Comparing the Results of Probability of Ceramic Head Fracture According to Weibull’s Theory with Inclusion of One or Three Principal Stresses

摘要

This paper focuses on the assessment of probability of ceramic head hip joint endoprothesis fracture. The Weibull's weakest link theory with inclusion of one or all three principal stresses was used for calculations of probability of failure and the results were compared. The test of head of the hip joint endoprothesis according to ISO 7206 was modelled. Three variants were considered. In the first variant, the head of hip joint endoprothesis ended up without any imperfections from ideal geometry. In other two variants, the ceramic head had shape imperfection from nominal conicity. Principal stresses needed for the calculation of probability of failure were calculated by finite element method. The results with the use of linear and quadratic solid elements were compared and better option was chosen for the next calculations. The influence of allowed penetration, density of the mesh on the results of stresses and probability of failure was assessed. The Gaussian quadrature of 13th order was used for integration over the surface of unit hemisphere in space of principal stresses which was needed for computation of probability of failure with inclusion of all principal stresses. The influence of imperfection from nominal conicity on probability of failure of the head hip joint endoprothesis was calculated and the relative difference between the results of Weibull's weakest link theory with the inclusion of one or all three principal stressed was analyzed.