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It has widely been acknowledged that no structures can be designed to be risk free, and therefore reliability analysis plays an essential role in the design of engineering structures. The recent focus has been placed on structures made of brittle heterogenous (a.k.a. quasibrittle) materials, such as ceramics, composites, concrete, rock, cold asphalt mixture, and many more at the microscale. This paper presents a level excursion model for the analysis of probabilistic failure of quasibrittle structures, in which the failure statistics is calculated as a first passage probability. The model captures both the spatial randomness of local material resistance and the random stress field induced by microstructures (e.g. randomly distributed flaws). The model represents a generalization of the classical weakest-link model at the continuum limit and it recovers the classical Weibull distribution as an asymptotic distribution function. The paper discusses two applications of the model. The model is first applied to the strength distribution of polycrystalline silicon (poly-Si) MEMS specimens. It is shown that the model agrees well with the experimentally measured strength distributions of poly-Si MEMS specimens of different sizes. The model predicts a complete size effect curve of the mean structural strength transitioning from a vanishing size effect at the small-size limit to the classical Weibull size effect at the large-size limit. The second application is concerned with the left tail of strength distribution of quasibrittle structures. By taking into account both random stress and strength fields, the model is used to investigate the origin of the power-law tail distribution of structural strength. [ABSTRACT FROM AUTHOR]

The feasibility of characterizing asphalt mixtures' rheological and failure properties at low temperatures by means of the Bending Beam Rheometer (BBR) is investigated in this paper. The main issue is the use of thin beams of asphalt mixture in experimental procedures that may not capture the true behavior of the material used to construct an asphalt pavement. For the rheological characterization, three-point bending creep tests are performed on beams of different sizes. The beams are also analyzed using digital image analysis to obtain volumetric fraction, average size distribution, and spatial correlation functions. Based on the experimental results and analyses, it is concluded that representative creep stiffness values of asphalt mixtures can be obtained from testing at least three replicates of the thin (BBR) mixture beams. Failure properties are investigated by performing strength tests using a modified Bending Beam Rheometer (BBR), capable of applying loads at different loading rates. Histogram testing of BBR mixture beams and of larger beams is performed and the failure distribution is analyzed based on the size effect theory for quasibrittle materials. Different Weibull moduli are obtained from the two specimens sizes, which indicates that BBR beams do not capture the representative volume element (RVE) of the material. [ABSTRACT FROM AUTHOR]

Low temperature cracking of asphalt pavements is a major distress in cold regions. Accurate assessment of strength of asphalt mixtures at low temperatures is of great importance for ensuring the structural integrity of asphalt pavements. It has been shown that asphalt mixtures behave in a quasibrittle manner at low temperatures and consequently its nominal strength strongly depends on the structure size. The size effect on the strength of asphalt mixtures can be directly measured by testing geometrically similar specimens with a sufficiently large size range. Recent studies have shown in theory that for quasibrittle structures, which fail at the macrocrack initiation from one representative volume element, the mean size effect curve can also be derived from the scaling of strength statistics based on the finite weakest link model. This paper presents a comprehensive experimental investigation on the strength statistics as well as the size effect on the mean strength of asphalt mixtures at −24 °C. It is shown that the size effect on mean structural strength can be obtained by strength histogram testing on specimens of a single size. The present study also indicates that the three-parameter Weibull distribution is not applicable for asphalt mixtures. [ABSTRACT FROM AUTHOR]

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 < 10-10 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 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. [ABSTRACT FROM AUTHOR]

This paper presents a general size effect equation for the strength of hybrid structures, which are made of two dissimilar quasibrittle materials with a thin and weak bimaterial interface. Depending on the material mismatch and structure geometry, a singular stress field could occur at the bimaterial corner. For structures with strong stress singularities, an energetic size effect is derived based on the equivalent linear elastic fracture mechanics and asymptotic matching. For structures without stress singularities, a finite weakest link model is adopted to derive the size effect. A general scaling equation that bridges the limits of strong and zero stress singularities is formulated by combining the energetic scaling of fracture of the bimaterial corner and the finite weakest link model. [ABSTRACT FROM AUTHOR]

In this study, a discrete element computational model is applied to simulate the fracture behavior of asphalt mixtures at low temperatures. In this model, coarse aggregates are explicitly represented by rigid spherical particles. The bonds that connect these particles represent the fine aggregate matrix (FAM), which is defined as the combination of asphalt binder and fine aggregates. The bending beam rheometer (BBR) tests are performed to determine the strength and Young's modulus of FAM at low temperatures. The model is then used to simulate the semi-circular bend (SCB) tests on the mixtures. The model is verified by a series of BBR and SCB tests on both conventional and graphite nano-platelet modified asphalt materials. The comparison between the experimental and simulated results indicates that the peak load capacity of the SCB specimens is primarily governed by the tensile strength of the FAM. However, in order to capture the entire load-displacement curve of the SCB specimens, one needs to employ a softening constitutive model of the FAM, which requires the information on its fracture energy. Several experimental methods for measuring the fracture energy of FAM are discussed for future prediction of the complete load-displacement response of asphalt mixtures at low temperatures. [ABSTRACT FROM AUTHOR]