Large dilatational hyperelasticity of glasses en route to cavitation failure

Abstract

Materials deform elasto-plastically and fail under various loading conditions, typically quantified by the stress triaxiality, which is the ratio between the dilatational (hydrostatic) stress and the deviatoric (shear-like) one. We show that the elasto-plastic deformation of glasses approaching failure qualitatively differ for large and small stress triaxiality levels. Specifically, in the former limit, glasses reveal a strong hyperelastic (nonlinear elastic) response with minute plasticity, largely independently of the quenching rate across the glass transition. Yet, glassy disorder gives rise to significant elastic (reversible) nonaffine deformation, accompanied by the formation of micro-cavities. A small fraction of the latter is irreversible, i.e., survives unloading prior to the onset of failure, and may serve as nucleation sites for failure in the form of large-scale cavitation, upon which the glass loses a significant fraction of its load-bearing capacity. These results are contrasted with glass behavior in the limit of vanishing stress triaxiality and their universality across different glass formers is demonstrated. Finally, the implications of our findings for understanding glass deformation and failure under realistic stress conditions are discussed.

Figures (7)

• Figure 1: (a) Stress-strain curves of the same glass sample ($N\!=\!10^6$ particles) under dilation (green, left $y$-axis) and shear (brown, right $y$-axis), see also visual inset in panel (b). The hydrostatic pressure $-P$ (shear stress $\sigma$) is plotted against the dilatational (shear) strain parameter $\epsilon$ ($\gamma$), both normalized such that the dimensionless zero-strain modulus equals unity, where $K_0$ ($\mu_0$) is the bulk (shear) modulus and ${\,\mathchar'26\mkern-12mu d}$ is space dimensionality (here ${\,\mathchar'26\mkern-12mu d}\!=\!3$). $\epsilon_{\rm c}$ corresponds to the large-scale cavitation strain under dilation (see Fig. \ref{['fig:fig6']}). See SI Appendix for details and definitions. (b) The corresponding strain-dependent bulk and shear moduli (up to the value of $\epsilon_{\rm c}$), see legend.
• Figure 2: (a) The dimensionless measure of nonaffine deformation $\eta_{_{\rm n.a.}}$ vs. strain under both dilation and shear (as in Fig. \ref{['fig:fig1']} but with $N\!=\!10^5$), see text for details and discussion. (b) The corresponding accumulated number of structural rearrangements (instabilities).
• Figure 3: (a-b) The same as Fig. \ref{['fig:fig1']}a, but with unloading to zero strain added (the unloading points are marked by diamonds and guiding arrows are added). (c-d) The same as panels (a-b), but for a deeply annealed (slowly quenched) glass sample. See text for discussion.
• Figure 4: (a) A stress-strain curve sketch, showing a loading portion (solid green line) followed by unloading (dashed-dotted orange line). It features a reversible structural rearrangement (event) and an irreversible one, resulting in a residual plastic strain $\epsilon_{\rm p}$. The sketch refers to dilation such that the slope corresponds to ${\,\mathchar'26\mkern-12mu d} K_0$ (see Fig. \ref{['fig:fig1']}a) and the irreversible stress drop to $\Delta{P}$. (b) A table showing the fraction of irreversible events among the population of the first structural rearrangements in two glass ensembles of $M\!=\!100$ samples each and $N\!=\!10^4$, corresponding to high/low $T_{\rm p}$ values (horizontal direction) and loaded in shear/dilation (vertical direction). See text for discussion. (c) The distribution of dimensionless stress drops $s$ under both dilation and shear (see legend), obtained for $M\!=\!100$ high $T_{\rm p}$ and $N\!=\!10^5$ glasses up to $3\%$ strain.
• Figure 5: (a-b) The same stress-strain curves as in Fig. \ref{['fig:fig3']}a,c respectively, where the first-principles zero-strain expansion of Eq. \ref{['eq:nonlinear_expansion']} up to first order (solid line) and second order (dashed line) are superposed. See text for discussion.