Residual stress prediction in selective laser melting

A critical review of simulation strategies
  • Leonardo Bertini
  • Francesco Bucchi
  • Francesco Frendo
  • Mattia Moda
  • Bernardo Disma MonelliEmail author


This review focuses on the analysis of numerical models aimed at predicting the residual stress-strain field produced by the selective laser melting process. Our first intent is to favor an intuitive understanding of the underlying physics and then to provide an overview of the available simulation strategies specifying their field of application. In fact, given the complexity and the multi-scale nature of the process, various tailored models are needed for the assessment and prediction of defects and manufacturing issues arising during the building phase. Regarding the estimation of residual stresses, the available models were reviewed and classified on the basis of the dimensional scale of the simulated phenomena. Meso-scale models perform the detailed simulation of the scanning process, but the high computational cost currently prevents their application on the whole build volume (the current limit on the scanning volume is approximately 100 mm3 with dynamic mesh coarsening techniques). Macro-scale models have been developed to overcome this limit by introducing deep simplifications of the thermo-structural problem. From our review, it appears that meso-scale modeling has reached a significant maturity, while a widely adopted strategy for macro-scale simulations has not emerged yet.


Additive manufacturing Powder bed fusion Multi-scale modeling Finite element simulation Residual stress Distortion 



Difference operator

Vector differential operator


Same order of magnitude


Identity matrix


Stefan–Boltzmann constant


Nusselt number


Fourier number


Position vector




Beam power


Scanning speed


Laser energy absorptivity




Thermal conductivity

\(\mathbf {q}^{\prime \prime }\)

Heat flux density

\(q^{\prime \prime \prime }\)

Heat generation per unit volume


Heat transfer coefficient


Characteristic length




Dynamic viscosity


Specific heat at constant pressure


Emissivity of the grey body


Enthalpy of fusion per unit volume


Enthalpy of vaporization






Boiling point


Poisson’s ratio


Volume energy density


Thermal diffusivity


Layer thickness


Distance between adjacent tracks


Generalized beam diameter


Surface normal unit-vector






Coefficient of thermal expansion


Surface tension


Standard acceleration due to gravity


Biot number


Marangoni number


Grashof number


Cauchy stress tensor


Green-Lagrangian strain tensor


Displacement field

\( \ddot{\mathbf{u}} \)

Acceleration field


Thermal specific heat matrix


Thermal conductivity matrix


Structural damping matrix


Structural stiffness matrix


Thermoelastic damping matrix


Thermoelastic stiffness matrix


Nodal temperature vector


Nodal displacement vector


Thermal body force vector


Thermal gradient force vector


Structural nodal loads vector


Thermal nodal loads vector


Optical penetration depth

\(q_{\text {I}}^{\prime \prime }\)



