A thermomechanically generalized Bodner-Partom model is developed. It is used to determine the fraction of plastic work that is not dissipated into heat and is stored in the material and to find a numerical solution to the dynamic thermomechanical problem for a disk under radial impulsive loading and to analyze the change in temperature due to thermomechanical coupling Keywords: stress waves, temperature, cold work, plastic material, disk, impulsive loading, finite-element method Introduction. Deformation, especially at high strain rates, can cause reversible (thermoelastic) and irreversible (dissipative) changes in temperature [24,30,31]. Such processes arouse theoretical and practical interest because of two circumstances. First, high and very high strain rates may give rise to localized regions of large plastic strains and high temperatures (adiabatic shear bands) [20,23,26], which lead to failure. Local thermal phenomena may also occur under monotonic quasistatic tension to large plastic strains (Lüders bands) [21,23]. Second, strain-induced thermal effects reflect some important aspects of the behavior of materials that are either difficult or fundamentally impossible to analyze with purely mechanical models. Of such are stored energy of cold work (SECW), dissipation of mechanical energy into heat, etc. Thermal effects are also helpful in diagnostics and analysis of damage kinetics, structural changes, etc. [15,22].The major problem in evaluating thermal effects in nonlinear materials is identification of the stored and dissipated fractions of the total plastic energy. Systematic research of these issues originated in the calorimetric tests conducted by Taylor and Quinney [29]. Later studies on SECW are reviewed in [8,10,18]. Fundamental results on the kinetics of accumulation and dissipation of plastic energy obtained by microcalorimetric methods are reported in [12,21]. However, most studies on the subject use quasistatic loading. A few publications on dynamic processes [6,19,27] use rather approximate approaches and estimations.In the present paper, we use the thermodynamically generalized Bodner-Partom model [4,10] to evaluate the fraction of plastic work of AMg-6 alloy that is not dissipated into heat, but is stored in the material through hardening and to find a numerical solution to the thermomechanical dynamic problem for a disk under radial impulsive loading and to study the issues of energy accumulation and dissipation and associated temperature changes.1. Thermodynamics. The constitutive equations of nonlinear plastic materials (such as metals) in thermodynamic formulation is based on general Green-Naghdy theory [17] concretized in [4,10].The local balance equations for momentum and energy written in terms of Cartesian coordinates Ox x x 1 2 3 are σ ρ
A coupled dynamic problem of thermomechanics is formulated based on a thermodynamically consistent modification of the Bodner-Partom model. This formulation is used to analyze the thermomechanical state of an aluminum cylinder under axial impulsive loading. The problem is solved by the finite-element method. Time integration is performed by the Crank-Nicholson scheme. Reversible and irreversible thermal changes are studied Keywords: thermomechanical coupling, finite element, physically nonlinear cylinder, impulsive loading Many modern structural members have cylindrical form and during operation and processing experience impulsive loads, which, as a rule, induce residual inelastic strains and stresses. Since inelastic deformation is accompanied by thermal effects due to the dissipation of mechanical energy, thermal strains should be taken into account in studying such processes. This is the reason why the correct description of the complex thermomechanical behavior of a material is of great importance.Recently, the so-called unified viscoplastic models [2, 13] have intensively been used, along with the classical models [12]. These models most accurately describe the high-rate deformation of materials. The most popular among them is the Bodner-Partom model [4,9,13], which has been validated by a great many experimental and theoretical data. Making the Bodner-Partom model and the thermodynamics of irreversible processes consistent, we can study thermomechanically coupled processes such as dissipative heating [11].Here we use a thermodynamically consistent modification of this model to describe numerically the propagation of stress waves and the formation of residual stresses and strains in aluminum cylindrical bodies under an impulsive load.
