Classic cracking mechanism

The classical HCK mechanism on bifunctional catalysts separates the metallic action from that of the acid by assigning the metallic function to the creation of an olefin from paraffin and the isomerization and cracking of the olefins to the acid function. Both reactions are occurring through carbenium ions [102],... 

In the cases of mesoporous silica, AMS and quartz chip, the 0.5 C3/C4 ratio being close to unity means that two reactions proceed with almost equal probability to each other. This is in accordance with the classical radical mechanism of alkane cracking supposing that the energy required to form tertiary radical is not so different from that required for secondary radical and that both radicals are cracked by P-scission mechanism shown below [13]. Thus, the results shown in Fig. 4 strongly suggest that isohexane is cracked via the radical mechanism on the mesoporous silica catalysts, or, in other words, MCM-41, both with and without aluminum impurity, and FSM-16 exhibit radical type catalytic function. 

Interestingly, the ductile-brittle transition observed for the MIM system provided an opportunity to assess the material fracture toughness, which was not possible using classical fracture mechanics tests due to the intrinsic brittleness of the MIM system. The measurement of the critical crack length, Lc, in the contact plane at the onset of brittle propagation allows estimation of a fracture toughness K C = a x+JnLc in the order of 0.85 MPa m1/2, i.e. much less than that of a poly(methylmethacrylate) homopolymer (1.20 MPa m1/2). 

The application of classical fracture mechanics in the case of pastes means that the strength is not controlled by total porosity but by a size of largest pores, playing the role of cracks . This idea was proposed by several authors, for example by Mindess [95] and Wittmarm [96]. 

A mechanism in which grains where the basal planes are parallel to the applied load serve as classic crack-bridges (not shown) [162],... 

Classical fracture mechanics presumes the presence of a single crack whose propagation proceeds in notch direction and thus can be described by only one parameter. This condition is not fulfilled in multidirectional laminates with their complex damage patterns. More recent fracture mechanic models adopt the concept of damage zones. 

Groth (1988) used a fracture mechanics approach without considering a preexisting crack. He formulated a fracture criterion based on an equivalent generalized stress intensity factor similar to that in classical fracture mechanics. Comparing it to a critical value, joint fi-acture may be predicted. However, the critical stress intensity factor needs first to be tuned with an experimental test which makes this approach questionable. 

The new approach to crack theory used in the book is intriguing in that it fails to lead to physical contradictions. Given a classical approach to the description of cracks in elastic bodies, the boundary conditions on crack faces are known to be considered as equations. In a number of specific cases there is no difflculty in finding solutions of such problems leading to physical contradictions. It is precisely these crack faces for such solutions that penetrate each other. Boundary conditions analysed in the book are given in the form of inequalities, and they are properly nonpenetration conditions of crack faces. The above implies that similar problems may be considered from the contact mechanics standpoint. 

Monel, the classic nickel-copper alloy with the metals in the ratio 2 1, is probably, after the stainless steels, the most commonly used alloy for chemical plant. It is easily worked and has good mechanical properties up to 500°C. It is more expensive than stainless steel but is not susceptible to stress-corrosion cracking in chloride solutions. Monel has good resistance to dilute mineral acids and can be used in reducing conditions, where the stainless steels would be unsuitable. It may be used for equipment handling, alkalies, organic acids and salts, and sea water. 

As shown, the ratio was very high on zeolite catalysts, while that on mesoporous silica was as low as those on AMS and quartz chip. The high ratio on zeolites can not be explained by classical mechanism of acid-catalyzed cracking supposing higher stability of tertiary carbenium ion and its cracking by P-scission, because this supposition predicts that the reaction (2) proceeds in preference to the reaction (1). Rather, a-scission of carbocation [12] may rationalize the higher C3/C4 ratio on zeolite catalysts. 

The diffusion, adsorption and chemical steps for the dehydrogenation and cracking reactions of light alkanes catalyzed by zeolites were studied using a combined classical mechanics (MM, MD and MC) / quantum mechanics approach. 

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. 

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