A crystal plasticity model for strain-path changes in metals

A model is proposed that deals with the transient mechanical anisotropy during strain-path changes in metals. The basic mechanism is assumed to be latent hardening or softening of the slip systems, dependent on if they are active or passive during deformation, reflecting microstructural mechanisms that depend on the deformation mode rather than on the crystallography. The new model captures the experimentally observed behaviour of cross hardening in agreement with experiments for an AA3103 aluminium alloy. Generic results for strain reversals qualitatively agree with two types of behaviour reported in the literature – with or without a plateau on the stress–strain curve. The influence of the model parameters is studied through detailed calculations of the response of three selected parameter combinations, including the evolution of yield surface sections subsequent to 10% pre-strain. The mathematical complexity is kept to a minimum by avoiding explicit predictions related directly to underpinning microstructural changes. The starting point of the model is a combination of conventional texture and work hardening approaches, where an adapted full-constraints Taylor theory and a simple single-crystal work-hardening model for monotonic strain are used. However, the framework of the model is not restricted to these particular models.     

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.     

DP钢板应变路径多步演变下的弹塑性力学行为

针对DP高强双相钢板在复杂载荷作用下的弹塑性力学特征,提出利用三步拉伸力学实验,对比分析单轴循环加载和非等轴加载下材料的各向异性硬化、永久软化和弹性模量衰减特性等力学行为,揭示应变路径多步演变下的弹塑性力学特性.研究结果表明:材料再加载初期的瞬态行为与应变路径有关,在初期瞬态阶段显示出明显的各向异性,且再加载角度、预应...     

Constitutive modelling of the high strain rate behaviour of interstitial-free steel

A physically based modelling and experimental investigation of the work hardening behaviour of IF steel covering a wide range of strain rates including complex strain path and/or strain rate changes are presented. In order to obtain isothermal stress–strain curves at high strain rates, a procedure has been proposed with the aid of finite element analysis. The result reveals that the apparent excess of the flow stress after a jump in strain rate, which is frequently observed in bcc metals, is in fact due to the thermal softening at large strains, and that the flow stress after a jump in strain rate tends asymptotically to the values corresponding to the curve at the new strain rate. The strain rate affects not only the short-range stress but also the long-range stress via the strain-rate dependant evolution of dislocation structures. The proposed model is based on the dislocation model of intragranular hardening proposed by Teodosiu and Hu [Teodosiu, C., Hu, Z., 1995. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen, S., Dawson, P. R., (Eds.), Proceedings of Numiform'95 on Simulation of Materials Processing: Theory, Methods and Applications. Balkema, Rotterdam, pp. 173–182] and extended to strain rate sensitive one with applying the results of the thermal activation analysis. A satisfactory agreement has been achieved between model predictions and experimental results.     

Investigation of advanced strain-path dependent material models for sheet metal forming simulations

Sheet metal forming processes often involve complex loading sequences. To improve the prediction of some undesirable phenomena, such as springback, physical behavior models should be considered. This paper investigates springback behavior predicted by advanced elastoplastic hardening models which combine isotropic and kinematic hardening and take strain-path changes into account. A dislocation-based microstructural hardening model formulated from physical observations and the more classical cyclic model of Chaboche have been considered in this work. Numerical implementation was carried out in the ABAQUS software using a return mapping algorithm with a combined backward Euler and semi-analytical integration scheme of the constitutive equations. The capability of each model to reproduce transient hardening phenomena at abrupt strain-path changes has been shown via simulations of sequential rheological tests. A springback analysis of strip drawing tests was performed in order to emphasize the impact of several influential parameters, namely: process, numerical and behavior parameters. The effect of the two hardening models with respect to the process parameters has been specifically highlighted.     

ON NONPROPORTIONAL CYCLIC PLASTIC BEHAVIOR OF STEEL 40

An experimental investigation was carried out on the flow characteristicand hardening of steel 40 subjected to complex combined axial-torsional cyclicstraining. For a specific cyclic strain path, the steel has mainly cyclic softeningbehavior when the strain amplitude is small. While with an increase of the effectivestrain amplitude, the softening becomes small, but there is the cyclic softening eventhough the steel is subjected to the cyclic loading by a square strain path. However, thesteel has cyclic additional hardening by a nonproportional path, compared with theproportional cycling. Generally, the additional hardening is small and its historicaleffect is not obvious at small strain amplitude. The additional hardening is remarkableby a cross-triangular strain path of large strain amplitude. The memory of the historyof nonproportional cyclic loading, the direction of plastic flow and the plastic modulusof the steel were also studied.     

