Giant configurational softening controls atomic-level process of shear banding in metallic glasses

While the shear banding is a ubiquitous feature for metallic glasses and other disordered solids, the underlying material softening mechanism is still an open question requiring physical interpretation at atomic level. Here, through a set of atomistic simulations, we clarify the origin of flow localization, i.e., the birth of a shear band. The local thermal temperature induced by atomic vibration and configurational temperature attributed to structural disordering are proposed to quantify critical degree of thermal and configurational softening, respectively. The comparison between configurational softening and thermal softening being two potential causes for shear banding emergence is then examined at atomic scale. Numerical evidence from atomistic simulations indicates that configurational-softening-induced strain burst is the dominant instability mode as evidenced through a very large value of configurational temperature rise that commensurate with glass transition temperature. It is also found that configurational softening takes precedence over thermally activated ones. Configurational softening is thus conceivably acting as the root cause for the onset of strain localization and shear banding, while the subsequent thermal softening is its consequence. These results provide important insights into the puzzle about the material weakening mechanism underlying shear banding.

Figure 1

The stress-strain curve of ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ metallic glass under strain rate of ${10}^8{\mathrm{s}}^{-1}$. The insets A–E are deformation patterns at strain of 0.05 (initial deformation), 0.10 (elastic limit), 0.112 (shear localization), 0.114 (shear banding formation), and 0.15 (plastic flow), respectively. Here atoms are colored according to the magnitude of $D_{min}^2$ with color scale ranging from 0 ${\AA }^2$ (blue) to 5 ${\AA }^2$ (red).

Figure 2

Softening localization during shear banding process. Evolution of local thermal temperature ${\overline{T}}_{\mathrm{t}}^i$ (a) as well as configurational temperature ${\overline{T}}_{\mathrm{c}}^i$ (b) in shear band and the surrounding matrix. (c) Direct comparison of evolution of thermal softening and configurational softening in the shear band.

Figure 3

Projected views of the atomic configurations during deformation. I–VIII display the spatial distributions of atomic thermal temperature (a) and configurational temperature (b) at various shear strains just before the formation of mature shear band. The strain ranges from I to VIII is from macroscopic strain of 0.1 to 0.114, with strain interval between the successive frames is 0.002.

Figure 4

Inhomogeneous analysis for thermal and configurational softening processes. [(a) and (b)] Statistical distributions of the reduced data normalized by mean value for ${\overline{T}}_{\mathrm{t}}^i$ as well as ${\overline{T}}_{\mathrm{c}}^i$ at various applied strains. (c) The evolution of the degree of localization parameter. Here ${\mathrm{\Psi }}_{T_{\mathrm{t}}}$ corresponds to thermal softening while ${\mathrm{\Psi }}_{T_{\mathrm{c}}}$ is related to configurational softening. (d) The skewness of the non-Gaussian profile as a function of applied strains for ${\overline{T}}_{\mathrm{t}}^i$ and ${\overline{T}}_{\mathrm{c}}^i$ field.

Figure 5

Correlation matrix $\mathrm{CM}\left({\gamma }^{\prime },{\gamma }^{\prime \prime }\right)$ of ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ MG under shear loading. The color coding corresponds to values of $\mathrm{CM}\left({\gamma }^{\prime },{\gamma }^{\prime \prime }\right)$ for ${\overline{T}}_{\mathrm{t}}^i$ (a) and ${\overline{T}}_{\mathrm{c}}^i$ (b).

Figure 6

The radial distribution functions at different levels of macroscopic strain.

Figure 7

Spatial distribution of nonaffine displacement along direction of $y$ axis. The data is obtained from snapshot at strain of 0.15 when mature shear band has already formed. Here 160 $\AA <y<210\AA$ denotes the position of shear band.

Figure 8

(a) Evolution of configurational temperature in the shear band against variation in cooling history. (b) Shear stress-strain curves of ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ samples with different cooling rates. The cooling rates applied during sample preparation are varying from $1\times {10}^{10}$ to $1\times {10}^{13}$ K/s.