Statistical micro-macro approach for the strength of aged brittle materials

Failure of brittle materials is due to the unstable propagation of a dominant crack and, therefore, their macroscopic strength is governed by the presence of surface microdefects. The defectiveness scenario continuously changes during the service life due to natural aging, mainly associated with processes of abrasion and corrosion. Developing the original idea by Freudenthal [1], we propose a micromechanically-motivated approach to pass, in statistical terms, from the population of micro-cracks to the population of macroscopic strengths. Assuming a uniform distribution of non-interacting flaws without preferred orientation, whose size statistically follows a Pareto distribution, the population of strengths shall vary according to a 2-parameter Weibull distribution. This is the most used statistics for brittle materials, even though its ability to interpret the left-hand-side tails of the population is a subject of debate. Furthermore, an upper-Truncation of the Pareto distribution for crack lengths leads to a left-Truncated Weibull distribution, which can much better interpret the tails of the population of strengths for some brittle materials, such as structural float glass [2]. The micro-macro approach can also interpret the observed variation of material strength during service life due to abrasion or corrosion. In fact, such phenomena are associated with a modification of the defectiveness scenario. In particular, corrosion leads to a surface dissolution and, hence, to a constant length reduction for all the surface micro-cracks. This effect is beneficial, especially for the highest fractiles of strength, associated with the smallest crack lengths. On the other hand, abrasion produces new surface cracks. A very hard abrasion process can overtake the initial defectiveness scenario, so that the strength population shall be governed by the new micro-cracks population. Instead, if the abrasion is "mild", the new crack population superimposes on the original one, resulting in a bi-modal Weibull distribution of strengths. Finally, some abrasion processes, such as sandblasting, can originate additional semi-spherical defects, which could provoke the shielding of pre-existing cracks. Here, this approach is used to justify the observed modification in the statistical strength population for corroded or abraded glass, induced also during the float production process. Further applications may include ceramics, glass-ceramics and polycrystalline silicon ME.