Cavitational stress

Particle Diameter Because plastic deformation depends on stress concentration in the whole volume between particles and not directly on the stress at the particles, D is not of primary importance. The only precondition is that for a given particle volume content, the particles must be small enough to ensure that A is less than the critical value according to equation 1. Therefore, the most important function of particles is to produce a dense pattern of microvoids. Recently, an increase of the toughness of modified PA with increasing tendency to form microvoids inside the particles (with decreasing stress to crack the particles or with decreasing cavitation strain) was found (6). The cavitation stress of an elastomer is dependent on its modulus (27). 

This balance between interfacial propagation and bulk deformation has been described for linear elastic materials [56] and results from the competition between two mechanisms the velocity of propagation of an interfacial crack, which is controlled by the critical energy release rate Gc, and the bulk deformation, which is controlled by the cavitation stress and hence essentially by the elastic modulus E or G. In the hnear elastic model, the key parameter is the ratio GJE, which represents the distance over which an elastic layer needs to be deformed before being fuUy detached from the hard surface. This model has been verified experimentally for elastic gels [57]. 

The critical stress predicted by Eq. (14) depends only on the elastic modulus and not at all on the strength of the elastomer. In agreement with this, cavitation stresses in bonded rubber blocks under tension (Figs. 8 and 9) [35], and near rigid inclusions, at points where a triaxial tension is set up (Figs. 

Figure 11.30a shows how competition between the various deformation mechanisms affects the yield stress. The solid line denotes Gic, the critical value of Ci at the onset of shear yield, whether before (the first straight section, calculated with Eq. 11.17) or after cavitation. The cavitation stress curve was calculated with Eq. 11.14 scaled accordingly to fit experimental data of the real PA6/rubber blend. Einally, the craze initiation stress curve, similar to those shown in Eig. 11.23, was calculated with Eq. 11.25. 

In the first stage the PB cylinders are strongly deformed till the cavitation stress of PB is reached. As a consequence, the PB cylinders cavitate resulting in the formation of voids. 

Unlike the shear yield process, crazing is an inherently non-isovolume event. Cavitation of the material requires a dilatational component of the stress tensor, such as occurs in triaxial stress systems that may be foimd in samples subjected to plane strain conditions. In addition, it is foimd in practice that there is a time dependency on the appearance of crazing. That is, there is generally a time delay between application of the load and the first visible appearance of a craze. A number of models have been proposed which require either a critical cavitation stress, a critical strain, or the presence of inherent microvoids, which can grow under the applied local stress or strain. 

Further, to check if the residual stress in MEH is due solely to heat treatment, thin sections of ME were also examined and relatively weak residual stresses/strains around microspheres were also found. An epoxy shrinks during cirring [55] and thus it is likely that the residual stresses were caused by shrinkage in this case, since it was not subjected to heat treatment. Consequently, it appeals that the toughness increase in both ME and MEH is due partially to the contribution of the compressive residual stresses even though, in the case of ME, its effect would be very weak. Cavitation occurred in the case of ME as discussed this indicates that the tensile cavitation stress is stronger than the compressive residual stress, which is Case II a < a (Inequality 3.16). 

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