A unified viscoplastic model for the inelastic flow of alkali halides

Abstract The present paper proposes a novel viscoplastic model to describe the inelastic behaviour of polycrystalline alkali halides. This model is of the unified type. It consists of a kinetic law and three evolution laws associated with three state variables, B, R and K. Variables B and R are internal stresses, which usually oppose the applied stress, and which induce kinematic and isotropic hardening respectively. The variable K is a scalar used to normalize the active stress, thus contributing to the isotropic hardening of the material. The proposed unified model is physically based, and allows a correct representation of both transient and steady-state flow under diverse loading conditions. It is valid for both instantaneous (plastic) and delayed (creep) components of the inelastic strains. Various phenomenological attributes of the model are discussed and compared to the theoretical and experimental behavior of polycrystalline alkali halides.

[1]  U. F. Kocks Laws for Work-Hardening and Low-Temperature Creep , 1976 .

[2]  C. E. Pugh,et al.  Progress in Developing Constitutive Equations for Inelastic Design Analysis , 1983 .

[3]  Z. Mroz,et al.  On the creep-hardening rule for metals with a memory of maximal prestress , 1984 .

[4]  F. A. Leckie,et al.  Constitutive Relationships for the Time-Dependent Deformation of Metals , 1976 .

[5]  L. Anand Constitutive Equations for the Rate-Dependent Deformation of Metals at Elevated Temperatures , 1982 .

[6]  M. Kawai,et al.  Effects of Prior Creep on Subsequent Plasticity of Type 316 Stainless Steel at Elevated Temperature , 1983 .

[7]  M. Kawai,et al.  Effects of Prior Plasticity on Subsequent Creep of Type 316 Stainless Steel at Elevated Temperature , 1986 .

[8]  A. Nicolas,et al.  Crystalline plasticity and solid state flow in metamorphic rocks , 1976 .

[9]  H. Mughrabi,et al.  Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals , 1983 .

[10]  P. Perzyna Thermodynamic Theory of Viscoplasticity , 1971 .

[11]  R. D. Krieg,et al.  Summary and Critique , 1987 .

[12]  M. Faruque,et al.  On modelling steady state and transient creep of polycrystalline solids , 1988 .

[13]  Nobutada Ohno,et al.  A constitutive equation of creep based on the concept of a creep-hardening surface , 1982 .

[14]  J. Čadek,et al.  Dislocation structure in the high temperature creep of metals and solid solution alloys: a review , 1986 .

[15]  W. B. Jones,et al.  A Physically Based Internal Variable Model for Rate Dependent Plasticity , 1987 .

[16]  A. Richter,et al.  15 – Microstructures and Textures in Evaporites , 1985 .

[17]  Alan K. Miller,et al.  An Inelastic Constitutive Model for Monotonic, Cyclic, and Creep Deformation: Part I—Equations Development and Analytical Procedures , 1976 .

[18]  W. Nix,et al.  Time-dependent deformation of metals , 1985 .

[19]  M. Ashby,et al.  Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics , 1982 .

[20]  Z. Mroz Phenomenological Constitutive Models for Metals , 1986 .

[21]  P. Haasen,et al.  Plastic Deformation and Hardening of Polycrystalline Halides , 1984 .

[22]  Z. Bažant,et al.  Stress Analysis for Creep , 1983 .

[23]  B. Ladanyi,et al.  Effect of simulated sampling disturbance on creep behaviour of rock salt , 1987 .

[24]  Chandrakant S. Desai,et al.  Viscoplastic model for geologic materials with generalized flow rule , 1987 .

[25]  U. F. Kocks Strain Hardening and ‘Strain-Rate Hardening’ , 1982 .

[26]  S. R. Bodner,et al.  Viscoplastic Constitutive Equations for Copper with Strain Rate History and Temperature Effects. , 1978 .

[27]  Y. Estrin,et al.  An extension of the Bodner-Partom model of plastic deformation , 1986 .