Dislocation density based constitutive model for ultrasonic assisted deformation

The mechanical behaviour of metallic materials subjected to plastic deformation is altered with the superposition of ultrasonic vibrations. A significant effect is the reduction of flow stress or acoustic softening. This phenomenon is utilized in metal forming and other deformation based manufacturing processes. Experimental investigations on ultrasonic assisted tensile tests focus on the effect of ultrasonic vibrations along the longitudinal axis of the specimen, whereas the manufacturing processes employs in transverse directions. In the present work, transverse ultrasonic vibrations are imposed during a uniaxial tensile test using an aluminium alloy. The trend of acoustic softening due to transverse direction vibrations is similar to that along longitudinal direction. A dislocation density based constitutive model is extended to model the softening due to ultrasonic effect. The predicted results agree well with the experimental observations.     

Strain localization analysis using a large deformation anisotropic elastic–plastic model coupled with damage

Sheet metal forming processes generally involve large deformations together with complex loading sequences. In order to improve numerical simulation predictions of sheet part forming, physically-based constitutive models are often required. The main objective of this paper is to analyze the strain localization phenomenon during the plastic deformation of sheet metals in the context of such advanced constitutive models. Most often, an accurate prediction of localization requires damage to be considered in the finite element simulation. For this purpose, an advanced, anisotropic elastic–plastic model, formulated within the large strain framework and taking strain-path changes into account, has been coupled with an isotropic damage model. This coupling is carried out within the framework of continuum damage mechanics. In order to detect the strain localization during sheet metal forming, Rice’s localization criterion has been considered, thus predicting the limit strains at the occurrence of shear bands as well as their orientation. The coupled elastic–plastic-damage model has been implemented in Abaqus/implicit. The application of the model to the prediction of Forming Limit Diagrams (FLDs) provided results that are consistent with the literature and emphasized the impact of the hardening model on the strain-path dependency of the FLD. The fully three-dimensional formulation adopted in the numerical development allowed for some new results – e.g. the out-of-plane orientation of the normal to the localization band, as well as more realistic values for its in-plane orientation.     

Finite element modeling of plastic anisotropy induced by texture and strain-path change

Consideration of plastic anisotropy is essential in accurate simulations of metal forming processes. In this study, finite element (FE) simulations have been performed to predict the plastic anisotropy of sheet metals using a texture- and microstructure-based constitutive model. The effect of crystallographic texture is incorporated through the use of an anisotropic plastic potential in strain-rate space, which gives the shape of the yield locus. The effect of dislocation is captured by use of a hardening model with four internal variables, which characterize the position and the size of the yield locus. Two applications are presented to evaluate the accuracy and the efficiency of the model: a cup drawing test and a two-stage pseudo-orthogonal sequential test (biaxial stretching in hydraulic bulging followed by uniaxial tension), using an interstitial-free steel sheet. The experimental results of earing behavior in the cup drawing test, maximum pressure and strain distribution in bulging, and transient hardening in the sequential test are compared against the FE predictions. It is shown that the current model is capable of predicting the plastic anisotropy induced by both the texture and the strain-path change. The relative significance of texture and strain-path change in the predictions is discussed.     

Ductility of interstitial-free steel under high strain rate tension: Experiments and macroscopic modeling with a physically-based consideration

In this paper, an experimental investigation and a constitutive modeling of the mechanical response of an interstitial-free (IF) steel over a wide range of strain rates (from 0.001/s to 750/s) are presented. Tensile tests at relatively high strain rates, exceeding 100/s, are performed at an initial room temperature, using the so-called one bar technique developed on the basis of the Hopkinson bar method. At a high strain rate, a distinct upper yield limit is observed, and the subsequent flow stress increases remarkably. Furthermore, the ductility is reduced significantly in comparison to the case of low strain rate tension. In order to express such a complicated material response of IF steel, we develop a new constitutive model that takes into account effects of a change in the mobile dislocation density and thermal softening. The model can be easily applicable to large-scale engineering computations, because it is macroscopically formulated. We try to reproduce the tensile response including a diffuse neck formation at high strain rates, using the proposed constitutive model and finite element method. The results indicate that a change in the mobile dislocation density, together with thermal softening, has substantial effects on apparent work hardening behavior at high strain rates, although the change in the mobile dislocation density is transcribed at macroscopic scale in the model. Finally, we discuss characteristics of true stress–true strain curves at various strain rates, and their correlation with the plastic instability behavior.     

