Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Recent Problems of Heat-Transfer Simulation in Technological Processes of Selective Laser Melting and Fusion

  • 17 Accesses

Abstract

The thermal processes arising upon the implementation of the additive technologies of selective laser melting and the fusion of metals and alloys are analyzed. An adequate description of the heat transfer upon the implementation of additive technological processes associated with high-intensity local heating by a moving laser beam and the phase transitions generated by a semifinished powder product, crystallization, and the concomitant effects in the growing element is the key to gaining insight into the microstructure and the efficient properties of the obtained material and the prevention of residual deformation (shrinkage) of the item. Currently, the main causes of unpredictable production defects are deviations of the shape of the final item from the preset geometry and high-amplitude residual stresses, which can initiate destruction of the item under loads significantly lower than those calculated, as well as the occurrence of the microscopic defects (pores, layer interfaces, etc.) are. The development of mathematical models that, on the one hand, are sufficiently accurate to predict the listed phenomena and, on the other hand, allow practical implementation in engineering calculations is the basis for the further development of the laser-melting and fusion of metal materials. At the same time, analysis of the current state of the problem shows that development of efficient numerical methods providing acceptable computational costs while maintaining accuracy is the key element in the practical implementation of the models. A method based on multiscale, interconnected modeling of the mechanical and the thermal state of the growing body—at the local level in the melt pool domain, at the intermediate level in the vicinity of the melt pool and the adjacent layers, and at the level of the entire product as a whole—seems to be efficient; here, the computing process at the global level can be based on a combination of the finite-element method (indisputable in practice) and analytical calculations providing local refinement of the solution.

This is a preview of subscription content, log in to check access.

REFERENCES

  1. 1

    Shishkovskii, I.V., Osnovy additivnykh tekhnologii vysokogo razresheniya (Fundamentals of High-Resolution Additive Technology), St. Petersburg: Piter, 2016.

  2. 2

    Frazier, W.E., J. Mater. Eng. Perform., 2014, vol. 23, no. 6, p. 1917.

  3. 3

    Alcisto, J., Enriquez, A., Garcia, H., et al., J. Mater. Eng. Perform., 2011, vol. 20, no. 2, p. 203.

  4. 4

    Guessasma, S., Zhang, W., Zhu, J., et al., Int. J. Simul. Multidiscip. Des. Optim., 2015, vol. 6, p. 9A

  5. 5

    Jared, B., Aguilo, M.A., Beghini, L.L., et al., Scr. Mater., 2017, vol. 135, p. 141.

  6. 6

    Galenko, P., Kharanzhevskii, E., and Danilov, D., Fiz. Met. Metalloved., 2002, vol. 94, no. 2, p. 100.

  7. 7

    Kharanzhevskii, E., et al., Prochn. Plast., 2009, vol. 18, no. 5, p. 534.

  8. 8

    Hwa-Hsong, T., Ming-Lu, C., and Hiao-Chuan, Y., J. Eur. Ceram. Soc., 2011, vol. 31, no. 8, p. 1383.

  9. 9

    Slarko, D. and Matic, K., Ann. DAAAM Proc., 2010, p. 1527.

  10. 10

    Dilberoglu, U., Gharehpapagh, B., Yaman, U., et al., Procedia Manuf., 2017, vol. 11, p. 545.

  11. 11

    Wohlers, T. and Cornet, T., History of additive manufacturing, Wohlers Report, 2014.

  12. 12

    Wohlers, T. and Caffrey, T., Manuf. Eng., 2013, vol. 150, no. 6, p. 67.

  13. 13

    Dickens, P., et al., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX: Univ. Texas, 1992, p. 280.

  14. 14

    Michaels, S., Sachs, E.M., and Cima, M., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX: Univ. Texas, 1992, p. 244.

  15. 15

    Dave, V.R., Matz, J.E., and Eagar, T.W., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX: Univ. Texas, 1992, p. 64.

  16. 16

    Atwood, C., Griffith, M., Harwell, L., et al., in Proc. Int. Congress on Applications of Lasers Electro-Optics, 1998. https://doi.org/10.2351/1.5059147

  17. 17

    Wong, K. W. and Hernandez, A., ISRN Mech. Eng., 2012, vol. 2012, 208760.

  18. 18

    Quadrennial Technology Review 2015, Washington, DC: US Department of Energy, 2015.

  19. 19

    Brandt, M., Laser Additive Manufacturing: Materials, Design, Technologies, and Applications, Sawston: Woodhead, 2017.

  20. 20

    Stavropoulos, P. and Foteinopoulos, P., Manuf. Rev., 2018, vol. 5, no. 2. https://doi.org/10.1051/mfreview/2017014

  21. 21

    Kruth, J.P., Froyen, L., Van Vaerenbergh, J., et al., J. Mater. Process. Technol., 2004, vol. 149, p. 616.

  22. 22

    Murr, L., Gaytan, S., and Ramirez, D.A., J. Mater. Sci. Technol., 2012, vol. 28, no. 1, p. 1.

  23. 23

    Simchi, A., Petzoldt, F., and Pohl, H., J. Mater. Process. Technol., 2003, vol. 141, p. 319.

  24. 24

    Hederick, E., in Proc. of the MST11, Additive Manufacturing of Metals, Columbus, OH, 2011.

  25. 25

    Kelly, S.M., Metall. Trans. A, 2004, vol. 35, p. 1869.

  26. 26

    Wang, F., Williams, S., Colegroveet, P., et al., Metall. Trans. A, 2013, vol. 44, p. 968.

  27. 27

    Zheng, B., Zhou, Y., Smugeresky, J.E., et al., Metall. Trans. A, 2008, vol. 39, p. 2228.

  28. 28

    Vilaro, T., Colin, C., and Bartout, J.D., Metall. Trans. A, 2011, vol. 42, p. 3190.

  29. 29

    Zheng, B., Zhou, Y., Smugeresky, J.E., et al., Metall. Trans. A, 2008, vol. 39, p. 2237.

  30. 30

    Kobryn, P. and Semiatin, S., JOM, 2001, vol. 53, no. 9, p. 40.

  31. 31

    Formalev, V.F., High Temp., 2012, vol. 50, no. 6, p. 744.

  32. 32

    Formalev, V. and Rabinskii, L., High Temp., 2014, vol. 52, no. 5, p. 675.

