as a bridging zone subject to tractions that provide the extra toughness needed to prevent unstable fracture. Composite failure occurs only when the matrix in the plastic band stretches to its rapture strain. This constitutes a large-scale bridging (LSB) phenomenon, which can be analyzed using standard LSB mechanics [19-21]. The results for TMCs are indicated in Figure 5 . That is, notch degradation is ameliorated at larger notch sizes. But there is still a strong sensitivity of TMC performance to small notches. This problem can be obviated in design, but re-emerges as an issue in fatigue, through its effect on the fatigue threshold.
Low transverse strengths constrain designs and limit application. An understanding of the transverse responses is essential to effective implementation. These properties are dominated by the matrix and the interfaces. They have monolith counterparts. Cracking and delamination occur in CMCs [8,31]. Yielding and plastic straining obtain in TMCs . But in both cases the fibers and the interfaces require that new factors be addressed.
For TMCs there are two principal factors. (i) The interface has minimal tensile strength, such that debonding occurs when the transverse stress exceeds the residual compression induced by thermal expansion mismatch [17,61,63]. At this “elastic limit,” σe, there is a reduction in the transverse modulus to about half its initial value [17,61]. (ii) At larger strains, matrix yielding occurs, but the hydrostatic tensions in the matrix induced by the fibers are an appreciable fraction of the matrix yield strength, despite interface debonding. This stress state accentuates plastic hole growth and leads to low transverse ductility (relative to monoliths having the same composition and microstructure) . The elastic