Non-Schmid effects and finite wavelength instabilities in single crystal metals

A long standing postulate in crystal plasticity of metals, known as Schmid law, states that yielding commences once the resolved shear stress on a slip plane reaches a critical value. While non-Schmid effects have previously been reported experimentally (mostly in alloys) and in molecular-dynamics simulations, we examine the validity of this assumption through phonon stability analysis. We subject four distinct single crystal metals to a combined shear-hydrostatic deformation and identify the onset of plasticity with the onset of an instability. We find significant shear-normal coupling in single crystal metals, reflecting non-Schmid effects in defect nucleation. Also, it is a widespread assumption in the literature (Liu et al., 2010; Van Vliet et al., 2003) that the instabilities in single crystal metals are of long wavelength. In contrast, we show that short wavelength instabilities are abundant. Our results illustrate the potential pitfalls of relying on the widely used elastic stability analysis for investigating defect nucleation. © 2018 Elsevier Ltd. All rights reserved. When a perfect single crystal is subjected to a deformation such that the energy at a lattice site exceeds the Peierls energy barrier, dislocations are nucleated there and move towards the boundary [1]. Dislocation nucleation in a perfect crystal can be identified with the onset of an instability under appropriate loading conditions, which breaks the local translation symmetry. Thus studying lattice instabilities provide fundamental insights into the mechanics of defect nucleation in single crystals, which is identified with the onset of plasticity. This article investigates two important aspects of the nature of defect nucleation in metallic crystals: (I) Schmid Law; (II) the type of instabilities. Schmid law in crystal plasticity, which governs dislocation motion [2–4], was proposed by Boas and Schmid in 1934. It states that glide on a given slip system commences when its resolved shear stress reaches a critical value [4,5]. Later, Bridgman conducted several experiments on a sample under various hydrostatic pressures and concluded that the yield stress is independent of the hydrostatic pressure [6]. However, in 1983, Christian [7] observed non-Schmid effects experimentally in iron and other bodycentered cubic (BCC) metals. Similar behaviors were observed in several alloys [8–10], like Ni3Al and NiTi [11,12], and crystal plasticity models based on non-Schmid effects have been proposed [3,11,13]. These models attribute non-Schmid effects to the non-closed packedness present in BCC single crystals. Molecular * Corresponding author. E-mail address: [email protected] (J.J. Rimoli). dynamics simulations have also been employed to study nonSchmid effects in various materials [2,4,14]. Although non-Schmid effects have been previously reported, various aspects of them are still an active field of research [10,15–17]. The aforementioned models and numerical studies were either phenomenological, like most models in crystal plasticity or based on molecular dynamics simulations at finite temperature. Several other researchers have employed lattice instability techniques to study homogeneous defect nucleation in crystalline solids [18–24]. Barring a few notable exceptions [25,26], instabilities are generally found to be of the long wavelength type and multiple authors have incorporated an elastic stability analysis to check for such long wavelength instabilities under complex loading conditions [19–21]. We aim to scrutinize the validity of such approaches by investigating the nature of instabilities in perfect