MatProps: Material Properties Database and Associated Access Library

Metallic shaped charge jets (SCJ) have been studied for many decades across multiple communities for applications ranging from military warheads to earth penetrators for accessing oil-rich areas [1]. Researchers have had varied success in modeling these jets using simulation codes such as CTH, ALEGRA, and ALE3D. Recently, a large amount of work has been performed at the US Army Research Lab investigating the behavior of jets with increasingly sophisticated experimental diagnostics. Advances in computational resources, code enhancements, and material models have allowed us to model jets and probe uncertainties caused by algorithms, equations of state (EOS), constitutive models, and any of the available parameters each one provides. In this work we explore the effects that various EOS and constitutive models have on the development and characteristics of a 65-mm diameter, 2D copper SCJ using the Sandia National Laboratories’ multiphysics hydrocode, ALEGRA [2]. Specifically, we evaluate the tabular SESAME 3320 [3], 3325 [4-5], and 3337 [6] EOS models, analytic EOS (ANEOS) 3331 [7], as well as the Johnson-Cook (JC) [8], Zerilli-Armstrong (ZA) [9], Preston-Tonks-Wallace (PTW) [10], Steinberg-Guinan-Lund (SGL) [11-12], and Mechanical Threshold Stress (MTS) [13] constitutive models. Note that while the SGL model supports rate-dependence, there is no current characterization for copper, thus we are using rate-independent version. We do not consider the MieGrüneisen equation of state here as we expect parts of the jet to be near or cross into melt.

Intelligent finite element method: An evolutionary approach to constitutive modeling

A model of a wide-range semi-empirical equation of state for metals is presented. The specific heat and Gruneisen coefficients of ions and electrons are functions of temperature and density. At low temperatures, the heat capacity varies according to Debye theory. The removal of the degeneration of the electron gas with increasing temperature is taken into account. The effect of ionization on the thermodynamic functions is effectively taken into account. The equation of state allows the calculation of states in a two-phase liquid-vapor region. This model was used to develop the equations of state for Ta, W, Al, and Be. For its range of applicability, the equation of state contains a relatively small number of free parameters, most of which have a physical meaning. Comparison of calculations of various isolines using equations of state with experimental data and calculations based on other models show that the equations of state for Ta, W, Al, and Be, describe most experimental data for these substances. At ultrahigh pressures and temperatures, calculations using the equations of state are in good agreement with calculations using the Thomas-Fermi model with corrections.

Summary form only given. A description of the thermodynamic properties of matter in a wide range of temperatures and pressures is of fundamental as well as practical interests. The equations of state for metals over the range from normal conditions to extremely high energy densities are necessary for hydrodynamic simulations of processes in plasmas under pulsed power influences. In this report, a new semiempirical equations-of-state model, which takes into account melting, evaporation and ionization effects, is proposed. Wide-range equations of state for some metals (aluminum, gold, tungsten and others) are constructed on the basis of model developed. Calculation results are compared with available high-temperature, high-pressure experimental data. Most essential dynamic experiments are described. The equations of state can be used efficiently in numerical simulations of different physical processes in the metals at high energy densities.

Dynamic constitutive model and ignition behavior of enhanced Al/PTFE

Constitutive model is the most commonly used method to describe the material deformation behavior during machining process. This paper aims to investigate the material dynamic deformation during high speed machining of 7050-T7451 aluminum alloy with the aid of split Hopkinson pressure bar (SHPB) system and finite element (FE) analysis. First, the quasi static and dynamic compression behaviors of 7050-T7451 aluminum alloy are tested at different loading conditions with a wide range of strain rates (0.001 s, 4000 s, 6000 s, 8000 s, and 12,000 s) and temperatures (room temperature, 100 °C, 200 °C, 300 °C, and 400 °C). The influences of temperature on strain and strain rate hardening effects are revealed based on the flow stress behavior and microstructural alteration of tested specimens. Second, a modified Johnson–Cook (JCM) constitutive model is proposed considering the influence of temperature on strain and strain rate hardening. The prediction accuracies of Johnson–Cook (JC) and JCM constitutive models are compared, which indicates that the predicted flow stresses of JCM model agree better with the experimental results. Then the established JC and JCM models are embedded into FE analysis of orthogonal cutting for 7050-T7451 aluminum alloy. The reliabilities of two material models are evaluated with chip morphology and cutting force as assessment criteria. Finally, the material dynamic deformation behavior during high speed machining and compression test is compared. The research results can help to reveal the dynamic properties of 7050-T7451 aluminum alloy and provide mechanical foundation for FE analysis of high speed machining.

