Statistical Fracture Mechanics, formalism of few natural ideas is applied to simulation of crack trajectories in brittle material. The “diffusion approximation” of the crack diffusion model represents crack trajectories as a one-dimensional Wiener process with advantage of well-developed mathematical formalism and simplicity of creating computer generated realizations (fractal dimension d = 1.5). However, the most of reported d values are in the range 1.1-1.3. As a result, fractional integration of Wiener processes is applied for lowering d and to generate computer simulated trajectories. Case studies on numerical simulation of experimentally observed crack trajectories in sandstone (discs tested in indirect tensile strength test) and concrete (compact tension specimens tested in the quasi-static splitting tensile test) are presented

Crack trajectories under different loading conditions and material microstructural features play an important role when the conditions of crack initiation and crack growth under fatigue loading have to be evaluated. Unavoidable inhomogeneities in the material microstructure tend to affect the crack propagation pattern, especially in the short crack regime. Several crack extension criteria have been proposed in the past decades to describe crack paths under mixed mode loading conditions. In the present paper, both the Sih criterion (maximum principal stress criterion) and the R-criterion (minimum extension of the core plastic zone) are adopted in order to predict the crack path at the microscopic scale level by taking into account microstress fluctuations due to material inhomogeneities. Even in the simple case of an elastic behaviour under uniaxial remote stress, microstress field is multiaxial and highly non-uniform. It is herein shown a strong dependence of the crack path on the material microstructure in the short crack regime, while the microstructure of the material does not influence the crack trajectory for relatively long cracks.

Risk modeling and analysis is one of the most important stages in project success. There are many approaches for risk assessment and an investigation of existing methods helps in developing new models . This paper is an extensive literature survey in risk modeling and analysis methods with main focus on fuzzy risk assessment.

The oxidation resistance of iron-based alloys depends on the formation of thin protective films consisting of reaction products between the alloys and the ambient atmosphere. The high corrosion resistance of Fe-Cr-Mo alloys has been attributed to the rapid formation of a uniform, highly protective passive film. The pipes hardness and resistance to various forms of corrosion are determined by the composition of the oxide layer that plays an important role in determining the lifetime of the pipes themselves. The thermal stability of the oxide layer is influenced by its composition and thickness as well as by the bond to the underlying metal. Determining factors for the high temperature corrosion are generally: temperature, metallurgy, TAN (chloridric and naphthenic acid), local flow conditions, sulphur compounds.