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The hardening behaviour of metals is generally described in terms of a stress-strain curve derived from experiments. In this paper, a linear method to identify the stress-strain curve starting from full-field measurement data is presented. This method can be applied to any stress state using a generic yield function, the only requirement is that the full-fieldmeasurement is extended up to the border of the specimen. The method is presented and validated using a finite element model of a notched specimen. Moreover, experiments were performed on specimens cut from a BH340 steel sheet to illustrate the viability to actual cases. Two geometries were considered, a standard uniaxial test, where the method was used to evaluate the post-necking behaviour, and a notched specimen with a heterogeneous strain field. The proposed method, named linear stress-strain curve identification (LSSCI), can be a useful tool in combination with inverse methods to identify the constitutive behaviour of metals in large strain plasticity. [ABSTRACT FROM AUTHOR]

The influence of strain rate on the stress–strain behaviour of an AISI 304 austenitic stainless steel sample was investigated. For this purpose, uniaxial tensile tests were performed at room temperature for different strain rates. Microstructural measurements of transformed martensitic phase as a function of plastic strain, and thermal analyses of the specimens were carried out as well. It was found that increasing the strain rate from 10−4 to 10−1 s−1 leads to a 25% improvement in uniform elongation. Moreover, a ‘curve-crossing’ phenomenon was observed for the hardening behaviour measured at different strain rates. These results were rationalized in terms of martensitic phase transformation suppressed by a temperature increase in the specimens deformed with high strain rates. [ABSTRACT FROM AUTHOR]

Abstract: Advanced macroscopic models give a good description of initial plastic behavior of most metallic materials like initial anisotropy. However, the modeling of anisotropic hardening, in particular for non-proportional loading paths, still is a difficult task for these models. The complex distortion of the yield locus is related to the activation and cross-hardening of different slip systems, depending on crystallographic orientations. These physical mechanisms are taken into account in polycrystalline models. The novel approach consists in: (i) drastically reducing the number of crystallographic orientations, (ii) applying a specific parameter calibration procedure to obtain a good agreement with all stress–strain and transverse strains curves of an extended experimental database including pseudo-experimental tests. In the present study, the methodology has been applied to a strongly anisotropic aluminum alloy (Part I) and to an initially isotropic fcc material (Part II, submitted to Int. J. Plasticity). Very good modeling is achieved with 8 and 14 crystallographic orientations, respectively, in particular for the Lankford ratios along different loading directions. The additional hardening for non-proportional loadings, such as simple shear followed by tension, can be modeled. The effects of texture evolution are also qualitatively investigated. It must be emphasized that the objective of the methodology is not to obtain results at the microscopic scale or material science level. The polycrystalline models are used in the same way as macroscopic models are, provided the computation times are similar. In order to validate the methodology and to evaluate its performance, finite element calculations of a deep drawing test have been performed. The CPU time of the polycrystalline model is only twice larger than the one with an advanced anisotropic macroscopic model. The calculated cup heights with six ears are in good agreement with the experimental measurements. [Copyright &y& Elsevier]

Abstract: Finite element (FE) simulations of the simple shear test were conducted for 1050-O and 6022-T4 aluminum alloy sheet samples. Simulations were conducted with two different constitutive equations to account for plastic anisotropy: Either a recently proposed anisotropic yield function combined with an isotropic strain hardening law or a crystal plasticity model. The FE computed shear stress–shear strain curves were compared to the experimental curves measured for the two materials in previous works. Both phenomenological and polycrystal approaches led to results consistent with the experiments. These comparisons lead to a discussion concerning the assessment of anisotropic hardening in the simple shear test. [Copyright &y& Elsevier]

Uniaxial and simple shear stress–strain curves were obtained for a 1050-O aluminum alloy sheet sample in different specimen orientations with respect to the material symmetry axes. For uniaxial tension, a strong anisotropy of strain hardening was observed leading to about 30% difference in uniform tensile elongation between the extreme conditions. For simple shear, the hardening was also significantly different. These results were rationalized with an analysis that accounts for dislocation substructure observations, crystallographic texture measurements and polycrystal modeling of texture-induced strength evolution. [Copyright &y& Elsevier]

Abstract: The present study aims at characterizing the post-necking strain hardening behavior of three sheet metals having different hardening behavior. Standard tensile tests were performed on sheet metal specimens up to fracture and heterogeneous logarithmic strain fields were obtained from a digital image correlation technique. Then, an appropriate elasto-plastic constitutive model was chosen. Von Mises yield criterion under plane stress and isotropic hardening law were considered to retrieve the relationship between stress and strain. The virtual fields method (VFM) was adopted as an inverse method to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields. The results show that the choice of a hardening law which can describe the hardening behavior accurately is important to derive the true stress–strain curve. Finally, post-necking hardening behavior was successfully characterized up to the initial stage of localized necking using the VFM with Swift and modified Voce laws. [Copyright &y& Elsevier]