Utilizing a proper material model for describing the mechanical behavior of any material is key for a successful simulation of friction stir processing (FSP) where temperature, strain, and strain rate gradients vary abruptly within, and when moving away, from the stirring zone. This work presents a comparison of how faithfully do three different constitutive equations reproduce the state variables of strain, strain rate, and temperature in an FEM simulation of a test-case FSP (1000 rpm spindle speed, and 90 mm/min feed). The three material models considered in this comparison are namely: Johnson-Cook (JC), Sellars-Tegart (ST), and Zerilli-Armstrong (ZA). Constants for these constitutive equations are obtained by fitting these equations to experimental mechanical behavior data collected under a range of strain rates and temperatures of twin-rolled cast wrought AZ31B sheets.It is widely recognized that JC-based models over predicts stress values in the stir zone whereas ST-based models are incapable of capturing work hardening outside of the stir zone. Therefore, a ZA model, being a physical based-HCP specific model, is hereby investigated for its suitability as a material model that would overcome such drawbacks of JC-and ST-based models. The equations from the constitutive models under consideration are fed into an FEM model built using DEFORM 3D to simulate the traverse phases of a friction stir process. Amongst these three material models, comparison results suggest that the HCP-specific ZA model yield better predictions of the state variables: strain, strain rate, and temperature, and, consequently, the estimated values for flow stresses.

Roma Plastilina (RP) # 1 clay has been used as a backing material in ballistic testing of body armor. Column-drop tests are conducted to assess the suitability of RP # 1 clay for ballistic tests. In the current study, deformations of RP # 1 clay induced by projectiles employed in column-drop tests are simulated using finite element models based on the Johnson-Cook (J-C) material model and a new constitutive model. Both the J-C and new models account for strain hardening, strain rate hardening and temperature softening effects exhibited by RP # 1 clay. However, the three effects are treated separately in the J-C model, while the coupling between the temperature and strain rate effects is considered in the new model, which contains seven material constants. The simulations are conducted using the explicit dynamic solver LS-DYNA, and a user-defined material module along with a computational algorithm is developed for the new model and implemented in LS-DYNA. The effect of the hydrostatic pressure is incorporated in the current simulations through using an equation of state (EOS) (with three different types), unlike in existing studies. The numerical results based on both the J-C and new constitutive models reveal that the hydrostatic pressure effect is insignificant for RP # 1 clay under the dynamic loading conditions in the column-drop tests. In addition, it is found that for RP # 1 clay tested at 37 °C the simulation results for the final penetration depth based on both the J-C and new models agree well with the experimental value. However, for RP # 1 clay tested at 23 °C (the room temperature), the permanent depth of penetration predicted using the J-C model differs significantly from what was measured experimentally, while that predicted by the new constitutive model is very close to the experimental value.

Metals (Al, Fe, Cu, Pb), polyethylene, and other plastic materials with a density of about 1 g/cm3 are commonly used as liners and screens in solving dynamic-compression problems that involve phase transitions. In this paper, the equations of state are presented in the form of formulas, graphs, and tables for the pressurep and energyE as functions of temperatureT and density ρ. These equations have a meaningful theoretical form and are based on the measured initial sound velocityc 0, densityρ 0, Gruneisen parameter Γ, heat capacityc p, sublimation energyU evp, and the known pressure dependence of the compression modulus ϱK/ϱp. These equations of state are in satisfactory agreement with available experimental data on shock compression. According to the same scheme, the equations of state are derived for carbon and boron nitride. However, in this case, the situation turned out to be much more complicated due to the existence of phase transitions from the hexagonal form into wurtzite and cubic forms. In deriving the equation of state, the equilibrium curve between the graphite-like and diamond phases on the phase diagram was additionally used. As a result of realization of the aforementioned scheme, the equations of state obtained (i.e., formulas, graphs, and tables) are in satisfactory agreement with experimental data.

The paper presents the results of research undertaken to investigate cold forming process for 40HM constructional steel suitable for heat treatment. In the first part of the paper, mechanical properties of this steel and its industrial applications are described. The second part of the paper presents the results of the analysis of flow curves for two kinds of steel specimens: those that were subjected to annealing and those that did not undergo any heat treatment. It was found that the application of heat treatment had a significant effect on improving the forming conditions for this steel at room temperature. The experimental flow curves obtained in a compression test were described by constitutive equations illustrating the dependence between flow stresses and strain value. In order to determine the equation coefficients, the Generalized Reduced Gradient method implemented in Microsoft Excel was used. Based on the obtained equations, a material model will be developed to perform numerical simulations of cold forming for 40HM steel, using FEM-based software that aids the design of metal forming technologies.

The major objective of this work was the development of a reliable model to describe the volumetric properties of metals. In this regard, we have applied the Song and Mason equation of state (SM EOS) for alkaline earth metals, aluminium, Germanium, lead, antimony, Bismuth, chromium, manganese, rhodium, palladium, platinum and lanthanum. Three temperature-dependent parameters in the equation of state (EOS) have been calculated as functions of reduced temperature with the use of the law of corresponding states. It is shown that the knowledge of just surface tension and the liquid density at the normal melting point is sufficient to predict the EOS of these metals. In order to improve the predictive power of the mentioned EOS for metals, we have proposed using a simple modification. The comparison of predicted densities with literature data led to encouraging results. The average absolute deviation of calculated densities from literature values was found to be 0.29%.

