Instability Analysis and Free Volume Simulations of Shear Band Directions and Arrangements in Notched Metallic Glasses

As a commonly used method to enhance the ductility in bulk metallic glasses (BMGs), the introduction of geometric constraints blocks and confines the propagation of the shear bands, reduces the degree of plastic strain on each shear band so that the catastrophic failure is prevented or delayed, and promotes the formation of multiple shear bands. The clustering of multiple shear bands near notches is often interpreted as the reason for improved ductility. Experimental works on the shear band arrangements in notched metallic glasses have been extensively carried out, but a systematic theoretical study is lacking. Using instability theory that predicts the onset of strain localization and the free-volume-based finite element simulations that predict the evolution of shear bands, this work reveals various categories of shear band arrangements in double edge notched BMGs with respect to the mode mixity of the applied stress fields. A mechanistic explanation is thus provided to a number of related experiments and especially the correlation between various types of shear bands and the stress state.

Similar to the concept of crack tip process zones, notch brittleness or ductility depends on the development of a clean process zone in the vicinity of the notch, which could be plastic deformation in metals or crack bridging or branching in composites, and a messy process zone right at the notch roots which are governed by damage processes on or below the microstructural length scales1,2. For examples, notches may not deteriorate the composite failure strength when the crack bridging zone (e.g., arising from fiber pull-out) is larger than the notch size. The study of notch sensitivity in bulk metallic glasses (BMGs), however, is much more complicated because of the localized deformation into shear bands, which can easily extend beyond the plastic zone estimated from continuum plasticity theory3,4,5. If the shear bands are not confined, either because the stress field is not decaying rapidly from the notch or due to the lack of geometric constraints, the resulting notch toughness will be low. Thus one commonly used approach of improving failure resistance and notch ductility is the introduction of geometric constraints that block and/or deflect the shear bands. Consequently, the degree of plastic strain on each shear band becomes low so that the transition from the shear band to a crack is delayed.

The clustering of multiple shear bands in the vicinity of notch roots has been investigated extensively in experiments6,7. The double edge notched samples under tensile condition have exhibited shear bands that connect the notches in Fig. 1(a)8,9,10, or radial shear bands that extend far from the notch roots in Fig. 1(b)11,12. It is worth noting that experiments in Sarac et al.9 were Mode I tests on Zr-based BMG films with a grid of pores at the gauge section, which is equivalent to the double edge notched sample since the shear bands are localized in the bridge between the holes. These two types of shear bands have not been found to co-exist, as understood by our schematic illustration in Fig. 1(c). The semi-circular shear bands that connect the neighboring notches actually lead to out-of-plane shear offset, and these shear bands will grow into the bulk in an inclined direction off the sample surface normal. The radial shear bands from the notch roots are believed to lead to surface ledges at the surface of the notch root. However, a mechanistic justification of such shear band arrangements has not been fully understood, and it has been suggested that these shear band patterns play an important role in understanding the notech sensitivity in recent experiments7,8,13. In addition to these Mode I (tension or compression) tests, Hsueh et al.14,15 performed combined compression/shear tests with various degrees of mode mixity (i.e., the ratio of Mode II to Mode I components). As shown in Fig. 2(a), when the applied loading condition is near the Mode II, two categories of shear bands can be found near the stress concentration sites – one being long, radial shear bands that extend almost across the entire sample, and the other being heavily curves shear bands that do not extend far from the edges. The latter becomes less prominent in Fig. 2(b) when the contribution of Mode II is reduced. Based on the measured load-displacement curves, Hsueh et al.14,15 developed a continuum plasticity model that considers the pressure effect in the yield surface, which however cannot address the importance of the non-uniform deformation fields and the shear band arrangements in these experiments.