A new macroscopic strain hardening function based on microscale crystal plasticity and its application in polycrystal modeling (original) (raw)
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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.
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.
Numerical modeling of strain rate hardening effects on viscoplastic behavior of metallic materials
2017
The main goal of the present work is to provide a finite strain elasticviscoplastic framework to numerically account for strain, strain rate hardening, and viscous effects in cold deformation of metallic materials. The aim is to provide a simple and robust numerical framework capable of modeling the main macroscopic behavior associated with high strain rate plastic deformation of metals. In order to account for strain rate hardening effects at finite strains, the hardening rule involves a rate dependent saturation hardening, and it accounts for linear hardening prevailing at latter deformation stages. The numerical formulation, finite element implementation, and constitutive modeling capabilities are assessed by means of decremental strain rate testing and constant strain rate loading followed by stress relaxation. The numerical results have demonstrated the overall framework can be an efficient numerical tool for simulation of plastic deformation processes where strain rate history effects...
A crystal plasticity model for strain-path changes in metals
International Journal of Plasticity, 2008
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.
A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials
Journal of the Mechanics and Physics of Solids, 2010
A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.
Materials
The justification of the applicability of constitutive models to exploring technological processes requires a detailed analysis of their performance when they are used to describe loadings including the complex loading mode that is characteristic of these processes. This paper considers the effect of equivalent stress overshooting after the strain-path changes known to occur in metals and alloys. The macrophenomenological and multilevel models, which are based on crystal plasticity, account for this effect by applying anisotropic yield criteria at the macro- and mesolevels, respectively. We introduce a two-level constitutive statistical inelastic deformation model (identified for aluminum) that incorporates the popular simple phenomenological anisotropic hardening law for describing the behavior of FCC polycrystals. The results of the numerical simulation are in satisfactory agreement with existing experimental data. Statistical analysis of the motion of a mesostress in the stress s...
Acta Materialia, 2001
A polycrystalline aluminum sample with a quasi-2D single layer of coarse grains is plastically deformed in a channel die plane strain set-up at ambient temperature and low strain rate. The microtexture of the specimen is determined by analysis of electron back scattering patterns obtained in a scanning electron microscope. The spatial distribution of the plastic microstrains at the sample surface is determined by measurement of the 3D plastic displacement field using a photogrametric pixel-based pattern recognition algorithm. The initial microtexture is mapped onto a finite element mesh. Continuum and crystal plasticity finite element simulations are conducted using boundary conditions which approximate those of the channel die experiments. The experimental and simulation data are analyzed with respect to macromechanical and micromechanical effects on grain-scale plastic heterogeneity. The most important contributions among these are the macroscopic strain profile (friction), the kinematic hardness of the crystals (individual orientation factors), the interaction with neighbor grain, and grain boundary effects. Crystallographic analysis of the data reveals two important points. First, the macroscopic plastic strain path is not completely altered by the crystallographic texture, but modulated following soft crystals and avoiding hard crystals. Second, grain-scale mechanisms are strongly superimposed by effects arising from the macroscopic profile of strain. The identification of genuine interaction mechanisms at this scale therefore requires procedures to filter out macroscopically induced strain gradients. As an analysis tool, the paper introduces a micromechanical Taylor factor, which differs from the macromechanical Taylor factor by the fact that crystal shear is normalized by the local rather than the global von Mises strain.
Journal of Physics: Conference Series, 2014
The problem of constructing a physically based hardening laws of mono-and polycrystalline samples in multi-level theories using crystal plasticity is considered, these hardening laws should allow describing the process of the defect structure evolution of the material due to the intensive inelastic deformations. It is also should be applicable to the description of simple and cyclic loading. An approach to the construction of a general and a particular form of hardening law is proposed, which takes into account the interaction of full and split dislocations with each other, forming and destruction of dislocation barriers, annihilation of dislocations during reverse loading. Using the obtained hardening law, the known experimental effects of simple and cyclic loading are described.