A statistical analysis of the second 'pop-in' behaviour of the spherical-tip nanoindentation of Zr-based bulk metallic glasses

Statistical analyses of the shear stresses, tau(y), at which the first 'pop-ins' occur during the spherical tip nano-indentation of a wide variety of materials is often conducted to understand the micromechanisms of incipient plasticity. In an earlier paper, we reported such a study on data generated on several different Zr-based bulk metallic glasses (BMGs) using a wide range of experimental variables, such as the tip radius, R-i, loading rate, P(over dot), and structural state of the glass. In the present work, we analyse the second pop-in stress, tau(2), data employing the expectation maximization algorithm in conjunction with the Akaike Information Criterion to examine which of the single and mixed (bimodal) versions of the Gaussian, Lognormal and Weibull (both 2 and 3 parameter) statistical models best describes the stochasticity of tau(2). Results show that the 3-parameter Weibull distribution also captures the stochasticity of tau(2), just as it does for tau(y). For datasets of tau(2) that are generated with larger R-i and P(over dot), the bimodal 3-parameter Weibull distribution is a better descriptor of the dispersion. While Weibull exponent, m, of tau(2) datasets is marginally higher than that of Ty, their kernel density estimates (KDEs) are similar. However, there is a relative shift of the KDEs of tau(2) to smaller values compared to that of tau(y). From mechanistic arguments, tau(2) is determined as the stress to nucleate a second shear band over a previously formed shear band and its stochasticity is attributed solely to the mechanical heterogeneity of the material within it. On this basis, the average shear strength of the shear band is estimated to be similar to 8-11% and 15-17% lower than the strength of the undeformed BMG in the as cast condition and structurally relaxed conditions, respectively. This study provides an understanding of how plasticity develops in BMGs during nanoindentation.