Invertible structured deformations and the geometry of multiple slip in single crystals (original) (raw)

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)

Deformation behavior of an idealized crystal

1975

The deformation behavior of an idealized crystal made by stacking of parallel slip planes is studied. Each slip plane is assumed to contain active sources of dislocations leading to a constant density of non-interacting dislocations in the plane which glide through randomly distributed localized point obstacles, representing small precipitates. The dislocation is assumed to have a constant line tension and the dislocation-obstacle interaction is taken to have a simple step form. Using results of computer simulation of thermally activated glide through random arrays of point obstacles the deformation is modeled as a function of temperature and applied stress, determining the strain rate and the morphological characteristics of slip. Stress-strain rate and flow stress-temperature relations are discussed. * Let the dislocation under the applied stress T encounter a configuration of point obstacles denoted by i (Figure 1). Between two adjacent

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).

Uniform rearrangement in defective crystals

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992

We show that an abstract notion of defectiveness yields the slip mechanism of classic plasticity theory by reasoning in purely kinematical terms, and we catalogue the canonical forms of slip that occur in this way. There appears, in consequence, a precise version of the idea of elastic-plastic decomposition.

A model for crystal plasticity based on micro-slip descriptors

Continuum Mechanics and Thermodynamics, 2002

Within the framework of multi-field theories of damage mechanics we address the problem of crystal plasticity without introducing either the usual decomposition of the deformation gradient into elastic and plastic parts, or the associated concept of intermediate (or lattice) configuration. In comparison with the standard presentations of crystal plasticity we use a more refined kinematical description able to assess the effects of any dislocation on the macro-motion of the body. We apply the principle of virtual working to obtain the balance equations; the first and the second principles of thermodynamics to get suitable restrictions for the constitutive relations. A numerical simulation is worked out to illustrate the main features of the model.