On the strain-rate dependence of flow stress in crystals with high intrinsic lattice friction (original) (raw)
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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
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.
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).
Physical Mesomechanics, 2010
The paper briefly considers the structure of internal variable constitutive relations. The mesoscale model required for determination of macroscale internal variables is taken to be one of the crystal plasticity (Lins model), in which critical shear stress along slip systems assumes great importance. In this work, evolution equations for critical shear stress that take into account dislocation annihilation and reactions with the formation of Lomer Cottrell barriers are proposed thus making possible description of the Bauschinger effect and additional hardening under complex loading. The potentialities of the model are demonstrated by numerical simulation of monotonic and cyclic uniaxial loading of polycrystals.
An improved method of calculating the lattice friction stress using an atomistic model
Journal of Physics C: Solid State Physics
We present an efficient and accurate method of calculating the lattice friction barrier to dislocation motion. This method makes use of an atomistic model of the dislocation core structure. Results of calculations for the lattice friction barrier and the Peierls stress of t u < 110) edge dislocations in the ionic crystals MgO and KCI are presented and compared with experiment.
C h a p t e r 8 / Deformation and Strengthening Mechanisms 8.6 SLIP IN SINGLE CRYSTALS
A further explanation of slip is simplified by treating the process in single crystals, then making the appropriate extension to polycrystalline materials. As mentioned previously, edge, screw, and mixed dislocations move in response to shear stresses applied along a slip plane and in a slip direction. As was noted in Section 7.2, even though an applied stress may be pure tensile (or compressive), shear components exist at all but parallel or perpendicular alignments to the stress direction (Equation 7.4b). These are termed resolved shear stresses, and their magnitudes depend not only on the applied stress, but also on the orientation of both the slip plane and direction within that plane. Let represent the angle between the normal to the slip plane and the applied stress direction, and the angle between the slip and stress directions, as indicated in .7; it can then be shown that for the resolved shear stress R R ϭ cos cos (8.1)
Slip avalanches in crystal plasticity: scaling of the avalanche cut-off
Journal of Statistical Mechanics: Theory and Experiment, 2007
Plastic deformation of crystals proceeds through a sequence of intermittent slip avalanches with scale-free (power-law) size distribution. On macroscopic scales, however, plastic flow is known to be smooth and homogeneous. In the present letter we use a recently proposed continuum model of slip avalanches to systematically investigate the nature of the cutoff which truncates scale-free behavior at large avalanche sizes. The dependence of the cutoff on system size, geometry, and driving mode, but also on intrinsic parameters such as the strain hardening rate is established. Implications for the observability of avalanche behavior in microscopic and macroscopic samples are discussed.
Dynamic crystal plasticity: An Eulerian approach
Journal of the Mechanics and Physics of Solids, 2010
In this paper an Eulerian rate-dependent single crystal model that accounts for highstrain rates, large strains and rotations is developed. The viscoplastic law as well as the evolution equations for the lattice are written in terms of vectorial and tensorial quantities associated with the current configuration. The viscoplastic law is obtained from Schmid law using an overstress approach. Such an expression for the viscoplastic law is motivated by the microdynamics of crystal defects. A general analysis of the plane-strain response of the proposed rigid-viscoplastic single crystal model is presented. It is shown that only one differential equation, involving the orientation of one composite in-plane slip system, is necessary to describe the lattice evolution. Several two-dimensional boundary value problems, such as equal-channel die extrusion and channel die compression are selected to illustrate the predictive capabilities of the model. The results show that even at relatively low strain rates the viscosity plays an important role in the development of localized deformation modes. At high crosshead velocity, the plastic properties and crystal anisotropy are less important while inertia effects are dominant. Finally, the grains interaction is investigated by analyzing the compression of a grains multicrystal. the large lattice rotations that occur in the dynamic flow regime may not be accurately captured. As concerns the flow rule, a Norton-type power-law is generally used. This law is adequate for the description of low strain rate behavior. Because Norton law is very stiff, current rate-dependent formulations may predict unrealistic slip rates (see for example, , and further discussion in Section 3 of this paper).
The asymmetry of the flow stress in Ni3(Al,Ta) single crystals
Acta Metallurgica, 1984
Flow stress measurements were performed on single crystalline Ni,(Al, Ta) as a function of temperature, orientation, strain rate and sense of the applied uniaxial stress to check the predictions of the Paidar er al. model [ha merall. 32,435 (1984)]. It was found that the critical resolved shear stress (CRSS) for (11 l)[TOl] slip depends not only on the test temperature and orientation of the samples, as other investigators have previously observed, but also on the sense of the applied stress. The orientation dependence of the tension/compression asymmetry, including the regions where the asymmetry is a maximum (positive), a minimum, and where it disappears, is as predicted by the model. The applied stress changes the activation enthalpy of cross slip primarily through its effect on constricting the Shockley partials during cross slip and only secondarily on directly promoting (111) to (010) cross slip. A maximum attainable CRSS for (111) [TO11 slip, the saturation stress, is also in agreement with the model. It was also found that the CRSS for (11 l)[TOl] slip is strain rate independent, but the CRSS for (OOl)[TlO] slip shows a strong positive strain rate dependence. The temperature at which the peak in the flow stress vs temperature curve occurs increases with increasing strain rate and decreases with increasing ratio of RSS on (OOl)[TlO] divided by that on (lll) [TOl]. When the deformation occurs by (OOl)[TlO] slip the stress-strain curve exhibits clearly defined, continuous yield points.