Effect of the strain rate sensitivity index and variable profile blanks in a welded envelope on the thickness distribution of spherical shells manufactured by free superplastic forming

O.P. Tulupova, A.A. Kruglov, F.U. Enikeev, G.R. Murzina, V.R. Ganieva show affiliations and emails
Received 26 December 2025; Accepted 13 April 2026;
Citation: O.P. Tulupova, A.A. Kruglov, F.U. Enikeev, G. R. Murzina, V.R. Ganieva. Effect of the strain rate sensitivity index and variable profile blanks in a welded envelope on the thickness distribution of spherical shells manufactured by free superplastic forming. Lett. Mater., 2026, 16(2) 166-172
BibTex   https://doi.org/10.48612/letters/2026-2-166-172

Abstract

The problem to diminish the thickness non-uniformity of spherical vessels manufactured by means of superplastic forming of an envelope consisting from two circular blanks welded along their periphery is considered by means of computer simulations.This paper uses computer simulation to address the problem of reducing thickness non-uniformity in spherical vessels produced by superplastic forming of an envelope consisting of two circular blanks welded at the periphery. The boundary value problem in mechanics of solids is formulated in terms of high temperature creep using standard power law of superplasticity. Finite element simulations are carried out using the ANSYS ED code. The geometry of the initial blank and the value of the strain rate sensitivity index, m, have been varied in the calculations. A special Python computer program was written to treat the results of the finite element calculations. Finite element calculations using the ANSYS program enable one to obtain the coordinates of the spherical vessel, which have been treated then in the Python computer program. As a result, the thickness distribution of the spherical vessel has been obtained. Edge welded envelopes consisting of two circular blanks of a conical profile have been used for calculations. The blank profile was varied under fixed value of the strain rate sensitivity index, m and a flow stress corresponding to the point of inflection of the sigmoidal superplastic curve. Four variants of blanks with varying central thicknesses and conical profiles were considered. Analysis of the results showed that in three of the four variants, the difference in the thickness of the spherical shells decreases monotonously with increasing index m. However, when the thickness of the blanks in the center is 1.33 times greater than their thickness at the periphery, as m increases from 0.5 to 0.7, the thickness difference does not decrease, but increases from 14 % to 16 %. As the thickness increases in the center of the blanks, the strain localization zone in the spherical shell moves from the pole to the equator.

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Funding

1. IMSP RAS state assignment - No. 124022900007-9