This diploma thesis deals with probability of fracture ceramic head of total hip endoprosthesis during tests by the standard ISO 7206-5. In the first part is made stress analysis with method of finite elements in program ANSYS. Six types of ceramic head with different geometry was analysed for ideal geometry of head and shaft, and also for shape imperfections from nominal conical shaft and head. The final values of principal stress from stress analysis were entry values for the second part – probability of fracture analysis. Weibull weakest-link theory was applied, namely 3-Parameter and 2-Parameter Weibull distribution.

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The scope of the presented master thesis was the experimental study of multi-filament yarns made of AR-glass and used for textile-reinforced concrete. The behavior under the tensile loading was investigated by laboratory tests. A high number of yarn specimens (over 300) of six different lengths (from 1 cm to 74 cm) was tested to obtain statistically significant data which were subsequently corrected and statistically processed. The numerical model of the multi-filament bundle was studied and applied for prediction of the yarn performance and for later results interpretation. The model of n parallel filaments describes the behavior of a bundle with varying parameters representing different sources of disorder of the response and provides the qualitative information about the influence of their randomization on the overall bundle response. The aim of the carried experiment was to validate the model presumptions and to identify the model parameters to fit the real load-displacement curves. Unfortunately, due to unsuccessful correction of measured displacements devalued by additional non-linear contribution of the unstiff experiment device the load-displacement diagrams were not applicable to model parameters identification. The statistical evaluation was carried only for the maximal load values and the effect of the specimen size (length) on its strength was demonstrated. The size effect curve did not exclude the existence of spatial correlation of material mechanical properties modifying the classical statistical Weibull theory.