The main goal of this work is the analysis of the procedure for material characterization aimed at elasto-visco-plastic models and their implementation in FEM codes. This will be done in order to perform stress analysis of structural components under repeated cyclical loads and high temperatures The overall development involves theoretical, numerical and experimental methodologies. The study of state of the art of material models, available in FEM codes, has allowed the evaluation of the limits of stress analysis on components subjected to repeated cyclical loads and high temperature. The initial study has also highlighted the necessity to implement complex material models. Traditionally this lack has been faced through the use of factors of safety, which are developed and refined on the basis of the experience and historical backgrounds. For systems where efficient design is of the utmost importance (for example the minimum weight design of an aircraft structure), it is possible that the traditional factors of safety may be overly conservative, so that optimal efficiency cannot be achieved. The implementation of complex material models allows simulating the real material behaviour and taking into account the non-linear interaction between creep and fatigue for structural analysis and life prediction. The results are more dependable and allow reducing the traditional factors of safety, consequently lead to a significant improvement in the designing of structural components. The process of material characterization has been developed through the following phases: designing the necessary experimental data base, choosing the constitutive laws, describing the iterative procedure for determining the coefficients of material model and the procedure of model validation, performed by comparisons between experimental data and simulated ones. It has been described how a poor experimental data base influences the material characterization process and the limits of an automatic procedure. Guidelines have been provided for designing experimental tests able to identify the optimized model parameters. In this way, it will be possible to determine material models with wide range of validity and to allow reducing time and costs of a characterization process. A methodology of structural analysis has been developed through the comparison with procedures of tested validity, in way to allow a correct and safe implementation of elasto-visco-plastic material models. An elasto-visco-plastic analysis on a combustion chamber of aeronautical engine has been performed and component life determined, taking into account the interaction between fatigue and creep.

When fluid phase behavior over a large region of states is considered, excess function models are no longer appropriate. They are designed to address mixing effects at constant density or pressure. Effects of varying density are most conveniently treated in terms of an equation of state. The thermodynamic relations for computing fluid phase behavior from an equation of state in combination with ideal gas properties are well established; cf. Section 2.1. Although they are more demanding computationally than excess function models, there are now many well-tested computer codes available that allow the computation of fluid phase behavior from an equation of state. Basically, this approach is free from any of the restrictions associated with the use of excess function models. In principle, an equation of state model is generally applicable, including simple and complicated molecules, and, in particular, mixtures of small and large molecules, as in polymer solutions. In practice, different equation of state models are used for different applications and no general model suitable for all applications has yet emerged. The generality of the equation of state approach requires full generality of the potential energy model. A formulation in terms of contact energies, adequate for excess function models, is unsufficient. Rather, the potential energy will in principle depend on the distances between the molecular centers, on the orientations of the molecules, and, in the most general case, also on their internal coordinates. In this book we shall concentrate on equation of state models for systems composed of small molecules, such as those typically encountered in the gas industries.

Constitutive Model for the Subsequent Time-Dependent Deformations of Type 304 Stainless Steel at Room Temperature

The dimensionless material parameter R introduced by Wu and Jing into the Rice-Walsh equation of state (EOS) deduced from the shock Hugoniot data for porous Al and Cu was shown to be well approximated by a function of pressure alone. This data processing was extended to several metals including Mo, Ni, Co, Cr, Pb, Ta, W, and Fe using porous shock data basically published by Russian researchers. It was again found that the parameter R/p for all metals decays smoothly with shock pressure p and displays small experimental scatter in the high pressure region. It is then possible to construct the Rice-Walsh EOS using the empirically determined function R(p) and its known full-density shock Hugoniot and to reproduce porous shock Hugoniot for these metals. For most degrees of porosity, the agreement between the porous data and the calculated Hugoniots using the empirical function described was very good, while anomalous Hugoniots of Mo and Ni with extremely high porosity exhibit appreciable discrepancies. In this paper, the Wu-Jing parameter as a function of pressure together with thermal contribution was introduced to extend the Rice-Walsh EOS to explain Hugoniots with extremely high porosities. Extended EOS was also formulated with newly introduced thermal variables, which enabled the calculation of the cold compression curve for these metals. The present analysis suggested that the Rice-Walsh type EOS is, in most cases, a preferable choice for analysis with its simple form, pressure-dependent empirical Wu-Jing parameter and its compatibility with porous shock data. Extended Rice-Walsh EOS is only necessary for anomalous Hugoniots.