Comparison of equilibrium-based plasticity models and a Taylor-like hybrid formulation for deformations of constrained crystal systems (original) (raw)
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Effect of rate sensitivity on slip system activity and lattice rotation
Acta Metallurgica, 1988
Viscoplastic constitutive models are used for crystals subjected to large strains and high strain-rates; they are based on the assumption that plastic strain occurs by viscous crystallographic slip. Rate-sensitivity and strain-rate effects on crystallographic shears and lattice rotations are investigated; it is shown that large strain-rate sensitivities such as those observed at very high strain rates and at high temperatures may increase the total number of significantly active slip systems and decrease the amount of plastic spin. This leads to contrasted texture evolutions in tension and simple shear which are described.
Modeling the mechanical response of polycrystals deforming by climb and glide
Philosophical Magazine, 2010
This paper presents a crystallographically-based constitutive model of a single crystal deforming by climb and glide. The proposed constitutive law is an extension of the rate-sensitivity approach for single crystal plasticity by dislocation glide. Based on this description at single crystal level, a homogenization-based polycrystal model for aggregates deforming in a climb-controlled thermal creep regime is developed. To illustrate the capabilities of the proposed model, we present calculations of effective behavior of olivine and texture evolution of aluminum at warm temperature and low strain rate. In both cases, the addition of climb as a complementary single-crystal deformation mechanism improves the polycrystal model predictions.
Comparisons of crystal hardening laws in multiple slip
International Journal of Plasticity, 1985
This paper brings together and concisely reviews results from recent analytical investigations on single crystals (variously clone alone or with students) in which predictions from different theoretical hardening laws are contrasted and compared with experimental studies. Finitely deforming f.c.c, crystals in both constrained and unconstrained multiple-slip configurations are considered. Four crystal hardening laws are given prominence. Two of these belong to a class of theories in which the physical hardening moduli relating rates-of-change of critical strengths (in the 24 crystallographically equivalent slip systems) to slip-rates are taken as symmetric. These are G. I. Taylor's classic isotropic hardening rule (proposed in 1923), which is almost universally adopted in the metallurgical literature for various approximate analyses of single and poly-crystal deformation, and a 2-parameter modification of Taylor's rule that has an empirical basis in the qualitative features of experimentally determined latent hardening in single slip. The other two hardening laws featured here belong to a class of theories that were introduced in 1977 by this author. This class requires the above modu[i to be nonsymmetric and explicitly dependent upon the current stress state in such a manner that the following consequences are assured. (1) The deformation-dependent hardening of latent slip systems necessarily develops anisotropically if there is relative rotation of gross material and underlying crystal lattice. (2) The theories admit self-adjoint boundary value problems for crystalline aggregates, hence a variational formulation. (The fact that symmetric physical hardening moduli do not permit variational formulations of polycrystalline problems was shown at the 1972 Warsaw Symposium.) The two members of this class considered here are the original (and simplest possible) theory of rotation-dependent anisotropy, which was proposed by this author in 1977 and commonly has been referred to as the "simple theory," and a modification of this theory introduced in 1982 by Peirce, Asaro and Needleman that lies between Taylor's rule and the simple theory in its predictions for finitely deforming f.c.c, crystals. (In a series of five papers during 1977-79, the simple theory was shown to universally account for the experimental phenomenon of "overshooting" in single slip in both f.c.c, and b.c.c, crystals.) Theoretical results from the various hardening rules are contrasted and compared with finite strain experiments in the metallurgical literature. Both tensile-loaded crystals in 4, 6 and 8-fold symmetry orientations and compressively loaded crystals under conditions of channel die constraint are treated. A postulate of minimum plastic work introduced in 1981 plays a prominent role in the theoretical analyses, in many cases providing a unique solution to the slip system inequalities and deformation constraints (where applicable). The rather remarkable ability of the simple theory to reconcile diverse qualitative features of both constrained and unconstrained finite deformation of f.c.c, crystals is demonstrated. Finally, conditions for total loading (all systems active) in 6-fold symmetry are investigated, and certain concepts regarding the selection of active systems under prescribed straining are critically assessed. i i4
On the selection of active slip systems in crystal plasticity
International Journal of Plasticity, 2005
The capabilities of existing rate-independent and rate-dependent constitutive models to select the active slip systems at the corners of non-smooth theories play a crucial role in predicting localisation phenomena. Even though the description of crystal plasticity within the context of modern continuum mechanics goes back to the early 1960s, there is no universally accepted solution as to how to identify a unique set of active slip systems. Furthermore, some recently proposed integration schemes have neither been compared with other methods nor tested under complex multiaxial stress conditions thus rendering a direct assessment difficult. In this work, the predictive capabilities of existing crystal plasticity and visco-plasticity formulations and algorithms when subjected to complex multiaxial loading paths are investigated, and their relative accuracies established. In order to compare consistently the performance of different models, a generic thermodynamics-based crystallographic framework, which incorporates current formulations as special cases, is proposed. Several two-dimensional boundary value problems for elasto-plastic and elasto-viscoplastic FCC crystals are selected as benchmark cases. The effects of multiaxial loading paths, latent hardening, and dissipated energy on the selection of active slip systems at sharp yield surface corners are investigated. The differences in the predicted behaviour were found to be associated with both the particular form of the single crystal formulations and the algorithms used in their numerical implementations. Experimental data (E.P. Busso).
