ABSTRACT
Fig. 2. Physical (a) and typical modeled (b) configurations of the bridging zone.
Fibre reinforced britde matrix composites 119
opening displacement. This equation is usually solved numerically for the unknown traction distribution. The key contributions in development of these models are: Rose, L.R.F., 1987; Budiansky and Amazigo, 1989; Budiansky, Hutchinson and Evans, 198 6; Marshal, Cox and Evans, 1985; Marshall and Cox, 1987; and many others. The energy approach was initiated by Aveston, J., Cooper, G.A., and Kelly, Α., 1971. The distributed traction approach turned out to be useful, and it played a significant role in understanding the fundamental aspects of the fiber reinforcement mechanism and in establishing the basic quantitative description of the process. However, it neglects certain micromechanical features of the process which are important in accurate evaluation of this reinforcing mechanism. Therefore, this method has its setbacks, which must be mentioned. The analysis based on smeared-out bridging fiber forces gives an approximate average value of the stress intensity factor for the matrix crack. This approach cannot give intermediate values of the driving stress intensity factor as the crack progresses between the fibers. In order to have reliable data on the strength, toughness, and fracture resistance of the ceramic matrix composites, one has to be able to obtain maximal and minimal values of the intermediate local stress intensity factors. Additionally, continuously distributed traction models use the force on the fiber - fiber pullout relationship as a local stress - displacement relationship, while the experimental measurements are obtained using the net force on the fiber. These models neglect the contributions of local stress intensity factors acting along the rim of the interface of fibers and the crack
crack front
Fig. 3. Crack front propagating through fiber reinforced matrix; it moves to the right. Cross section A-A indicates the plane considered in the analysis.
