Theory Of Thermoviscoplasticity Research Articles

Mathematical Simulation of Cyclic Thermoviscoplastic Deformation and Fracture of Materials

Fundamental concepts and equations of the thermoviscoplasticity (inelasticity) theory are examined. Material functions are chosen, the basic experiment and identification method for the material functions, closing the thermoviscoplasticity theory, are formulated. Thermoviscoplasticity theory potentials for describing deformation and fracture of structural steels and alloys at different cyclic thermomechanical loads are demonstrated.

Thermoviscoplastic cyclic deformation and fracture of materials

The paper considers the main theses and equations of the modern theory of thermoviscoplasticity (inelasticity). The authors highlight material functions, formulate the basic experiment and method for identifying the material functions which enclose the theory of thermoviscoplasticity. The possibility of the theory are illustrated to adequately describe the processes of deformation and fracture of structural steels and alloys in a variety of modes of thermal power cyclic loading.

Analysis of the influence of various effects on criteria for adiabatic shear band localization in single crystals

The paper aims at the investigation of the influence of various effects on criteria for shear band localization in inelastic single crystals. This investigation is based on an analysis of acceleration waves and takes advantage of a notion of the instantaneous adiabatic acoustic tensor. Particular attention is focussed on the analysis of the effects as follows: (i) spatial covariance and plastic spin; (ii) thermomechanical coupling; (iii) non-Schmid; (iv) evolution of substructure; (v) nondissipative thermal term; (vi) cooperative phenomena (synergetic). The theory of thermoviscoplasticity of inelastic single crystals is presented within a framework of the rate type covariance constitutive structure with a finite set of the internal state variables. By assuming that the mechanical relaxation time is equal to zero the thermo-elasto-plastic (rate independent) response of single crystals is accomplished. An adiabatic inelastic flow process of the single crystal is formulated and investigated. Symmetric double slip and single slip processes are considered. The formulation of macroscopic adiabatic shear bands is investigated. The criteria for adiabatic shear band localization for a single slip process are presented in exact analytical form. For a symmetric double slip process these criteria are estimated numerically. The discussion of the influence of various effects is presented, and the comparison of the results obtained with available experimental observations is given.

Numerical modelling of localized fracture of inelastic solids in dynamic loading processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. By applying ideas of synergetics it can be shown that as a result of instability hierarchies a system is self-organized into a new shear band pattern system. This leads to the conclusion that inelastic solid body considered during the dynamics process becomes a two-phase material system. Particular attention is focussed on attempt to construct a physically and experimentally justified localized fracture theory that relates the kinetics of material failure on the microstructural level to continuum mechanics. The description of the microstructural damage process is based on dynamic experiments with carefully controlled load amplitudes and duration. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history-dependent, non-linear process. The theory of thermoviscoplasticity is developed within the framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of microdamage mechanism and thermomechanical coupling. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the unconditionally stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial–boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretized problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elasto–viscoplastic model the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging over 103−104 s−1 is presented. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data. © 1997 John Wiley & Sons, Ltd.

Localized Fracture in Inelastic Polycrystalline Solids under Dynamic Loading Processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by micro-damage and thermal softening during dynamic plastic flow processes. The theory of thermoviscoplasticity is developed within a framework of the rate type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of micro-damage mechanism and thermomechanical coupling. The micro-damage mechanism has been treated as a sequence of nucleation, growth, and coalesence of microcracks. The micro-damage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature, and history dependent, nonlinear process. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent micro-damage mechanism is considered. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well posed. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem), as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elastoviscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging from 10-1-104 s-1 is presented. Three particular examples have been considered; namely, a dynamic adiabatic process for a thin-walled steel tube and dynamic adiabatic and quasi-static processes for a thin steel plate. In each case, a thin shear band region of finite width which undergoes significant deformations and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data.

Determination of the parameters of the Bodner-Partom model for thermoviscoplastic deformation of materials

