Residual stresses in a thermoelastic cylinder resulting from layer-by-layer surfacing

S. A. Lychev   ; Montaser Fekry

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 3, pp. 63-90

Résumé

The article investigates the residual stresses arising in a thermoelastic cylinder as a result of layer-by-layer deposition of material on its lateral surface. Residual stresses are defined as the limiting values of internal stresses developing during the technological process. Internal stresses are caused by incompatible deformations that accumulate in the body as a result of joining parts with different temperatures. For the analysis of internal stresses, an analytical solution of the axisymmetric quasi-static problem of thermoelasticity for a layer-by-layer growing cylinder is constructed. It is shown that the distribution of residual stresses depends on the scenario of the surfacing process. In this case, the supply of additional heat to the growing body can significantly reduce the unevenness of the temperature fields and reduce the intensity of residual stresses. The most effective is uneven heating, which can be realized, for example, by the action of an alternating current with a tunable excitation frequency. This is illustrated by the calculations performed using the constructed analytical solution.

Détail

Keywords: additive manufacturing, residual stresses, growing solids, thermoelasticity, analytical solutions.

Bibliographie

[1] P. Mercelis, J. P. Kruth, “Residual stresses in selective laser sintering and selective laser melting”, Rapid Prototyping Journal, 12:5 (2006), 254–265 | DOI

[2] D. Buchbinder et al., “Investigation on reducing distortion by preheating during manufacture of aluminum components using selective laser melting”, Journal of Laser Applications, 26:1 (2014), 012004 | DOI

[3] M. F. Zaeh, G. Branner, “Investigations on residual stresses and deformations in selective laser melting”, Production Engineering, 4:1 (2010), 35–45 | DOI

[4] T. Vilaro et al., “As-Fabricated and Heat-Treated Microstructures of the Ti-6Al-4V Alloy Processed by Selective Laser Melting”, Metallurgical and materials transactions A, 42:10 (2011), 3190–3199 | DOI

[5] J.P. Kruth et al., “Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method”, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 226:6 (2012), 980–991 | DOI

[6] G. N. Levy, R. Schindel, J. P. Kruth, “Rapid manufacturing and rapid tooling with layer manufacturing (LM) technologies, state of the art and future perspectives”, CIRP Annals-Manufacturing Technology, 52:2 (2003), 589–609 | DOI

[7] T. DebRoy et al., “Additive manufacturing of metallic components-Process, structure and properties”, Progress in Materials Science, 92 (2018), 112–224 | DOI

[8] J. P. Kruth, M. C. Leu, T. Nakagawa, “Progress in additive manufacturing and rapid prototyping”, CIRP Annals-Manufacturing Technology, 47:2 (1998), 525–540 | DOI

[9] W. Meiners, K. Wissenbach, A. Gasser, Shaped body especially prototype or replacement part production, DE Patent, 1998, 19 pp. https://patents.google.com/patent/DE19649865C1/en

[10] A. Klarbring, T. Olsson, J. Stalhand, “Theory of residual stresses with application to an arterial geometry”, Archives of Mechanics, 59:4-5 (2007), 341–364 https://am.ippt.pan.pl/am/article/viewFile/v59p341/pdf | Zbl

[11] S. Lychev, K. Koifman, Geometry of Incompatible Deformations: Differential Geometry in Continuum Mechanics, De Gruyter, 2018 | DOI | Zbl

[12] A. Yavari, “A Geometric Theory of Growth Mechanics”, Journal of Nonlinear Science, 20:6 (2010), 781–830 | DOI | Zbl

[13] N. Kh. Arutiunian, A. D. Drozdov, V. E. Naumov, Mechanics of growing viscoelastoplastic bodies, Nauka, M., 1987 (In Russ.)

