13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- On bifurcation of homogenous deformation in metallic glasses Yan Chen & Lanhong Dai* State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Science, Beijing, 100190, China * Corresponding author: lhdai@lnm.imech.ac.cn Abstract At temperatures well below the glass transition and at high stresses, the homogenous deformation in metallic glasses (MGs) usually develops to a critical point, at which the discontinuity in deformation rate is incipient across nano-scale shear bands. However, such a bifurcation condition of homogeneous deformation concerning the unique properties of MGs is still lacking for general stress state. In this paper, a new constitutive is introduced for MGs accounting for the pressure-sensitivity, dilatancy and structural evolution; the shear banding is regarded as the appearance of instability in the constitutive description of inelastic deformation. Tying the bifurcation theory to the new model, the general condition of deformation localization is derived. The shear band initiation and failure orientation are then precisely predicted for MGs by constructing a bridge between the microscopic origin and the loss-of-ellipticity instability in the constitutive law in continuum mechanics. Keywords Metallic glasses, Bifurcation, Shear band 1. Introduction Metallic glass (MG) represents a relatively young class of structural materials with a combination of excellent properties. Due to their random atomic structure, plastic deformation in MGs is usually accommodated by localized shear bands. These nanoscale shear bands as a precursor of crack lead to a fast fracture of material, which presents little plasticity at room temperature. Being a key process to understand the underlying plasticity of MGs, shear banding, including its origin and propagation, has attracted lots of attention for last decades[1-5]. Although the precise physical picture of how it originates from the internal structure remains elusive, it is well accepted that the shear banding of MGs occurs as a consequence of formations and self-organizations of shear plastic flow events [3, 6-8]. Those flow events are essentially local arrangements of atoms around free volume sites, termed shear transformation zones (STZs) or flow defects [9-12]. The transition from local plastic events to macroscopic shear-band instability is dominated by the stress-driven free volume softening and assisted by thermal softening [1, 2, 13-15]. Regardless of micro-mechanisms, at the continuum level, the shear banding, a physically material unstable event, can be regarded as the appearance of instability in the macroscopic constitutive description of inelastic deformation [16-19]. It is accepted that the homogenous deformation in MGs develops to a critical point, at which the discontinuity in deformation rate is incipient across nano-scale shear bands, at temperatures well below the glass transition and at high stresses. Tying the bifurcation theory to a pressure-sensitive dilatant constitutive model, Rudnicki and Rice [17] derived both the general conditions for shear localization and the orientation of shear band in the stress space. Based on this, the shear band direction as an important feature in shear band formation was predicted for MGs by Gao et al. [20], which closely depends on the pressure coefficient, the dilatancy factor, and etc. In nature, shear banding as a material instability is greatly correlated to atomic structural change. Such a picture is also realized by Ruan et al. [21] who embody the atomic structural change by the plastic strain and the associated dilatation for MGs. On the other hand, through perturbation analysis of constitutive instability, the conditions for the shear instability for a given stress state (usually simple shear) can be also obtained for MGs [1, 2, 13]. These analyses confirm the important role of free volume, as a state variable, in the constitutive instability. However, such a bifurcation condition of homogeneous deformation concerning the unique
RkJQdWJsaXNoZXIy MjM0NDE=