Crack magnitude

Using Equ. (3.1), we can now compute the optimum frequency for cracks in various depths (see Fig. 3.2). For comparison, the optimum excitation frequency for a planar wave or a sheet inducer (300 x 160 mm) is also displayed. One finds that for a planar excitation source, a much lower excitation frequency is required, which causes a reducfion in the response signal of the crack of up to an order of magnitude in case of a small circular coil. 

Therefore, the magnitude of the stress at small distances from the crack tip is a function of the crack length, a, and the remotely appHed stress. O. Close to the crack tip (r ft) the stress can be scaled usiag a parameter called the stress intensity factor, K (9—11) ... 

The MTO process employs a turbulent fluid-bed reactor system and typical conversions exceed 99.9%. The coked catalyst is continuously withdrawn from the reactor and burned in a regenerator. Coke yield and catalyst circulation are an order of magnitude lower than in fluid catalytic cracking (FCC). The MTO process was first scaled up in a 0.64 m /d (4 bbl/d) pilot plant and a successfiil 15.9 m /d (100 bbl/d) demonstration plant was operated in Germany with U.S. and German government support. 

If no laminae have failed, the load must be determined at which the first lamina fails (so-called first-ply failure), that is, violates the lamina failure criterion. In the process of this determination, the laminae stresses must be found as a function of the unknown magnitude of loads first in the laminate coordinates and then in the principal material directions. The proportions of load (i.e., the ratios of to Ny, to My,/ etc.) are, of course, specified at the beginning of the analysik The loaa parameter is increased until some individual lamina fails. The properties, of the failed lamina are then degraded in one of two ways (1) totally to zero if the fibers in the lamina fail or (2) to fiber-direction properties if the failure is by cracking parallel to the fibers (matrix failure). Actually, because of the matrix manipulations involved in the analysis, the failed lamina properties must not be zero, but rather effectively zero values in order to avoid a singular matrix that could not be inverted in the structural analysis problem. The laminate strains are calculated from the known load and the stiffnesses prior to failure of a lamina. The laminate deformations just after failure of a lamina are discussed later. 

The occurrence of stress-corrosion cracking in the martensitic steels is very sensitive to the magnitude of the applied stress. For instance, a 13% chromium martensitic steel tested in boiling 35% magnesium chloride solution (125.5°C) indicated times to failure that decreased abruptly from more than 25(X)h to less than 0.1 h as the applied stress was increased from 620 MPa to about 650 MPa (Fig. 8.25). However, the effects of stress on time to failure are not always so dramatic. For instance, in the same set of experiments times to failure for a 17Cr-2Ni martensitic steel gradually decreased from more than 800 h to about 8 h as the applied stress was increased from 500 MPa to 800 MPa. 

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