  33. 33

    Formalev, V., Kuznetsova, E., and Rabinskiy, L., High Temp., 2015, vol. 53, no. 4, p. 548.

  34. 34

    Formalev, V. and Kolesnik, S., J. Eng. Phys. Thermophys., 2016, vol. 89, no. 4, p. 975.

  35. 35

    Formalev, V., Kolesnik, S., Kuznetsova, E., and Rabinskii, L., High Temp., 2016, vol. 54, no. 3, p. 390.

  36. 36

    Formalev, V., Kolesnik, S., and Kuznetsova, E., High Temp., 2016, vol. 54, no. 6, p. 824.

  37. 37

    Formalev, V., Kuznetsova, E., Kolesnik, S., and Pegachkova, E., Int. J. Pure Appl. Math., 2016, vol. 111, no. 2, p. 303.

  38. 38

    Formalev, V., Kolesnik, S., and Kuznetsova, E., High Temp., 2017, vol. 55, no. 5, p. 761.

  39. 39

    Formalev, V., Kolesnik, S., and Kuznetsova, E., Period. Tche Quim., 2018, vol. 15, no. 1 (suppl.), p. 426.

  40. 40

    Formalev, V., Kolesnik, S., and Kuznetsova, E., High Temp., 2018, vol. 56, no. 3, p. 393.

  41. 41

    Formalev, V., Kolesnik, S., and Kuznetsova, E., High Temp., 2018, vol. 56, no. 5, p. 727.

  42. 42

    Formalev, V. and Kolesnik, S., J. Eng. Phys. Thermophys., 2019, vol. 92, no. 1, p. 52.

  43. 43

    Murr, L., Martinez, E., Gaytan, S.M., et al., Metall. Trans. A, 2011, vol. 42, p. 3491.

  44. 44

    Lambrakas, S. and Cooper, K., J. Mater. Eng. Perform., 2009, vol. 18, no. 3, p. 221.

  45. 45

    Lambrakas, S.G. and Cooper, K., J. Mater. Eng. Perform., 2010, vol. 19, no. 3, p. 321.

  46. 46

    Lambrakas, S. and Milewski, J., Sci. Technol. Weld. Joining, 2002, vol. 7, no. 3, p. 137.

  47. 47

    Ruttert, B., Ramsperger, M., Mujica Roncery, L., et al., Mater. Des., 2016, vol. 110, p. 720.

  48. 48

    Mower, T.M. and Long, M.J., Mater. Sci. Eng.: A, 2016, vol. 651, p. 198.

  49. 49

    Tammas-Williams, S., Withers, P.J., Todd, I., et al., Metall. Trans. A, 2016, vol. 47, no. 5, p. 1939.

  50. 50

    Tammas-Williams, S., Withers, P.J., Todd, I., et al., Scr. Mater., 2016, vol. 122, p. 72.

  51. 51

    Tammas-Williams, S., et al., Addit. Manuf., 2017, vol. 13, p. 93.

  52. 52

    Yan, C., Liu, W., Tang, Z., et al., Opt. Laser Technol., 2018, vol. 106, p. 427. https://doi.org/10.1016/j.optlastec.2018.04.034

  53. 53

    Khaidarov, G., Zh. Fiz. Khim., 1983, vol. 57, no. 10, p. 2528.

  54. 54

    Weisskopf, V., Am. J. Phys., 1985, vol. 53, p. 19.

  55. 55

    Weisskopf, V., Am. J. Phys., 1985, vol. 53, p. 618.

  56. 56

    Khaidarov, G., Khaidarov, A., and Mashek, A., Vestn. S.-Peterb. Univ., Ser. 4: Fiz., Khim., 2011, no. 1, p. 3.

  57. 57

    Eotvos, L., Ann. Phys., 1886, vol. 27, p. 448.

  58. 58

    Khaidarov, G., et al., Vestn. S.-Peterb. Univ., Ser. 4: Fiz., Khim., 2012, no. 1, p. 24.

  59. 59

    Luo, Z. and Zhao, Y., Addit. Manuf., 2018, vol. 21, p. 318. https://doi.org/10.1016/j.addma.2018.03.022

  60. 60

    Matthiews, M.J., Guss. G., Khairallah, S.A., et al., Acta Mater., 2016, vol. 114, p. 33.

  61. 61

    Thijs, L., Verhaeghe, F., Craeghs, T., et al., Acta Mater., 2010, vol. 58, p. 3302.

  62. 62

    Su, X. and Yang, Y., J. Mater. Process. Technol., 2012, vol. 212, p. 2074.

  63. 63

    Aboulkhair, N., Maskery, I., Tuck, C., et al., J. Mater. Process. Technol., 2016, vol. 230, p. 88.

  64. 64

    Gusarov, A., Yadroitsev, I., Bertrand, Ph., et al., Appl. Surf. Sci., 2007, vol. 254, p. 975.

  65. 65

    Fang, J.X., Dong, S.I., Wang, Y.J., et al., Mater. Des., 2015, vol. 87, p. 807. https://doi.org/10.1016/j.matdes.2015.08.061

  66. 66

    Doumanidis, C. and Kwak, Y.M., J. Manuf. Sci. Eng., 2001, vol. 123, no. 1, p. 45.

  67. 67

    Vásquez, F., Ramos-Grez, J., and Walczak, M., Int. J. Adv. Manuf. Technol., 2012, vol. 59, p. 1037.

  68. 68

    Chiumenti, M., Neiva, E., Salsi, E., et al., Addit. Manuf., 2017, vol. 18, p. 171. https://doi.org/10.1016/j.addma.2017.09.002

  69. 69

    Islam, M., Purtonen, T., Piili, H., et al., Phys. Procedia, 2013, vol. 41, p. 835. https://doi.org/10.1016/j.phpro.2013.03.156

  70. 70

    Fu, C. and Guo, Y., J. Manuf. Sci. Eng., 2014, vol. 136, 061004.

  71. 71

    Babaytsev, A., Prokofiev, M., and Rabinskiy, L., Int. J. Nanomech. Sci. Technol., 2017, vol. 8, no. 4, p. 359.

  72. 72

    Rabinskiy, L. and Tushavina, O., Period. Tche Quim., 2018, vol. 15, no. 1 (suppl.), p. 321.

  73. 73

    Baureifi, A., Scharowsky, T., and Korner, C., J. Mater. Process. Technol., 2014, vol. 214, no. 11, p. 2522.

