Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity

Abstract The effects of stress triaxiality and initial porosity on void growth and coalescence are studied in this paper. The representative material volume (RMV) is modeled by two approaches: (1) a unit cell containing a discrete, spherical void at its center, and (2) a unit cell having the same void volume fraction and obeying the Gurson–Tvergaard constitutive relation. The macroscopic stress–strain response and the void growth and coalescence behavior of the voided cell are obtained from detailed finite element analyses and the results show strong dependencies on stress triaxiality and the initial void volume fraction. The micromechanics parameters of the GT model, q 1 and q 2 , are calibrated to minimize the differences between the predicted void growth rate and macroscopic stress–strain relation by the GT model and the corresponding finite element results of the voided RMV. The calibrated values of q 1 and q 2 as functions of the stress triaxiality and the initial porosity are obtained for an idealized material under the axi-symmetric condition. Furthermore, discussions are made on the description of the triaxial stress state of the RMV. It is found that the effect of stress triaxiality on void growth and coalescence cannot be uniquely described by the stress triaxiality factor, defined as the ratio of the hydrostatic stress and the effective stress, alone. Multiple stress states with different principal stress ratios ρ 1 (= Σ 1 / Σ 2 ) and ρ 2 (= Σ 3 / Σ 2 ) can result in the same stress triaxiality ratio, and the macroscopic stress–strain response and the void growth and coalescence behavior of the voided RMV are different for each stress state. In order to characterize the effects of stress triaxiality on void growth and the macroscopic stress–strain behavior of the RMV, the principal stress ratios must be specified and consequently, the q -parameters of the GT model should be expressed as functions of ρ 1 and ρ 2 .

[1]  W. Brocks,et al.  Verification of the transferability of micromechanical parameters by cell model calculations with visco-plastic materials , 1995 .

[2]  V. Tvergaard.  On localization in ductile materials containing spherical voids , 1982, International Journal of Fracture.

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

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

[5]  Zhiliang Zhang,et al.  ANALYZING DUCTILE FRACTURE USING DUAL DILATIONAL CONSTITUTIVE EQUATIONS , 1994 .

[6]  Claudio Ruggieri,et al.  Numerical modeling of ductile crack growth in 3-D using computational cell elements , 1996 .

[7]  Pierre Suquet,et al.  Continuum Micromechanics , 1997, Encyclopedia of Continuum Mechanics.

[8]  R. H. Van Stone,et al.  Microstructural aspects of fracture by dimpled rupture , 1985 .

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

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

[11]  Rodney Hill,et al.  The essential structure of constitutive laws for metal composites and polycrystals , 1967 .

[12]  G. Rousselier,et al.  Ductile fracture models and their potential in local approach of fracture , 1987 .

[13]  P. Thomason,et al.  Three-dimensional models for the plastic limit-loads at incipient failure of the intervoid matrix in ductile porous solids , 1985 .

[14]  Alan Needleman,et al.  Void growth and coalescence in porous plastic solids , 1988 .

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

[16]  Viggo Tvergaard,et al.  Constraint effects on the ductile-brittle transition in small scale yielding , 1996 .

[17]  Jean-Baptiste Leblond,et al.  Theoretical models for void coalescence in porous ductile solids. II. Coalescence “in columns” , 2001 .

[18]  Jean-Baptiste Leblond,et al.  Recent extensions of Gurson's model for porous ductile metals , 1997 .

[19]  Xiaosheng Gao,et al.  Cell model for nonlinear fracture analysis – I. Micromechanics calibration , 1998 .

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

[21]  Jean-Baptiste Leblond,et al.  Approximate Models for Ductile Metals Containing Nonspherical Voids—Case of Axisymmetric Oblate Ellipsoidal Cavities , 1994 .

[22]  Ke-Shi Zhang,et al.  Numerical analysis of the influence of the Lode parameter on void growth , 2001 .

[23]  Jonas Faleskog,et al.  Micromechanics of coalescence—I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids , 1997 .

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

[25]  A. Needleman,et al.  Mesh effects in the analysis of dynamic ductile crack growth , 1994 .

[26]  Xiaosheng Gao,et al.  Cell model for nonlinear fracture analysis – II. Fracture- process calibration and verification , 1998 .

[27]  A. Pineau,et al.  Coalescence-Controlled Anisotropic Ductile Fracture , 1999 .

[28]  R. H. Dodds,et al.  Simulation of ductile crack growth using computational cells: numerical aspects , 2000 .

[29]  W. Brocks,et al.  Application of the Gurson Model to Ductile Tearing Resistance , 1995 .

[30]  Robert H. Dodds,et al.  Ductile tearing in part-through cracks: experiments and cell-model predictions , 1998 .

[31]  Ian C. Howard,et al.  PREDICTION OF THE FIRST SPINNING CYLINDER TEST USING DUCTILE DAMAGE THEORY , 1993 .

[32]  Viggo Tvergaard,et al.  An analysis of ductile rupture modes at a crack tip , 1987 .

[33]  David J. Smith,et al.  Constraint Effects in Fracture : Theory and Applications ASTM STP 1244 , 1995 .

[34]  C. Shih,et al.  Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales , 1995 .