Cyclic behaviour of short glass fibre reinforced polyamide: Experimental study and constitutive equations

Polymer matrix composites are widely used in the automotive industry and undergo fatigue loadings. The investigation of the nonlinear cyclic behaviour of such materials is a required preliminary work for a confident fatigue design, but has not involved many publications in the literature. This paper presents an extensive experimental study conducted on a polyamide 66 reinforced with 35 wt% of short glass fibres (PA66 GF35), at room temperature. The material was tested in two conditions: dry-as-moulded (DAM) and at the equilibrium with air containing 50% of relative humidity (RH50).An exhaustive experimental campaign in tensile mode has been carried out, including various strain or stress rates, complex mechanical histories and local thermo-mechanical recordings. Such an extended database allowed us to highlight several complex physical phenomena: viscoelastic effects at different time scales, irrecoverable mechanisms, non-linear kinematic hardening, non-linear viscous flow rule, cyclic softening.Taking into account this advanced analysis, a constitutive model describing the cyclic behaviour is proposed. As the experimental database only includes uniaxial tensile tests, the general 3D anisotropic frame is reduced to an uniaxial model valid for a specific orientation distribution. The robust identification process is based on tests which enable the uncoupling between the underlined mechanical features. This strategy leads to a model which accurately predicts the cyclic behaviour of conditioned as well as dry materials under complex tensile loadings.     

Experimental study of the cyclic visco-elasto-plastic behaviour of a polyamide fibre strap

Experimental tensile tests were performed on polyamide-based (PA66) woven strap samples. A strain measuring device was used to measure the strain in the middle and effective part of the woven tensile sample. The tests were performed, on the one hand under monotonous tension at different strain rates and on the other hand under sophisticated cyclic loading histories, including relaxation and creep sequences. The analysis of experimental results was made through a visco-elasto-hysteresis model, based on the superimposition of three stress components. The proposed method allows for characterizing the steady state viscous stress as a function of strain and strain rate, the time-independent irreversible behaviour and the instantaneous modulus increasing with the strain. Based on the visco-elasto-hysteresis model, an analysis enabled us to understand and predict the change in relaxation and creep orientations during complex loading histories.     

A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase B.C.C. polycrystals

Accurate and reliable predictions of yield surfaces and their evolution with deformation require a better physical representation of the important sources of anisotropy in the material. Until recently, the most physical approach employed in the current literature has been the use of polycrystalline deformation models, where it is assumed that crystallographic texture is the main contributor to the overall anisotropy. However, recent studies have revealed that the grain-scale mesostructural features (e.g. cell-block boundaries) may have a large impact on the anisotropic stress-strain behaviour, as evidenced during strain-path change tests (e.g. cross effect, Bauschinger effect).In previous papers, the authors formulated an extension of the Taylor-type crystal plasticity model by incorporating some details of the grain-scale mesostructural features. The main purpose of this paper is to study the evolution of yield surfaces in single-phase b.c.c. polycrystals during deformation and strain-path changes using this extended crystal plasticity model. It is demonstrated that the contribution of the grain-scale substructure in these metals on yield loci is comparable in magnitude to the effects caused by the differences in texture. Furthermore, it is shown that the shape of yield loci cannot be predicted accurately by the traditional polycrystalline deformation model with equal slip hardening. The trends predicted by the extended crystal plasticity model are in much better agreement with the experimental evidence reported in the literature than those represented in classical treatments by isotropic and kinematic hardening.     

Time-dependent ratchetting experiments of SS304 stainless steel

The time-dependent strain cyclic characteristics and ratchetting behaviours of SS304 stainless steel were investigated by uniaxial/multiaxial cyclic loading tests at room and elevated temperatures (350 and 700 °C). The effects of loading rate, peak/valley strain or stress holds, ambient temperature and non-proportional loading path on the cyclic softening/hardening and ratchetting behaviours of the material were discussed. It is shown that: the cyclic deformation of the material presents remarkable time-dependence at room temperature and 700 °C; the cyclic hardening feature and ratchetting strain depend significantly on straining or stressing rate, hold-time, ambient temperature and the non-proportionality of loading path; the time-dependent ratchetting is resulted from the slight opening of hysteresis loop and visco-plasticity together, and the viscosity is a dominating factor at 700 °C; at 350 °C, abnormal rate-dependence and quick shakedown of ratchetting are observed due to the dynamic strain aging of the material at this temperature. Some significant conclusions are obtained, which are useful to construct a constitutive model to describe the time-dependent ratchetting behaviour of the material. It is also stated that the unified visco-plastic constitutive model discussed here cannot provide reasonable simulation to the time-dependent ratchetting at 700 °C, especially to that with certain peak/valley stress hold, since the effect of the high viscosity on time-dependent ratchetting cannot be properly described by using a unified visco-plastic flow rule.     

