Rigid inclusions

Fig. 7.18. Source of shrinkage stresses (a) rigid inclusion embedded in a matrix (b) resin pockets surrounded by fibers in hexagonal and square arrays. After Hull (1981).

Daniel, I.M. and Durelli (1962). Shrinkage stresses around rigid inclusions. Exper. Mech. 2, 240-255. 

When the material is composed of a soft phase with rigid inclusions, the strain rate is written in the form ... 

Yonn, C.K., and Chen, I.W., Superplastic flow of two-phase ceramics containing rigid inclusions-zirconia/mullite composites , J. Am. Ceram. Soc., 1990, 73, 1555—... 

C. K. Yoon and I.-W. Chen, Superplastic Flow of Two-Phase Ceramics Containing Rigid Inclusions-Zirconia/Mullite Composites, J. Am. Ceram. Soc., 73[6], 1555-1565 (1990). 

When a strain is applied to a soft elastic material containing discrete rigid inclusions adhering to the matrix, the average local strain in the matrix must exceed the macroscopic applied strain. Mullins and Tobin... 

Still completely blocked, but para chlorination has the same rate as it has in free solution. With 10 mM j5-cyclodextrin anisole is only 59% bound, not 72%, and the para/ortho chlorination ratio becomes only 3.8 1, not 21.6 1 as with a-cyclodextrin. Thus, the catalysis of para chlorination in the a-cyclodextrin complex is promoted by rigid inclusion of the anisole into a tight-fitting cavity. 

FIGURE 10.10 Cavitation near a rigid inclusion (schematic). 

FIGURE 10.11 Critical applied stress, Oc, for cavitation near rigid inclusions (see Figure 10.10) versus Young s modulus, E, of the elastomer. (From Oberth and Bruenner (1965).)... 

Cavitation near small rigid inclusions is more difficult to induce (Gent and Park, 1984), probably because the volume of rubber subjected to a critical triaxial tension is too small to contain relatively large precursor voids. And larger stresses are necessary to expand small voids less than about 0.5 p,m in diameter. 

Holes and pores are extreme examples of a mismatch in elastic behavior. In many cases one is concerned with inclusions, and solutions for ellipsoidal inclusions are available. For the case of spherical inclusions, it is useful to classify inclusions into those that are more rigid or more compliant than the matrix. For more-compliant spherical inclusions, the stress distribution is similar to that of a spherical pore but the maximum stress is less extreme. For more-rigid inclusions, the maximum tensile stress moves to the poles of the inclusion (0=0 or tt). 

Bordia RK, Scherer GW (1988) On contrained sintoing, 3. Rigid inclusions. Acta Metall 36 2411-2416... 

A. R. Boccaccini andE. A. Olevsky, Effect of Rigid Inclusions on Sintering Anisotropy of Composite Glass Powder Compacts,/. Mar. Proc. Technol. 96,92-101 (1999). 

In Sections 12.1 and 12.2 several important aspects of matrix and interface behavior, such as the effects of an inclusion on modulus and the effect of interfacial adhesion, were described. It is also appropriate to discuss specific molecular effects of rigid inclusions (particulate or fibrous) on a matrix, in order to demonstrate continuity between all types of reinforcements. Effects of environmental exposure on composite behavior are also briefly considered. 

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. 

Yolcu C, Desemo M (2012) Membrane-mediated interactions between rigid inclusions an effective field theory. Phys Rev E 86 031906... 

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