Euclidean norm


Euler’s number


Precision of a normal distribution


Enthalpy per unit volume


Average diameter of powder particles


Compliance elastic tensor


Yield stress


Cauchy traction vector



  1. 1.
    Adam GAO, Zimmer D (2014) Design for additive manufacturing—element transitions and aggregated structures. CIRP J Manuf Sci Technol 7(1):20–28. CrossRefGoogle Scholar
  2. 2.
    Adam GAO, Zimmer D (2015) On design for additive manufacturing: evaluating geometrical limitations. Rapid Prototyp J 21(6):662–670. CrossRefGoogle Scholar
  3. 3.
    Alessandro F, Luca R, Alessandro M (2014) Modelling for predicting seam geometry in laser beam welding of stainless steel. Int J Therm Sci 79:194–205. CrossRefGoogle Scholar
  4. 4.
    Ali H, Ghadbeigi H, Mumtaz K (2018) Effect of scanning strategies on residual stress and mechanical properties of Selective Laser Melted Ti6Al4V. Mater Sci Eng: A 712:175–187. CrossRefGoogle Scholar
  5. 5.
    Alrbaey K, Wimpenny D, Tosi R, Manning W, Moroz A (2014) On optimization of surface roughness of selective laser melted stainless steel parts: a statistical study. J Mater Eng Perform 23(6):2139–2148. CrossRefGoogle Scholar
  6. 6.
    Antony K, Arivazhagan N, Senthilkumaran K (2014) Numerical and experimental investigations on laser melting of stainless steel 316L metal powders. J Manuf Process 16(3):345–355. CrossRefGoogle Scholar
  7. 7.
    Averyanova M, Cicala E, Bertrand P, Grevey D (2012) Experimental design approach to optimize selective laser melting of martensitic 17-4 PH powder: part I – single laser tracks and first layer. Rapid Prototyp J 18(1):28–37. CrossRefGoogle Scholar
  8. 8.
    Badrossamay M, Childs T (2007) Further studies in selective laser melting of stainless and tool steel powders. Int J Mach Tools Manuf 47(5):779–784. CrossRefGoogle Scholar
  9. 9.
    Bartolomeu F, Buciumeanu M, Pinto E, Alves N, Carvalho O, Silva F, Miranda G (2017) 316L stainless steel mechanical and tribological behavior – a comparison between selective laser melting, hot pressing and conventional casting. Add Manuf 16:81–89. Google Scholar
  10. 10.
    Bate PS, Wilson DV (1986) Analysis of the bauschinger effect. Acta Metall 34(6):1097–1105. CrossRefGoogle Scholar
  11. 11.
    Bejan A (2013) Convection heat transfer. Wiley, New York. zbMATHCrossRefGoogle Scholar
  12. 12.
    Bejan A, Kraus AD (2003) Heat transfer handbook. Wiley, New YorkGoogle Scholar
  13. 13.
    Bourell D, Coholich J, Chalancon A, Bhat A (2017) Evaluation of energy density measures and validation for powder bed fusion of polyamide. CIRP Ann 66(1):217–220. CrossRefGoogle Scholar
  14. 14.
    Casavola C, Campanelli SL, Pappalettere C, Campanelli L, Pappalettere C (2008) Experimental analysis of residual stresses in the selective laser melting process. In: Proceedings of the XIth International Congress and Exposition, vol 3, pp 1479–1486Google Scholar
  15. 15.
    Casavola C, Campanelli SL, Pappalettere C (2009) Preliminary investigation on distribution of residual stress generated by the selective laser melting process. J Strain Anal Eng Des 44 (1):93–104. CrossRefGoogle Scholar
  16. 16.
    Cengel YA (2002) Heat transfer: a practical approach. Mcgraw-Hill, TxGoogle Scholar
  17. 17.
    Cervera G, Bugeda M, Lombera G (1999) Numerical prediction of temperature and density distributions in selective laser sintering processes. Rapid Prototyp J 5(1):21–26. CrossRefGoogle Scholar
  18. 18.
    Cheng B, Shrestha S, Chou K (2016) Stress and deformation evaluations of scanning strategy effect in selective laser melting. Add Manuf 12:240–251. Google Scholar
  19. 19.
    Conti P, Cianetti F, Pilerci P (2018) Parametric finite elements nodel of SLM additive manufacturing process. Procedia Struct Integr 8:410–421. CrossRefGoogle Scholar
  20. 20.
    Contuzzi N, Campanelli SL, Ludovico AD (2011) 3D finite element analysis in the selective laser melting process. Int J Simul Modell 10(3):113–121. CrossRefGoogle Scholar
  21. 21.
    Criales LE, Arısoy YM, Özel T (2016) Sensitivity analysis of material and process parameters in finite element modeling of selective laser melting of Inconel 625. Int J Adv Manuf Technol 86(9-12):2653—-2666. CrossRefGoogle Scholar