Non-uniform deformation after prestrain

The deformation behaviour of prestrained metal sheets is analysed in this work. The non-uniform deformation observed during reloading in tension was studied, by following deformation in different regions of the samples. It takes into account the presence of geometrical defects in the samples and explains the importance of mechanical behaviour. A simplified analysis was used, to model the behaviour in tension of a metallic specimen with geometrical imperfection. The flow behaviour is described using a Swift law equation, which includes strain-rate sensitivity. A modified law was used for prestrained materials and this incorporates the plastic prestrain value, adjusted to the path change. The model predicts imperfection growth kinetics with strain, and strain saturation in the homogeneous region, due to the onset of necking.     

A modified swift law for prestrained materials

A modified Swift law to describe the evolution of the mechanical behaviour in reloading of prestrained materials is proposed in this work. This equation is deduced from the original Swift law by including a parameter that accounts for the effect of strain path change. This parameter depends on the value of the yield stress and the subsequent work-hardening behaviour in reloading. The new equation predicts well the general mechanical behaviour in the second path for copper and steel. In particular, it predicts accurately the strain value for which necking occurs during reloading and fits experimental stress-strain curves well. The flow equation formulated remains sufficiently simple to be applied in finite element modelling of prestrained materials. However, since the parameter, which is needed for the modified Swift law, must be previously known, the strain path change itself cannot be part of the simulation.     

Elasto-visco-plastic modeling of mild steels for sheet forming applications over a large range of strain rates

A physically based elasto-visco-plastic constitutive model is presented and compared to experimental results for three different mild steels. The experiments consist of tensile tests ranging from quasi-static conditions up to strain rates of 10³ s^?1 as well as quasi-static simple and reverse shear tests at different amounts of pre-strain. Additional two-step sequential mechanical tests (Bauschinger and orthogonal effects) have been performed to further evaluate the ability of the model to describe strain-path changes at moderate/large strains. The model requires significantly fewer material parameters compared to other visco-plasticity models from the literature, while being able to describe some of the main features of the strain-rate sensitivity of mild steels. Accordingly, the parameter identification is simple and intuitive, requiring a relatively small set of experiments. The strain-rate sensitivity modeling is not restricted to a particular hardening law and thus provides a general framework in which advanced hardening equations can be adopted.     

Nonlinear analysis of beam–column joints using softened truss model

The aim of this study is to expand the application of the nonlinear softened truss model for membrane elements on beam–column joints. The softened truss model employs three equations for equilibrium, three for compatibility and four equations for the constitutive laws of materials. The constitutive equations for both the concrete and steel are based on the actually observed stress–strain relationships. The model has three important attributes. The first is the nonlinear association of stress and strain. The second, and conceivably more noteworthy, is the softening of concrete in compression due to tensile strains in the perpendicular direction. The third is that the influence of the concrete tensile stresses between cracks on the average stress–strain relationship for reinforcing steel and the influence of orthogonal tensile stresses on the compression stress–strain relationship for concrete can be considered in the model. For beam–column joints, one of the most important factors influencing the behaviour is certainly the bond conditions of the beam bars. In this study, the softened truss model is expanded to take into account the influence of this important factor into account. In the revised version of the model, full strain compatibility does not exist between the steel reinforcement and the surrounding concrete and thus the factors influencing the bond-slip between concrete and reinforcement is adequately considered. The improved softened truss model is applied on 51 exterior beam–column joint tests. It is apparent from the results that the revised model gives very accurate predictions of the shear strength of joints and is an improvement on the existing version of the model proposed by Hsu.     

Further application of endochronic constitutive equation to loading with non-proportional axial-torsional strain-path

A combined theoretical-experimental investigation of the stress response to complex, non-proportional strain-paths in the axial-torsional strain space is reported in this paper. Type 304 stainless steel tubular specimens have been tested at a constant strain rate of 5 × 10^?4 per second. Two strain-paths have been investigated. The first path involves a cyclic axial straining and unstraining following a shear prestraining, and the second strain-path is cyclic in shear after a prestraining in tension.The endochronic theory with a plastic strain defined intrinsic time has been shown to be capable of predicting the stress response to the two strain-paths considered.