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A computational model of melt pool morphology for selective laser melting process

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Abstract

Selective laser melting (SLM) is a promising metal additive manufacturing technology, which holds widespread applications in numerous fields. Unfortunately, it is arduous to predict the real geometry of SLM part, which impedes its further development, while the morphology of melt pool, influenced and determined by process parameters, poses a crucial influence on the overall part geometry. Nonetheless, the association between process parameters and melt pool morphology is still unclear. Hence, it is indispensable to explore relevant solution to address this issue. For this purpose, this paper proposes a new model to directly establish the mathematical relationship between process parameters and melt pool structure for SLM process. In this model, the status of melt pool is first qualitatively analyzed via the defined synthetic process index, and three types of melting states are differentiated including low melting, intermediate melting, and high melting, which could cover different melt pool modes. Then, the computational model involving more physical mechanisms integrating mass conversion, heat exchange, and temperature field is constructed. Melt pool critical geometries including the height, width, depth, and length could be computed through the model. In order to validate the correctness of the proposed model, published experimental observations and existing models are compared. Calculation results from the proposed model show high consistency with the experimental samples and better accuracy than existing empirical models. Its applicability in melt pool classification and prediction is also verified, laying foundation for geometric simulation of SLM object which is successively shaped melt-pool by melt-pool.

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(adapted from Scime and Beuth [9]) of IN718. a Severe keyhole defect. b Normal morphology (all graphs are presented at the same size scale)

Fig. 11

(adapted from Yang et al. [28]) of TC4. a Severe keyhole defect. b Normal morphology. c Balling defect (all graphs are presented at the same size scale)

Fig. 12

(adapted from Kamath et al. [30]) of 316L. a Normal morphology. b Slightly balling (all graphs are presented at the same size scale)

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Abbreviations

\(a\) :

Thermal diffusivity (m2/s)

\(A\) :

Maximum cross-sectional area of melt pool (m2)

\({A}_{g}\) :

Contact area between melt pool and gas interface (m2)

\({A}_{s}\) :

Contact area between melt pool and solid interface (m2)

\(C\) :

Material specific heat capacity (J/(kgK))

\({C}_{l}\) :

Liquid specific heat capacity (J/(kgK))

\({C}_{s}\) :

Solid specific heat capacity (J/(kgK))

\({C}_{lackfusion}\) :

Critical normalized enthalpy of lack of fusion

\(d\) :

Melt pool depth (m)

\(D\) :

Laser beam diameter (m)

\({E}_{i}\) :

Specific internal energy of melt pool (J/kg)

\({E}_{s}\) :

Specific internal energy of solidification melt pool (J/kg)

\(h\) :

Melt pool height (m)

\({H}_{\mathrm{sl}}\) :

Melting enthalpy (J/m3)

\(\Delta H/{H}_{\mathrm{sl}}\) :

Normalized enthalpy

\(k\) :

Thermal conductivity (W/(mK))

\(K\) :

Temperature gradient (K/m)

\(l\) :

Melt pool length (m)

\({L}_{t}\) :

Layer thickness (m)

\(P\) :

Laser beam power (W)

\({Q}_{gc}\) :

Convection energy between melt pool and gas environment (J)

\({Q}_{gr}\) :

Radiation energy between melt pool and environment (J)

\({Q}_{sc}\) :

Conduction energy between melt pool and solid environment (J)

\(t\) :

Time (s)

\(T\) :

Transient melt pool temperature (K)

\({T}_{b}\) :

Material boiling temperature (K)

\({T}_{m}\) :

Material melting temperature (K)

\({T}_{o}\) :

Initial temperature (K)

\({T}_{ms}\) :

Steady-state melt pool temperature (K)

\(v\) :

Scanning speed (m/s)

\(V\) :

Melt pool volume (m3)

\(w\) :

Melt pool width (m)

\({\alpha }_{g}\) :

Thermal convection coefficient (W/(m2K))

\({\alpha }_{s}\) :

Equivalent thermal convection coefficient (W/(m2K))

\({\beta }_{h/d}\) :

Melt pool shape ratio of height to depth

\({\beta }_{l/w}\) :

Melt pool shape ratio of length to width

\({\beta }_{w/d}\) :

Melt pool shape ratio of width to depth

\(\varepsilon\) :

Thermal radiation coefficient

\(\eta\) :

Absorptivity of solid material

\({\eta }^{*}\) :

Absorptivity of powder material

\(\lambda\) :

Steady-state melt pool temperature coefficient

\({\lambda }_{melting}\) :

Melting degree index

\({\mu }_{HM}\) :

Critical coefficient of high melting state

\({\mu }_{IM}\) :

Critical coefficient of intermediate melting state

\({\mu }_{defect}^{keyhole}\) :

Critical coefficient of over-melting state

\({\mu }_{defect}^{lackfusion}\) :

Critical coefficient of under-melting state

\(\rho\) :

Material density (kg/m3)

\({\rho }_{p}\) :

Material density of powder state (kg/m3)

\({\rho }_{s}\) :

Material density of solid state (kg/m3)

\(\sigma\) :

Stefan-Boltzmann constant (W/(m2K4))

\(\tau\) :

Ratio of laser exposure time to thermal diffusion time

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Funding

This research is funded by the National Natural Science Foundation of China (grant number 52005021).

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, Beihang University, Beijing, 100191, China

    Kai Guo, Lihong Qiao, Zhicheng Huang & Yuda Cao

  2. LURPA, ENS Paris-Saclay, Université Paris-Sud, Université Paris-Saclay, 94235, Cachan, France

    Nabil Anwer

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Contributions

Kai Guo: conceptualization, methodology, investigation, visualization, writing–original draft. Lihong Qiao: conceptualization, methodology, writing–review and editing, supervision. Zhicheng Huang: methodology, writing–review and editing, supervision, project administration. Nabil Anwer: writing–review and editing, supervision. Yuda Cao: writing–review and editing.

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Correspondence to Zhicheng Huang.

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Appendices

Appendix 1. Material properties for IN718, TC4, and 316L

Table 4 Material parameters of IN718, TC4, and 316L for calculation
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Appendix 2. Fitting constant values for IN718, TC4, and 316L

Table 5 Fitting values of constants in melt pool ratio equations for different materials
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Appendix 3. Adopted energy absorptivity under different machines and process conditions for IN718, TC4, and 316L

Table 6 Adopted energy absorptivity under different machines and process conditions for IN718
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Table 7 Adopted energy absorptivity under different machines and process conditions for TC4
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Table 8 Adopted energy absorptivity under different machines and process conditions for 316L
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Guo, K., Qiao, L., Huang, Z. et al. A computational model of melt pool morphology for selective laser melting process. Int J Adv Manuf Technol 121, 1651–1673 (2022). https://doi.org/10.1007/s00170-022-09366-y

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