*3.3. Mode III Shear Morphology*

Unlike the mode II shear, the mode III shear deformation occurs in the direction perpendicular to the shear propagation plane. This shear mode is less constrained and has some "degree of freedom" in the propagation direction, which can result not only in the appearance of local deviations of the SB path but also in its segmentation. A typical example of such an SB is represented in Figure 3. Each segmen<sup>t</sup> of the mode III SB is labelled numerically from #1 to #7 and consists of two parts: (i) the arched step with a constant shear offset ranging from 500 to 50 nm and (ii) the tip with a monotonic decrease in the offset height from 50 nm to zero (Figure 3a).

**Figure 3.** The typical behaviour of the mode III shear band (SB) in the compressed Pd-based bulk metallic glass (BMG) specimen. The 3D surface map obtained with the scanning white-light interferometry (SWLI) technique (**a**) shows a segmented nature of a mode III shear (275 μm length). The slope map reveals fine scratches (marked by red arrows) extending through SBs and showing the absence of a mode II shear component (**b**). The scanning electron microscope (SEM) image of the mode III SB shows 40◦ inclination to the surface (**c**). Shear offsets 1 to 7 measured by SWLI are represented on the bar chart (**d**). The schematic (**e**) illustrates a dislocation-based interpretation of the shear morphology formed in three consecutive steps I, II, and III, and the corresponding isometric and top views of the resulting shear. In this case, the circled arrows indicate the positions of screw dislocation lines, and the "plus"/"minus" signs indicate the tensile and compressive stress components of a macro-dislocation, respectively.

One should keep in mind that the shear plane of the observed SB is inclined with respect to the scanned specimen surface (Figure 3c). Thus, the shear o ffset values (Figure 3d) are larger than the vertical (Z-axis) step height values by a factor of around 1.4. This, however, does not change the mode III shear behaviour qualitatively. Such a shear band propagates in a progressive manner (at sharp contrast with simultaneous sliding), which has been shown in Reference [27]. Unlike the straight single-line mode II shear, the mode III shear path is segmented into short consequent fragments, so that each propagation event occurs one after another.

Considering that the SB tip induces a long-range stress field, one can easily rationalize the above observations. The mode III shear initiates from a stress concentrator, located at the edge of the specimen (Figure 3c). The plane of the maximum shear stresses is inclined at approximately 45◦ to the loading axis (40◦ in the case of compression). The SB tends to align itself with this plane, but the resulting trajectory is not straightforward. This is due to the fact that a path of the mode III shear in a BMG is the result of the superposition of external far-field stress and the stress field of the mode III shear itself (Figure 1c). A sum of two perpendicular acting forces—one from the external stress and one from the dislocation-induced peak stress—results in the tortuous path, which one can observe clearly for each segment.

Even in polycrystalline materials, the planar discontinuities, such as cracks, may propagate along a smoothly curved non-crystallographic path due to a specific superposition of triaxial stresses. Compare, for example, the S-shaped cracks, which are frequently observed in hydrogen embrittled steels [47].

The curved morphology of the SB indicates that the Volterra-type macro-dislocation associated with the shear band deviates from the preferred maximum macroscopic shear stress plane. The more the SB deviates from this plane, the lesser is the driving force for its propagation, which vanishes at some point, and the shear front stops (Figure 3e(I)). The next shear segmen<sup>t</sup> starts from the stress concentrator located at the intersection of the maximum shear plane and the previous shear path (Figure 3e(II)). In this scenario, each new SB segmen<sup>t</sup> increases the total o ffset at the surface, extends the overall SB length, deviates from the general mode III plane, and stops (Figure 3e(III)).

Another exciting feature of the mode III SB step morphology is that the individual segments tend to curve in the same direction. This observation can be logically explained by the stress fields of SB's tips. Each tip of the terminated SB can be described as a Volterra-type screw macro-dislocation, which is shown in Figure 3e—isometric view. The screw shear tips form an energetically favourable dislocation-like ladder (just like that in crystals) with alternating negative and positive stresses (see Figure 3e, top view). This happens due to the attraction of the opposite sign stress components—an example of dislocations interaction in a BMG.
