Abstract
Reviewing the numerical simulation of the process of non-proportional elastic-plastic deformation of steel 45 by a knot of constant curvature, taking into account the complex nature of deformation under complex subcritical loading by axial compressive force and torque for a thin-walled circular cylindrical shell. The theory of Quas and simple processes of A. A. Ilyushin and the mathematical model of V. Zubchaninov were applied taking into consider the parameters of the complex loading for plane trajectories To assess the accuracy of accepted theories, the simulation results are compared with experimental results, received on the automated complex СNcomputer in the laboratory of the faculty of «Strength of materials and theory of elasticity and plasticity» of the Tver state technical University. Was introduced the scheme of calculations disproportionate plastic deformation of steel 45 using the proposed mathematical model showed a satisfactory result and recommended for further use. Remarks, that in the described processes the lack of some parameters complex loading in approximations reduces the accuracy of the final calculated values, differences significantly compared to the experimental data.
Highlights
The fundamental system-forming of the theory of processes elastic-plastic deformation of materials and basic equations are accepted by formulas [1,2,3,4,5,6,7,8, 10, 11]:
- 7 experimental points are marked with circles, solid lines are marked with curves, which were built according to the considered mathematical model of the theory of processes in flat tasks, taking into account the approximation of the process functional (15) all the parameters of the complexity of the process s, к1, 10 for flat trajectories and a generalized effect of baushinger
Numerical calculations on the presented mathematical model of the theory of processes using functional approximations (15) and (16) quite well correspond to the experimental data for this type of trajectory from scalar data
Summary
Angle of approach 1 , which characterizes the deviation of the stress vector from the tangent to the trajectory of the deformation at each point is a functional of the parameters of the complexity of the process 1 1(s, 10, k1) . This angle reflects the effect of the vector properties of the material on the deformation process, а (s, 10, k1) , being a functional of the same parameters - the influence of scalar properties of the material.
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