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Many modern engineering structures are made of brittle heterogenous (quasibrittle) materials, such as concrete, composites, and tough ceramics. Recent studies have shown that the strength distribution of quasibrittle structures varies from a Gaussian distribution modified by a power-law tail to a Weibull distribution as the structure size increases, and such size dependence can be well captured by a finite weakest link model. This paper investigates the implication of the size-dependent strength distribution on the reliability-based analysis and design of quasibrittle structures by considering a linear failure limit state. The size effect on the statistical properties of structural strength directly leads to a size-dependent Cornell index, which could give a reasonable estimation of the failure risk in some cases. To improve the prediction of the structural failure risk, the size dependence of the strength distribution is further incorporated into the computation of the Hasofer–Lind index, where it is shown that the transformation method for the non-Gaussian random structural strength is dependent on the structure size and geometry. By assuming that the applied load follows a Gaussian distribution, approximate size effect equations are developed for the central and nominal safety factors through asymptotic matching. The proposed formulation of the size effect on reliability indices and safety factors is applied to analyze the failure of the Malpasset arch dam. [ABSTRACT FROM AUTHOR]

The design of various engineering structures, such as buildings, infrastructure, aircraft, ships, as well as microelectronic components and medical implants, must ensure an extremely low probability of failure during their service lifetime. Since such a low probability is beyond the means of histogram testing, we must rely on some physically based probabilistic model for the statistics of structural lifetime. Attention is focused on structures consisting of quasibrittle materials. These are brittle materials with inhomogeneities that are not negligible compared with the structure size, as exemplified by concrete, fiber composites, tough ceramics, rocks, sea ice, bone, wood, and many more at the micro- or nano-scale. This paper presents a finite weakest-link model of the fatigue lifetime of quasibrittle structures that fail at the fracture of one representative volume element (RVE). In this model, the probability distribution of critical stress amplitude is first derived by assuming a prescribed number of loading cycles and a fixed stress ratio. The probability distribution of fatigue lifetime is then deduced from the probability distribution of critical stress amplitude through the Paris law for fatigue crack growth. It is shown that the present theory matches well with the experimentally measured lifetime histograms of various engineering and dental ceramics, which systematically deviate from the two-parameter Weibull distribution. The theory indicates that the mean fatigue lifetime of quasibrittle structures must strongly depend on the structure size and geometry. Finally, the present model indicates that the probability distribution of fatigue lifetime can be determined from the mean size effect analysis. [ABSTRACT FROM PUBLISHER]

Highlights: [•] This paper investigates the effect of stress singularities on the scaling of fracture of hybrid structures. [•] The scaling mechanism transits from energetic to statistical as the stress singularities get weaker. [•] The energetic-statistical scaling relation agrees well with the numerical simulations by a stochastic cohesive crack model. [Copyright &y& Elsevier]

Abstract: Ensuring a small enough failure probability is important for the design and selection of restorative dental ceramics. For this purpose, the two-parameter Weibull distribution, which is based on the weakest link model with infinitely many links, is usually adopted to model the strength distribution of dental ceramics. This distribution has been thoroughly validated for perfectly brittle materials. However, dental ceramics are generally quasibrittle because the inhomogeneity size is not negligible compared to the size of the ceramic part. For such materials, the experimental histograms of many quasibrittle materials have been shown to exhibit strong deviations from the two-parameter Weibull distribution. As a remedy, the three-parameter Weibull distribution, which has a nonzero threshold, has been proposed. However, the improvement of the fits of histograms of quasibrittle materials has been only partial. Instead of making the threshold non-zero, the correct remedy is to consider the weakest link model to have a finite number of links, each of them representing one finite-size representative volume element of material. This model has recently been justified on the basis of the probability of random jumps of atomic lattice cracks over the activation energy barriers on the free energy potential of the lattice. It is shown that, in similarity to other quasibrittle materials, this new model allows excellent fits of the experimental strength histograms of various types of dental ceramics. [Copyright &y& Elsevier]