A plasticity-damage theory for large deformation of solids—I. Theoretical formulation

Abstract A coupled theory of continuum damage mechanics and finite strain plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic damage, the matrix representation is restricted to isotropy. A linear transformation is shown to exist between the effective deviatoric Cauchy stress tensor and the total Cauchy stress tensor. It is also shown that a linear transformation between the deviatoric Cauchy stress tensor and its effective counterpart is not possible as this will lead to plastic incompressibility in damaged materials. In addition, an effective elasto-plastic stiffness tensor is derived that includes the effects of damage. The proposed model is applied to void growth through the use of Gurson's yield function. It is also shown how a modified Gurson function can be related to the proposed model. Some interesting results are obtained in this case.

[1]  Sia Nemat-Nasser,et al.  Decomposition of strain measures and their rates in finite deformation elastoplasticity , 1979 .

[2]  S. Murakami,et al.  Mechanical Modeling of Material Damage , 1988 .

[3]  C. L. Chow,et al.  Ductile fracture characterization with an anisotropic continuum damage theory , 1988 .

[4]  S. Nemat-Nasser.  On Finite Plastic Flow of Crystalline Solids and Geomaterials , 1983 .

[5]  Wang June,et al.  An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates , 1985 .

[6]  George Z. Voyiadjis,et al.  A coupled theory of damage mechanics and finite strain elasto-plasticity—II. Damage and finite strain plasticity , 1990 .

[7]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[8]  V. Tvergaard.  Material failure by void coalescence in localized shear bands , 1982 .

[9]  J. Lemaître.  A CONTINUOUS DAMAGE MECHANICS MODEL FOR DUCTILE FRACTURE , 1985 .

[10]  J. Betten.  Applications of tensor functions to the formulation of constitutive equations involving damage and initial anisotropy , 1986 .

[11]  E. H. Lee,et al.  Some comments on elastic-plastic analysis , 1981 .

[12]  Jean-Louis Chaboche,et al.  CONTINUUM DAMAGE MECHANICS :PRESENT STATE AND FUTURE TRENDS , 1987 .

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

[14]  C. L. Chow,et al.  An anisotropic theory of elasticity for continuum damage mechanics , 1987 .

[15]  S. Murakami,et al.  Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory , 1983 .

[16]  F. A. Leckie,et al.  Representation of Mechanical Behavior in the Presence of Changing Internal Structure , 1988 .

[17]  C. L. Chow,et al.  An anisotropic theory of continuum damage mechanics for ductile fracture , 1987 .

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

[19]  Dusan Krajcinovic,et al.  The Continuous Damage Theory of Brittle Materials, Part 1: General Theory , 1981 .

[20]  J. Chaboche.  Continuum Damage Mechanics: Part II—Damage Growth, Crack Initiation, and Crack Growth , 1988 .

[21]  J. Chaboche.  Continuum Damage Mechanics: Part I—General Concepts , 1988 .

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

[23]  E. Onat.  Representation of mechanical behavior in the presence of internal damage , 1986 .

[24]  Panos D. Kiousis,et al.  Stress rate and the lagrangian formulation of the finite-strain plasticity for a von mises kinematic hardening model , 1987 .

[25]  G. Voyiadjis,et al.  Eulerian constitutive model for finite deformation plasticity with anisotropic hardening , 1989 .

[26]  Dusan Krajcinovic,et al.  Constitutive Equations for Damaging Materials , 1983 .

[27]  F. Sidoroff,et al.  Damage Induced Elastic Anisotropy , 1982 .

[28]  George Z. Voyiadjis,et al.  A coupled theory of damage mechanics and finite strain elasto-plasticity. I : Damage and elastic deformations , 1990 .

[29]  J. Lemaître.  How to use damage mechanics , 1984 .

[30]  George Z. Voyiadjis,et al.  Degradation of elastic modulus in elastoplastic coupling with finite strains , 1988 .

[31]  A. Gurson.  Plastic flow and fracture behavior of ductile materials incorporating void nucleation, growth and interaction , 1988 .

[32]  George Z. Voyiadjis,et al.  Experimental determination of the material parameters of elasto-plastic workhardening metal alloys , 1984 .

[33]  Hans-Werner Ziegler.  A Modification of Prager's Hardening Rule , 1959 .

[34]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—I. Formulation , 1987 .