Abstract: The mechanical behaviours under reversed strain of low carbon steels and aluminium alloys are reviewed and modelled with a simple approach based on the evolutionary laws of two dislocation densities related respectively to the forward and the backward straining. In essence, it is the competition between the annihilation of the dislocations that were created during the prestrain and the storage of newly created dislocations that lead to the observed stagnation of the hardening rate. Textural effects as well as back stresses are shown to extend or to reduce the stress–strain plateau but are not responsible for it. [Copyright &y& Elsevier]

A stress integration algorithm is provided for a novel homogeneous-yield-function-based anisotropic hardening (HAH) model. The new model is an extension of the original HAH model that describes cross-hardening or softening of a sheet metal under an orthogonal strain path change. A semi-explicit integration scheme for the stress update is utilized to efficiently handle the gradient of the distorted yield surface during complex strain path changes, as originally proposed by Lee et al. (2012). Validations of the algorithm developed were conducted by comparing the predicted stress–strain curves of dual-phase (DP) 780 and extra-deep-drawing-quality (EDDQ) steels with experimental stress–strain responses observed under cross-loading conditions. Finally, the accuracy of the proposed finite element (FE) formulations was assessed by r -value prediction and preparation of iso-error maps. [ABSTRACT FROM AUTHOR]

Abstract: Polycrystal aggregates subjected to plastic forming exhibit large changes in the yield stress and extended transients in the flow stress following strain path changes. Since these effects are related to the rearrangement of the dislocation structure induced during previous loading, here we propose a crystallographically-based dislocation hardening model for capturing such behavior. The model is implemented in the polycrystal code VPSC and is applied to simulate strain path changes in low carbon steel. The path changes consist of tension followed by shear at different angles with respect to the preload direction, and forward simple shear followed by reverse shear. The results are compared to experimental data and highlight the role that directional dislocation structures induced during preload play during the reload stage. [Copyright &y& Elsevier]

Abstract: In this work, the springback behavior of the commercial 6022 aluminum alloy in temper aging (T4) is investigated taking into account that the sheets, prior to deformation process, are initially pre-strained and then submitted to various sitting times at room temperature. The unconstrained cylindrical bending test based on the NUMISHEET2002 proceedings as presented by Yoon et al. [Yoon JW, Pourboghrat F, Chung K, Yang DY. Springback prediction for sheet metal forming process using a 3D hybrid membrane/shell method. International Journal of Mechanical Sciences 2002;44:2133–53] is selected as validation benchmark. For finite element simulations, the geometry is modeled by solid-shell finite elements using the formulation of Alves de Sousa et al. [Alves de Sousa RJ, Yoon JW, Cardoso RPR, Fontes Valente RA, Grácio JJ. On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations. International Journal of Plasticity 2007;23:490–515; Alves de Sousa RJ, Cardoso RPR, Fontes Valente RA, Yoon J-W, Natal Jorge RM, Grácio JJ. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part I—Geometrically linear applications. International Journal for Numerical Methods in Engineering 2005;62:952–77; Alves de Sousa RJ, Cardoso RPR, Fontes Valente RA, Yoon JW, Grácio JJ, Natal Jorge RM. A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness: Part II—Nonlinear applications. International Journal for Numerical Methods in Engineering 2006;67:160–88]. The material behavior is described based on the work of Correia et al. [Correia JPM, Simões F, Gracio JJ, Barlat F, Ahzi S. A simple hardening rule accounting for time-dependent behavior in Al–Mg–Si alloys. Materials Science Engineering A 2007;456:170–9]. The results of conducted experiments and numerical simulations are compared. It can be concluded about the good agreement between experiments and simulations attesting the effectiveness of the material model utilized to describe the time-dependent hardening behavior. [Copyright &y& Elsevier]

Abstract: The present work deals with the development of a simple but efficient hardening rule for Al–Mg–Si alloys taking into account the evolution of mechanical response with time when tests are interrupted. The new hardening rule is derived from the classical Swift law through a time dependent hardening exponent. The model predicts accurately the evolution of the stress level with the sitting period as well as other phenomena such as the strain hardening rate stagnation after reloading and critical values of time dependence initiation. [Copyright &y& Elsevier]

Abstract: Strain reversal tests are performed at large strains on an AA1050 aluminium alloy and a low carbon steel deformed in simple shear. The forward and reverse loading are performed either at room temperature or at −120 °C. A transient stagnation in the hardening rate is recorded at reloading for both materials in any temperature sequence. Only the extent of the plateau is material and temperature sensitive. A dislocation cell structure is always observed in the prestrained aluminium alloy. In contrast, the dislocation distribution is homogeneous in the steel when prestrained at low temperature. As the dislocation substructure evolution upon strain reversal is different for these cases, it is concluded that structural features like cell disintegrations are not responsible but merely correlated to the measured transient stagnation of the hardening rate. [Copyright &y& Elsevier]