Modeling anisotropic strain hardening and deformation textures in low stacking fault energy fcc metals

The main issues and challenges involved in modeling anisotropic strain hardening and deformation textures in the low stacking fault energy (SFE) fcc metals (e.g. brass) are reviewed and summarized in this paper. The objective of these modeling efforts is to capture quantitatively the major differences between the low SFE fcc metals and the medium (and high) SFE fcc metals (e.g. copper) in the stress–strain response and the deformation textures. While none of the existing models have demonstrated success in capturing the anisotropy in the stress–strain response of the low SFE fcc metals, their apparent success in predicting the right trend in the evolution of deformation texture is also questionable. There is ample experimental evidence indicating that the physical mechanism of the transition from the copper texture to the brass texture is represented wrongly in these models. These experimental observations demonstrate clearly the need for a new approach in modeling the deformation behavior of low SFE fcc metals. This paper reports new approaches for developing crystal plasticity models for the low SFE fcc metals that are consistent with the reported experimental observations in this class of metals. The successes and failures of these models in capturing both the anisotropic strain hardening and the deformation textures in brass are discussed in detail.     

A void–crack nucleation model for ductile metals

A phenomenological void–crack nucleation model for ductile metals with secondphases is described which is motivated from fracture mechanics and microscale physicalobservations. The void–crack nucleation model is a function of the fracture toughness of theaggregate material, length scale parameter (taken to be the average size of the second phaseparticles in the examples shown in this writing) , the volume fraction of the second phase, strainlevel, and stress state. These parameters are varied to explore their effects upon the nucleationand damage rates. Examples of correlating the void–crack nucleation model to tension data in theliterature illustrate the utility of the model for several ductile metals. Furthermore, compression,tension, and torsion experiments on a cast Al–Si–Mg alloy were conducted to determinevoid–crack nucleation rates under different loading conditions. The nucleation model was thencorrelated to the cast Al–Si–Mg data as well.     

Achieving high strength and high ductility in nanostructured metals: Experiment and modelling

Engineering nanostructures in metallic materials such as nanograins and nanotwins can promote plastic performance significantly. Nano/ultrafine-grained metals embedded in coarse grains called bimodal metals and nanotwinned polycrystalline metals have been proved to possess extensively improved yield strength whilst keeping good ductility. This paper will present an experimental study on nanostructured stainless steel prepared by surface mechanical attrition treatment (SMAT) with surface impacts of lower strain rate (10 s^?1–10³ s^?1) and higher strain rate (10⁴ s^?1–10⁵ s^?1). Microstructure transition has been observed from the original γ-austenite coarse grains to α′-martensite nanograins with bimodal grain size distribution for lower strain rates to nanotwins in the ultrafine/coarse grained austenite phase for higher strain rates. Meanwhile, we will further address the mechanism-based plastic models to describe the yield strength, strain hardening and ductility in nanostructured metals with bimodal grain size distribution and nanotwinned polycrystalline metals. The proposed theoretical models can comprehensively describe the plastic deformation in these two kinds of nanostructured metals and excellent agreement is achieved between the numerical and experimental results. These models can be utilized to optimize the strength and ductility in nanostructured metals by controlling the size and distribution of nanostructures.     

Thermal analysis of thin multi-layer metal films during femtosecond laser heating

Multi-layer metals films are widely used in modern engineering applications such as gold-coated metal mirrors used in high power laser systems. A transient heat flux model is derived to analyze multi-layer metal films under laser heating. The two separate system composed of electrons and the lattice is considered to take into account the electron–lattice interaction. The present model predicted the effects of underlying chromium’s thermal properties on temperature rise of the top gold layer. The effects of two adjacent and different metals with different electron–lattice coupling factors are analyzed for the heating mechanism of different lattices. The derived transient model combined with the two different conservation equations for the lattice and electrons are applied for the ultra short-pulse laser heating of a multi-layer film composed of gold and chromium.     

Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling

The elastic–plastic behaviors of three body-centered cubic metals, tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel, are presented over a wide range of strains (15%), strain rates (10⁻⁶–10⁴ s⁻¹) and temperatures (77–600°F). Johnson-Cook and Zerilli-Armstrong models were found inadequate to describe the observations. A new viscoplastic model is proposed based on these experimental results. The proposed constitutive model gives good correlations with these experimental results and strain-rate jump experiments. In the next paper (Liang, R., Khan A.S., 2000. Behaviors of three BCC metals during non-proportional multi-axial loadings and predictions using a recently proposed model. International Journal of Plasticity, in press), multi-axial loading results on these materials and comparison with the proposed model will be presented.     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

The Mechanical Threshold Stress model for various tempers of AISI 4340 steel

Numerical simulations of high strain rate and high temperature deformation of pure metals and alloys require realistic plastic constitutive models. Empirical models include the widely used Johnson–Cook model and the semi-empirical Steinberg–Cochran–Guinan–Lund model. Physically based models such as the Zerilli–Armstrong model, the Mechanical Threshold Stress model, and the Preston–Tonks–Wallace model are also coming into wide use. In this paper, we determine the Mechanical Threshold Stress model parameters for various tempers of AISI 4340 steel using experimental data from the open literature. We also compare stress–strain curves and Taylor impact test profiles predicted by the Mechanical Threshold Stress model with those from the Johnson–Cook model for 4340 steel. Relevant temperature- and pressure-dependent shear modulus models, melting temperature models, a specific heat model, and an equation of state for 4340 steel are discussed and their parameters are presented.     

Enzyme–metal nanocomposites for antibacterial applications

Metal nanoparticles have been used as antibacterial agents widely, and the combined use of enzymes and metal nanoparticles promotes antibacterial activity, achieving a synergistic effect. Additionally, enzymes decrease the amounts of metals and increase biocompatibility, thereby reducing toxicity of metals. However, the efficiency of enzymes is hindered when coupled with metals, which causes deactivation in the function of enzymes. How can a balance be struck between metals and enzymes? Although the antibacterial mechanism of metal nanoparticles is relatively clear, how enzyme–metal nanocomposites work against bacteria is not conclusive. Here, we describe several examples on the synthesis of enzyme–metal nanocomposites via co-immobilization or in situ reduction and summarize how enzyme–metal nanocomposites combat microorganisms.     

A thermo-mechanically-coupled theory accounting for hydrogen diffusion and large elastic–viscoplastic deformations of metals

In this paper we develop a thermodynamically-consistent coupled-theory which accounts for diffusion of hydrogen, diffusion of heat, and large elastic–viscoplastic deformations of metals. The theory should be of utility in the analysis of hydrogen diffusion in elastic–plastically-deforming solids, an analysis which is an essential prerequisite for theoretical and numerical efforts aimed at modeling the integrity of structural components used for hydrogen gas storage and distribution.     

Numerical analysis and elastic–plastic deformation behavior of anisotropically damaged solids

The present paper is concerned with the numerical modelling of the large elastic–plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. Numerical simulations of the elastic–plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic–plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed.     

Modeling the thermoelastic–viscoplastic response of polycrystals using a continuum representation over the orientation space

Conventional methodologies towards polycrystal plasticity use an aggregate of single crystals and this choice of the aggregate affects the response of the polycrystal. In order to address this issue, a continuum approach is presented for the representation of polycrystals through an orientation distribution function over the orientation space. Additionally, a constitutive framework for thermoelastic–viscoplastic response of metals based on polycrystal plasticity is presented along with a coupled macro–micro, fully implicit Lagrangian finite element algorithm. Numerical examples that highlight the accuracy, performance and benefits of the proposed approach are presented.     

