Yielding in multicomponent metallic glasses: Universal signatures of elastic modulus heterogeneities

Sheared multicomponent bulk metallic glasses are characterized by both chemical and structural disorder that define their properties. We investigate the behavior of the local, microstructural elastic modulus across the plastic yielding transition in six Ni-based multicomponent glasses, that are characterized by compositional features commonly associated with solid solution formability. We find that elastic modulus fluctuations display consistent percolation characteristics pointing towards universal behavior across chemical compositions and overall yielding sharpness characteristics. Elastic heterogeneity grows upon shearing via the percolation of elastically soft clusters within an otherwise rigid amorphous matrix, confirming prior investigations in granular media and colloidal glasses. We find clear signatures of percolation transition with spanning clusters that are universally characterized by scale-free characteristics and critical scaling exponents. The spatial correlation length and mean cluster size tend to diverge prior to yielding, with associated critical exponents that exhibit fairly weak dependence on compositional variations as well as macroscopic stress-strain curve details.

Figure 1

Three-dimensional softness maps of the (b) CoNiFe and (c) CoNiCrFe compositions at applied shear strain ${\gamma }_{xy}\simeq 0.1$ and the corresponding stress-strain curves ${\sigma }_{xy}$ vs ${\gamma }_{xy}$ in (a). The colors in (b) and (c) indicate different clusters including elastically unstable regions with $\mu \le 0$. The slope in (a) indicates the softening modulus $h_{\min }$. Upon shearing, negative-$\mu$ clusters form percolating networks (in brown) on approach to failure that tend to correlate with the (postfailure) macroscopic properties.

Figure 2

Cluster size statistics corresponding to the CoNiFe and CoNiCrFe glasses. (a), (c) Cluster size distribution $n_s$. (b), (d) Scatter plot of cluster size $s$ and associated radius of gyration $r_s$ at different strains ${\gamma }_{xy}=0.03$ ($•$), 0.07 ($\blacksquare$), 0.1 ($⬩$). The dashed-dotted lines denote power laws $n_s\propto s^{-\tau }$ with (a) $\tau =2.0$, (c) $\tau =2.1$, and $s\propto r_s^{d_f}$ with (b) $d_f=2.3$, (d) $d_f=2.6$.

Figure 3

Mean cluster size $S$ plotted against $p$ associated with the (a) CoNiFe and (c) CoNiCrFe glasses. The graphs in (b) and (d) are the same as (a) and (c) but plot $S$ as a function of $1-p/p_{\text{max}}$ with (a) $p_{\text{max}}=0.14$ and (c) $p_{\text{max}}=0.20$. The (red) curves indicate binning averaged data. The dashed-dotted lines denote power laws $S\propto {(p_{\text{max}}-p)}^{-\gamma }$ with (b) $\gamma =2.89$ and (d) $\gamma =2.20$.

Figure 4

Correlation length $\xi$ plotted against $p$ corresponding to the (a) CoNiFe and (c) CoNiCrFe glasses. The graphs in (b) and (d) are the same as (a) and (c) but plot $\xi$ as a function of $1-p/p_{\text{max}}$ with (a) $p_{\text{max}}=0.14$ and (c) $p_{\text{max}}=0.20$. The (red) curves indicate binning averaged data. The dashed-dotted lines denote power laws $\xi \propto {(p_{\text{max}}-p)}^{-\nu }$ with (b) $\nu =1.26$ and (d) $\nu =0.51$.

Figure 5

Scatter plot of softening modulus $h_{\text{min}}$ and scaling exponents (a) $\gamma$ (b) $\nu$ corresponding to the FeNi ($•$), CoNiFe($\blacksquare$), CoNiCrFe ($⬩$), CoCrFeMn ($▴$), CoNiCrFeMn ($◂$), and ${\mathrm{Co}}_5{\mathrm{Cr}}_2{\mathrm{Fe}}_{40}{\mathrm{Mn}}_{27}{\mathrm{Ni}}_{26}$ ($▸$) bulk metallic glasses.