Failure of metal structures is caused by cracks appearing and growing in the material until the strength of the structure is compromised. The way in which such cracks grow in metal has been researched extensively; the great majority of this work concentrates on long cracks, that is cracks of the order of 1mm or longer.
This research explores new ways of modelling reliability by developing a model for short crack propagation and interactions in steel. Short crack propagation is affected by the microstructural properties of the material, and differs significantly from the growth of long cracks. Interactions consist of cracks growing into one other to form longer cracks. This is an important mechanism for damage accumulation, and is termed coalescence. During a substantial portion of useful structural lifetime, short cracks are present in the material. These form and grow under everyday stresses that are experienced by the structure. For this reason, predictions as to when the length of the cracks will compromise the strength of the structure are of interest.
Data on the growth and coalescence of short cracks has been provided by the Department of Mechanical and Manufacturing Engineering, Trinity College Dublin.
A model is developed for short crack propagation which takes into account the microstructural features of the material. This gives reasonable reliability predictions when coalescence is not a dominant feature. A further model is developed for coalescence. This is combined with the model for growth, using auxiliary variables for unobserved parameters of interest.
The analysis is carried through in a Bayesian framework. Markov Chain Monte Carlo (MCMC) techniques are used to sample from the posterior distribution of the parameters of the model.
Recommendations are made as to the nature of the spatial data that may be easily recorded in the future, in order that reliability predictions may be improved.