming problems using an implicit non-local gradient model , 2006 .

[39]  A. Needleman,et al.  Analysis of the cup-cone fracture in a round tensile bar , 1984 .

[40]  Paulo A.F. Martins,et al.  Fracture predicting in bulk metal forming , 1996 .

[41]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[42]  M. H. Baluch,et al.  Towards a canonical elastoplastic damage model , 1994 .