Matrix fracture energy

In (15.36) rm is the matrix fracture energy, t is the interfacial shear strength, and Ex is the axial modulus of the composite. In (15.37) e refers to the effective properties of the composite, which, for unidirectional fiber reinforcement, can be calculated with good approximation by the rule of mixtures. 

Although the two approaches are very similar, the value of A Tc in Boccaccini s model does not depend on the interfacial shear strength t, as a result of the model chosen for the value of matrix cracking stress. Blissett et al. (1997) suggested that their method was valid for the UD material providing that some key parameters (interfacial shear stress, matrix fracture energy) were determined independently. 

On the other hand, the fracture energy of the composite, is composed from those of the fibre, and matrix related term, the latter differs from that of the matrix fracture energy in the unfilled state [1265]. Therefore ... 

As shown in Fig. 10, the nail solution applies to relatively weak interfaces, G c 1 J/m, where all the fracture events occur on one plane and the matrix holding the molecular nails does not deform but offers frictional resistance. In the next section, we explore how the fracture energy can increase by several orders of magnitude as we proceed from nails to nets. 

An important consideration is the effect of filler and its degree of interaction with the polymer matrix. Under strain, a weak bond at the binder-filler interface often leads to dewetting of the binder from the solid particles to formation of voids and deterioration of mechanical properties. The primary objective is, therefore, to enhance the particle-matrix interaction or increase debond fracture energy. A most desirable property is a narrow gap between the maximum (e ) and ultimate elongation ch) on the stress-strain curve. The ratio, e , eh, may be considered as the interface efficiency, a ratio of unity implying perfect efficiency at the interfacial Junction. 

The introduction of rubber particles increases the fracture energy of the networks at room temperature, but also decreases the temperature of the ductile-brittle transition (Van der Sanden and Meijer, 1993). This ductile-brittle transition is strongly dependent on the nature (and Tg) of the rubber-rich phase and the amount of rubber dissolved in the matrix. The lowest ductile-brittle transition is obtained with butadiene-based copolymers (Tg — 80°C), compared with butylacrylate copolymers (Tg —40°C). 

A threshold of interfacial adhesion between both phases is needed to (a) promote the cavitation mechanism and (b) activate the crack-bridging mechanism. For rubbery particles, the former contributes much more than the latter to the total fracture energy. Adhesion is achieved by the use of functionalized rubbers that become covalently bonded to the matrix. Higher toughness values have been reported by the use of functionalized rubbers (Kinloch, 1989 Huang et al., 1993b). However, these experimental results also reflect the effect of other changes (particle size distribution,... 

Poly(vinyl acetate) (PVAc) is very often used for low-profile applications. At low PVAc contents, the continuous matrix is a polyester network with PVAc inclusions. Increasing the PVAc amount leads first to a bicon-tinuous structure, and then to a phase-inverted system (Chapter 8). The low-profile action is observed in the concentration range where bicontinuous structures are formed (Pascault and Williams, 2000). However, the fracture energy attains a maximum value for lower PVAc concentrations (Bucknall et al., 1991). 

Liquid reactive rubbers were also used for UP and vinyl ester formulations (Suspene et al., 1993 Siebert et al., 1996). Increases in fracture energy and fatigue- crack resistance were reported for some systems, although no significant improvements were observed for some other systems. These different behaviors are probably related to the heterogeneous structure of the matrix (Chapter 7). Toughening mechanisms in three-phase systems are not yet well established. 

With 10 wt% of dispersed acrylic rubbers (average diameter 0.4 gm), the fracture energy of an epoxy network was largely improved. GIc increased from 180 Jm 2 for the neat matrix to 420 Jm 2 for the modified formulation. The addition of 10 wt% CTBN led to a value of 240 J m-2 but, with the addition of 10 wt% CSR particles, increased the value to 490Jm-2. 

The interphase provided by the adhesion promoter may be hard or soft and could affect the mechanical properties. A soft interphase, for example, can significantly improve fatigue and other properties. A soft interphase will reduce stress concentrations. A rigid interphase improves stress transfer of resin to the filler or adherend and improves interfacial shear strength. Adhesion promoters generally increase adhesion between the resin matrix and substrate, thus raising the fracture energy required to initiate a crack. 

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