UDC 539.376 The problem of describing thermoviscoplastic deformation of materials arises in modeling the behavior of structural elements under intensive loading and elevated temperature conditions, which in particular are characteristic of various industrial treatments such as welding, forging, etc. [3, 14, 18]. A rather complete review of results obtained within approaches to modeling the indicated processes is given in [5, 6]. Most of them to some degree use the concept of the yield surface and representation of the strain rate as the sum of terms corresponding to the processes of elastic and instantaneous plastic deformation and creep deformation. At the same time, it is commonly accepted that plastic deformation essentially is a time-dependent process. Attempts to develop a theory of plasticity taking into account the time and temperature dependence led to the creation of so-called unified theories. In these theories, all the characteristics of inelastic deformation are represented in a single inelastic strain term. In the evolution equation for inelastic deformation, internal variables appear whose number depends both on the hardening mechanisms (isotropic, directional) and the complexity of the loading histories under consideration. In such a formulation, the model does not explicitly contain a yield condition and related loading and unloading conditions. Thus the dependence of plastic flow on the strain rate under monotonic and cyclic loading, and also creep and stress relaxation, are determined from a single system of equations. Unified theories include those in [4, 9, 10, 15, 16]. The results of experimental study of these theories for the case of a uniaxial stress state are presented in [2, 8, 10]. It has been established that the given theories describe well the substantially nonlinear, temperature-dependent behavior of metals under complex thermomechanical loading. References [13, 19] are devoted to generalization to the case of multiaxial states. A number of papers are also available which make it possible to give a positive empirical evaluation based on comparison of finite-element calculations using the indicated models and the experimental data in problems of stress concentration and crack propagation [17], and also residual weld stresses [18]. Comparison of the major models in this class [2] shows that quantitatively and qualitatively, the thermoviscoplastic behavior of metals is described most exactly by the Bodner-Partom model [10, 11]. The paper [8] is devoted to development of a flow chart for determining the parameters of this model. In approaching this problem, we should bear in mind two facts reflecting the specifics of the model: first of all, the responsibility for the characteristic aspects of the inelastic behavior, such as the yield stress and directly several parameters of the model; secondly, the sensitivity of the model to the quality of the experimental data and the values of a number of its parameters. From this standpoint, the flow chart proposed in [8] involves assumptions and procedures (in particular, the procedure for differentiation of the experimentally obtained so-called ~,-curves) lead~g to errors in determination of the model parameters. In this paper, we develop a correct procedure for determining the desired parameters of the Bodner-Partom theory of thermoviscoplasticity, which we illustrate using the example of the AMG-6 aluminum alloy. 1. Equations of the Bodner-Partom Model. The system of constitutive equations for the Bodner-Partom model

Nonlinear finite element simulation of thermoviscoplastic deformation of C4 solder joints in high density packaging under thermal cycling

A nonlinear finite element model has been used to simulate the thermally induced viscoplastic deformation of the controlled collapse chip connection (C4) solder joints in a high density single chip module (SCM). The dependence of solder joint deformation on the tin content was demonstrated for various lead-rich Pb-Sn alloys with the tin content varying from 2 wt% to 10 wt%. A thermoviscoplasticity theory was introduced for modeling inelastic stress-strain response of the Pb-Sn alloys. In the theory, the creep and plasticity were separately considered and formulated. The Garafalo hyperbolic sine law was used to model the creep behavior, while the Prandtl-Reuss equation was used for the rate independent plastic deformation. The modeled SCM consists of a 5 mm silicon chip attached to 50 mm alumina substrate by an array of C4 with diameter of O.1 mm on a 0.2 mm I/O pitch. A cyclic temperature load of 0 to 100/spl deg/C at frequency of 3 cycles per hour was applied to the SCM, and a nonlinear finite element program ABAQUS was used to numerically study the effect of the tin content on the stress-strain response of the C4. It is concluded that the decrease of the tin content induces a decrease of the equivalent creep strain and Mises stress, but an increase of the equivalent plastic strain for the edge C4 in the SCM. >

Thermoviscoplasticity Based on Overstress Applied to the Analysis of Fibrous Metal-Matrix Composites

The vanishing fiber diameter (VFD) model together with the thermovisco plasticity theory based on overstress (TVBO) are used to analyse the thermomechanical behavior of unidirectional fibrous metal-matrix composites. Fiber and matrix can both be transversely-isotropic, thermoelastic-viscoplastic. All material constants can depend on current temperature. Yield surfaces and loading/unloading conditions are not used in the theory in which the inelastic strain rate is solely a function of the overstress, the difference between stress and the equilibrium stress, a state variable of the theory. The three- dimensional equations are derived and specialized for various simple loading cases such as isothermal uniaxial and biaxial proportional and nonproportional loadings. The predic tions of this viscoplasticity theory during loading compare favorably with results from the rate-independent plasticity theory. In addition it is capable of predicting creep, relaxation and rate sensitivity.

A Numerical Simulation of the Effects of Volume Fraction, Creep and Thermal Cycling on the Behavior of Fibrous Metal-Matrix Composites

A previously derived cyclic neutral thermoviscoplasticity theory for fi brous metal-matrix composites (Yeh and Krempl [1]), which combines the vanishing fiber diameter (VFD) model with the thermoviscoplasticity theory based on overstress (TVBO) is specialized for transversely isotropic, thermoelastic fibers and an isotropic, thermovis coplastic matrix. Numerical experiments are used to illustrate the predictive capability of the theory. Simulations include the influence of volume fraction on the monotonic and cyclic loading behavior in the fiber and transverse directions with creep holds for B/A1 and B/Ti unidirectional composites and thermal cycling of B/A1. The three-dimensional theory permits the calculation of the actual Poisson's ratio in the tests. The results compare favor ably with sparsely available experimental results.