  22. 22.
    Dai D, Gu D (2014) Thermal behavior and densification mechanism during selective laser melting of copper matrix composites: simulation and experiments. Mater Des 55:482–491. CrossRefGoogle Scholar
  23. 23.
    Dai K, Shaw L (2002) Distortion minimization of laser-processed components through control of laser scanning patterns. Rapid Prototyp J 8(5):270–276. CrossRefGoogle Scholar
  24. 24.
    Dai K, Shaw L (2004) Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders. Acta Mater 52(1):69–80. CrossRefGoogle Scholar
  25. 25.
    Denlinger ER, Irwin J, Michaleris P (2014) Thermomechanical modeling of additive manufacturing large parts. J Manuf Sci Eng 136(6):061007. CrossRefGoogle Scholar
  26. 26.
    Denlinger ER, Heigel JC, Michaleris P (2015) Residual stress and distortion modeling of electron beam direct manufacturing Ti-6Al-4V. Proc Inst Mech Eng Part B: J Eng Manuf 229(10):1803–1813. CrossRefGoogle Scholar
  27. 27.
    Denlinger ER, Heigel JC, Michaleris P, Palmer TA (2015) Effect of inter-layer dwell time on distortion and residual stress in additive manufacturing of titanium and nickel alloys. J Mater Process Technol 215:123–131. CrossRefGoogle Scholar
  28. 28.
    Denlinger ER, Gouge M, Irwin J, Michaleris P (2017) Thermomechanical model development and in situ experimental validation of the Laser Powder-Bed Fusion Process. Add Manuf 16:73–80. Google Scholar
  29. 29.
    Ding J, Colegrove P, Mehnen J, Ganguly S, Almeida PMS, Wang F, Williams S (2011) Thermo-mechanical analysis of wire and arc additive layer manufacturing process on large multi-layer parts. Comput Mater Sci 50(12):3315–3322. Google Scholar
  30. 30.
    Ding J, Colegrove P, Mehnen J, Williams S, Wang F, Almeida PS (2014) A computationally efficient finite element model of wire and arc additive manufacture. Int J Adv Manuf Technol 70(1-4):227–236. CrossRefGoogle Scholar
  31. 31.
    Dunbar AJ, Denlinger ER, Gouge MF, Michaleris P (2016) Experimental validation of finite element modeling for laser powder bed fusion deformation. Add Manuf 12:108–120. Google Scholar
  32. 32.
    Dunbar AJ, Denlinger ER, Heigel J, Michaleris P, Guerrier P, Martukanitz R, Simpson TW (2016) Development of experimental method for in situ distortion and temperature measurements during the laser powder bed fusion additive manufacturing process. Add Manuf 12:25–30. Google Scholar
  33. 33.
    Foroozmehr A, Badrossamay M, Foroozmehr E, Golabi S (2016) Finite element simulation of selective laser melting process considering optical penetration depth of laser in powder bed. Mater Des 89:255–263. CrossRefGoogle Scholar
  34. 34.
    Ghosh S, Choi J (2005) Modeling and experimental verification of transient/residual stresses and microstructure formation in multi-layer laser aided DMD process. J Heat Transf 128(7):662–679. CrossRefGoogle Scholar
  35. 35.
    Goldak J, Chakravarti A, Bibby M (1984) A new finite element model for welding heat sources. Metall Trans B 15(2):299–305. CrossRefGoogle Scholar
  36. 36.
    Goldak JA, Akhlaghi M (2005) Computational welding mechanics. Springer, Boston. Google Scholar
  37. 37.
    Gong H, Rafi K, Starr T, Stucker B (2013) The effects of processing parameters on defect regularity in Ti-6Al-4V parts fabricated by selective laser melting and electron beam melting. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 424–439Google Scholar
  38. 38.
    Gürtler F J, Karg M, Leitz KH, Schmidt M (2013) Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method. Phys Procedia 41:881–886. CrossRefGoogle Scholar
  39. 39.
    Gu H, Gong H, Pal D, Rafi K, Starr T, Stucker B (2013) Influences of energy density on porosity and microstructure of selective laser melted 17-4PH stainless steel. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 474– 489Google Scholar
  40. 40.
    Gusarov AV (2005) Modelling of radiation transfer in metallic powders at laser treatment. Int J Heat Mass Transfer 48(16):3423–3434. zbMATHCrossRefGoogle Scholar
