МОДЕЛЮВАННЯ ПОВЕДІНКИ ЛОКАЛЬНО НАВАНТАЖЕНОЇ ПОЛОСИ З ПСЕВДО-ПРУЖНО-ПЛАСТИЧНОГО МАТЕРІАЛУ ПРИ ВЕЛИКИХ ПЛАСТИЧНИХ ДЕФОРМАЦІЯХ

Abstract

Introduction. Currently, a number of models are known to describe the thermomechanical behavior of functionally inhomogeneous materials, in particular alloys with shape memory (SPF) [3; 4]. Most of them are based on classical ideas, ie aim to directly describe the experimental data obtained on different macrosamples under simple and complex loads. However, as established in experimental studies, the behavior of the material at a point in the body in the General case may be different from the behavior of the sample as a whole [5]. In the considered problems the numerical procedure of calculation of the diagram of material which represents a curve which surrounds a family of diagrams of the material constructed for certain laws of change of speed of a front of rupture of deformations is developed. Purpose. The aim of the work is to apply a nonlinear phenomenological model, which describes the properties of alloys with shape memory and thermo-pseudo-plastic behavior (TPPM) of the material at the point to the problem of modeling a locally loaded strip of pseudo-elastic-plastic material at large plastic deformations. Compare the results of modeling in geometrically linear and nonlinear formulations for large plastic deformations. Results. The behavior of the locally loaded weakened strip of pseudo-elastic-plastic material under its non-stationary loading is modeled in the work. The authors used a nonlinear phenomenological model of the material to solve the above problem, which allows to describe a number of experimental data on different samples under different conditions. A comparison of the results obtained in geometrically linear and nonlinear formulations with large plastic deformations. Conclusion. Modeling the behavior of pseudo-elastic-plastic material with large plastic deformations requires the use of nonlinear mathematical models that could more accurately describe and predict the behavior of such a body. The behavior of the locally loaded weakened strip of pseudo-elastic-plastic material under its non-stationary loading is modeled in the work. The authors used a nonlinear phenomenological model of the material to solve the above problem, which allows to describe a number of experimental data on different samples under different conditions. A comparison of the results obtained in geometrically linear and nonlinear formulations with large plastic deformations. Numerically compared intensity fields at symmetric and asymmetric loading It is established that at plastic deformations up to 6% (small deformations) the discrepancy of results in points of localization of deformation does not exceed 5%. With increasing values of plastic deformation (more than 7%, large deformations), the discrepancy of the results can increase significantly and in the vicinity of the possible creation of the neck to reach 20%.