In contrast to the case of known environments, path planning in unknown environments, mostly for humanoid robots, is yet to be opened for further development. This is mainly attributed to the fact that obtaining thorough sensory information about an unknown environment is not functionally or economically applicable. This study alleviates the latter problem by resorting to a novel approach through which the decision is made according to fuzzy Markov decision processes (FMDP), with regard to the pace. The experimental results show the efficiency of the proposed method.

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A disc-type specimen containing a central bean-shaped slit, called the U-notched Brazilian disc specimen, was utilized to measure experimentally the mode II notch fracture toughness of a type of commercial polycrystalline graphite. First, 24 U-notched Brazilian disc graphite specimens were fabricated for four different notch tip radii, and the monotonic fracture tests were performed under pure mode I and pure mode II loading conditions; 12 for each loading mode. The recorded fracture loads were converted to the corresponding notch fracture toughness values, and the ratio mode II notch fracture toughness/mode I notch fracture toughness was experimentally determined. Then, assuming that the experimental values of mode I notch fracture toughness are known, the mode II notch fracture toughnesses were theoretically predicted by means of two brittle fracture criteria, namely the existing U-notched maximum tangential stress and the newly developed U-notched mean stress. A very good agreement was found to exist between the theoretical and the experimental results. Also, found in this research was that both the criteria could predict well the experimentally measured fracture initiation angles.

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