Most probable fracture strength/stress

We will discuss these fracture properties of disordered solids, modelled by the random percolation models, and concentrate on their statistics, given by the cumulative failure strength distribution F a) under stress a, and the most probable fracture strength erf of such samples. We will discuss separately the cases for weak disorder p 1) and strong disorder p Pc)-The scaling properties of <7f near p pc and the nature of the competition between the percolation and extreme statistics here, will be discussed in detail. 

On the epoxy side of the interface, high fracture toughness and low residual stresses 72,73) are a requirement for optimum transverse strength in graphite and glass-epoxy 1A) composites. Since the adsorption of epoxy components has been shown to be probable, the local structure of the epoxy at the interphase will most likely not be the same as in the bulk. This local anisotropy caused by the interphase is a limitation in the predictive capability of micromechanical models which do not include the interphase as a component. 

This is the most commonly used form of WeibuU resistance probability. WeibuU modulus m is indicative of strength scatter Oq is indicative of strength level and corresponds to fracture stress with a failure probabiUty of 63.2%. It is closely related to the mean strength of the distribution by <7m = <7oT(l + 1/m), with T( ) = Jg°° (see also Appendix H). For a WeibuU modulus in the range... 

The statistical description of the strength was introduced by Weibull. In his model the assumption is made that failure is due to sudden catastrophic growth of pre-existing defects corresponding to local failure stresses. Failure at the most serious defect, i.e. the defect with the lowest fracture stress, leads to immediate failure of the fiber. It is further assumed that the defects are uniformly distributed throughout the fiber. The cumulative failure probability function, P, which represents the fraction of fibers that fail at or below a stress cr is, according to Weibull, given by... 

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