Influence of non-glide stresses on plastic flow: from atomistic to continuum modeling

Abstract

The Schmid law, which is accurate for face-centered-cubic (fcc) metals, assumes that only the shear stress acting in the slip plane in the slip direction controls the plastic deformation. Hence, it is implicitly assumed that the critical resolved shear stress (CRSS) for the slip is not affected by any other components of the applied stress tensor. This rule is almost ubiquitously utilized in large-scale continuum computations of plastically deforming single and polycrystals. On the other hand, in materials with more complex structures and for some orientations of the dislocation line the cores can spread onto several non-parallel planes. The most widely-known example is the screw dislocation in bcc metals, though this phenomenon is quite universal in structures that are not close packed. Signatures of such core configurations commonly include unexpected deformation modes and slip geometries, strong and unusual dependence of flow stresses on temperature and strain rate, a high Peierls stress, and, in general, a breakdown of the Schmid law. In this paper, we first summarize results of atomistic computer simulations of the response of 1/2 1 1 1 screw dislocations to the applied shear stresses. The calculations have been made using central-force many-body potentials and tight-binding based bond-order potentials for molybdenum. While the core structure found is not the same for the two descriptions of atomic interactions, both lead to a very similar orientation dependence of the critical resolved shear stress for the dislocation motion which takes place along the most highly stressed {1 1 0} plane. This dependence reveals the break down of the Schmid law invoked by the effect of shear stresses acting in another {1 1 0} plane, which are called non-glide stresses. These results are then transferred to macroscopic level by formulating single crystal yield criteria that include the effects of non-glide components of the stress tensor. These criteria form a basis for multislip yield criteria and flow relations for continuum analyses. Using this approach we demonstrate that the effects of non-glide stresses that have their origin at the level of individual dislocations also have significant effect on polycrystalline response, including a significant tension-compression asymmetry.

Advances in anisotropy and formability

“…For equal yield stresses in tension and compression c=0, hence the proposed criterion reduces to the von Mises yield criterion. It was shown that this isotropic yield criterion describes with great accuracy the crystal plasticity simulation results of Hosford and Allen [140] and of Vitek et al [286] for randomly oriented polycrystals (for more details, see Cazacu and Barlat [75]). The isotropic criterion (13) was further extended such as to incorporate anisotropy using the generalized invariants approach i.e.…”

Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

“…This means that the CPFE method has evolved as an attempt to employ some of the extensive knowledge gained from experimental and theoretical studies of single-crystal deformation and dislocations to inform the further development of continuum field theories of deformation. The general framework supplied by variational crystal plasticity formulations provides an attractive vehicle for developing a comprehensive theory of plasticity that incorporates existing knowledge of the physics of deformation processes [8][9][10] into the computational tools of continuum mechanics [11,12] with the aim of developing advanced and physically based design methods for engineering applications [13].…”

Investigation of slip system activity in iron at room temperature by SEM and AFM in-situ tensile and compression tests of iron single crystals

“…Alternative flow criteria to the classical Schmid law form which are investigated in different contexts, see for example (Vitek et al, 2004) but also (Franciosi and Zaoui, 1991;Franciosi and Berbenni, 2008), can also require, in general, reconsideration of the underlying hardening mechanisms. In the particular case of BCC crystals, it has been discussed in details in ) that when the critical stress to attain slip activity is no more a pure shear on a slip plane but a stress combination, the hardening model becomes more complex than the simple (and widely efficient) forest model and is still to be explicated.…”