Micromechanics for Random System and Its Application to Small Crack Problems

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1. Analysis of Strength Characteristic by Considering Random Microstructure in Ceramics : The modification factor for the stress intensity factor was derived as a new mechanical parameter in a random system so that the influence of microstructures in ceramic could be reflected in the parameter. To evaluate the modification factor, numerical analyses on the crack-tip stress field were conducted by taking account of variations in the stiffness and size of individual grains as the difference of microstructures. The stress filed was significantly affected by the stiffness of grains around the grain at the crack-tip, but hardly influenced by the grain-size. The modification factor obtained from the aforementioned analyses was found to become smaller for a longer crack length. Using the simulated distribution of the modification factor, the strength distribution was estimated based on the criterion using the resistance curve concept. The estimated strength distribution was able to show an average tendency in experimental results well.2. Analysis of Fatigue Characteristic by Considering Random Microstructures in Metallic Materials : Deformed hexagons were adopted as elements in modeling metallic polycrys-talline materials. In modeling a microstructure with two phases, the phases were selected from elements by using random numbers so that the selection should correspond to the proportion of each phase occupied in the microstructure. For polycrystalline materials composed of such elements, a crack growth model was constructed based on the competition between the linkage mode of initiated cracks and by the propagation mode of an individual crack. Using the model, notched components for four kinds of metallic materials with different microstructures under multiaxial fatigue were statistically simulated by using a Monte Carlo procedure. It was shown that the distribution range of the simulated life sufficiently covered the failure life observed experimentally.