  41. 41.
    Gusarov AV, Smurov I (2009) Two-dimensional numerical modelling of radiation transfer in powder beds at selective laser melting. Appl Surf Sci 255(10):5595–5599. CrossRefGoogle Scholar
  42. 42.
    Gusarov AV, Yadroitsev I, Bertrand P, Smurov I (2007) Heat transfer modelling and stability analysis of selective laser melting. Appl Surf Sci 254(4):975–979. CrossRefGoogle Scholar
  43. 43.
    Gusarov AV, Yadroitsev I, Bertrand P, Smurov I (2009) Model of radiation and heat transfer in laser-powder interaction zone at selective laser melting. J Heat Transfer 131(7):072101. CrossRefGoogle Scholar
  44. 44.
    Han J, Yang J, Yu H, Yin J, Gao M, Wang Z, Zeng X (2017) Microstructure and mechanical property of selective laser melted Ti6Al4V dependence on laser energy density. Rapid Prototyp J 23(2):217–226. CrossRefGoogle Scholar
  45. 45.
    Harrison NJ, Todd I, Mumtaz K (2015) Reduction of micro-cracking in nickel superalloys processed by selective laser melting: a fundamental alloy design approach. Acta Mater 94:59–68. CrossRefGoogle Scholar
  46. 46.
    Heigel JC, Michaleris P, Reutzel EW (2015) Thermo-mechanical model development and validation of directed energy deposition additive manufacturing of Ti-6Al-4V. Add Manuf 5:9–19. Google Scholar
  47. 47.
    Hodge NE, Ferencz RM, Solberg JM (2014) Implementation of a thermomechanical model for the simulation of selective laser melting. Comput Mech 54(1):33–51. MathSciNetCrossRefGoogle Scholar
  48. 48.
    Hodge NE, Ferencz RM, Vignes RM (2016) Experimental comparison of residual stresses for a thermomechanical model for the simulation of selective laser melting. Add Manuf 12:159–168. Google Scholar
  49. 49.
    Hsu CT, Cheng P, Wong KW (1994) Modified Zehner-Schlunder models for stagnant thermal conductivity of porous media. Int J Heat Mass Transfer 37(17):2751–2759. zbMATHCrossRefGoogle Scholar
  50. 50.
    Hussein A, Hao L, Yan C, Everson R (2013) Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Mater Des 52:638–647. CrossRefGoogle Scholar
  51. 51.
    Hutton DV (2004) Fundamentals of finite element analysis. McGraw-Hill, New YorkGoogle Scholar
  52. 52.
    Ibraheem AK, Brian D, Withers PJ (2002) Thermal and residual stress modelling of the selective laser sintering process. MRS Proc 758:1–6. CrossRefGoogle Scholar
  53. 53.
    ISO 11146-2:2005(E) (2005) Lasers and laser-related equipment – test methods for laser beam widths, divergence angles and beam propagation ratios – general astigmatic beams. International standard, International Organization for Standardization, Geneva, CHGoogle Scholar
  54. 54.
    Jamshidinia M, Kong F, Kovacevic R (2013) The coupled CFD-FEM model of electron beam melting\({\circledR }\) (EBM). In: ASME District F - Early Career Technical Conference Proceedings.
  55. 55.
    Keller N, Ploshikhin V (2014) New method for fast predictions of residual stress and distortions of AM parts. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 1229–1237Google Scholar
  56. 56.
    Khairallah SA, Anderson A (2014) Mesoscopic simulation model of selective laser melting of stainless steel powder. J Mater Process Technol 214(11):2627–2636. CrossRefGoogle Scholar
  57. 57.
    Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 108:36–45. CrossRefGoogle Scholar
  58. 58.
    King W, Anderson AT, Ferencz RM, Hodge NE, Kamath C, Khairallah SA (2015) Overview of modelling and simulation of metal powder bed fusion process at Lawrence Livermore National Laboratory. Mater Sci Technol 31(8):957–968. CrossRefGoogle Scholar
  59. 59.
    King WE, Anderson AT, Ferencz RM, Hodge NE, Kamath C, Khairallah SA, Rubenchik AM (2015) Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev 2(4):041304. CrossRefGoogle Scholar
  60. 60.
    Knowles CR, Becker TH, Tait RB (2012) Residual stress measurements and structural integrity implications for selective laser melted TI-6AL-4v. South Afr J Ind Eng 23(3):119–129. Google Scholar
  61. 61.
    Kolossov S, Boillat E, Glardon R, Fischer P, Locher M (2004) 3D FE simulation for temperature evolution in the selective laser sintering process. Int J Mach Tools Manuf 44(2-3):117–123. CrossRefGoogle Scholar
