Universal behaviour in compressive failure of brittle materials

Brittle failure limits the compressive strength of rock and ice when rapidly loaded under low to moderate confinement. Higher confinement or slower loading results in ductile failure once the brittle-ductile transition is crossed. Brittle failure begins when primary cracks initiate and slide, creating wing cracks at their tips(1-3). Under little to no confinement, wing cracks extend and link together, splitting the material into slender columns which then fail. Under low to moderate confinement, wing crack growth is restricted and terminal failure is controlled by the localization of damage along a narrow band. Early investigations proposed that localization results from either the linkage of wing cracks(1-3) or the buckling of microcolumns created between adjacent wing cracks(4,5). Observations of compressive failure in ice(6) suggest a mechanism whereby localization initiates owing to the bending-induced failure of slender microcolumns created between sets of secondary cracks emanating from one side of a primary crack. Here we analyse this mechanism, and show that it leads to a closed-form, quantitative model that depends only on independently measurable mechanical parameters. Our model predictions for both the brittle compressive strength and the brittle-ductile transition are consistent with data from a variety of crystalline materials, offering quantitative evidence for universal processes in brittle failure and for the broad applicability of the model.