On the strength reliability of statistically heterogeneous materials with microstructure at diverse scales

The paper examines the effects of microstructure realized at diverse scales on the overall strength reliability of the material. Reliability, or more precisely indirect reliability evaluated herein through the spatial fluctuations of strength, is shown to depend strongly on the scale-wise distribution of heterogeneity as well as on the size of a specimen or structure. In particular, for a polycrystalline material with pores, the overall (indirect) strength reliability increases as (a) the average grain size decreases relevant to the that of the pores, (b) the variance of the grain size decreases relevant to that of the pores, and (c) the size of a specimen or structure or material building block decreases. Under certain conditions, it is possible to reach near-zero or even zero variance, implying perfect reliability. The major conclusion is that scales interact with each other and that affects the overall fluctuations in material properties, thus providing renewed opportunities for tailoring the reliability of materials. The major conclusion is amenable to experimental investigation and verification for different heterogeneity scenarios.