  62. 62.
    Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978–987. CrossRefGoogle Scholar
  63. 63.
    Körner C, Bauereiß A, Attar E (2013) Fundamental consolidation mechanisms during selective beam melting of powders. Modell Simul Mater Sci Eng 21(8):085011. CrossRefGoogle Scholar
  64. 64.
    Krol TA, Westhäuser S, Zäh M F, Schilp J, Groth G (2011) Development of a simulation-based process chain – strategy for different levels of detail for the preprocessing definitions. Simul Notes Eur 21(3-4):135–140. CrossRefGoogle Scholar
  65. 65.
    Krol TA, Seidel C, Schilp J, Hofmann M, Gan W, Zaeh MF (2013) Verification of structural simulation results of metal-based additive manufacturing by means of neutron diffraction. Phys Procedia 41:849–857. CrossRefGoogle Scholar
  66. 66.
    Kruth JP, Levy G, Klocke F, Childs THC (2007) Consolidation phenomena in laser and powder-bed based layered manufacturing. CIRP Ann 56(2):730–759. CrossRefGoogle Scholar
  67. 67.
    Labudovic M, Hu D, Kovacevic R (2003) A three dimensional model for direct laser metal powder deposition and rapid prototyping. J Mater Sci 38(1):35–49. CrossRefGoogle Scholar
  68. 68.
    Lee Y, Zhang W (2015) Mesoscopic simulation of heat transfer and fluid flow in laser powder bed additive manufacturing. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 1154–1165Google Scholar
  69. 69.
    Li C, Fu C, Guo Y, Fang F (2016) A multiscale modeling approach for fast prediction of part distortion in selective laser melting. J Mater Process Technol 229:703–712. CrossRefGoogle Scholar
  70. 70.
    Li R, Shi Y, Liu J (2009) Effects of processing parameters on the temperature field of selective laser melting metal powder. Powder Metall Metal Ceram 48(3-4):186–195. CrossRefGoogle Scholar
  71. 71.
    Li Y, Gu D (2014) Parametric analysis of thermal behavior during selective laser melting additive manufacturing of aluminum alloy powder. Mater Des 63:856–867. CrossRefGoogle Scholar
  72. 72.
    Li Y, Gu D (2014) Thermal behavior during selective laser melting of commercially pure titanium powder: numerical simulation and experimental study. Add Manuf 1-4:99–109. Google Scholar
  73. 73.
    Liebisch A, Merkel M (2016) On the numerical simulation of the thermal behavior during the selective laser melting process. Mater Werkst 47(5-6):521–529. CrossRefGoogle Scholar
  74. 74.
    Lindgren LE, Lundbäck A, Fisk M, Pederson R, Andersson J (2016) Simulation of additive manufacturing using coupled constitutive and microstructure models. Add Manuf 12:144–158. Google Scholar
  75. 75.
    Liu FR, Zhang Q, Zhou WP, Zhao JJ, Chen JM (2012) Micro scale 3D FEM simulation on thermal evolution within the porous structure in selective laser sintering. J Mater Process Technol 212(10):2058–2065. CrossRefGoogle Scholar
  76. 76.
    Liu H, Sparks T, Liou F, Dietrich DM (2015) Residual stress and deformation modelling for metal additive manufacturing processes. In: Proceedings of the world congress on mechanical, chemical and material engineering, vol 245, pp 1-9Google Scholar
  77. 77.
    Loh LE, Chua CK, Yeong WY, Song J, Mapar M, Sing SL, Liu ZH, Zhang DQ (2015) Numerical investigation and an effective modelling on the selective laser melting (SLM) process with aluminium alloy 6061. Int J Heat Mass Transfer 80:288–300. CrossRefGoogle Scholar
  78. 78.
    Ma L, Bin H (2007) Temperature and stress analysis and simulation in fractal scanning-based laser sintering. Int J Adv Manuf Technol 34(9-10):898–903. CrossRefGoogle Scholar
  79. 79.
    Mackenzie JK, Shuttleworth R (1949) A phenomenological theory of sintering. Proc Phys Soc Sect B 62 (12):833–852. CrossRefGoogle Scholar
  80. 80.
    Marimuthu S, Clark D, Allen J, Kamara AM, Mativenga P, Li L, Scudamore R (2013) Finite element modelling of substrate thermal distortion in direct laser additive manufacture of an aero-engine component. Proc Inst Mech Eng Part C: J Mech Eng Sci 227(9):1987–1999. CrossRefGoogle Scholar
  81. 81.
