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By G. Fowles, G. Cassiday

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J VECTORS OF A SEMI-ELLIPTICAL SURFACE CRACK IN A PRESSURE VESSEL. 2 shows a semi-elliptical surface crack in a pressure vessel. The crack exists on the inner surface of the vessel. 3 shows the dimensions and coordinates of the pressure vessel. As finite element analyses are carried out by using cylindrical coordinates, the J r and Jz components are evaluated. 4. 9). 33, is the shape recommended by ASME. For each shape of crack, two analyses are carried out: one in which the crack surfaces are unpressurized and the other in which they are pressurized.

4. Analytical investigations strongly suggest that J and COD can be em- ployed as characterizing parameters for crack initiation and growth. The nu- merical studies based on an incremental theory of plasticity revealed that J is path independent everywhere except very near the crack tip for some amount of crack growth. g. compact specimen, the path independence of J is observed for growth up to 6% of the original uncracked ligament. It is noted that the slope of the J-resistance curve (dJ~da) is approximately constant for a relatively short interval of crack extension, while the slope of the COD-resistance curve (do~da, also called the average or nominal crack opening angle) and the local crack opening angle (COA) remain practically constant over the range of crack extension explored in our experimental and analytical investigations.

J 'l,. 'l,. 'l,. (16) A r+rs-rendr+rs We also consider the case where the area of the fracture process region is diminishing and the contour integral along r reduces to Jk =J{Wenk-Ti(oui/oXk)}dr+JJ{crij( r+r 8 en d is equal to zero. Equation (16) aEij/oXk)+(PUi-Fi)(oui/aXk)}dA (17) A We further assume: the fracture region is ignored; the crack extends in 27 the direction parallel to the crack surfaces; the stress-strain relation of the material is elastic; and body forces, inertia of the material, and crack surface tractions are absent.

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Analytical Mechanics [SOLUTIONS MANUAL] by G. Fowles, G. Cassiday

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