Fracture mechanics of composite materials

Abstract

The above circumstances lead to models based on a discussion of the structure of a composite being used most frequently in the fracture mechanics of composite materials. In view of the stochastic properties of the elements in the structure, especially the dispersion in the strength of the fibers, stochastic fracture models are widely used [4-7]. Nevertheless, there has been no success so far in suggesting models which predict the strength of a composite and the dimensions of the permissible defects. Furthermore, there has been no success in reconciling the proposed models qualitatively with the results of tests on specimens containing cracks or notches. The purpose of this study is to fill this gap partially. In this paper semideterministi c models are developed, distinguished by being based on probability considerations, butthe final results are presented in deterministic form. These results are related to the average or most probable values of the macroscopically measurable quantities, which can be compared with the average data from experiments. The most appreciable difference in the proposed approach is that a crack in a composite is considered as a formation which, owing to delamination, has extension in the direction of reinforcement, its dimension in this direction entering explicitly or implicitly into all the principal relationships. The proposed equations have a qualitative approximate nature. As is frequently done, we shall carry out the operations at the physical level of rigor [8]. In particular, we shall omit factors on the order of unity (except for cases where these factors are necessary for qualitative conclusions) and discard small terms. For macroscopic quantities we shall give "almost certain ~ estimates, Le., with a probability on the order of unity, and we shall identify the deterministic quantities with distribution medians, with quantilers on the order of 1 - e -1 = 0.632.. , etc.