    Marion JB, Heald MA (1995) Classical electromagnetic radiation. Saunders College Publishing, PhiladelphiaGoogle Scholar
  82. 82.
    Martukanitz R, Michaleris P, Palmer T, DebRoy T, Liu ZK, Otis R, Heo TW, Chen LQ (2014) Toward an integrated computational system for describing the additive manufacturing process for metallic materials. Add Manuf 1-4:52–63. Google Scholar
  83. 83.
    Masmoudi A, Bolot R, Coddet C (2015) Investigation of the laser-powder-atmosphere interaction zone during the selective laser melting process. J Mater Process Technol 225:122–132. CrossRefGoogle Scholar
  84. 84.
    Masoomi M, Thompson SM, Shamsaei N (2017) Laser powder bed fusion of Ti-6Al-4V parts: thermal modeling and mechanical implications. Int J Mach Tools Manuf 118-119:73–90. CrossRefGoogle Scholar
  85. 85.
    Matsumoto M, Shiomi M, Osakada K, Abe F (2002) Finite element analysis of single layer forming on metallic powder bed in rapid prototyping by selective laser processing. Int J Mach Tools Manuf 42(1):61–67. CrossRefGoogle Scholar
  86. 86.
    Mercelis P, Kruth JPJ (2006) Residual stresses in selective laser sintering and selective laser melting. Rapid Prototyp J 12(5):254–265. CrossRefGoogle Scholar
  87. 87.
    Merriam-Webstercom (2018) Irradiance.
  88. 88.
    Mertens R, Vrancken B, Holmstock N, Kinds Y, Kruth JP, Van Humbeeck J (2016) Influence of powder bed preheating on microstructure and mechanical properties of H13 tool steel SLM parts. Phys Procedia 83:882–890. CrossRefGoogle Scholar
  89. 89.
    Moat RJ, Pinkerton AJ, Li L, Withers PJ, Preuss M (2011) Residual stresses in laser direct metal deposited Waspaloy. Mater Sci Eng: A 528(6):2288–2298. CrossRefGoogle Scholar
  90. 90.
    Mower TM, Long MJ (2016) Mechanical behavior of additive manufactured, powder-bed laser-fused materials. Mater Sci Eng: A 651:198–213. CrossRefGoogle Scholar
  91. 91.
    Mukherjee T, Zhang W, DebRoy T (2017) An improved prediction of residual stresses and distortion in additive manufacturing. Comput Mater Sci 126:360–372. CrossRefGoogle Scholar
  92. 92.
    Neugebauer F, Keller N, Ploshikhin V, Feuerhahn F, Koehler H (2014) Multi scale FEM simulation for distortion calculation in additive manufacturing of hardening stainless steel. In: Proceedings of the International Workshop on Thermal Forming and Welding Distortion, vol 54Google Scholar
  93. 93.
    Papadakis L, Loizou A (2013) A thermo-mechanical modeling reduction approach for calculating shape distortion in SLM manufacturing for aero engine components. In: Proceedings of the 6th International Conference on Advanced Research in Virtual and Rapid Prototyping, pp 613–618.
  94. 94.
    Papadakis L, Branner G, Schober A, Richter KH, Uihlein T (2012) Numerical modeling of heat effects during thermal manufacturing of aero engine components. In: Proceedings of the World Congress on Engineering 2012, vol 3Google Scholar
  95. 95.
    Papadakis L, Loizou A, Risse J, Schrage J (2014) Numerical computation of component shape distortion manufactured by selective laser melting. Procedia CIRP 18:90–95. CrossRefGoogle Scholar
  96. 96.
    Parry L, Ashcroft IA, Wildman RD (2016) Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-mechanical simulation. Add Manuf 12:1–15. Google Scholar
  97. 97.
    Paul R, Anand S, Gerner F (2014) Effect of Thermal deformation on part errors in metal powder based additive manufacturing processes. J Manuf Sci Eng 136(3):031009. CrossRefGoogle Scholar
  98. 98.
    Pitassi D, Benedetti M, Savoia E, Fontanari V, Molinari A, Luchin V, Zappini G (2018) Finite element thermal analysis of metal parts additively manufactured via selective laser melting. Finite Element Method, 6.
  99. 99.
    Prashanth K, Scudino S, Klauss H, Surreddi K, Lȯber L, Wang Z, Chaubey A, Ku̇hn U, Eckert J (2014) Microstructure and mechanical properties of Al–12Si produced by selective laser melting: effect of heat treatment. Mater Sci Eng: A 590:153–160. CrossRefGoogle Scholar
  100. 100.
    Pupo Y, Monroy KP, Ciurana J (2015) Influence of process parameters on surface quality of CoCrMo produced by selective laser melting. Int J Adv Manuf Technol 80(5-8):985–995. CrossRefGoogle Scholar