  74. 74

    Ippolito, R., Iuliano, L., and Gatto, A., CIRP Ann., 1995, vol. 44, p. 157.

  75. 75

    Yang, H., Hwang, P., and Lee, S., Int. J. Mech. Tools Manuf., 2002, vol. 42, p. 1203.

  76. 76

    Wu, A., Brown, D.W., Kumar, M., et al., Metall. Mater. Trans. A, 2014, vol. 45, p. 6260.

  77. 77

    Li, Y. and Gu, D., Mater. Des., 2014, vol. 63, p. 856. https://doi.org/10.1016/j.matdes.2014.07.006

  78. 78

    Olakanmi, E.O., Cochrane, R.F., and Dalgarno, K.W., Prog. Mater. Sci., 2015, vol. 74, p. 401. https://doi.org/10.1016/j.pmatsci.2015.03.002

  79. 79

    Lavery, N., et al., in Pre-Proc. of Sustainable Design and Manufacturing 2014 Conf. (SDM-14), 2014, p. 651.

  80. 80

    Lui, J., Jalalahmadi, B., Guo, Y.B., et al., Rapid Prototyping J., 2018, vol. 24, no. 8, p. 1245.

  81. 81

    Moges, T., Ameta, G., and Wtherell, P., J. Manuf. Sci. Eng., 2018, vol. 141, no. 4, 040801.

  82. 82

    Furumoto, T., Ogura, R., Hishida, K., et al., J. Mater. Process. Technol., 2017, vol. 245, p. 207. https://doi.org/10.1016/j.jmatprotec

  83. 83

    Roberts, I., Investigation of residual stresses in the laser melting of metal powders in additive layers manufacturing, Ph.D. Thesis, West Midlands: Univ. Wolverhampton, 2012.

  84. 84

    Denlinger, E.R., Heigel, J.C., and Michaleris, P., Proc. Inst. Mech. Eng.,Part B, 2015, vol. 229, no. 10, p. 1803.

  85. 85

    Denlinger, E.R., Irwin, J., and Michaleris, P., J. Manuf. Sci. Eng., 2014, vol. 136, no. 6, 061007.

  86. 86

    Lindgren, L.E., Lundbäck, A., Fisk, M., et al., Addit. Manuf., 2016, vol. 12, p. 144.

  87. 87

    Mamelov, A., Modeling of additive manufacturing with reduced computational effort, M. Sci. Thesis, Lulea, Sweden: Lulea University of Technology, 2016.

  88. 88

    Riedlbauer, D., Steinmann, P., and Mergheim, J., Comput. Mech., 2014, vol. 54, p. 109.

  89. 89

    Patil, N., Pal, D., Khalid Rafi, H., et al., J. Manuf. Sci. Eng., 2015, vol. 137, 041001.

  90. 90

    Manzhirov, A. and Lychev, S., Dokl. Phys., 2012, vol. 57, no. 4, p. 160.

  91. 91

    Manzhirov, A. and Lychev, S., in Aktual’nye problemy mekhaniki. 50 let Institutu problem mekhaniki im. A.Yu. Ishlinskogo RAN (Actual Problems of Mechanics: 50 Years of the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences), Moscow: Nauka, 2015, p. 426.

  92. 92

    Manzhirov, A., Procedia Manuf., 2017, vol. 7, p. 59.

  93. 93

    Lychev, S. and Manzhirov, A., in Proc. World Congress on Engineering (WCE), London, 2014, vol. 2, p. 1327.

  94. 94

    Zinovieva, O., Zinoviev, A., and Ploshikhin, V., Comput. Mater. Sci., 2018, vol. 141, p. 207.

  95. 95

    Zinovieva, O., Zinoviev, A., and Ploshikhin, V., in Proc. European Solid Mechanics Conf., Bologna, 2018, p. 560.

  96. 96

    Mani, M., Lane, B.M., Alkan Donmez, M., et al., Int. J. Prod. Res., 2016, vol. 55, no. 5, p. 1400. https://doi.org/10.1080/00207543.2016.1223378

  97. 97

    Kruth, J.-P., Mercelis, P., van Vaerenbergh, J., et al., Virtual Model.Rapid Manuf., 2008, p. 521.

  98. 98

    Tang, L. and Landers, R., J. Manuf. Sci. Eng., 2010, vol. 132, no. 1, 011010.

  99. 99

    Song, L. and Mazumder, J., IEEE Trans. Control Syst. Technol., 2011, vol. 19, no. 6, p. 1349.

  100. 100

    Song, L., Bagavath-Singh, V., Dutta, B., et al., Int. J. Adv. Manuf. Technol., 2011, vol. 58, nos. 1–4, p. 247.

  101. 101

    Craeghs, T., Bechmann, F., Berumen, S., et al., Phys. Procedia, 2010, vol. 5, p. 505.

  102. 102

    Craeghs, T., Yasa, E., and Kruth, J.P., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX, 2011, p. 212.

  103. 103

    Craeghs, T., Clijsters, S., Kruth, J.-P., et al., Phys. Procedia, 2012, vol. 39, p. 753.

  104. 104

    Mumtaz, K. and Hopkinson, N., J. Mater. Process Technol., 2010, vol. 210, no. 2, p. 279.

  105. 105

    Ning, Y., Wong, Y.S., Fuh, J.Y.H., et al., IEEE Trans. Autom. Sci. Eng., 2006, vol. 3, p. 73.

  106. 106

    Wang, X., Rapid Prototyping J., 1999, vol. 5, no. 3, p. 129.

  107. 107

    Manesh, M., Wong, Y.S., Fuh, J.Y.H., et al., Int. J. Adv. Manuf. Technol., 2006, vol. 31, nos. 3–4, p. 374.

  108. 108

    Rosenthal, D., in Proc.Congres National des Sciences, Brussels, 1935, p. 1277.

  109. 109

    Rosenthal, D., Weld. J., 1938, vol. 17, no. 4, p. 2.

  110. 110

    Rosenthal, D., Weld. J., 1941, vol. 20, no. 5, p. 220.

  111. 111

    Rosenthal, D., Trans.ASME, 1946, vol. 43, no. 11, p. 849.

  112. 112

    Eagar, T. and Tsai, N., Weld. J., 1983, vol. 62, no. 12, p. 5346.

  113. 113

    Vasinonta, A., Beuth, J., and Griffith, M., in Proc. of the Solid Freeform Fabrication Symp., 1999, p. 383.

