Abstract
Probability models are developed for the failure of parallel brittle fibres embedded in a relatively soft plastic matrix. A loss of load-bearing occurs in the region surrounding a fibre break, resulting in a concentration of stress in neighbouring fibres. These stress concentrations cannot be measured directly, but by assuming them to be a chosen function of unknown parameters, the failure of the composite may be modelled. It is then shown how the stress concentration parameters may be estimated using the method of maximum likelihood. The technique is illustrated using experimental data for different materials, and in particular, it is shown how the stress concentration parameters vary with fibre spacing. The appearance of breaks along a fibre is, in nature, a point process. Load-sharing between two fibre processes will lead to a degree of nearly coincidental breaks. The degree to which 'coincidences' or 'matchings' occur in two independent point processes is examined. An unusually high degree of matching can be defined, and used to infer that processes are not independent. The exact analysis for a fibre-break process is intractable, but several approximate alternatives are studied, and compared with real and simulated data. The probability models for composite failure rely on assumptions about the underlying strength of the fibres. Principally, the 'weakest-link' property is assumed, frequently characterised by use of the Weibull distribution. A non-parametric test of this property is devised, and specially designed experiments show that weakest-link is apparently open to considerable doubt. It is shown that the existence of different causes of failure, all of which may not be present all of the time, give rise to some new types of failure model. It is demonstrated that these do not have the weakest-link property, even when based on the Weibull distribution, and that they are consistent with some experimental results.