Расчет оптимальной толщины трубы, подверженной наружной коррозии под напряжением

Many structures are under simultaneous action of mechanical stresses and chemically active agents. Such conditions can cause a process of so-called mechanochemical corrosion, which rate linearly depends on the principal stresses. In this paper we consider the case of external uniform corrosion. Designing structures without taking into account mechanochemical corrosion can lead to their premature destruction, as well as the assignment of a large margin for the thickness of structures - to wasteful material consumption and weighting of structures. Therefore, from the point of view of safety and economics, it is important to be able to accurately calculate the initial dimensions of the structure necessary to ensure the required service life. The presented article is devoted to the calculation of the optimum thickness of a linearly elastic cylindrical tube under external and internal pressure. The dependence of the initial dimensions of the structure on the required service life is found, which allows finding the optimum dimensions of the product, and this subsequently ensures the prevention of unfavorable outcomes during its exploitation. The graphs illustrating these results are constructed, and also the influence of external and internal pressure on the durability of the structures under consideration is studied. The strengthening effect of external pressure is proved at a fixed internal pressure. In the present paper the problem is reduced to an ordinary differential equation with respect to the required radius of the tube. The solution is constructed for such proportions of pipe dimensions and external and internal pressures, at which the maximum voltage in terms of absolute magnitude is the circumferential stress.