  114. 114

    Vasinonta, A., Beuth, J.L., and Griffith, M.L., J. Manuf. Sci. Eng., 2001, vol. 123, no. 4, p. 615.

  115. 115

    Wang, Q., Li, J., Gouge, M., et al., J. Manuf. Sci. Eng., 2016, vol. 139, no. 2, 021013.

  116. 116

    Sammons, P., Bristow, D., and Landers, R., J. Manuf. Sci. Eng., 2013, vol. 135, no. 5, 054501.

  117. 117

    Cao, X. and Ayalew, B., in Proc. American Control Conference (ACC) IEEE, 2015. https://doi.org/10.1109/acc.2015.7171895

  118. 118

    Zeng, K., Pal, D., and Stacker, B., in Proc. of the 23rd Annual Int. Solid Freeform Fabrication Symp, Add-it. Manuf. Conf. CFF2012, 2012, p. 796.

  119. 119

    Markl, M. and Korner, C., Annu. Rev. Mater. Res., 2014, vol. 46, p. 1.

  120. 120

    Schoinochoritis, B., Chantzis, D. and Salonitis, K., Proc. Inst. Mech. Eng.,Part B, 2015, vol. 23, no. 1, p. 96.

  121. 121

    Rai, A., Markl, M., and Korner, C., Comput. Mater. Sci., 2016, vol. 124, p. 37.

  122. 122

    Rai, A., Helmer, I.L., and Korner, C., Addit. Manuf., 2017, vol. 13, p. 124.

  123. 123

    Rolchigo, M., Mendoza, M.Y., Samimi, P., et al., Metal. Mater. Trans. A, 2017, vol. 48, p. 3606.

  124. 124

    Gu, D. and Yan, P., J. Appl. Phys., 2015, vol. 118, 233109.

  125. 125

    Yuan, P. and Gu, D., J. Phys. D: Appl. Phys., 2015, vol. 48, no. 3, 035303.

  126. 126

    Manvatkar, V., De, A., and Debroy, T., Mater. Sci. Technol., 2015, vol. 31, no. 8, p. 924.

  127. 127

    David, S.A. and Debroy, T., Science, 1992, vol. 257, no. 5069, p. 497.

  128. 128

    DebRoy T. and David, S., Rev. Modern Phys., 1995, vol. 67, p. 85.

  129. 129

    Wang, H., Shi, Y., and Gong, S., J. Phys. D: Appl. Phys., 2006, vol. 39, no. 21, p. 4722.

  130. 130

    Morville, S., Carin, M., Peyre, P., et al., J. Laser Appl., 2012, vol. 24, 032008.

  131. 131

    Li, S., Xiao, H., Liu, K., et al., Mater. Des., 2017, vol. 119, p. 351. https://doi.org/10.1016/j.matdes.2017.01.065

  132. 132

    Gan, Z., Yu, G., He, X., et al., Int. J. Heat Mass Transfer, 2015, vol. 104, p. 28. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.049

  133. 133

    Saadlaoui, Y., Feulvarch, É., Delache, A., et al., C. R. Mec., 2018, vol. 346, no. 11, p. 999.

  134. 134

    Chan, C., Mazumder, J., and Chen, M., J. Appl. Phys., 1988, vol. 64, p. 6166.

  135. 135

    Leblond, J.B., Amin El-Sayed, H. and Bergheau, J.M., C. R. Mec., 2013, vol. 341, p. 770.

  136. 136

    Yu, G., Gu, D., Dai, D., et al., J. Phys. D: Appl. Phys., 2016, vol. 49, no. 13, 135501.

  137. 137

    Korner, C., Attar, E., and Heinl, P., J. Mater. Process Technol., 2011, vol. 211, no. 6, p. 978.

  138. 138

    Bergheau, J.M. and Fortunier, R., Finite Element Simulation of Heat Transfer, Wiley, 2008.

  139. 139

    Feulvarch, E., Bergheau, J.M., and Leblond, J.B., Int. J. Numer. Math., 2009, vol. 78, p. 1492.

  140. 140

    Williams, R.J., Davies, C.M., and Hooper, P.A., Addit. Manuf., 2018, vol. 22, p. 416. https://doi.org/10.1016/j.addma.2018.05.038

  141. 141

    Li, C., Fu, C.H., Guo, Y.B., et al., J. Mater. Process. Technol., 2016, vol. 229, p. 703.

  142. 142

    Moran, T.P., Li, P., Warner, D.H., et al., Addit. Manuf., 2018, vol. 21, p. 215. https://doi.org/10.1016/j.addma.2018.02.015

  143. 143

    Zhang, Z., Huang, Y., Rani Kasinathan, A., et al., Opt. Laser Technol., 2019, vol. 109, p. 297.

  144. 144

    Roberts, L., Wang, C.J., Esterlein, R., et al., Int. J. Mach. Tools Manuf., 2009, vol. 49, p. 916.

  145. 145

    Antony, K., Arivazhagan, N., and Senthilkumaran, K., J. Manuf. Process., 2014, vol. 16, no. 3, p. 345.

  146. 146

    Criales, L.E., Arisoy, Y.M., Lane, B., et al., Addit. Manuf., 2017, vol. 13, p. 14.

  147. 147

    Schilp, J., Seidel, C., Krauss, H., et al., Adv. Mech. Eng., 2014, vol. 6, 217584.

  148. 148

    Fathi, A., Toyserkani, E., Khajepour, A., and Durali, M., J. Phys. D: Appl. Phys., 2006, vol. 39, p. 2613.

  149. 149

    Nie, Z., Wang, G., McGuffin-Cawley, J.D., et al., J. Mater. Process. Technol., 2016, vol. 235, p. 171. https://doi.org/10.1016/j.jmatprotec.2016.04.006

  150. 150

    Shi, Q., Gu, D., Xia, M., et al., Opt. Laser Technol., 2016, vol. 84, p. 9.

  151. 151

    Gladush, G. and Smurov, I., Fizicheskie osnovy lazernoi obrabotki materialov (Physical Fundamentals of Laser Processing of Materials), Moscow: Fizmatlit, 2017.

  152. 152

    Gusarov, A., Yadrovtsev, I., Bertrand, Ph., et al., J. Heat Transfer, 2009, vol. 131, no. 7, 072101.

  153. 153

    Liu, S., Zhu, H., Peng, G., et al., Mater. Des., 2018, vol. 142, p. 319.

