Abstract
A mathematical model is developed for the stress state of a casting when a cavity is formed by a cylindrical rod. Formulas for the radial and azimuthal stresses and also the contact-force distribution permit prediction of the forces between the casting and the rod, with different rigidities expressed by the longitudinal elastic modulus. The stress is found to be greatest in layers of the casting in contact with the rod surface. The dependence of the radial and azimuthal stresses in the casting and the distributed contact force on various factors—the temperature gradient, the rigidity of the casting and the sand–clay casting mixture, and the geometric parameters of the casting (the wall thickness and external radius)—is considered. The influence of these factors on the stress–strain state of the casting wall—specifically, the equivalent stress obtained by means of the second strength hypothesis—is assessed.
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