Shape discontinuity

Figure 14.13 Geometry of the plastic hinge that forms due to the shape discontinuity and produces overcurvature...

The Zoo norm graphed over one span is symmetric, and it looks as though the maximum is at the central point of a span. In fact it is not quite. abs(f(x)) is itself a function, with V-shaped discontinuities of slope at the roots of f(x). 

SiC whiskers were initially developed in the early 1960s. However, their use was originally to be applied to the reinforcement of metal matrices, such as aluminum. These metal matrix composites were only a small commercial success, mainly because of the high cost of the whiskers. The first application of whisker reinforcement to ceramics, and in particular alumina, did not occur until the 1980 s. For the purposes of this article, SiC whiskers will be defined to be acicular or needle-like shaped, discontinuous, nearly single crystals. 

Some of the problems often encountered during ultrasonic inspection of plane specimens are also found on cylindrical specimens. For example, problems associated with the directional characteristic of the ultrasonic transducer. Furthermore, the discontinuity influences the shape and propagation direction of a reflected pulse, causing wave mode transformation. In addition, the specimen influences the shape and amplitude of the reflected pulse by sound absorption. 

Secondly, the linearized inverse problem is, as well as known, ill-posed because it involves the solution of a Fredholm integral equation of the first kind. The solution must be regularized to yield a stable and physically plausible solution. In this apphcation, the classical smoothness constraint on the solution [8], does not allow to recover the discontinuities of the original object function. In our case, we have considered notches at the smface of the half-space conductive media. So, notche shapes involve abrupt contours. This strong local correlation between pixels in each layer of the half conductive media suggests to represent the contrast function (the object function) by a piecewise continuous function. According to previous works that we have aheady presented [14], we 2584... 

Electromagnetic Evaluation of Material Discontinuities Shape and Severity. 

This work presents the theoretieal results and their experimental verifications concerning two possible methods for predicting the material discontinuities shape and severity. The methods are developed for the case of the eddy current transducer with orthogonal coils, for two situations for long crack-tjfpe discontinuities, a metod based on the geometrical diffraction has been used, while in the ease of short discontinuities the holographic method is prefered. 

The purpose of the nondestructive control consists in detecting local modifications of the material parameters which, by their presence can endanger the quality of the half-finished or finished products. The electromagnetic nondestructive control permits to render evident surface and subsurface discontinuities in the electroconductive material under test. The present tendency of this control is to pass from a qualitative evaluation (the presence or absence of the material discontinuities which give at the output of the control equipment a signal higher or at least equal to that coming from a standard discontinuity whose shape and severity has been prescribed by the product standards) to a quantitative one, which enables to locate as exactly as possible the discontinuity and to make predictions over its shape and severity. 

Let us consider a conductive material with the conductivity a, in which have been machined relatively small discontinuities shaped like dead hole. The surface has been inspected with a transducer with orthogonal coils connected in an impedance bridge [11]. 

Accordingly, due to the presence of the maximum for z =d -h, the holographic procedure enables to determine not only shape and location of small discontinuities, but also their subsurface depth. 

This work presents two methods to determine the shape and severity of material discontinuities detected by means of the eddy current nondestructive control. 

The curious shape of the computed parts of the curves suggests that there is, in each case, a discontinuity of slope. However, examination of the results shows that there is, in fact, a switch in the dominant eigenvalue as the Lewis number changes. Above a certain value of the Lewis number this is real and moves to the right as decreases. But eventually it crosses with a pair of complex eigenvalues moving to the left and these, which become the dominant eigenvalues for smaller values of, cause... 

Nondestmctive evaluation, also termed nondestmctive testing or nondestmctive inspection, is extensively used in weld testing (14). Nondestmctive tests do no impair the serviceabiUty of the material or component under stress. The most widely used tests for evaluation of welds are Hquid penetrant, magnetic particle, ultrasonics, and radiography. Acoustic-emission tests are increasingly used. Nondestmctive tests detect and characterize, in terms of size, shape, and location, the various types of weld discontinuities that can occur. 