Nonlinear kinematic hardening rule parameters — relationship to substructure evolution in polycrystalline nickel

General cyclic plasticity results and detailed analyses of experimental data from constant plastic strain amplitude, completely reversed, tension–compression tests on polycrystalline nickel with two grain sizes are reported. These analyses focus on kinematic hardening behavior and are based on Armstrong–Frederick-type kinematic hardening rules and Masing-type assumptions. Juxtaposition of these analyses with observations of specimen surface relief and substructure evolution using TEM provides a context for discussion of mechanisms and modeling of nonlinear kinematic hardening and its relationship to heterogeneous microstructure in metals.     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

Experimental studies on yield behavior of steel under rapid heating

The yield behavior of steels under different heating rates and pre-stress levels is studied experimentally. The yield temperatures are found to increase with the heating rates and decrease with the pre-stress values. Two remarkable changes in the microstructures of tested steels are the grain elongation along the loading direction owing to the plastic deformation, and the grain refineries owing to the recrystallization. The micrographic features prove the above remarks. An equation of plastic strain rates of metals can estimate the yield temperature of metals under various heating rates. An extended Johnson–Mehl equation of recrystallization is derived, which includes the influence of heating rates.     

Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of bcc and fcc mechanisms of metals

Combination of physically based constitutive models for body centered cubic (bcc) and face centered cubic (fcc) metals developed recently by the authors [Voyiadjis, G.Z., Abed, F.H., 2005. Microstructural based models for bcc and fcc metals with temperature and strain rate dependency. Mech. Mater. 37, 355–378] are used in modeling the plastic deformation of AL-6XN stainless steel over a wide range of strain rates between 0.001 and 8300 s⁻¹ at temperatures from 77 to 1000 K. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the plastic flow model for both the isothermal and adiabatic plastic deformation. In addition, the experimental observations of AL-6XN conducted by Nemat-Nasser et al. [Nemat-Nasser, S., Guo, W., Kihl, D., 2001. Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures, J. Mech. Phys. Solids 49, 1823–1846] are utilized in understanding the underlying deformation mechanisms. The plastic flow is considered in the range of temperatures and strain rates where diffusion and creep are not dominant, i.e., the plastic deformation is attributed to the motion of dislocations only. The modeling of the true stress–true strain curves for AL-6XN stainless steel is achieved using the classical secant modulus for the case of unidirectional deformation. The model parameters are obtained using the experimental results of three strain rates (0.001, 0.1, and 3500 s⁻¹). Good agreement is obtained between the experimental results and the model predictions. Moreover, the independency of the present model to the experiments used in the modeling is verified by comparing the theoretical results to an independent set of experimental data at the strain rate of 8300 s⁻¹ and various initial temperatures. Good correlation is observed between the model predictions and the experimental observations.     

The quantum hypernetted chain model of warm dense matter

Modeling warm dense matter, where a combination of partial ionization, partial electron degeneracy, and strong ion–ion and ion–electron coupling occur, is a frontier of equation of state research. We present the quantum hypernetted chain model which can be applied to studies of liquid metals, warm dense matter, and plasmas. This is an all-electron model that considers a mixture of a classical fluid of ions (with bound electrons) and a quantum electron fluid. The model describes self-consistently the structure of the ion fluid as well as the bound states of the ions and the non-linear response of the electron fluid. We present our initial results and compare them with experimental and ab initio results for liquid metals and low-temperature plasmas.     

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.     

Necking and softening as a consequence of latent continuum damage

Necking and softening in ductile polycrystalline metals are modeled as consequences of continuum damage (CD) that consists in braking through of barriers resisting plastic deformation. Our model describes these materials as two-phase continua consisting of microdomains with easy glide and barriers with decreasing continuity in the course of deformation. Macroscopic homogeneity and increase of macroscopic stress with increasing deformation are conditioned by sufficient continuity of these barriers. Our model describes the whole course of engineering stress–strain diagrams up to rupture and the differences in the diagrams for test specimens of different length. The model is compared to experimental data measured on two materials − sorbitic steel and an AlMg3 alloy.     

Inverse error propagation and model identification for coupled dynamic problems with application to electromagnetic metal forming

The purpose of this work is the development and application of strategies to identify material model parameters for metals at high strain-rates using data obtained from high-speed electromagnetic metal forming. To this end, a staggered algorithm for the finite-element-based numerical solution of the coupled electromagnetic-mechanical boundary-value problem has been developed based on mixed Eulerian–Lagrangian multigrid methods. On this basis, the parameter determination together with a sensitivity analysis and error estimation are carried out. After verifying the validity of this approach using synthetic data sets, it is applied to the identification of material parameters using experimental results from electromagnetic tube forming.