  101. 101.
    Rangaswamy P, Griffith ML, Prime MB, Holden TM, Rogge RB, Edwards JM, Sebring RJ (2005) Residual stresses in LENS\({\circledR }\) components using neutron diffraction and contour method. Mater Sci Eng: A 399(1-2):72–83. CrossRefGoogle Scholar
  102. 102.
    Read N, Wang W, Essa K, Attallah MM (2015) Selective laser melting of AlSi10Mg alloy: process optimisation and mechanical properties development. Mater Des (1980-2015) 65:417–424. CrossRefGoogle Scholar
  103. 103.
    Ren J, Liu J, Yin J (2011) Simulation of transient temperature field in the selective laser sintering process of W/Ni powder mixture. In: Computer and Computing Technologies in Agriculture IV. Springer, pp 494–503.
  104. 104.
    Roberts IA, Wang CJ, Esterlein R, Stanford M, Mynors DJ (2009) A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing. Int J Mach Tools Manuf 49(12-13):916–923. CrossRefGoogle Scholar
  105. 105.
    Safronov VA, Khmyrov RS, Kotoban DV, Gusarov AV (2016) Distortions and residual stresses at layer-by-layer additive manufacturing by fusion. J Manuf Sci Eng 139(3):031017. CrossRefGoogle Scholar
  106. 106.
    Sames WJ, List FA, Pannala S, Dehoff RR, Babu SS (2016) The metallurgy and processing science of metal additive manufacturing. Int Mater Rev 61(5):315–360. CrossRefGoogle Scholar
  107. 107.
    Scherer GW (1977) Sintering of low density glasses: i theory. J Am Ceram Soc 60(5-6):236–239. CrossRefGoogle Scholar
  108. 108.
    Scherer GW (1977) Sintering of low density glasses: III, Effect of a distribution of pore sizes. J Am Ceram Soc 60(5-6):243–246. CrossRefGoogle Scholar
  109. 109.
    Scherer GW (1986) Viscous sintering under a uniaxial load. J Am Ceram Soc 69 (9):206–207. CrossRefGoogle Scholar
  110. 110.
    Scherer GW, Bachman DL (1977) Sintering of low density glasses: II, Experimental study. J Am Ceram Soc 60(5-6):239–243. CrossRefGoogle Scholar
  111. 111.
    Schilp J, Seidel C, Krauss H, Weirather J (2014) Investigations on temperature fields during laser beam melting by means of process monitoring and multiscale process modelling. Adv Mech Eng 6:217584. CrossRefGoogle Scholar
  112. 112.
    Schoinochoritis B, Chantzis D, Salonitis K (2015) Simulation of metallic powder bed additive manufacturing processes with the finite element method: a critical review. Proc Inst Mech Eng Part B: J Eng Manuf 231(1):96–117. CrossRefGoogle Scholar
  113. 113.
    Seitz F (1940) The modern theory of solids. McGraw-Hill Inc., New YorkzbMATHGoogle Scholar
  114. 114.
    Shapiro M, Dudko V, Royzen V, Krichevets Y, Lekhtmakher S, Grozubinsky V, Shapira M, Brill M (2004) Characterization of powder beds by thermal conductivity: effect of gas pressure on the thermal resistance of particle contact points. Part Part Syst Charact 21(4):268–275. CrossRefGoogle Scholar
  115. 115.
    Shen N, Chou K (2012) Thermal modeling of electron beam additive manufacturing process: powder sintering effects. In: International Manufacturing Science and Engineering Conference, ASME, pp 287–295.
  116. 116.
    Sih SS, Barlow JW (1994) The prediction of the thermal conductivity of powders. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 397–401Google Scholar
  117. 117.
    Sih SS, Barlow JW (1995) Emissivity of powder beds. In: Proceedings of the Solid Freeform Fabrication Symposium, pp 402–408Google Scholar
  118. 118.
    Song B, Dong S, Liao H, Coddet C (2012) Process parameter selection for selective laser melting of Ti6Al4V based on temperature distribution simulation and experimental sintering, vol 61.
  119. 119.
    Starr TL, Gornet TJ, Usher JS (2011) The effect of process conditions on mechanical properties of laser-sintered nylon. Rapid Prototyp J 17(6):418–423. CrossRefGoogle Scholar
  120. 120.
    Strano G, Hao L, Everson RM, Evans KE (2013) Surface roughness analysis, modelling and prediction in selective laser melting. J Mater Process Technol 213(4):589–597. CrossRefGoogle Scholar
  121. 121.
    Thümmler F, Oberacker R (1993) An introduction to powder metallurgy. The Institute of Materials, UKGoogle Scholar
  122. 122.