The aspect ratio E/IE refers to the shape of the particles in the discontinuous phase. It is the average dimension of this phase parallel to the plane of the film E divided by the average dimension perpendicular to the film W. Plates in the plane of the film would have a high aspect ratio. Spheres or cubes would have an aspect ratio equal to 1. 

Fibrous Composites. These composites consist of fibers in a matrix. The fibers may be short or discontinuous and randomly arranged continuous filaments arranged parallel to each other in the form of woven rovings (coUections of bundles of continuous filaments) or braided (8). In the case of chopped strand mat the random arrangement is planar. In whisker (needle-shaped crystals or filaments of carbon and ceramics) reinforced materials the arrangement is usually three-dimensional and the resulting composites are macroscopically homogeneous. 

Liquids Slurries Pastes and sludges Free-flowing powders Granular, crystalbne, or fibrous solids Large sobds, special forms and shapes Continuous sheets Discontinuous sheets... 

No industrially significant reaction has 3 > 0,3 (or with y = 20, and D/a = 1, 5 > 5) and only above this value are the interesting S-shaped curves possible. Of the three values of T, the effectiveness at one value of the Thiele modulus < >, the middle one is an artificial, non-existent solution. The two other values for T show the possibility of discontinuity inside the pellet. While this is possible, it is very unlikely to occur. 

CP-1 was assembled in an approximately spherical shape with the purest graphite in the center. About 6 tons of luanium metal fuel was used, in addition to approximately 40.5 tons of uranium oxide fuel. The lowest point of the reactor rested on the floor and the periphery was supported on a wooden structure. The whole pile was surrounded by a tent of mbberized balloon fabric so that neutron absorbing air could be evacuated. About 75 layers of 10.48-cm (4.125-in.) graphite bricks would have been required to complete the 790-cm diameter sphere. However, criticality was achieved at layer 56 without the need to evacuate the air, and assembly was discontinued at layer 57. The core then had an ellipsoidal cross section, with a polar radius of 209 cm and an equatorial radius of309 cm [20]. CP-1 was operated at low power (0.5 W) for several days. Fortuitously, it was found that the nuclear chain reaction could be controlled with cadmium strips which were inserted into the reactor to absorb neutrons and hence reduce the value of k to considerably less than 1. The pile was then disassembled and rebuilt at what is now the site of Argonne National Laboratory, U.S.A, with a concrete biological shield. Designated CP-2, the pile eventually reached a power level of 100 kW [22]. 

Fig. 17 shows the adsorption isotherms of all (undimerized and dimerized) particles. Except for a very fast increase of adsorption connected with filling of the first adlayer, the adsorption isotherm for the system A3 is quite smooth. The step at p/k T 0.28 corresponds to building up of the multilayer structure. The most significant change in the shape of the adsorption isotherm for the system 10, in comparison with the system A3, is the presence of a jump discontinuity at p/k T = 0.0099. Inspection of the density profiles attributes this jump to the prewetting transition in the... 

Gels of various particle sizes can be made by varying the stirring rate, the shape of the stir blades used, the concentration of the suspending agents, and, to a lesser degree, the ratio of the continuous water phase to the discontinuous organic phase. 

Decomposition rates of (Ni,Co) mellitates [1110] increase with increase in nickel content. The a—time curves for the pure components and the mixed mellitates were deceleratory throughout and there was no discontinuity in shape with changes in composition. Rates of decomposition of the solid solutions were appreciably greater than those expected from the decomposition of the individual components present (Fig. 19). The values of E determined for the initial stages of the decomposition of mixtures were close to that found for the nickel salt (184 kJ mole 1) and in the latter stages tended to increase towards that for cobalt mellitate (251 kJ mole-1). Values of A showed a systematic decrease with increase in cobalt content. 

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