  154. 154

    Yin, L., Zhu, H., Ke, L., et al., Comput. Mater. Sci., 2012, vol. 53, no. 1, p. 333.

  155. 155

    Mukherjee, T., Zhang, W., and Debroy, T., Comput. Mater. Sci., 2017, vol. 126, p. 360. https://doi.org/10.1016/j.commatsci.2016.10.003

  156. 156

    Foroozmehr, A., Badrossamay, M., Foroozmehr, E., et al., Mater. Des., 2016, vol. 89, p. 255.

  157. 157

    Wu, C., Wang, H., and Zhang, Y., Weld. Res., 2006, p. 284.

  158. 158

    Bondakar, M., Molavi-Zarandi, M., Chamanfar, A., et al., J. Manuf. Process., 2017, vol. 26, p. 339.

  159. 159

    Papadakis, L., Loizou, A., Risse, J., et al., in High Value Manufacturing: Advanced Research in Virtual and Rapid Prototyping, da Silva Bártolo, P.J., Eds., Boca Raton, FL: CRC, 2014, p. 613.

  160. 160

    Goldak, J., Chakravarti, A., and Bibby, M., Metall. Trans. B, 1984, vol. 15, no. 2, p. 299.

  161. 161

    Bartel, T., Guschke, I., and Menze, A., in Proc. European Solid Mechanics Conf., Bologna, 2018, p. 1283.

  162. 162

    Nunes, A.C., Jr., Weld. Res., 1983, vol. 68, no. 6, p. 165.

  163. 163

    Dunbar, A.J., Skulina, D., Pantělejev, L., et al., Addit. Manuf., 2016, vol. 12, p. 108. https://doi.org/10.1016/j.addma.2016.08.003

  164. 164

    Ilin, A., Logvinov, R., Kulikov, A., et al., Phys. Procedia, 2014, vol. 52, p. 638.

  165. 165

    Gusarov, A. and Kruth, J.P., Int. J. Heat Mass Transfer, 2005, vol. 48, p. 3423.

  166. 166

    Baillis, D. and Sacadura, J.F., J. Quant. Spectrosc. Radiat. Trasfer, 2000, vol. 47, p. 327.

  167. 167

    Zhang, Y., Guillemot, G., Bernacki, M., et al., Comput. Methods Appl. Mech. Eng., 2018, vol. 331, p. 514. https://doi.org/10.1016/j.cma.2017.12.003

  168. 168

    Bruna-Rosso, C., Demir, A., and Previtali, B., Mater. Des., 2018, vol. 156, p. 143.

  169. 169

    Ladani, L., Romano. J., Brindley, W., et al., Addit. Manuf., 2017, vol. 14, p. 13.

  170. 170

    Krivilev, M., et al., Vestn. Udmurt. Univ., Ser. Fiz. Khi-m., 2010, no. 1, p. 42.

  171. 171

    Kharanzhevskii, E. and Krivilyov, M., Phys. Met. Metall., 2011, vol. 111, no. 1, p. 53.

  172. 172

    Kostenkov, S. and Kharanzhevskii, E., Vestn. Udmurt. Univ., Ser. Fiz. Khim., 2012, no. 1, p. 13.

  173. 173

    Kostenkov, S., Kharanzhevskii, E., and Krivilev, E., Phys. Met. Metall., 2012, vol. 113, no. 1, p. 93.

  174. 174

    Krivilev, M., Kharanzhevskii, E., Gordeev, G.A., et al., in Upravlenie bol’shimi sistemami (Management of Large Systems), vol. 31, Moscow: Inst. Problem Upravleniya im. V.A. Trapeznikova, Ross. Akad. Nauk, 2010, p. 299.

  175. 175

    Sotov, A., Cand. Sci. (Eng.) Dissertation, Samara: Samara Univ., 2017.

  176. 176

    Tran, H. and Lo, Y., J. Mater. Process. Technol., 2018, vol. 255, p. 411.

  177. 177

    Gusarov, A., High Temp., 2009, vol. 47, no. 3, p. 375.

  178. 178

    Boley, C., Khairallah, S., and Rubenchik, A., Appl. Opt., 2015, vol. 54, p. 2477.

  179. 179

    Hopkins, A., Stillinger, F.H., and Torquato, S., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2013, vol. 88, 022205.

  180. 180

    King, W., Barth, H.D., Castillo, V.M., et al., J. Mater. Process. Technol., 2014, vol. 214, no. 12, p. 2915.

  181. 181

    Meier, C., Penny, R.W., Zou, Y., et al., Annu. Rev. Heat Transfer, 2016, vol. 20, p. 241.

  182. 182

    Wei, L.C., Ehrlich, L.E., Powell-Palm, M.J., et al., Addit. Manuf., 2018, vol. 21, p. 201. https://doi.org/10.1016/j.addma.2018.02.002

  183. 183

    Wang, X.C.,Laoui, T., Bonse, J., et al., Int. J. Adv. Manuf. Technol., 2002, vol. 19, p. 351.

  184. 184

    Meakin, P. and Jullien, R., J. Phys. (Paris), 1987, vol. 48, p. 1651.

  185. 185

    Hu, Z. and Manadevan, B., Int. J. Adv. Manuf. Technol., 2017, vol. 93, p. 2855.

  186. 186

    Gusarov, A. and Kovalev, E., Fiz. Khim. Obrab. Mater., 2009, no. 1, p. 70.

  187. 187

    Gusarov, A. and Kovalev, E., Fiz. Khim. Obrab. Mater., Fiz. Khim. Obrab. Mater., 2009, no. 2, p. 66.

  188. 188

    Wang, X. and Kruth, J.P., in Proc. Int. Conf. Math. Model. Simul. Meth. Technol., 2000, p. 673.

  189. 189

    Fischer, P., Romano, V., Weber, H.P., et al., Acta Mater., 2003, vol. 51, no. 6, p. 1651.

  190. 190

    Zhou, J., Zhang, Y., and Chen, J.K., Int. J. Heat Mass Transfer, 2009, vol. 52, nos. 13–14, p. 3137.

  191. 191

    Yan, W., Smith, J., Ge, W., et al., Comput. Mech., 2015, vol. 56, no. 2, p. 265.

  192. 192

    Chen, Q., Guillemot, G., Gandin, C.-A., et al., Addit. Manuf., 2017, vol. 16, p. 124.