Analysis and Application of a Coupled Thermoviscoplasticity Theory

Coupled thermoviscoplasticity equations are developed based on the rational theory of thermodynamics. A power-form internal state variable constitutive equation is proposed. Limitation of the proposed constitutive equation is discussed and simulation results of cyclic loading of 1070 steel at different temperatures and strain rates are presented. The developed coupled equations and the proposed constitutive equation are implemented into a finite element program which is used to investigate the thermomechanical problem of cyclic loading of a constrained-ended cylinder.

A COUPLED, ISOTROPIC THEORY OF THERMOVISCOPLASTIC1TY BASED ON TOTAL STRAIN AND OVERSTRESS AND ITS PREDICTIONS IN MONOTONIC TORSIONAL LOADING

A coupled, isotropic, infinitesimal theory of thermoviscoplasticity was proposed in [32, 33] and applied to a variety of simple loadings including both mechanical and thermal straining. In this paper we develop this theory by postulating specific forms of the mechanical constitutive equation and the internal energy rate. The heat conduction equation is then obtained from the internal energy rate and the first law of thermodynamics. The predictions of the theory in torsion are examined qualitatively and through numerical experiments. Torsion is simulated at loading rates differing by four orders of magnitude, and both jump-increases and jump-decreases in loading rate are also examined. The theory predicts an initial thermoelastic response followed by nonlinear, rate-dependent plastic behavior. The adiabatic temperature response in torsion is initially isothermal and is followed by inelastic heating. Significant differences are found between the mechanical responses to stress-and strain-controlled loading. ...

A theory of thermoviscoplasticity based on infinitesimal total strain

A theory of three-dimensional infinitesimal isotropic thermoviscoplasticity is proposed and investigated in several homogeneous deformations. The theory is represented by both a mechanical constitutive equation and a constitutive assumption for the heat equation; these equations are separately postulated but are coupled through their common linear dependence upon the stress rate and strain rate tensors and the time rate of temperature change, and through their common nonlinear dependence upon the stress and strain tensors and the absolute temperature. Throughout this theory total strain is used and the strain tensor is not decomposed into a sum of elastic and inelastic contributions. The concept of the yield surface is not employed and the transition from initially linear thermoelastic behavior to nonlinear inelastic behavior is continuous.Through qualitative discussion and quantitative examples, this proposed system of constitutive equations is shown to represent: initial linear thermoelastic behavior followed by inelastic rate sensitive work hardening; linear thermoelastic behavior between stress, strain and temperature in pure hydrostatic loading; initial cooling in uniaxial tension, initial heating in uniaxial compression, and initial isothermal behavior in torsion prior to inelastic deformation; subsequent self-heating in any monotonie loading following the onset of inelastic behavior; axial stress (strain) build-up due to temperature change uniformly induced by monotonic and cyclic torsional loading. Also represented are stress (strain) rate sensitivity; temperature rate sensitivity; creep and relaxation; and nonlinear dependence of the spacing between stress-strain curves at different stress (strain) rates upon the value of the stress (strain) rate tensor in constant-rate loading. Stress-strain curves corresponding to different constant strain (stress) rate loadings ultimately attain the same slope. Defined and physically meaningful limits are obtained in the cases of very slow and very fast loading rates in monotonie radial loading. Associated with limitingly slow loading is an equilibrium stress-strain curve, and in relaxation the stress relaxes to an equilibrium value associated with this curve.Illustrative specializations to cases of uniaxial, torsional, pure hydrostatic and radial deformation histories are considered and numerical results are obtained by postulating specific choices of material functions, and by numerically integrating the resulting system of first-order nonautonomous, nonlinear stiff differential equations. Results are presented in terms of graphs to show the influence of various test histories and material parameters as well as the capability of the model.In cyclic deformation the proposed equations of the model are modified according to previously established concepts to account for history dependence in the sense of plasticity. This is accomplished by updating a material parameter associated with the equilibrium stress-strain curves in such a manner that the material response predicted by the model remains continuous .and smooth. The ability to represent hardening in materials is illustrated. In torsional cycling a significant net increase in temperature can be induced. A possible thermoinelastic explanation for the Ronay effect is given.

A unified theory of thermoviscoplasticity of crystalline solids

A unified theory of thermoviscoplasticity of crystalline solids is presented. In particular it is shown that a thermodynamics for ‘viscoplastic’ materials can be accommodated within the framework of modern mechanics of materials with memory. The basic physical concepts are derived from the consideration of dislocation behaviour of crystalline solids. Relationships of the present approach to several of the existing theories of plasticity are examined.

A variational principle for non-linear thermoviscoplasticity

A general variational principle associated with the non-linear theory of thermoviscoplasticity is presented. In particular, this paper shows that the use of Vainberg's theorem on non-linear potential operators and a special bilinear form using the convolution of two functions makes possible a variational formulation for non-linear initial-and-boundary value problems. Several alternate principles and their relationship with the existing variational principles are also discussed.