Sensitivity of polycrystal plasticity to slip system kinematic hardening laws for Al 7075-T6
Materials Science and Engineering: A, 2017
The prediction of formation and early growth of microstructurally small fatigue cracks requires use of constitutive models that accurately estimate local states of stress, strain and cyclic plastic strain. However, little research has attempted to systematically consider the sensitivity of overall cyclic stressstrain hysteresis and higher order mean stress relaxation and plastic strain ratcheting responses introduced by the slip system back-stress formulation in crystal plasticity, even for face centered cubic (FCC) crystal systems. This paper explores the performance of two slip system level kinematic hardening models using a finite element crystal plasticity implementation [1]. The two kinematic hardening formulations aim to reproduce the cyclic deformation of polycrystalline Al 7075-T6 in terms of both macroscopic cyclic stress-strain hysteresis loop shape, as well as ratcheting and mean stress relaxation under strain-or stress-controlled loading with mean strain or stress, respectively. The first formulation is an Armstrong-Frederick type hardening-dynamic recovery law for evolution of the back stress [2]. This approach is capable of reproducing observed deformation under completely reversed uniaxial loading conditions, but overpredicts the rate of cyclic ratcheting and associated mean stress relaxation. The second formulation corresponds to a multiple back stress Ohno-Wang type hardening law [3] with nonlinear dynamic recovery. The adoption of this back stress evolution law greatly improves the capability to model experimental results for polycrystalline specimens subjected to cycling with mean stress or strain. The relation of such nonlinear dynamic recovery effects are related to slip system interactions with dislocation substructures.
Crystals, 2021
In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with...
1999
To bridge length scales in plastic flow of polycrystalline fcc metals, the salient features of 3D polycrystalline elastoviscoplasticity at the crystal level (mesoscale) were studied to determine the relative influences on macroscale behaviour. This 3D study builds upon the 2D planar doubleslip analysis performed by Horstemeyer and McDowell in which the relative influence of the constitutive-law features on macroscale properties in polycrystal plasticity were quantified for oxygen-free, high-conductivity copper. The mesoscale constitutive-law features considered include single-crystal elastic properties, slip-system-level hardening law, latent hardening, slip-systemlevel kinematic hardening, and intergranular constraint relation. Volume-averaged macroscale responses included the effective flow stress, plastic spin, elastic moduli, hardening behaviour, and axial extension (for the free-end torsion case). Each response was evaluated at 10% and 50% effective strain levels under rectilinear shear straining. In the existing literature, only one type of behaviour (e.g. texture or stress-strain response) is typically considered when assessing these various elements of the constitutive framework. In this paper, we develop a more comprehensive understanding of the relative importance of constitutive-law features as deformation proceeds. This study suggests that the design of experiments methodology is a valuable tool to assist in selecting relevant features for polycrystalline simulations and for development of macroscale unified-creepplasticity models. In general, the results indicated that the intergranular constraint and kinematic hardening were more influential overall than the type of constitutive model used, whether isotropic or anisotropic elasticity was used, and whether or not latent hardening was used. Finally, 3D results were similar to the previous 2D planar double-slip study of Horstemeyer and McDowell, except that latent hardening had a stronger influence on the 3D macroscale responses than the 2D macroscale responses.
A ‘stack’ model of rate-independent polycrystals
International Journal of Plasticity, 2011
A novel 'stack' model of a rate-independent polycrystal, which extends the 'ALAMEL' model of is proposed. In the 'stack' model, stacks of N neighboring 'ALA-MEL' domains collectively accommodate the imposed macroscopic deformation while deforming such that velocity and traction continuity with their neighbors is maintained. The flow law and consistency conditions are derived and an efficient solution methodology based on the linear programming technique is given. The present model is applied to study plastic deformation of an idealized two-dimensional polycrystal under macroscopically imposed plane-strain tension and simple shear constraints. Qualitative and quantitative variations in the predicted macroscopic and microscopic response with N are presented. The constraint on individual 'ALAMEL' domains diminishes with stack size N but saturates for large N. Computational effort associated with the present model is analyzed and found to be well within one order of magnitude greater than that required to solve the classical Taylor model. Furthermore, implementation of the consistency conditions is found to reduce computation time by at least 50%.
International Journal of Plasticity, 1986
A modification of the simple theory of rotation-dependent anisotropy is applied to the analysis of f.c.c, crystals, in both constrained and unconstrained multiple-slip orientations, with the object of resolving the question of uniqueness of solution. Specifically, tensile loading in each of 4-, 6-and 8-fold symmetry and [1101 loading in channel die compression for each of [i101 and [001] lateral constraint are investigated. It is established that the modified simple theory, augmented by the postulate of minimum plastic work, uniquely predicts equal multiple-slip and lattice stability (relative to the force axis or axes) in all cases.