Rubber particles stress concentration

A novel theory has been developed which directly relates the abrasion of rubber by a knife edge to its crack-growth characteristics. The approach is based on fracture mechanics which has been successfully used to interpret other failure processes in rubbers. The theory treats the removal of the rubber when a steady state has been reached in the development of the abrasion pattern in the rubber surface. It is suggested that crack growth occurs into the rubber from stress concentrations in the abrasion pattern. An important point is that once a steady state is established the detailed way in which the particles of rubber are finally detached is unimportant. The crack growth behaviour of the rubber is measured independently using established techniques. 

Craze Nucleation Theory. In various ways it has been suggested that the role of the rubber particles is that of stress concentrators. Thus, Schmitt and Keskkula (33) believe that the multiplicity of stress concentrators (i.e., a multitude of weak points) produce a large number of small cracks rather than a few large ones more energy is needed to propagate a large number of small cracks, and stress fields of the various... 

Further, the Goodier equations predict that hard particles and voids produce higher stress concentrations (i.e., stronger craze nucleation) than rubbers, and thus hard particles and voids should toughen even better than rubbers if nucleation were the operative mechanism. This is not observed experimentally. The nucleation theory is thus seen to have substantial drawbacks. 

Rubber Content. In the theories of toughening where the role of rubber particles is (a) to absorb energy directly or (b) to induce matrix yielding through stress concentration or hydrostatic tension effects, energy absorption should increase linearly with the number of rubber particles (proportional to rubber content if particle size is invariant). On the other hand, if dynamic craze/crack branching is the operative mechanism, evidence of an exponential law may be expected. The exponential form of the law may be derived as follows. 

For a single rubber particle in an infinite uniaxial tensile stress field, it was demonstrated that there is a stress concentration effect with a factor around 2, at the particle equator (Fig. 13.1). 

Figure 13.1 Stress concentration around a single rubber particle.

Figure 13.9 Sequence of events in a croid formation, (a) Initial state at the crack tip. (b) Cavitation ofthe rubber particles dueto loading head of the crack tip. (c) Cavitation of rubber particles near the already cavitated particles due to stress-concentration effect. The croid is forming, (d) Croids are propagating ahead ofthe crack and inside the craze-like damaged zone many shear bands develop between cavitated rubber particles. (Sue, 1992 with kind permission from Kluwer Academic Publisher.)...

A good dispersion of rubber particles appears to favor the nucleation and growth of a large number of thick crazes uniformly distributed in the polystyrene matrix. This is believed to be an efficient source of energy absorption for the material under mechanical loading. The concepts of stress field overlap and critical volume of stress concentration zone for craze initiation were introduced to explain the observed mechanical behavior of HIPS. 

An impact modifier is a rubber phase dispersed in particulate form throughout the matrix of a polymer solid. Unlike plasticizers, the rubber particles retain their intrinsic properties as a separate phase. The glass transition temperature of the parent matrix is not lowered by the addition of an impact modifier. The rubber particles do two things to the parent matrix phase (2,3,4) they act as stress concentrators (i.e., a large strain will start in the matrix near the interface) and they enhance the multi-axiality in stress. As multiaxial tensile strength near the interface further enhances dilatation, which shortens the mechanical relaxation time, the otherwise brittle polymer solid of the matrix will undergo plastic deformation in the vicinities of the rubber particles. 

ABS and HIPS. The yield stress vs. W/t curves of ABS and HIPS are very similar. They are somewhat surprising because the yield stresses reach their respective maximum values near the W/t (or W/b) where plane strain predominates. This behavior is not predicted by either the von Mises-type or the Tresca-type yield criteria. This also appears to be typical of grafted-rubber reinforced polymer systems. A plausible explanation is that the rubber particles have created stress concentrations and constraints in such a way that even in very narrow specimens plane strain (or some stress state approaching it) already exists around these particles. Consequently, when plane strain is imposed on the specimen as a whole, these local stress state are not significantly affected. This may account for the similarity in the appearance of fracture surface electron micrographs (Figures 13a, 13b, 14a, and 14b), but the yield stress variation is still unexplained. 

Stress concentrations around isolated spherical inclusions in an isotropic matrix have been calculated by Goodier (10), but apparently there is no satisfactory theory for the problem of concentrated dispersions. A simple approach would be to use Goodier s equation and to allow for the effect of the high concentration of rubber particles simply by adding the calculated stress concentrations that arise from neighboring particles. 

At quasi-static rates of loading the effect of the rubber particle is twofold. First, the stress concentrations near the rubber particles induce... 

At the same stress amplitude, rubber modified polymers fail sooner in fatigue than do the unmodified polymers even though they have superior resistance to fatigue crack propagation. This is a result of much earlier initiation of crazing, localized plastic deformation, and subsequent crack development due to the stress concentrating effect of the dispersed second phase particles. 

Thus, more likely, cavitation of the rubber particles has a limited effect upon yielding of these materials. Yielding may occur due to the stress concentration around the particles since the magnitude of this mechanism is higher when the density and the fineness of the particles are also high. 

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