Toughening theories

Recognizing that the extensive art in rubber toughening teaches that only adherent rubbers toughen (nonadherent rubber particles act like voids), we nevertheless tested the above conclusions of the dilatation theory by attempting to toughen styrene acrylonitrile copolymer (S/AN) with dispersions of voids and with dispersions of hard particles. 

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. 

When fracture occurs out of the linear domain (fracture with yielding), e.g., for highly toughened thermosets or at high temperatures, it is still possible to apply fracture mechanics, with the energetic theory. For instance, the J-integral may be used for bulk materials (Williams, 1984) or Essential Work for Fracture for thin films (Mai and Powell, 1991 Liu and Nairn, 1998). 

There are some additional applications of the theory which are presently under investigation. These are the effects of drawing on fibers for which the three-dimensional theory with transverse symmetry is applicable and the toughening mechanism in high impact polystyrene for which the flaw spectrum may be viewed as caused by the size, orientation, and spacing distributions of the rubber particles. 

Bragaw, C. C., The Theory of Rubber Toughening of Polymers, Advan. 

B. Budiansky, J. W. Hutchinson and J. C. Lambropoulus, Continuum theory of dilatant transformation toughening in ceramics, Int. J. Solids Struct, 19 (1983) 337-55. 

Thus, while it is clear that the elastic modulus of a material may not affect its crack resistance as indicated in Equation (16.1), a change in elastic modulus at an interface toughens the material by a factor of( 2/ i)- This theory was used to calculate the full lines for comparison with experiment in Fig. 16.7. 

Many of the entries in this book dealing with the science of a(fliesion and Theories of adhesion are relevant to composition materials in general. There are a number of articles that discuss specific aspects of composite materials that come within the scope of this book. Toughened adhesives, particnlarly Epoxide adhesives and Toughened acryiics, consist of polymers with a rubbery phase dispersed as small spheres within a more glassy matrix. Appropriate adhesion between the phases is crucial for effective toughening. 

Several theories have been proposed to explain the toughening effect of rubber particles on the brittle thermoset matrix. These are based on the fractographic features and fracture properties of rubber-toughened thermoset networks. Garg and Mai [113] proposed 13 mechanisms to explain the impact behaviour of rubber-toughened epoxy... 

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