Bifurcation stability of spherical shells under dispersed cracking in shear materials
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 78, Issue 2
Abstract
The present paper deals with the method for solution of the bifurcation stability of thin-walled structural elements of damage materials under single and cyclic loading. This method is developed by using a structural-probabilistic approach to modeling joint processes of cracking and deformation of materials. The phenomenon of the bifurcation stability in elastic part of deformation of thin-walled structures of damaging materials under cyclic loading, the values of which are smaller than corresponding static critical efforts, are considered. The main purpose of solving such problems is to determine of the limiting number of a given load, at which the structure loses stability. It should be mentioned, that the possibility of loss stability of thin-walled structures at loads less than the upper critical is related to the type of failure of the material, such as destruction by rupture or destruction by shear. In the case of destruction by rupture, when microcracks are parallel to the direction of compressive stress, this phenomenon does not take place, because in this type of damage under repeated compression of the same load a material behaves as a continuous medium. The density of microcracks is not increased. This type of stability loss is possible for thin-walled structures made of materials which are damaged by shear, when microcracks are formed on the sloping planes to the direction of the load. Under such type of microfractures, the effective cross-sectional area decreases. It leads to increase of true tangential stresses in the material under constant conditional stresses of repetitive loading. The proposed method consists of the following: construction of the constitutive equations for the damaged material by using the Eshelbi method for determining the effective elastic properties of the damaged medium; the model of microdamages accumulation basing on the Treska Saint-Venant, fracture criterion which is formulated in full true tangential stresses in random sections of structural elements and two-parameter power law distribution of limit values of shear microstrength of structural elements and procedures for solving problems bifurcation stability of spherical shells. It should be noted, that the true stresses differ from the conditional in that the former refer to the areas of the damaged medium whereas the latter to the areas of the continuous medium. On an example of uniformly compressed spherical shell it is shown that the structire can lose stability under loads smaller than the upper critical. From the expression for the critical stress it follows that the ambiguity of critical loads depends on the density of the accumulated damages in material in thin-walled structures, which is associated with the nature of the load. This phenomenon could be one of the possible reason of dispersion in the experimental data and the discrepancy between theoretical and experimental results. For steel spherical shell 15X2MF numerical results are obtained.
Authors and Affiliations
Dmytro Babich, Tetyana Dorodnykh
Keywords
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