Crack fracture, energy associated

For the in-situ phase-separation process, an increase in the TP molar mass modifies the phase diagram (it lowers cnl), increases the viscosity - which is a drawback for processing and impregnation of composites - but increases the fracture energy associated with the crack-bridging mechanism. 

The fracture energy, Gc, is related to the energy, AU, associated with crack growth by... 

The presence of a crack also increases the surface area. Griffith called the energy associated with a unit area of the crack the surface energy. Here we will call it the fracture energy for reasons that should become clear later. The fracture energy, T, associated with the crack may be expressed as... 

A test may typically involve the extraction of force P and energy associated with the initiation of crack extension from an instrumented impact load-deflection trace (see Fig. 7) for a test conducted in three-point bending mode (Charpy arrangement). The associated fracture stress can be calculated from... 

A second paradox is the use of the word shear to describe the fracture. It is evident from the calculation used to obtain Equation (15.5) that shear is not mentioned. The joint peels but does not slide or shear (Fig. 15.11). Only tension forces and displacements are needed to explain the failure of the joint. In fact, it would be far more logical to describe this failure as a tension failure, just as the Griffith equation describes tension failure. Of course, shear stresses exist around the crack tip, as in every crack geometry known, but the energy associated with these stresses remains constant as the crack moves and therefore cannot drive the crack. 

The key to this discrepancy is that interfacial fracture takes place under conditions very far from thermodynamic reversibility. Associated with the propagation of an interfacial crack are processes that result in substantial energy dissipation and it is this that produces usefully large values of the interfacial fracture energy. This dissipation may be relatively localised, close to the crack tip it may in some cases, however, take place over macroscopic volumes. The latter situation is common for polymer melts and concentrated solutions, as anyone who has pulled their finger out of a pot of glue will attest. 

Figure 14.4 Energy associated with fracture of a crack uniformly loaded in far-field tension in glass. From Ref. [4].

Ej is usually associated with crack initiation and, on a load-deflection curve, spans the area up to the maximum load, while Ep is believed to represent the apparent crack-propagation energy, appearing after the maximum load. Considering the curves of these ceramic materials shown in Fig. 1.72, it is clear that the load drops vertically and there is no additional area to represent Ep. This observation indicates that PSZ and SiC show typically elastic brittle fracture without plastic deformation and that ... 

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