Identification methodology and comparison of phenomenological ductile damage models via hybrid numerical–experimental analysis of fracture experiments conducted on a zirconium alloy

Abstract The present study details the methodology of the identification process of uncoupled damage formulations proposed by Bai and Wierzbicki (B&W model – Bai and Wierzbicki (2008) and Modified Mohr–Coulomb – Bai and Wierzbicki (2010) ) as well as the Lemaitre and enhanced Lemaitre coupled damage models. These uncoupled models were first implemented in the Finite Element (FE) software Forge2009®, then their parameters identifications were carried out. These identifications involve two steps: identification of hardening law parameters and identification of damage parameters. In the first step, the method to obtain the coefficient of a non-linear friction law in compression test is also presented. The second step differs between the above-mentioned models: the identification of uncoupled models is carried out through the experimental fracture strains of different loading paths, while the identification of Lemaitre’s model is based on the softening effect of damage. The latter model is enhanced by accounting for the influence of the Lode parameter to improve its ability to predict fracture in shear loading. The results show that, among the studied models, the proposed enhanced Lemaitre model gives overall best results in terms of fracture prediction for all the tests. The proportionality of studied loading paths is also discussed. It is shown that the compression is not suitable to identify the parameters of the studied uncoupled damage models.

[1]  Jacques Besson,et al.  Plastic potentials for anisotropic porous solids , 2001 .

[2]  V. Tvergaard.  Material Failure by Void Growth to Coalescence , 1989 .

[3]  E. Maire,et al.  Initiation and growth of damage in a dual-phase steel observed by X-ray microtomography , 2008 .

[4]  C. Schuh,et al.  The Mohr–Coulomb criterion from unit shear processes in metallic glass , 2004 .

[5]  Jean-Baptiste Leblond,et al.  Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities , 1993 .

[6]  Stelios Kyriakides,et al.  Determination of anisotropy and material hardening for aluminum sheet metal , 2012 .

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

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

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

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

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

[12]  Pierre-Olivier Bouchard,et al.  Ductile damage parameters identification for cold metal forming applications , 2011 .

[13]  David A. Surovik,et al.  On the path-dependence of the fracture locus in ductile materials - Analysis , 2012 .

[14]  I. Barsoum,et al.  Micromechanical analysis on the influence of the Lode parameter on void growth and coalescence , 2011 .

[15]  V. Palchik,et al.  Application of Mohr–Coulomb failure theory to very porous sandy shales , 2006 .

[16]  J. Leblond,et al.  Effect of void locking by inclusions upon the plastic behavior of porous ductile solids¿I: theoretical modeling and numerical study of void growth , 2004 .

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

[18]  Dirk Mohr,et al.  On the predictive capabilities of the shear modified Gurson and the modified Mohr–Coulomb fracture models over a wide range of stress triaxialities and Lode angles , 2011 .

[19]  Yonggang Huang,et al.  The modified Gurson model accounting for the void size effect , 2004 .

[20]  F. Mcclintock,et al.  Ductile fracture by hole growth in shear bands , 1966 .

[21]  Jacques Besson,et al.  Anisotropic ductile fracture: Part II: theory , 2004 .

[22]  Viggo Tvergaard,et al.  An analysis of ductile rupture in notched bars , 1984 .

[23]  W. Brocks,et al.  On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening , 2003 .

[24]  Otto Mohr,et al.  Abhandlungen aus dem Gebiete der technischen Mechanik , 1906 .

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

[26]  L. Xue,et al.  Constitutive modeling of void shearing effect in ductile fracture of porous materials , 2008 .

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

[28]  J. Lemaître,et al.  Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures , 2005 .

[29]  T. Pardoena,et al.  An extended model for void growth and coalescence , 2022 .

[30]  J. Hutchinson,et al.  Modification of the Gurson Model for shear failure , 2008 .

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

[32]  Yuanli Bai,et al.  Application of extended Mohr–Coulomb criterion to ductile fracture , 2009 .

[33]  Marc G. D. Geers,et al.  Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour , 2003 .

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

[35]  Dirk Mohr,et al.  Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals , 2010 .

[36]  Tie-jun Wang.  Unified CDM model and local criterion for ductile fracture—II. Ductile fracture local criterion based on the CDM model , 1992 .

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

[38]  H. W. Swift.  Plastic instability under plane stress , 1952 .

[39]  Jacques Besson,et al.  Continuum Models of Ductile Fracture: A Review , 2010 .

[40]  Jean-Baptiste Leblond,et al.  An improved Gurson-type model for hardenable ductile metals , 1995 .

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

[42]  P. Thomason,et al.  Ductile Fracture of Metals , 1990 .

[43]  C A Coulomb,et al.  ESSAI SUR UNE APPLICATION DES REGLES DE MAXIMIS ET MINIMIS A QUELQUES PROBLEMES DE STATIQUE RELATIFS A L'ARCHITECTURE (ESSAY ON MAXIMUMS AND MINIMUMS OF RULES TO SOME STATIC PROBLEMS RELATING TO ARCHITECTURE) , 1973 .

[44]  Dirk Mohr,et al.  Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading – Part II: Ductile fracture , 2012 .

[45]  Pierre-Olivier Bouchard,et al.  An enhanced Lemaitre model formulation for materials processing damage computation , 2011 .

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

[47]  Yonggang Huang,et al.  Accurate Dilatation Rates for Spherical Voids in Triaxial Stress Fields , 1991 .

[48]  V. Tvergaard.  Influence of voids on shear band instabilities under plane strain conditions , 1981 .

[49]  A. Needleman,et al.  Void Nucleation Effects in Biaxially Stretched Sheets , 1980 .

[50]  M. Fortin,et al.  A stable finite element for the stokes equations , 1984 .

[51]  Imad Barsoum,et al.  Rupture mechanisms in combined tension and shear : Experiments , 2007 .

[52]  John W. Hutchinson,et al.  Calibration procedures for a computational model of ductile fracture , 2010, Engineering Fracture Mechanics.

[53]  T. Wierzbicki,et al.  On fracture locus in the equivalent strain and stress triaxiality space , 2004 .