[14] S. A. Lychev, A. V. Manzhirov, “The mathematical theory of growing bodies. Finite deformations”, Journal of Applied Mathematics and Mechanics, 77:4 (2013), 421–432 | DOI | Zbl

[15] S. A. Lychev, A. V. Manzhirov, “Reference configurations of growing bodies”, Mechanics of Solids, 48:5, 553–560 | DOI

[16] S. A. Lychev, “Universal deformations of growing solids”, Mechanics of Solids, 46:6 (2011), 863–876 | DOI

[17] S. A. Lychev, A. V. Manzhirov, “Discrete and Continuous Growth of Hollow Cylinder. Finite Deformations”, Proceedings of the World Congress on Engineering, v. II, 2014, 1327–1332 http://www.iaeng.org/publication/WCE2014/WCE2014_pp1327-1332.pdf

[18] A. L. Levitin, S. A. Lychev, A. V. Manzhirov, M. Y. Shatalov, “Nonstationary vibrations of discretely accreted thermoelastic parallelepiped”, Mechanics of Solids, 47:6, 677–689 | DOI

[19] P. Ciarletta, M. Destrade, A. L. Gower, M. Taffetani, “Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition”, Journal of the Mechanics and Physics of Solids, 90 (2016), 242–253 | DOI

[20] A. E. Green, “Thermoelastic stresses in initially stressed bodies”, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 266:1324 (1962), 1–9 | DOI

[21] B. E. Johnson, A. Hoger, “The use of a virtual configuration in formulating constitutive equations for residually stressed elastic materials”, Journal of Elasticity, 41:3 (1995), 177–215 | DOI | Zbl

[22] A. Ozakin, A. Yavari, “A geometric theory of thermal stresses”, Journal of Mathematical Physics, 51:3 (2010), 032902 | DOI | Zbl

[23] S. Sadik, A. Yavari, “Geometric nonlinear thermoelasticity and the time evolution of thermal stresses”, Mathematics and Mechanics of Solids, 22:7 (2017), 1546–1587 | DOI | Zbl

[24] J. Wang, S. P. Slattery, “Thermoelasticity without energy dissipation for initially stressed bodies”, International Journal of Mathematics and Mathematical Sciences, 31 (2002) | DOI

[25] T. N. Lycheva, S. A. Lychev, “Spectral decompositions in dynamical viscoelastic problems”, PNRPU Mechanics Bulletin, 2016, no. 4, 120–150 (In Russ.) | DOI

[26] S. A. Lychev, “Geometric aspects of the theory of incompatible deformations in growing solids”, Mechanics for Materials and Technologies, Advanced Structured Materials, 46, eds. Altenbach H., Goldstein R., Murashkin E., Springer, Cham | DOI

[27] A. D. Polyanin, S. A. Lychev, “Decomposition methods for coupled 3D equations of applied mathematics and continuum mechanics: Partial survey, classification, new results, and generalizations”, Applied Mathematical Modelling, 40:4 (2016), 3298–3324 | DOI | Zbl

[28] S. Lychev, A. Manzhirov, M. Shatalov, I. Fedotov, “Transient Temperature Fields in Growing Bodies Subject to Discrete and Continuous Growth Regimes”, Procedia IUTAM, 23 (2017), 120–129 | DOI

[29] W. L. Weeks, Transmission and distribution of electrical energy, Harpercollins, 1981, 302 pp.

[30] F. John, Partial Differential Equations, Springer-Verlag, New York, 1982, 249 pp. https://www.studmed.ru/~john-f-partial-differential-equations_000d60bbee2.html | Zbl

[31] Mohamed I. A. Othman, Montaser Fekry, Marin Marin, “Plane waves in generalized magneto-thermoviscoelastic medium with voids under the effect of initial stress and laser pulse heating”, Structural Engineering and Mechanics, 73:6 (2020), 621–629 | DOI

[32] Mohamed I. A. Othman, Montaser Fekry, “Effect of Magnetic Field on Generalized Thermo-Viscoelastic Diffusion Medium with Voids”, International Journal of Structural Stability and Dynamics, 16:07 (2016), 1550033 | DOI | Zbl

[33] R. A. Silverman, Special Functions and Their Applications, Prentice Hall, Englewood Hills, New Jersey, 1972 https://fuchs-braun.com/media/8a9c1aa3b60768bffff808bfffffff0.pdf

[34] M. J. Donachie, Titanium: a technical guide, ASM international, 2000, 381 pp.