Size effect on strength and lifetime probability distributions of quasibrittle structures

Abstract

Abstract. 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 load is derived. Both the strength and lifetime cdfs are shown to be sizeand 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.

Influence of external and internal cooling at solidification on strength of brittle duralumin in compression

“…The same picture is observed in hammered or rolled elements: the surface layers undergo an intense deformation, which causes the described distribution of inherent stresses after cooling. The deplanation stresses will increase with increasing sample sizes, (due to a greater difference in the temperature of the inside and surface layers of the casting), which must also affect the scale effect [10,11].…”

Experimental Study of Postcritical Deformation and Failure of Steels at High Temperature

“…Вопросы экспериментального и теоретического изучения закономерностей закритического деформирования материалов привлекают внимание исследователей в связи с необходимостью исследования деформационных резервов материалов, повышения несущей способности и живучести конструкций и сооружений в процессе эксплуатации, а также более точного прогнозирования процессов разрушения и их устойчивости [1][2][3][4][5][6][7][8].…”