There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

J. Appl. Cryst.の発刊に際して

Polymer/layered silicate nanocomposites: a review from preparation to processing

Publisher Summary This chapter describes the mixed mode cracking in layered materials. There is ample experimental evidence that cracks in brittle, isotropic, homogeneous materials propagate such that pure mode I conditions are maintained at the crack tip. An unloaded crack subsequently subject to a combination of modes I and II will initiate growth by kinking in such a direction that the advancing tip is in mode I. The chapter also elaborates some of the basic results on the characterization of crack tip fields and on the specification of interface toughness. The competition between crack advance within the interface and kinking out of the interface depends on the relative toughness of the interface to that of the adjoining material. The interface stress intensity factors play precisely the same role as their counterparts in elastic fracture mechanics for homogeneous, isotropic solids. When an interface between a bimaterial system is actually a very thin layer of a third phase, the details of the cracking morphology in the thin interface layer can also play a role in determining the mixed mode toughness. The elasticity solutions for cracks in multilayers are also elaborated.

Mixed mode cracking in layered materials

There have been a number of review papers on layered silicate and carbon nanotube reinforced polymer nanocomposites, in which the fillers have high aspect ratios. Particulate–polymer nanocomposites containing fillers with small aspect ratios are also an important class of polymer composites. However, they have been apparently overlooked. Thus, in this paper, detailed discussions on the effects of particle size, particle/matrix interface adhesion and particle loading on the stiffness, strength and toughness of such particulate–polymer composites are reviewed. To develop high performance particulate composites, it is necessary to have some basic understanding of the stiffening, strengthening and toughening mechanisms of these composites. A critical evaluation of published experimental results in comparison with theoretical models is given.

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Klaus Friedrich

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