Ring cracks

The condensed cycloparaffin rings crack yielding n-butyl groups, containing, in part, the 13C label in a terminal CHg position (signal at 14.0). 

The kinetics of hydrocracking reactions has been studied with real feedstocks and apparent kinetic equations have been proposed. First-order kinetics with activation energy close to 50 kcal/gmol was derived for VGO. The reactions declines as metal removal > olefin saturation > sulfur removal > nitrogen removal > saturation of rings > cracking of naphthenes > cracking of paraffins [102],... 

The main undesired reactions, which occur essentially with normal TDP, are toluene hydrodealkylation, toluene-xylenes transalkylation and ring cracking. 

The desired reactions are shown in Figure 9.9. Deethylation of ethyl+ groups is a desired reaction because these ethyl+aromatics cannot lead to xylenes via transalkylation. The side reactions to avoid are demethylation, xylenes transalkylation with other aromatics and ring cracking. 

Fig. 17 Contact mechanics analysis of Herztian cracks within brittle materials.a Schematic description of a Hertzian cone crack induced under normal indentation by a rigid sphere, b Reduced plot of JC-field as function of cone crack length and for increasing loads pf < p// < pm during sphere-on-flat normal indentation of brittle materials. Arrowed segments denote stage of stable ring crack extension from Cf to cc (initiation), then unstable to ci at P = P,n (cone-crack pop-in) (From [67]). Branches (1) and (3) correspond to unstable crack propagation (dK/dc > 0), branches (2) and (4) to stable crack propagation (dK/dc < 0)...

The mechanism of these reactions must be obtained by reversing the steps of the ring-cracking mechanism (principle of microscopic reversibility) therefore, in the cases of limonene, or vinylcyclohexene, a rather unstable primary carbonium ion should form, and react with the olefinic double bond (Fig. 16a). Another possibility is offered by the addition of a proton to the cyclic double bond (Fig. 16b). 

All fracture surfaces were analysed by ffactographic means in order to identify fracture origins. In any case the fracture origins are at or very close to the surface. In the case of set C, the surface flaws identified by the dye penetrant and positioned in the highest loaded area of the specimens were fracture origins in every case. An example is shown in Fig. 6.b. The fracture origin is a Hertzian contact crack (a part of a ring crack), which had previously been detected before fracture (Fig. 6.a). 

I. Finnic and S. Vaidyanathan, Initiation and propagation of hertzian ring cracks. In Fracture Mechanics of Ceramics, eds., R. C. Bradt, D. P. FI. Hasselman, and F. F. Lange, New York, Plenum Press, 1974, p. 231. 

If the stresses are high enough, cracking occurs at blunt indenters but, in this case, the crack is initially circular (ring crack) but then extends into a cone geometry (Fig. 8.89). Experimentally, it is found that the load required to initiate a cone crack is given by... 

The same reasoning applies to an elastic surface coating which is indented by a rigid punch, as shown in Fig. 14.16(a). In this case the crack is caused by the squeezing of the film from the gap between the punch and the substrate. This causes a ring crack to be initiated just outside the punch contact region, as shown by some early experiments in 1974. ... 

Usually, in such indentation experiments, plastic flow also arises in the substrate under the film as shown in Fig. 14.20(b). This has been analyzed by Swain and his colleagues." As the indenter was pressed into the surface, ring cracks were observed just outside the indenter contact region. Sometimes radial cracks were also seen in the film." Subsequently, the substrate was pushed down... 

Figure 12.5 Contact damage (cracks) in the surface of ceramics, (a, b) Cracks caused by a blunt and (c, d) cracks caused by a sharp indenter. (a) Hertzian ring crack in silicon carbide (b) Crack caused in operation by the...

Fig. 1.69 Summary of outer ring crack diameters observed on ZrB2/SiC and HfB2/SiC...

Fig. 1.70 Optical microscope image of the ring crack generated by the 316 m s impact of a 762 pm diameter stainless steel ball on a HfB2/SiC surface [37], With kind permission of Springer...

The first of these considers elastic interactions only between the target and the streams of particles which produce ring cracks on the surface of the target. The ring cracks eventually intersect, and material is removed. This model does most closely suit the impingement of low velocity spherical particles. Clearly the Brinell static indentation test is most closely similar because overloaded Brinell spheres produce this type of damage (see 5.2.2). 

Following the above analytical conclusions, because the maximum tensile stress occurs at the periphery of the indentation, circle BB, it would be expected that at some critical load a crack would nucleate and propagate around the circumference BB. On a surface of glass or another amorphous material a ring crack is observed, but on highly anisotropic crystalline ceramics a less well traced crack is produced as the ring has a definite... 

When the indenter is more compliant, the maximum stress in the sample is increased due to the frictional forces but remains at the edge of the contact circle. Smaller diameter secondary cracks are sometimes produced as the indenter ball is unloaded in cases where Young s modulus of the ball exceeds that of the surface under test. If, as suggested above, friction is an important parameter, then on unloading there will be a reversal in the direction of frictional traction at the edge of the contact circle which will produce an increase in stress nearer to the contact radius which can, if there is a critical sized surface flaw in the vicinity, give rise to the secondary ring crack. 

Development of this type of crack is discussed in terms of the dimensions c/a<, as defined in Figure 5.10. The crack is known as a shallow ring crack for c/a < 10 , and as a cone crack within the ceramic when c/a > 10 . A good analytical curve has been developed by Mouginot and Mangis by plotting the variables G/2y against c/a where G is the... 

Equation (5.34) gives G in terms of cone edge length c and ring crack start radius rg. It can be re-expressed in terms of cone base diameter s... 

The Hertz method of determining Kc involves the use of an optically flat surface and a blunt— i.e., spherical— indenter. The sphere is pressed with a series of loads P until a critical load P ris found that gives a 50% chance of Hertz ring crack formation. In practice this is found by plotting the fracture probability against applied load for any given indenter radius a typical plot would look like Figure 5.18. 

---