  193. 193

    Masoomi, M., Thompson, S., and Shamsaei, N., Int. J. Mach. Tools Manuf., 2017, vols. 118–119, p. 73.

  194. 194

    Kaplan, A., Appl. Surf. Sci., 2012, vol. 258, p. 73.

  195. 195

    Bäuerle, D., Laser Processing and Chemistry, Berlin: Springer, 2011.

  196. 196

    Gladush, G.G. and Smurov, I., Physics of Laser Materials Processing: Theory and Experiment, Berlin: Springer, 2011.

  197. 197

    Yadroitsev, I., Bertrand, Ph., Antonenkova, G., et al., J. Laser Appl., 2013, vol. 25, 0252003.

  198. 198

    Yadroitsev, I., Thivillon, L., Bertrand, Ph., et al., Appl. Surf. Sci., 2007, vol. 254, p. 980.

  199. 199

    Gouge, M.F., Heigel, J.C., Michaleris, P., et al., Int. J. Adv. Manuf. Technol., 2015, vol. 79, nos. 1–4, p. 307. https://doi.org/10.1007/s00170-015-6831-x

  200. 200

    Kundakcioglu, E., Lazoglu, I., and Rawal, S., Int. J. Adv. Manuf. Technol., 2015, vol. 85, nos. 1–4, p. 493.

  201. 201

    Dai, K. and Shaw, L., Acta Mater., 2005, vol. 53, p. 4743.

  202. 202

    Zhang, Z., Farahmand, P., and Kovacevic, R., Mater. Des., 2016, vol. 109, p. 686. https://doi.org/10.1016/j.matdes.2016.07.114

  203. 203

    Marion, G., Cailletaud, G., Colin, C., et al., in Proc. 33rd Int. Congress on Applications of Lasers and Electro-Optics (ICALEO), San Diego, CA, 2014, paper 1801.

  204. 204

    Parry, L., Ashcroft, I.A., and Wildman, R.D., Addit. Manuf., 2016, vol. 12, p. 1. https://doi.org/10.1016/j.addma.2016.05.014

  205. 205

    Zhang, D., Int. J. Adv. Manuf. Technol., 2010, vol. 51, nos. 5–8, p. 649.

  206. 206

    Karkhin, V., Ilin, A.S., Pesch, H.J., et al., Sci. Technol. Weld. Joining, 2005, vol. 10, no. 5, p. 597.

  207. 207

    Duarte, C.A., Babuska, I., and Oden, J.T., Comput. Struct., 2000, vol. 77, p. 215.

  208. 208

    Duarte, C.A., Hamzeh, O.N., Liszka, T.J., et al., Comput. Methods Appl. Mech. Eng., 2001, vol. 190, nos. 15–17, p. 2227.

  209. 209

    Duarte, C.A. and Babuska, I., Int. J. Numer. Methods Eng., 2002, vol. 55, no. 12, p. 1477.

  210. 210

    Christensen, N., Davies, V., and Gjermudsen, R., Br. Weld. J., 1965, vol. 12, no. 2, p. 54.

  211. 211

    Bontha, S. and Klingbeil, N.W., J. Mater. Process. Technol., 2006, vol. 178, p. 135.

  212. 212

    Bontha, S., Klingbeil, N.W., Kobryn, P.A., et al., Mat-er. Sci. Eng., A, 2009, vols. 513–514, p. 311.

  213. 213

    Romanova, V., Zinovieva, O., Balokhonov, R., et al., AIP Conf. Proc., 2018, vol. 2051, 020256.

  214. 214

    Dobranich, D. and Dykhuizen, R., Scoping Thermal Calculations of the LENS Process: Internal Report, Sandia Natl. Lab., 1998.

  215. 215

    Dukhuizen, R. and Dobranich, D., Cooling Rates in the LENS Process: Internal Report, Sandia Natl. Lab., 1998.

  216. 216

    Rykalin, N. and Beketov, A., Weld. Prod., 1967, vol. 14, p. 42.

  217. 217

    Oreper, G., Eagar, T., and Szekely, J., Weld. J., 1983, vol. 62, no. 11, p. 307.

  218. 218

    Raganaswamy, P., Holden, T.M., Rogge, R.B., et al., J. Strain Anal. Eng. Des., 2003, vol. 38, no. 6, p. 519.

  219. 219

    Gockel, J., Klingbeil, N., and Bontha, S., Metall. Mater. Trans. B, 2016, vol. 47, no. 2, p. 1400.

  220. 220

    Yang, Y., Knol, M.F., van Keulen, F., et al., Addit. Manuf., 2018, vol. 21, p. 284.

  221. 221

    Carlsaw, H. and Jaeger, J., Conduction of Heat in Solid, Oxford: Oxford Univ. Press, 1967.

  222. 222

    Rykalin, N. and Nikolaev, A., Weld. World, 1971, vol. 93, nos. 3–4, p. 112.

  223. 223

    Pavelic, V., in Proc. Welding Inst. Conf. on Arc Physics and Weld Pool Behavior, London, 1979, p. 251.

  224. 224

    Peng, T.C., Sastry, S., and O’Neal, J., in Proc. Lasers in Metallurgy Symposium, 110th AIME Meeting, Chicago, IL, 1981, p. 279.

  225. 225

    Grosh, R. and Trabant, E., Weld. J., 1956, vol. 35, no. 8, p. 396.

  226. 226

    Stakgold, I., Green’s Functions and Boundary Value Problems, New York: Wiley, 1979.

  227. 227

    Ishizaki, K., Murai, K., and Kanbe, Y., Penetration in arc welding and convection in molten metal, Int. Inst. Welding (IIW), Doc. 212-77-66.

  228. 228

    Mills, G., Weld. J., 1979, vol. 58, no. 1, p. 21.

  229. 229

    Heiple, C. and Roper, J., Weld. J., 1982, vol. 61, no. 4, p. 97.

  230. 230

    Apps, R. and Milner, D., Br. Weld. J., 1955, vol. 2, no. 10, p. 475.

  231. 231

    Yan, C., Liu, W., Tang, Z., et al., Opt. Laser Technol., 2018, vol. 106, p. 427. https://doi.org/10.1016/j.optlastec.2018.04.034

  232. 232

    Karkhin, V., Teplovye protsessy pri svarke (Thermal Processes in Welding), St. Petersburg: St. Petersburg. Politekh. Univ., 2015, 2nd ed.

