TY - GEN
T1 - Size effect on strength and lifetime distributions of quasibrittle structures
AU - Bažant, Zdeněk P.
AU - Le, Jia Liang
PY - 2010
Y1 - 2010
N2 - 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 junction (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.
AB - 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 junction (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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U2 - 10.1115/IMECE2009-11824
DO - 10.1115/IMECE2009-11824
M3 - Conference contribution
AN - SCOPUS:78049409666
SN - 9780791843840
T3 - ASME International Mechanical Engineering Congress and Exposition, Proceedings
SP - 137
EP - 145
BT - Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2009, IMECE 2009
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2009 International Mechanical Engineering Congress and Exposition, IMECE2009
Y2 - 13 November 2009 through 19 November 2009
ER -