Numerical and analytical model of the stress-strain state during the expansion of thin-walled pipe blanks in a curved axisymmetric matrix


Аuthors

Feoktistov S. I.*, Andrianov I. K.**, Mar’in S. B.***

Komsomolsk-on-Amur State University (KnASU), 27, Lenin str., Komsomolsk-on-Amur, 681013, Russia

*e-mail: serg_feo@mail.ru
**e-mail: ivan_andrianov_90@mail.ru
***e-mail: maryinsb@mail.ru

Abstract

The study considers numerical and analytical modeling of the stress-strain state and force characteristics during expansion of the thin-walled pipe blanks in a curved axisymmetric matrix. The equilibrium equations of the momentless theory of thin axisymmetric shells with regard to the nonlinear plasticity, changes in wall thickness and contact friction are employed when developing the model. The computations are based on the numerical method of variable elasticity parameters, which allows determining stresses and strains; the thickness distribution in the meridian section; the amount of contact pressure, as well as to plot the change in the force distribution depending on the application point displacement of the force relative to the matrix. A mathematical model for the stress-strain state of pipe blanks estimating during expansion is developed for a matrix, which profile is described by an arbitrary function. The numerical technique for the stress-strain state computing is based on the variable elasticity parameters method, which allows solving the problem of expansion in an elastic-plastic formulation. Besides, the developed model accounts for the material compressibility during elastic strain. Based on the numerical computing results, the distribution of meridian and circumferential stresses and logarithmic strains, as well as the of logarithmic strains distribution over the workpiece wall thickness are presented. An assessment of the contact pressure during crimping is performed, a decrease in the relative thickness of the workpiece along the length during distribution is noted herewith. The iterative computation process convergence by the of variable elasticity parameters method was estimated by the position of stress intensities and logarithmic strain intensities relative to the deformation diagram of the material. The proposed problem solution of the pipe blanks expansion may find application in the field of aircraft engineering in the development of thin-walled shell structures for aviation purposes.

Keywords:

method of variable elasticity parameters, pipe expansion, nonlinear plasticity, variable wall thickness, contact friction, curved matrix

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