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

[29]  A. S. Argon,et al.  Steady-state creep of single-phase crystalline matter at high temperature , 1976 .

[30]  P. Haasen Dislocations and the plasticity of ionic crystals , 1985 .

[31]  P. Delobelle,et al.  Modeling of 316 Stainless Steel (17.12 Sph.) Mechanical Properties Using Biaxial Experiments—Part I: Experiments and Basis of the Model , 1987 .

[32]  Yuri Estrin,et al.  A unified phenomenological description of work hardening and creep based on one-parameter models , 1984 .

[33]  T. Lowe,et al.  Constitutive Equations for Rate-Dependent Plasticity* , 1985 .

[34]  D. H. Allen,et al.  On the use of internal state variables in thermoviscoplastic constitutive equations , 1985 .

[35]  Chandrakant S. Desai,et al.  Constitutive laws for engineering materials, with emphasis on geologic materials , 1984 .

[36]  G. James,et al.  An Experimental Comparison of Several Current Viscoplastic Constitutive Models at Elevated Temperature , 1987 .

[37]  E. W. Hart Constitutive Relations for the Nonelastic Deformation of Metals , 1976 .

[38]  M. Langer,et al.  Solution-mined salt caverns for the disposal of hazardous chemical wastes , 1988 .

[39]  J. Chaboche,et al.  On the Plastic and Viscoplastic Constitutive Equations—Part I: Rules Developed With Internal Variable Concept , 1983 .

[40]  T. Langdon,et al.  Creep of ceramics , 1983 .

[41]  T. Lowe,et al.  Modeling Internal Stresses in the Nonelastic Deformation of Metals , 1986 .

[42]  H. Evans,et al.  Dislocation creep in non-metallic materials , 1978 .

[43]  W. Nix,et al.  Mechanisms Controlling Creep of Single Phase Metals and Alloys , 1979 .

[44]  R. Krieg,et al.  A Unified Creep-Plasticity Model for Halite , 1982 .

[45]  J. Čadek,et al.  The back stress concept in power law creep of metals: A review , 1987 .

[46]  C. E. Pugh,et al.  Some trends in constitutive equation model development for high-temperature behavior of fast-reactor structural alloys , 1978 .

[47]  Dale S. Preece Borehole Creep Closure Measurements And Numerical Calculations At the Big Hill, Texas SPR Storage Site , 1987 .

[48]  F. Hansen,et al.  Creep of rocksalt , 1983 .

[49]  P. Delobelle Sur les lois de comportement viscoplastique à variables internes - Exemples de deux alliages industriels : inoxydable austénitique 17-12 SPH et superalliage INCO718 , 1988 .

[50]  Jean-Paul Poirier,et al.  Creep of Crystals: High-Temperature Deformation Processes in Metals, Ceramics and Minerals , 1985 .

[51]  S. R. Bodner,et al.  A survey of unified constitutive theories , 1985 .

[52]  M. F. Ashby,et al.  Mechanisms of Deformation and Fracture , 1983 .

[53]  É. M. Nadgornyi Dislocation Dynamics and Mechanical Properties of Crystals , 1988 .

[54]  Piotr Perzyna,et al.  The constitutive equations for rate sensitive plastic materials , 1963 .

[55]  P. E. Senseny,et al.  Influence of end effects on the deformation of salt , 1989 .

[56]  M. Ashby,et al.  A Microstructural model for primary creep , 1987 .

[57]  David H. Zeuch,et al.  Modeling and mechanistic interpretation of creep of rock salt below 200°C☆ , 1986 .

[58]  M. Ashby,et al.  On the power-law creep equation , 1980 .

[59]  W. Nix,et al.  Observations of anelastic backflow following stress reductions during creep of pure metals , 1981 .

[60]  P. Duval,et al.  Constitutive Relations for the Non Elastic Deformation of Polycrystalline Ice , 1980 .

[61]  Michael F. Ashby,et al.  Wear-rate transitions and their relationship to wear mechanisms , 1987 .