Analysis of the Sheet Shell's Curvature with Lame's Superellipse Method during Superplastic Forming


Article Preview

The prospects and novelty of using the expression of Lame's superellipse for approximating the curvature of shells in superplastic forming (SPF) and for predicting the geometry of a product are shown. Different versions of the SPF facilitate the realization of different radii of curvature of the shell contours, which differ significantly from the radius of the spherical segment. The regularities of the change in the radius of conjugation of the bottom and the wall of the spherical shell for various SPF variants are established.



Edited by:

Dr. Denis Solovev




O.S. Anishchenko et al., "Analysis of the Sheet Shell's Curvature with Lame's Superellipse Method during Superplastic Forming", Materials Science Forum, Vol. 945, pp. 531-537, 2019

Online since:

February 2019




[1] Giuliano, G., Superplastic Forming of Advanced Metallic Materials: Method and Applications. Oxford-Cambridge-Philadelfia-New Dehli, Woodhead Publishing Ltd.. (2011).

[2] Balasubramanian, M., Ramanathan, K., and Senthilkumar, V. S., Mathematical Modeling and Finite Element Analysis of Superplastic Forming of Ti-6Al-4 V Alloy in a Stepped Rectangular Die. Procedia Engineering. 64 (2013) 1209-1218.


[3] Zakhariev, I. Y., and Aksenov, S. A., Influence of a Material Rheological Characteristics on the Dome Thickness during Free Bulging Test. Journal of Chemical Technology and Metallurgy. 52 (5) (2017) 1002-1007.

[4] Giuliano, G., Constitutive Equation for Superplastic Ti–6Al–4V Alloy. Materials and Design. 29 (2008) 1330-1333.


[5] V. Kukhar, V. Artiukh, A. Prysiazhnyi, A. Pustovgar., Experimental Research and Method for Calculation of Upsetting-with-Buckling, Load at the Impression-Free (Dieless) Preforming of Workpiece. E3S Web of Conference. 33 (2018) 02031.


[6] Kazashi, Y., A Fully Discretised Filtered Polynomial Approximation on Spherical Shells. Journal of Computational and Applied Mathematics. 333 (2018) 428-441.


[7] Zhang, X., Rosin, P. L., Superellipse Fitting to Partial Data. Pattern Recognition. 36 (3) (2003) 743-752.


[8] Sadowsky, A. J., Rotter, A. M., Exploration of Novel Geometric Imperfection Forms in Buckling Failures of Thin-Walled Metal Silos under Eccentric Discharge. International Journal of Solids and Structures. 50 (5) (2012) 781-794.


[9] Anishchenko, A. S., and Sosnovskij, N. Yu., A Machine for Rolling and Coiling of the Ends of Tubular Blanks. Chemical and Petroleum Engineering. (1992) 30.


[10] Giuliano, G., Sorrentino, L., Turchetta, S., FEM Analysis of Superplastic PbSn60 Alloy Free Bulging Test. International Journal of Engineering and Technology (IJET). 7 (5) (2015) 1916-1920.

[11] Aksenov, S. A., Chumachenko, E. N., Kolesnikov, A. V., Osipov, S. A., Determination of Optimal Gas Forming Conditions from Free Bulging Tests at Constant Pressure. Journal of Materials Processing Technology. 217 (2015) 158-164.


[12] Grushko, A. V., Kukhar, V. V., Slobodyanyuk, Yu. O., Phenomenological Model of Low-Carbon Steels Hardening during Multistage Drawing. Solid State Phenomena. 265 (2017) 114-123.


[13] Ogorodnikov, V., Del, G., Spiridonov, L., Plasticity of Metal Subjected to Complex Loading. Izv. Vyssh. Uchebn. Zaved. Mashinostr, 12 (1974) 22–26.

[14] V.A. Titov, N.K. Zlochevskaya, A.Y. Kachan, Features of Integrated Manufacture of Blade Workpieces from Eutectically Strengthened Titanium Alloys. Metallurgist. 58(1-2) (2014) 141-148.


[15] Gao, F., Li, W., Meng, B., Wan, M., Zhang, X., and Han, X., Rheological Law and Constitutive Model for Superplastic Deformation of Ti-6Al-4V. Journal of Alloys and Compounds. 701 (2017) 177-185.


[16] Kukhar, V., Balalayeva, E., Nesterov, O., Calculation Method and Simulation of Work of the Ring Elastic Compensator for Sheet-Forming. MATEC Web of Conferences. 129 (2017) 01041.


[17] Balalayeva, E., Artiukh, V., Kukhar, V., Tuzenko, O., Glazko, V., Prysiazhnyi, A., Kankhva, V., Researching of the Stress-Strain State of the Open-Type Press Frame Using of Elastic Compensator of Errors of Press-Die, System. Advances in Intelligent Systems and Computing. 692 (2018) 220-235.


[18] Kukhar, V., Artiukh, V., Butyrin, A., Prysiazhnyi, A., Stress-Strain State and Plasticity Reserve Depletion on the Lateral Surface of Workpiece at Various Contact Conditions during Upsetting. Advances in Intelligent Systems and Computing. 692 (2018) 201-211.


[19] Asaadi, E., Heyns, P. S., Flow Stress Identification of Tubular Materials Using the Progressive Inverse Identification Method. Engineering Computations. 33 (5) (2016) 1472-1489.


[20] Cornfield, G. C., Johnson, R. H., The Forming of Superplastic Sheet Metal. International Journal of Mechanical Science. 12 (6) (1970) 479-490.

[21] Grushko, O.V., Development of usage of brinell hardness test method for flow stress definition during cold deformation. Metallurgical and Mining Industry. 5(1) (2013) 11-16.