ABSTRACT
Figure 1: Three typical fracture configurations taking place in ceramic matrix composites: a) short bridging zone; b) short fully bridged crack; c) long fully bridged crack. computational effort. The method is based on a specific situation taking place during composite failure which will be discussed here along with a background of methods currently used in the literature. The fracture process in ceramic matrix composites consists of a failing brittle matrix while the reinforcing fibers may remain intact. The portion of the cracked matrix with fibers intact forms the process zone. The intact fibers bridge the surfaces of the cracked matrix, retarding or possibly preventing future matrix crack growth. A typical failure process is initiated by formation of a crack in the matrix. The separation of the crack surfaces is constrained by the reinforcing fibers which may remain intact along the entire or a portion of the crack surfaces, forming the so-called bridging zone. These initial cracks may be formed during the manufacturing process or may be initiated during service. The three typical cases of fracture development are categorized by the length of the crack and the relative length of the bridging zone where fibers remain intact. The models of the fracture resistance development process address three essentially different cases: case (a), when the bridging zone is short as compared to the total crack length, or did not develop prior to loading of a preexisting crack; case (b), a situation when a small crack in the matrix develops and propagates under the applied uniform stress; and case (c), when the crack growth will progress under an increased load until the total crack length reaches the critical value, and the crack growth becomes unstable and continues under a constant or decreased load. These three cases, illustrated in Fig. 1, represent the fracture process on a microscale within the large component. The analytical description of this process is extremely important for future development of ceramic matrix composites and for the development of engineering fracture and strength design criteria for the practical application of these materials. The aim of theoretical analysis is to relate the fracture mechanics parameters acting on a microscale to the applied loading or fracture parameters obtained on a macroscale. The development of models relating the processes on micro-and macro-scales has taken a certain pattern over the last few years. The most typical approach adopted for these models is based on substitution of the action of discretely distributed fibers with the action of continuously distributed forces. Schematically, the difference between the physical configuration and the modeled configuration is illustrated in Fig. 2 and Fig. 3.
