Brownian motion, and Kramer's rate formula are included in the rate theory chapter. One suggestion (for a possible second edition) would be the inclusion of more applications that are carried through to quantitative conclusions, such as specific atomic based-computations of elastic behavior of crystals, including finite, nonlinear deformation (some examples can be found in Mechanics of Solids, edited by H. G. Hopkins and M. J. Sewell, Pergamon Press, 1982).

Engineering structures such as aircraft, bridges, dams, nuclear containments and ships, as well as computer circuits, chips and MEMS, should be designed for failure probability < 10−6–10−7 per lifetime. The safety factors required to ensure it are still determined empirically, even though they represent much larger and much more uncertain corrections to deterministic calculations than do the typical errors of modern computer analysis of structures. The empirical approach is sufficient for perfectly brittle and perfectly ductile structures since the cumulative distribution function (cdf) of random strength is known, making it possible to extrapolate to the tail from the mean and variance. However, the empirical approach does not apply to structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared to structure size. This paper presents a refined theory on the strength distribution of quasibrittle structures, which is based on the fracture mechanics of nanocracks propagating by activation energy controlled small jumps through the atomic lattice and an analytical model for the multi-scale transition of strength statistics. Based on the power law for creep crack growth rate and the cdf of material strength, the lifetime distribution of quasibrittle structures under constant loads is derived. Both the strength and lifetime cdf’s are shown to be size- and geometry-dependent. The theory predicts intricate size effects on both the mean structural strength and lifetime, the latter being much stronger. The theory is shown to match the experimentally observed systematic deviations of strength and lifetime histograms of industrial ceramics from the Weibull distribution.

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Metal-composite joints between steel ribs and advanced fiber-polymer composites are an effective structural system for hybrid ship hulls. Similar joints are of interest for fuel-efficient aircraft. The current designs of such joints are generally based on the strength criterion, which ignores fracture mechanics. Aimed at an efficient and reliable design, this study investigates the size effect on the strength of these joints theoretically, numerically and experimentally. The analytical formulation of the size effect is asymptotically anchored at the large-size limit in linear elastic fracture mechanics (LEFM). The bi-material corner of the joint is shown to have a singular stress field with complex singularity. The strength of the joint is determined by the energy criterion for the macrocrack initiation at the corner, from which the large-size asymptote of the size effect law has been derived. A general approximate size effect law, spanning all sizes and various joint angles, is further derived via asymptotic matching. Numerical analysis with cohesive fracture model is used to design the experiments. Experimental studies involve the testing of geometrically similar hybrid joint specimens with the size ratio of 1 : 4 : 12. The analytical, numerical and experimental studies all indicate that the strength of bimaterial metal-composite joints is subjected to a strong size effect.