Crack interactions and strength predictions in fibrous metal matrix composites

This work consists of two major parts. The first part presents a general and simple method of stress analysis in linear elastic media which contains randomly oriented cracks and complex crack configurations. The second part is concerned with strength prediction of notched, fibrous metal matrix composite plate specimens.; The crack interaction method evaluates stress intensity factors of these cracks and some features of the adjacent stress fields. It is based on a novel superposition scheme which considers a configuration of N cracks as N separate problems, each of which consists of a solitary crack in an infinite elastic medium, loaded by an unknown traction, induced by the applied external load and by mutual interaction with other cracks in the configuration. In the analysis, the unknown tractions are approximated by a polynomial series weighted by certain unknown coefficients. The polynomial series are referred to as base functions in the sequel. The mutual interaction among all cracks is accounted for by the stresses generated by an isolated crack at a location of another line crack when the former is subjected to the combination of appropriate base functions. The overall solution reduces to a system of linear algebraic equations. The method is formulated here in the context of two-dimensional elasticity, but it can be extended to three-dimensional problems.; Several examples which illustrate particular applications of the method are presented. These include H-crack and T-crack shapes which appear in studies of fracture of fibrous metal matrix composites. Comparison of the results with solutions that are available in the literature shows that the method gives accurate results even when a few base functions are selected in the analysis.; The experimental observations of deformation fields in notched, unidirectionally reinforced metal matrix plates indicate that these fields are dominated by discrete plastic zones which extend from the notch tip in the direction of the fiber. The zones are usually much longer than the notch and they accommodate large plastic shear strains. They blunt the crack tip and help to redistribute the adjacent crack-tip stress fields.; In the present work, a model of strength prediction which takes into account the plastic zone-induced stress is presented. Two types of metal matrix composites are selected in the analysis, the boron aluminum (B/Al) and alumina (Al{dollar}sb2{dollar}O{dollar}sb3{dollar}) aluminum (FP/Al) systems. The present analytical predictions on various specimens of different notch geometries are found to be in agreement with those found by experiments and by finite element analysis.