TY - JOUR
T1 - Subcritical crack growth law and its consequences for lifetime statistics and size effect of quasibrittle structures
AU - Le, Jia Liang
AU - Bažant, Zdeněk P.
AU - Bazant, Martin Z.
PY - 2009
Y1 - 2009
N2 - For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine the loading or time corresponding to a tolerable failure probability such as 10-6. Unfortunately, this is not so for quasibrittle structures, characterized by material inhomogeneities that are not negligible compared with the structure size (as is typical, e.g. for concrete, fibre composites, tough ceramics, rocks and sea ice). For such structures, the distribution of structural strength was shown to vary from almost Gaussian to Weibullian as a function of structure size (and also shape). Here we predict the size dependence of the distribution type for the lifetime of quasibrittle structures. To derive the lifetime statistics from the strength statistics, the subcritical crack growth law is requisite. This empirical law is shown to be justified by fracture mechanics of random crack jumps in the atomic lattice and the condition of equality of the energy dissipation rates calculated on the nano-scale and the macro-scale. The size effect on the lifetime is found to be much stronger than that on the structural strength. The theory is shown to match the experimentally observed systematic deviations of lifetime histograms from the Weibull distribution.
AB - For brittle failures, the probability distribution of structural strength and lifetime are known to be Weibullian, in which case the knowledge of the mean and standard deviation suffices to determine the loading or time corresponding to a tolerable failure probability such as 10-6. Unfortunately, this is not so for quasibrittle structures, characterized by material inhomogeneities that are not negligible compared with the structure size (as is typical, e.g. for concrete, fibre composites, tough ceramics, rocks and sea ice). For such structures, the distribution of structural strength was shown to vary from almost Gaussian to Weibullian as a function of structure size (and also shape). Here we predict the size dependence of the distribution type for the lifetime of quasibrittle structures. To derive the lifetime statistics from the strength statistics, the subcritical crack growth law is requisite. This empirical law is shown to be justified by fracture mechanics of random crack jumps in the atomic lattice and the condition of equality of the energy dissipation rates calculated on the nano-scale and the macro-scale. The size effect on the lifetime is found to be much stronger than that on the structural strength. The theory is shown to match the experimentally observed systematic deviations of lifetime histograms from the Weibull distribution.
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U2 - 10.1088/0022-3727/42/21/214008
DO - 10.1088/0022-3727/42/21/214008
M3 - Article
AN - SCOPUS:70450209303
SN - 0022-3727
VL - 42
JO - Journal Physics D: Applied Physics
JF - Journal Physics D: Applied Physics
IS - 21
M1 - 214008
ER -