  233. 233

    Borisov, V., Teoriya dvukhfaznoi zony metallicheskogo slitka (Theory of a Two-Phase Zone of a Metal Ingot), Moscow: Metallurgiya, 1987.

  234. 234

    Vinogradov, V. and Tyazhel’nikova, I., Vestn. Udmurt. Univ., Ser. Fiz. Khim., 2008, no. 1, p. 37.

  235. 235

    Lykov, A., Yavleniya perenosa v kapillyarno-poristykh telakh (Transport Phenomena in Capillary-Porous Bodies), Moscow: Gos. Izd. Tekh.-Teor. Lit., 1954.

  236. 236

    Krivilev, M., Kharanzhevskii, E., Gordeev, G.A., et al., in Upravlenie bol’shimi sistemami (Management of Large Systems), vol. 31, Moscow: Inst. Problem Upravleniya im. V.A. Trapeznikova, Ross. Akad. Nauk, 2010, p. 299.

  237. 237

    Galenko, P. and Danilov, D., Phys. Lett. A, 1997, vol. 235, p. 271.

  238. 238

    Vernott, P., C. R. Acad. Sci., 1958, vol. 246, no. 22, p. 3154.

  239. 239

    Cattaneo, C., C. R. Acad. Sci., 1958, vol. 247, no. 4, p. 431.

  240. 240

    Lykov, A., Teoriya teploprovodnosti (Heat Conduction Theory), Moscow: Vysshaya Shkola, 1967.

  241. 241

    Shashkov, A., Bubnov, A., and Yanovskii, S., Volnovye yavleniya teploprovodnosti (Wave Phenomena of Heat Conductunce), Moscow: URSS, 2004.

  242. 242

    Lykov, A., Teplomassoobmen. Spravochnik (Heat and Mass Transfer: A Reference Book), Moscow: Energiya, 1978.

  243. 243

    Sobolev, S., Phys.—Usp., 1991, vol. 34, no. 3, p. 217.

  244. 244

    Samarskii, A., Galaktionov, R.A., Kurdyumoiv, S.P., et al., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii (Exacerbation Modes in Problems for Quasilinear Parabolic Equations), Moscow: Nauka, 1987.

  245. 245

    Formalev, V., Kolesnik, S., and Kuznetsova, E., High Temp., 2015, vol. 53, no. 1, p. 68.

  246. 246

    Fergani, O., Berto, F., Welo, T., et al., Fatigue Fract. Eng. Mater. Struct., 2017, vol. 40, p. 971.

  247. 247

    Arutyunyan, N., Manzhirov, A., and Naumov, V., Kontaktnye zadachi mekhaniki rastushchikh tel (Contact Problems of the Mechanics of Growing Bodies), Moscow: Nauka, 1991.

  248. 248

    Lychev, S. and Lycheva, T., in Proc. 3rd Polish Congress of Mechanics & 21st Computer Methods in Mechanics, Gdansk, Poland, 2015, p. 923.

  249. 249

    Lychev, S.A. and Manzhirov, A.V., J. Phys.: Conf. Ser., 2009, vol. 181, 012096.

  250. 250

    Manzhirov, A., in Proc. ASME 2014 Int. Mechanical Engineering Congress and Exposition, Montreal, Canada, 2014. https://doi.org/10.1115/IMECE2014-36712

  251. 251

    Manzhirov, A., Lychev, S., and Gupta, N., Proc. Indian Natl. Sci. Acad., 2013, suppl. issue, part A, p. 529.

  252. 252

    Lychev, S. and Manzhirov, A., Mech. Solids, 2013, vol. 48, no. 5, p. 86.

  253. 253

    Manzhirov, A., Vestn. Nizhegorod. Univ. im. N.I. Lobachevskogo, 2011, no. 4-4, p. 1603.

  254. 254

    Manzhirov, A. and Lychev, S., Prikl. Mat. Mekh., 2013, vol. 77, no. 4, p. 585.

  255. 255

    Manzhirov, A. and Parshin, D., in Mekhanika deformiruemogo tverdogo tela: Sbornik trudov IX Vserossiiskoi konferentsii (Mechanics of a Deformable Solid Body: Proc. IX All-Russian Conf.), Voronezh, 2016, p. 31.

  256. 256

    Manzhirov, A. and Lychev, S., in Proc. World Congress on Engineering (WCE), London, 2014, vol. 2, p. 1404.

  257. 257

    Manzhirov, A. and Parshin, D., Mech. Solids, 2015, vol. 50, no. 5, p. 559.

  258. 258

    Manzhirov, A. and Parshin, D., Mech. Solids, 2015, vol. 50, no. 6, p. 657.

  259. 259

    Manzhirov, A. and Parshin, D., Mechanics of Solids, 2015, vol. 51, no. 6, p. 692.

  260. 260

    Lychev, S. and Mark, A., Izv. Saratov. Univ.,Novaya Ser.: Mat. Mekh. Inf., 2014, vol. 14, no. 2, p. 209.

  261. 261

    Manzhirov, A. and Parshin, D., Vestn. Chuvash. Gos. Ped. Univ. im. I.Ya. Yakovleva,Ser.: Mekh. Predel’nogo Sostoyaniya, 2015, vol. 3, p. 22.

  262. 262

    Lychev, S., Vestn. Nizhegorod. Univ. im. N.I. Lobachevskogo, 2011, no. 4, p. 1588.

  263. 263

    Manzhirov, A. and Parshin, D., Vestn. Samarsk. Gos. Univ.,Estestvennonauchn. Ser., 2007, vol. 54, no. 4, p. 290.

  264. 264

    Kuznetsov, S.I., Manzhirov, A.V., and Fedotov, I., Mech. Solids, 2011, vol. 46, no. 6, p. 139.

  265. 265

    Levitin, A., Lychev, S., and Saifutdinov, I., in Proc. World Congress on Engineering (WCE), London, 2014, vol. 2, p. 1196.

  266. 266

    Manzhirov, A. and Parshin, D., Proc. World Congress on Engineering (WCE), London, 2016, p. 1131.

  267. 267

    Bychkov, P. and Korchak E., in Mater. Mezhdunar. molodezhn. nauchnoi konferentsii “XLIII Gagarinskie chteniya,” Sektsiya “Mekhanika i modelirovanie materialov i tekhnologii” (Proc. Int. Youth Sci. Conference “XLIII Gagarin Readings,” Section “Mechanics and Modeling of Materials and Technologies”), Moscow, 2011, p. 16.

