We present an experimental and theoretical study of the fatigue failure of heterogeneous materials under cyclic compression considering asphalt as a specific example. Varying the load amplitude, experiments reveal a finite fatigue limit below which the specimen does not break, while approaching the tensile strength of the material a rapid failure occurs. In the intermediate load range, the lifetime decreases with the load as a power law. We introduce two novel theoretical approaches, namely, a fibre bundle model and a fuse model, and show that both capture the major microscopic mechanisms of the fatigue failure of heterogeneous materials, providing an excellent agreement with the experimental findings.

In several phenomena of practical interest, such as catalyst deactivation, fouling in heat transfer and other systems of technological and scientific relevance, an irregular surface accessed by diffusion can be progressively passivated. In a diffusion limited situation, an interface that works unevenly due to Laplacian screening is simultaneously and unevenly passivated. To study this phenomenon, we describe a process in which the regions of the surface that are initially working, are transformed into passive, reflecting zones. As a consequence, at each step, a new part of the interface becomes active. In turn, this new active zone is passivated, and so on. It is found that the length of the successive active zones remains approximately constant for a prefractal interface. The concept of active zone in Laplacian transport can then be successfully extended to elucidate this self-limiting behavior of the passivation process. A conjecture is then proposed which states that, in D = 2, the information dimension of the harmonic measure on a fractal supporting a "passivated or reflecting subfractal" (of smaller dimension) is equal to 1. This constitutes an extension of Makarov theorem. From our results, fractal geometry 381 Fractals 2004.12:381-387. Downloaded from www.worldscientific.com by CHINESE UNIVERSITY OF HONG KONG on 02/18/15. For personal use only. 382 B. Sapoval et al.is revealed as a potential candidate to engineer substrate morphologies that are robust to Laplacian passivation.

We investigate the two-dimensional transport of heat through viscous flow between two parallel rough interfaces with a given fractal geometry. The flow and heat transport equations are solved through direct numerical simulations, and for different conduction-convection conditions. Compared with the behavior of a channel with smooth interfaces, the results for the rough channel at low and moderate values of the Péclet number indicate that the effect of roughness is almost negligible on the efficiency of the heat transport system. This is explained here in terms of the Makarov's theorem, using the notion of active zone in Laplacian transport. At sufficiently high Péclet numbers, where convection becomes the dominant mechanism of heat transport, the role of the interface roughness is to generally increase both the heat flux across the wall as well as the active length of heat exchange, when compared with the smooth channel. Finally, we show that this last behavior is closely related with the presence of recirculation zones in the reentrant regions of the fractal geometry.

We investigate the diffusion-reaction behavior of two-dimensional pore networks at the critical percolation point. Our results indicate the existence of three distinct regimes of reactivity, determined by parameter xi[triple bond]D/(Kl2), where D is the molecular diffusivity of the reagent, K is its chemical reaction coefficient, and l is the length scale of the pore. First, when the diffusion transport is strongly limited by chemical reaction (i.e., D<>K), the flux of reagent reaches a saturation limit Phi(sat) that scales with the system size as Phi(sat) approximately L(alpha), with an exponent alpha approximately 1.89, corresponding to the fractal dimension of the sample-spanning cluster. We then show that the variation of flux Phi calculated for different network sizes at the second and third regimes can be adequately described in terms of the scaling relation, Phi approximately L(alpha)f(xi/L(z)), where the crossover exponent z approximately 2.69 is consistent with the predicted scaling law alpha=2betaz.

Polymethylmethacrylate is the material of choice for prosthetic bases. Depending on the type of polymerization, acrylic resins may present some mechanical weaknesses that may lead to the failure of a prosthesis. The microhardness and flexural strength of a dental material determine its applicability. The objective of the present investigation was to evaluate the in vitro Knoop microhardness and flexural strength of a thermopolymerizable (Probase Hot) and an autopolymerizable (Probase Cold) resin, according to ISO 20759-1: 2013.