Peridynamics is a non-local continuum mechanics modelling method, with fundamental equations built upon integrals as opposed to partial differentials, which gives benefits when modelling brittle fracture relative to other continuum mechanics modelling techniques. Notably absent from peridynamics literature is an investigation of the effect of fracture strength distributions (an important element of brittle fracture) in peridynamics. This thesis outlines a method for appropriately including fracture strength distributions in peridynamics, and presents a model of a UO2 fuel pellet fracturing in service using this method.
It was shown that using a Weibull distribution in peridynamics without adjusting the distribution of strengths to account for the difference in size between bonds and the part to be modelled produces inaccurate results. Using Weibull scaling to account for this did not alone solve this problem, as there was still a disconnect between the stress at which the first bond fails (stage 1 failure) and the stress at which the overall part modelled fails (stage 2 failure). Bond strengths were localised by linking bond strength to the material points they are connected to. Combining this localisation with using the most extreme strengths, the shape of the Weibull curve was accurately recreated in 1D peridynamics.
The method was applied in two dimensions, and it was shown that the method which had worked in one dimension is no longer adequate. It was found that edge length is the most appropriate size-scaling criteria, as opposed to total area of the two-dimensional model. The model was able to recreate Weibull distributions of fracture strain in a two dimensional tensile test using a Weibull modulus of 10, but was less accurate with lower Weibull moduli.
The effect of Weibull distributions on radial crack numbers in in-service UO2 nuclear fuel pellets was investigated. It was found that using a Weibull distribution of fracture strains in a peridynamics model of fuel pellets allows the model to more accurately predict the number of cracks expected at a given power. The model was compared to low-burnup post irradiation examination data.