Thesis is devoted to the improvement of the analytical-computational approach to the predicting of real stresses and loads at the moment of the uniform plastic stability loss. Accurate prediction of ultimate strength requires taking into account the actual dimensions of the loaded element and constructing a true deformation curve. Calculation of ultimate true stresses at the moment of the uniform plastic stability loss under uniaxial tension, based on Swift-Marchiniak criterion and the analytical relationship σ ̃=dσ ̃/dε between true stresses and tangent modulus in true stresses, known as a Considere scheme. There are also known attempts to use the Consider scheme for predicting the ultimate pressure in thin-walled pipes using the ratio σ ̃=□(1/2) dσ ̃/dε that contains a correction factor ½ of the tangent modulus. The task that was posed in this work was to develop a methodology for determining the limiting values of true stresses and loads in metal structural elements under complex stress state, which would take into account both the physical properties of the material and changes in the actual dimensions during uniform plastic deformation.
A system of equivalent coordinates is developed for the analytical description of the generalized stress-strain curve, which is consistent with classical approaches, as well as with the results of experiments. The proposed phenomenological model of the generalized stress-strain curve integrates the physical and mechanical properties of the material by introducing the parameter p. In particular cases, equivalent stresses and strains are reduced to classical ones: the greatest shear stresses and angular deformations τ_max,γ_max (p=1), and the intensities of stresses and strains σ_i,ε_i (p=2). Based on experimental data for a series of alloys, it has been established that there is such a calculated value of the parameter p, for which it is possible to construct a deformation curve with the smallest scattering of points. On the basis of the maximum load principle, analytical conditions are formulated for achieving the true ultimate strength for structural elements of typical geometric shapes (strip, plate, thin-walled cylinder and thin-walled axisymmetric shell) for the simplest types of loads. The principle of maximum load is used to obtain two types of dependencies: boundary conditions, the graphs of which are secants of true deformation diagrams, and tangent moduli. Boundary conditions obtained for thin-walled axisymmetric shells, are applicable to stress states close to internal pressure or axial tension. The tangent modules are used to construct a generalized condition for the loss of stability of the plastic deformation process of a thin-walled pipe with a combined load of internal pressure and tension. It has been analytically confirmed that the strength life of a thin-walled cylinder is the smallest for loading only by internal pressure. A slight additional load of the cylinder by axial tension increases the limit values of the actual design circular stresses for the pipe, but decreases them for an axisymmetric shell of positive Gaussian curvature.
Method for predicting the true ultimate strength of plastic isotropic structural materials under complex stress state, taking into account their geometry, is developed. A detailed description of the technique is made for a thin-walled pipe loaded with internal pressure and axial tension. The basic formula of the algorithm contains a correcting factor for the tangent module, which takes into account the physical and mechanical properties of the material, the type of stress state and the geometry of the element. To implement the technique, a generalized true stress-strain curve was constructed.
The developed technique is tested for thin-walled cylindrical pipes made of various types of plastic structural materials. For two grades of steels (carbon steel 45 and alloy steel 10MnН2MoV), an increase in the calculated strength threshold is shown with an insignificant additional tension of a pipe under pressure (σ_z/σ_θ =0,6..0,8). With increasing the ratio of wall thickness to diameter twice (from 0,08 to 0,16), the maximum calculated limit hoop stresses (at σ_z/σ_θ =0,6) decrease by 2–5%, which confirms the inexpediency of improving the strength of structural elements only by increasing their massiveness. Analysis of the results showed that it is possible to establish a balance between the actual geometry of the element and the load, which will solve the problem of finding the optimal ratio of "weight-strength", important for practical applications in aircraft, rocket and mechanical engineering.
The proposed method makes it possible to predict the strength of thin-walled pressure vessels; choose a realistic safety factor and make optimal engineering solutions at the design and operation stages of structural elements; to increase the efficiency and safety of using pipeline and shell-type saving systems.