  268. 268

    Bychkov, P.S., Kozintsev, V.M., Manzhirov, A.V., et al., Mech. Solids, 2017, vol. 52, no. 5, p. 524.

  269. 269

    Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry, New York: Interscience, 1963, vol. 1.

  270. 270

    Mukherjee, T., Zhang, W., and Debroy, T., Comput. Mater. Sci., 2017, vol. 126, p. 360. https://doi.org/10.1016/j.commatsci.2016.10.003

  271. 271

    Formalev, V. and Kolesnik, S., High Temp., 2013, vol. 51, no. 6, p. 795.

  272. 272

    Formalev, V. and Kolesnik, S., J. Eng. Phys. Thermophys., 2017, vol. 90, no. 6, p. 1302.

  273. 273

    Formalev, V. and Kolesnik, S., Int. J. Heat Mass Transfer, 2018, vol. 123, p. 994.

  274. 274

    Philo, A.M., Sutcliffe, C.J., Sillars, S., et al., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX, 2017, p. 1203.

  275. 275

    Keller, N. and Ploshikhin, V., in Proc. of the Solid Freeform Fabrication Symp., Austin, TX, 2014, p. 4.

  276. 276

    Alvarez, P., Ecenarro, J., Setien, I., et al., Int. J. Eng. Res. Sci., 2016, vol. 2, no. 10, p. 39.

  277. 277

    Ahmad, B., van der Veen, S.O., Fitzpatrick, M.E., et al., Addit. Manuf., 2018, vol. 22, p. 571.

  278. 278

    Hill, M.R. and Nelson, D.V., The Inherent Strain Method for Residual Stress Determination and Its Application to a Long Welded Joint, ASME, 1995, vol. 318.

  279. 279

    Bugatti, M. and Semeraro, Q., Addit. Manuf., 2018, vol. 23, p. 329.

  280. 280

    Kamara, A., Wang, W., Marimuthu, S., et al., Proc. Inst. Mech. Eng.,Part B, 2011, vol. 225, no. 1, p. 87.

  281. 281

    Yang, K.V., Rometsch, P., Davies, C.H.J., et al., Mate-r. Des., 2018, vol. 154, p. 275.

  282. 282

    Hitzler, L., Janousch, C., Schanz, J., et al., J. Mater. Process. Technol., 2017, vol. 243, p. 48. https://doi.org/10.1016/j.jmatprotec.2016.11.029

  283. 283

    Wei, L.C., Ehrlich, L.E., Powell-Palm, M.J., et al., Addit. Manuf., 2018, vol. 21, p. 201. https://doi.org/10.1016/j.addma.2018.02.002

  284. 284

    Trapp, J., Rubenchik, A.M., Guss, G., et al., Appl. Mater. Today, 2017, vol. 9, p. 341.

  285. 285

    Thermo-Mechanical Modeling of Additive Manufacturing, Gouge, M. and Michaleris, P., Eds., Oxford: Butterworth-Heinemann, 2017.

  286. 286

    Mukherjee, T., Wei, H.L., De, A., et al., Comput. Mater.- Sci., 2018, vol. 150, p. 304.

  287. 287

    Zhang, Y., Guillemot, G., Bernacki, M., et al., Comput. Methods Appl. Mech. Eng., 2018, vol. 331, p. 514. https://doi.org/10.1016/j.cma.2017.12.003

  288. 288

    Kakhramanov, R.M., Knyazeva, A.G., Rabinskiy, L.N., et al., High Temp., 2017, vol. 55, no. 5, p. 731.

  289. 289

    Denlinger, E.R., Gouge, M., and Irwing, J., et al., Addi-t. Manuf., 2017, vol. 16, p. 73. https://doi.org/10.1016/j.addma.2017.05.001

  290. 290

    Santos, L.S., Gupta, S.K., and Bruck, H.A., Simulation of buckling of internal features during selective laser sintering of metals, Addit. Manuf., 2018, vol. 23, p. 235. https://doi.org/10.1016/J.ADDMA.2018.08.002

  291. 291

    Afazov, S., Denmark, W.A.D., Toralles, B.L., et al., Addit. Manuf., 2017, vol. 17, p. 15.https://doi.org/10.1016/j.addma.2017.07.005

  292. 292

    Dunbar, A.J., Skulina, D., Pantělejev, L., et al., Addit. Manuf., 2016, vol. 12, p. 108. https://doi.org/10.1016/j.addma.2016.08.003

  293. 293

    Michopoulos, J.G., Iliopoulos, J.G., Steuben, J.C., et al., Addit. Manuf., 2015, vol. 22, p. 784. https://doi.org/10.1016/j.addma.2018.06.019

  294. 294

    Mirkoohi, E., Ning, J., Bocchini, P., et al., J. Manuf. Mater. Process., 2018, vol. 2, no. 3, p. 63.

  295. 295

    Formalev, V., Kuznetsova, E., and Kuznetsova, E., Period. Tche Quim., 2018, vol. 15, p. 377.

  296. 296

    Ding, J., Colegrove. P., Mehnen, J., et al., Int. J. Adv. Manuf. Technol., 2014, vol. 70, nos. 1–4, p. 227.

  297. 297

    Lindgren, L.E., Lundbäck, A., Fisk, M., et al., Addit. Manuf., 2016, vol. 12, p. 144.

  298. 298

    Foteinopoulos, P., Papacharalampopoulos, A., and Stavropoulos, P., CIRP J. Manuf. Sci. Tech, 2018, vol. 20, p. 66.

  299. 299

    Michaleris, P., Finite Elem. Anal. Des., 2014, vol. 86, p. 51. https://doi.org/10.1016/j.finel.2014.04.003

  300. 300

    Michaleris, P., Finite Elem. Anal. Des., 2014, vol. 86, p. 51. https://doi.org/10.1016/j.finel.2014.04.003

Download references

Funding

The work was supported by the Russian Foundation for Basic Research, project nos. 17-01-00837-a, 19-08-00938-a, 19-01-00695-a.

Author information

Correspondence to L. N. Rabinskiy.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhavoronok, S.I., Kurbatov, A.S., Rabinskiy, L.N. et al. Recent Problems of Heat-Transfer Simulation in Technological Processes of Selective Laser Melting and Fusion. High Temp 57, 916–943 (2019). https://doi.org/10.1134/S0018151X19060178

Download citation