Matrix cracking basic mechanics

The initial intent of this review is to address the mechanisms of stress redistribution upon monotonic and cyclic loading, as well as the mechanics needed to characterize the notch sensitivity.5 13 This assessment is conducted primarily for composites with 2-D reinforcements. The basic phenomena that give rise to inelastic strains are matrix cracks and fiber failures subject to interfaces that debond and slide (Fig. 1.1).14-16 These phenomena identify the essential constituent properties, which have the typical values indicated in Table 1.1. 

For numerical investigations of stress localizations in laminates, the discretizational effort can be reduced significantly if only the boundary needs to be discretized, as it is for e -ample the case in the classical boundary element method (BEM). But in this method a fundamental solution is needed which is in many cases difficult to achieve or even unknown. The Boundary Finite Element Method (BFEM) to be presented here does not require such a fundamental solution, because the element formulation is based on the finite element method (FEM), Thus the BFEM can be characterized to be a finite element based boundary discretization method. This method was originally developed from Wolf and Song [10] under the name Consistent Finite Element Cell Method for time-dependent problems in soil-mechanics. The basic assumption of this method is that a stiffness matrix describing the force-displacement relation at discrete degrees of freedom at the boundary of the continuum is scalable with respect to one point in three-dimensional space, the so-called similarity center, if similar contours within the continuum are considered. In contrast to this, the current work deals with the case of equivalent cross-sectional properties, i.e., that cross-sections parallel to the boundary can be described by the same stiffness matrix, which is the appropriate formulation for the case of the free-edge effect and the matrix crack problem. The boundary stiffness matrix results from a Matrix-Riccati equation. The field quantities inside of the continuum can be calculated from an ordinary differential equation. 

Basic Catalysis. The catalytic properties of alkali zeolites free of acidic sites have been investigated for the cracking of hexanes (25, 26). At 500 C K-Y zeolite cracks easily n-hexane and its isomers resulting in product distributions markedly different from those obtained over acidic zeolites or even by thermal cracking (pyrolysis). Free radical-type mechanism predominates on the zeolite surface. The relative rates of H atom abstraction (bimolecular) and B-scission (unimolecular) are greatly affected by the zeolite matrix. Zeolites also concentrate hydrocarbon reactants within the crystal, which enhances the rate of bimolecular reaction step. Comparison with silicalite (Al-free ZSM-5 zeolite) and quartz chips has been done in order to characterize the zeolitic effect. Silicalite behaves as inert quartz chips with no effect on the rate of H-abstraction step,... 

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