A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials (original) (raw)
Related papers
2021
A new phenomenological strain hardening function is proposed to describe the strain hardening behavior of metallic materials. The function is based on a simplification of an earlier established self and latent hardening crystal plasticity approach. The proposed function contains only four parameters, which can be readily obtained using an efficient numerical technique by fitting the experimental curve. Several applications on different materials are presented and good agreements with the experimental counterparts were obtained. One great advantage of the proposed empirical function is that its parameters can be directly used in polycrystal viscoplastic modeling (VPSC approach) for crystal plasticity-based incremental strain hardening simulations. For the conversion of the parameters between the macroscopic scale and the grain-level, the Taylor factor was used, which was re-defined for polycrystals in the present work. The VPSC simulations also led to good reproduction of the experimental strain hardening behavior for all investigated cases, with rapid convergence.
A new intermediate model for polycrystalline viscoplastic deformation and texture evolution
Acta Materialia, 2008
In this paper, we propose a model for large viscoplastic deformation of polycrystalline materials called /-model. The proposed interaction law is based on a new non-linear intermediate approach. In this formulation, we propose to minimize an error function which combines the deviations of the local fields from the corresponding macroscopic ones. A scalar weight parameter was introduced to span the entire solution domain between the upper and lower bound approaches. We applied this approach to predict the stress-strain response and texture evolution in face-centered cubic metals under tension, compression and plane strain compression. We analyzed the effect of the weight parameter in terms of slip activity, stress-strain responses and texture transitions such as copper-type vs. brass-type textures. A comparison between the self-consistent model (VPSC code) and the /-model is also performed in this paper. Some possible links between the / parameter and microstructural features are also discussed.
Hardening relations describe the increase in resistance to deformation during plastic flow. Three hardening relations are compared here in the context of conventional large-strain single-crystal viscoplasticity. The first is an isotropic hardening relation. The second is a hardening relation that is expressed as an ordinary differential equation in the slip resistance. The third is a new relation, originally developed in the context of gradient crystal plasticity, in which the slip resistance is expressed explicitly in terms of the accumulated slip on each slip system. The numerical solution of the governing equations is found using the finite element method coupled with a predictor-corrector type algorithm. The features of the hardening relations are elucidated using a series of numerical benchmark problems. The parameters for the hardening relations are calibrated using a model problem. Various crystal structures are investigated, including single-and double slip, and face-centred cubic crystals. The hardening relations are compared and their relative features discussed.
Materialwissenschaft und Werkstofftechnik, 2005
In this paper, we report predicted results for texture evolution in FCC metals under uniaxial compression test. These results are computed using a newly developed nonlinear rigid viscoplastic crystal plasticity model based on an intermediate interaction law. This interaction law is formulated by the minimization of a normalized error function which combines the local fields' deviations, from the macroscopic ones, obtained by the classical upper bound (Taylor) and lower bound (Sachs) models. This interaction law leads to results lying between the upper and lower bound approaches by simply varying a scalar weight function f (0 < f < 1). A simple interaction law based on the linear mixture of the fields from the Taylor and Sachs models is also used. The results from these both the linear and nonlinear intermediate approaches are shown in terms of texture evolution under uniaxial compression. These results are discussed in comparison with the well known experimental textures in compressed FCC metals. Finally, we show that the linear intermediate approach yields fairly acceptable texture predictions under compression and that the fully non-linear approach predicts much better results.
International Journal of Plasticity, 2013
A polycrystalline material, deformed to large plastic strains and subsequently reloaded along a distinct strain path, exhibits a change in flow stress and hardening behavior. Such changes upon reloading depend on the level of mechanical anisotropy induced by texture and sub-grain microstructure developed during prior loading. In order to comprehend such material behavior, we extend a previously developed rate-and temperature-sensitive hardening law for hexagonal single crystals that accounts explicitly for the evolution of dislocation densities by including the effects of reverse dislocation motion and de-twinning on strain hardening and texture evolution. The law is implemented within a visco-plastic self-consistent polycrystalline model and applied to simulate macroscopic behavior of polycrystalline beryllium during strain-path changes. We show that the model successfully captures the mechanical response and evolution of texture and twin volume fraction during pre-loading in compression and subsequent cross-reloading in compression along two orthogonal directions at two different strain rates. These predictions allow us to elucidate the role played by various slip and twin mechanisms, de-twinning, and reverse dislocation motion on strain hardening and texture evolution of beryllium during strain-path changes. The model is general and can be applied to any metal deforming by slip and twinning.
Procedia Engineering, 2014
Multi-scale modelling offers physical insights in the relationship between microstructure and properties of a material. The macroscopic anisotropic plastic flow may be accounted for by consideration of (a) the polycrystalline nature and (b) the anisotropic grain substructure. The latter contribution to anisotropy manifests itself most clearly in the event of a change in the strain path, as occurs frequently in multi-step forming processes. Under monotonic loading, both the crystallographic texture and the loading-dependent strength contribution from substructure influence the macroscopically observed strength. The presented multi-scale plasticity model for BCC polycrystals combines a crystal plasticity model featuring grain interaction with a substructure model for anisotropic hardening of the individual slip systems. Special attention is given to how plastic deformation is accommodated: either by slip of edge dislocation segments, or alternatively by dislocation loop expansion. Results of this multi-scale modelling approach are shown for a batch-annealed IF steel. Whereas both model variants are seen to capture the transient hardening after different types of strain path changes, the dislocation loop model offers more realistic predictions under a variety of monotonic loading conditions.
A polycrystal plasticity model based on the mechanical threshold
International Journal of Plasticity, 2002
A temperature and rate-dependent viscoplastic polycrystalmodel is presented.It uses a single crystal constitutive response that is based on the isotropic Mechanical Threshold Stress continuum model. This combination gives us theability to relate the constitutive model parameters between the polycrystaland continuum models. The individual crystal response is used to obtain themacroscopic response through the extended Taylor hypothesis. A Newton-Raphsonalgorithm is used to solve the set of fully implicit nonlinear equations for each crystal. The analysis also uses a novel state variable integration method which renders the analysis time step size independent for constant strain rate simulations. Material parameter estimates are obtained through an identification study, where the error between experimental and computed stress response is minimized. The BFGS method, which is used to solve theidentification problem, requires first-order gradients. These gradients arecomputed efficiently via the direct method of design sensitivity analysis.Texture augmentation is performed in a second identification study by changing crystal weights (volume fractions). #
Fourth World Congress …, 1998
The selfconsistent models for the prediction of the mechanical properties of polycrystals are conceived to account for the influence and evolution of several microestructural aspects like: the anisotropy of the constituent grains, the activity of the different microscopic deformation mechanisms, the volume fraction and the interaction between different phases, the crystallographic and morphologic texture, etc. In this work we present the basic equations of the viscoplastic selfconsistent polycrystal model; we show some specific applications to the prediction of: texture development, polycrystal yield surface, intergranular residual stresses; taking into account the effect of: slip geometry, mechanical twinning, recrystallization, grain shape and local correlations and we also discuss the implementation of inverse problem for this kind of formulation.