الفهرس 
الملخص العربي
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Abstract
In this work the olastic instability condition of a shell of evolution with a free outer surface and deformed by internal forces has been analysed. An expression for each plastic limit strain as a function of the anisotropy parameters, the strain hardening index and the principal stress ration is obtained. The theory of plastic anisotropy developed by Hill (1949) is used. It is shown that any case of anisotropy which may be ordinarily exoressed in normal anisotropy parameters, having R-vales lying between I and 2, can be expressed in terms of assumed values of planar anisotropy parameters. Using the obtained were expressions. predicted forming limit curves were constructed and the combined effect of the stress ratio and anisotropy or limit strains is studied. A comparison between the effect of anisotropy considerd either as normal anisotropy or planar anisotropy is also obtained. The effect of loading a sheet of metal, suffering planar anisotropy, in biaxial tension such that the maximum principal stress a, is applied at the direction of maximum anisotropy or at the direction normal to it. is also studied. A hydraulic bulging test-rig is designed and constructed by which snecimens of different anisotropic charactaristics were bulged up to the beginning of instability. The specimens were made of commercial steel produced in two different steel-factories and were subjected to two different annealing temperatures. Straind at the domes of the bulged specimens are measured using a specially designed and constructed x-y tracer.
Comparison between own predicted strain limit curves and experimental limit strains has given a fair agreement. It also shows the importance of taking planar anisotropy and directions of biaxial-tension loading into account for greater strain limits.