    Thompson MK, Moroni G, Vaneker T, Fadel G, Campbell RI, Gibson I, Bernard A, Schulz J, Graf P, Ahuja B, Martina F (2016) Design for additive manufacturing: trends, opportunities, considerations, and constraints. CIRP Ann 65(2):737–760. CrossRefGoogle Scholar
  123. 123.
    Trosch T, Strößner J, Völkl R, Glatzel U (2016) Microstructure and mechanical properties of selective laser melted Inconel 718 compared to forging and casting. Mater Lett 164:428–431. CrossRefGoogle Scholar
  124. 124.
    Vastola G, Zhang G, Pei QX, Zhang YW (2016) Controlling of residual stress in additive manufacturing of Ti6Al4V by finite element modeling. Add Manuf 12:231–239. Google Scholar
  125. 125.
    Vrancken B, Thijs L, Kruth JP, Van Humbeeck J (2012) Heat treatment of Ti6Al4V produced by selective laser melting: microstructure and mechanical properties. J Alloys Compd 541:177–185. CrossRefGoogle Scholar
  126. 126.
    Wang XC, Laoui T, Bonse J, Kruth JP, Lauwers B, Froyen L (2002) Direct selective laser sintering of hard metal powders: Experimental study and simulation. Int J Adv Manuf Technol 19(5):351–357. CrossRefGoogle Scholar
  127. 127.
    Wang Z, Denlinger E, Michaleris P, Stoica AD, Ma D, Beese AM (2017) Residual stress mapping in Inconel 625 fabricated through additive manufacturing: method for neutron diffraction measurements to validate thermomechanical model predictions. Mater Des 113:169–177. CrossRefGoogle Scholar
  128. 128.
    Wei K, Gao M, Wang Z, Zeng X (2014) Effect of energy input on formability, microstructure and mechanical properties of selective laser melted AZ91d magnesium alloy. Mater Sci Eng: A 611:212–222. CrossRefGoogle Scholar
  129. 129.
    Weirather J (2015) Project final report. Technical report, Technische Universitaet MuenchenGoogle Scholar
  130. 130.
    Wu AS, Brown DW, Kumar M, Gallegos GF, King WE (2014) An experimental investigation into additive manufacturing induced residual stresses in 316L stainless steel. Metall and Mater Trans A 45(13):6260–6270. CrossRefGoogle Scholar
  131. 131.
    Yadroitsev I, Gusarov A, Yadroitsava I, Smurov I (2010) Single track formation in selective laser melting of metal powders. J Mater Process Technol 210(12):1624–1631. CrossRefGoogle Scholar
  132. 132.
    Yadroitsev I, Krakhmalev P, Yadroitsava I (2014) Selective laser melting of Ti6Al4V alloy for biomedical applications: temperature monitoring and microstructural evolution. J Alloys Compd 583:404–409. CrossRefGoogle Scholar
  133. 133.
    Yin J, Zhu H, Ke L, Lei W, Dai C, Zuo D (2012) Simulation of temperature distribution in single metallic powder layer for laser micro-sintering. Comput Mater Sci 53(1):333–339. CrossRefGoogle Scholar
  134. 134.
    Zaeh MF, Branner G (2010) Investigations on residual stresses and deformations in selective laser melting. Prod Eng 4(1):35–45. CrossRefGoogle Scholar
  135. 135.
    Zaeh MF, Branner G, Krol T (2010) A three dimensional FE-model for the investigation of transient physical effects in selective laser melting. In: Innovative developments in design and manufacturing - advanced research in virtual and rapid prototyping – Proceedings of VRP4, Leiria, Taylor & Francis, pp 415–424.
  136. 136.
    Zeng K, Pal D, Gong HJ, Patil N, Stucker B (2015) Comparison of 3DSIM thermal modelling of selective laser melting using new dynamic meshing method to ANSYS. Mater Sci Technol 31(8):945–956. CrossRefGoogle Scholar
  137. 137.
    Zäh M F, Lutzmann S (2010) Modelling and simulation of electron beam melting. Prod Eng 4(1):15–23. CrossRefGoogle Scholar
  138. 138.
    Zhang DQ, Cai QZ, Liu JH, Zhang L, Li RD (2010) Select laser melting of W-Ni-Fe powders: simulation and experimental study. Int J Adv Manuf Technol 51(5-8):649–658. CrossRefGoogle Scholar
  139. 139.
    Zhang Y, Zhang J (2017) Finite element simulation and experimental validation of distortion and cracking failure phenomena in direct metal laser sintering fabricated component. Add Manuf 16:49–57. Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil and Industrial EngineeringUniversity of PisaPisaItaly

Personalised recommendations