Nonstationary axisymetric waves in a disk excited by an impulsive radial load are analyzed numerically. The nonlinear deformation of the material is described by the Bodner-Partom model. The model parameters are derived from experimental data for samples subjected to tension followed by compression over a wide range of strain rates. The temporal and spatial characteristics of the wave process are studied. The influence of hardening on wave focusing and residual strain distribution is examined Keywords: nonstationary waves, physically nonlinear material, disk, impulsive loading, finite-element methodIntroduction. Many structural members in modern technology are cylindrical bodies that, while in service, experience impulsive loads, which induce inelastic residual strains. Strength evaluation of such structures calls for stress-strain analysis methods that would allow for the rheological behavior of the material, the geometry of the body, and nonstationary loads acting on it.Analysis of residual stress-strain state (SSS) of bodies under impulsive loading is of considerable theoretical and practical interest [20,21]. These problems play a crucial role in the fatigue crack arresting techniques currently under development. They use an impulsive, explosion load with energy focused at the crack tip to induce compressive residual stresses and plastic strains [10].Research in this field is also motivated by the needs of explosion welding [5]; impulsive straightening of thin-walled structures, including welded ones [6,27]; surface hardening [15,22]; etc. In all these applications, the prime objective of calculations is to determine the appropriate process parameters. New technologies also require studying the influence of dynamic processes on the kinetics of microstructural transformations in materials [18, 28, etc].In studying nonstationary dynamic processes, reliable results can be obtained by accomplishing two basic tasks. One is to select and specify constitutive equations for fast (10 10
By way of numerical simulation, a method is developed to determine the parameters of the thermomechanical Bodner-Partom model of flow under high strain rate deformation using a split Hopkinson bar. The classical method is generalized in two directions. To evaluate the kinematic hardening parameters, the wave reflected from the free end of the bar is used. The thermomechanical parameters that are responsible for the stored energy of cold work are calculated from measurements of temperature changes in the specimen Keywords: split Hopkinson bar, Bodner-Partom model, Baushinger effect, temperature change, finite-element method, stored energy of cold workIntroduction. The coupling of mechanical and thermal fields is of theoretical and applied importance. While in service, many structural elements of modern engineering are subjected to cyclic or impulsive loads, which may induce inelastic residual strains and temperature changes, either reversible (thermoelastic) or irreversible (dissipative) [12,13,30]. Monotonic quasistatic, high strain rate, and very high strain rate loading may give rise to local regions of large inelastic strains and high temperature (thermal shear bands) [22,23,25,28], which may lead to failure.On the other hand, thermal effects of deformation represent a number of prominent aspects of material behavior, which are either difficult or impossible to analyze within the framework of purely mechanical models. Among them are stored energy of cold work, dissipation of mechanical energy as heat, etc. A conceptual factor is that a characteristic variable of an adiabatic process is temperature, which can be measured experimentally. Thermal effects also carry information useful for diagnostics and study of damage kinetics, structural transformations, etc. [18,26].The reliability of data obtained in studying nonstationary thermomechanically coupled dynamic processes in high strain rate (10 2 -10 3 sec -1 ) and very high strain rate (10 3 -10 6 sec -1 ) deformation is strongly dependent on the choice and individualization of constitutive equations. A criterion for choosing a model should be its capability of describing viscosity, dependence of the yield stress on the strain rate, hardening, thermal effects, damage, etc.A split Hopkinson bar is widely used to test dynamic properties [15,17,19,20,24]. The equipment developed in [21] to measure temperature in a sample through which a wave propagates allows us to study the effects of thermomechanical coupling.The thermodynamically consistent Bodner-Partom model [9][10][11] was used in [27] to determine, for AMg-6 aluminum alloy, the portion of the inelastic work that does not dissipate as heat and accumulates by hardening ("cold work"). The results obtained there were used for numerical simulation of thermal (temperature) effects in a disk under impulsive radial loading. An analysis revealed that a chief task in studying such effects is to individualize the parameters of a thermodynamic model of flow under high strain rate loading.In the present paper, we carry o...
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