ABSTRACT: A three-dimensional thermo-mechanical coupling model has been developed to simulate a single-layer multi-track selective laser melting process using the finite element method. The model takes into account the powder melting, vaporization, solidification, cooling and shrinkage processes. The modeling results show that the component of the residual stresses is generally larger along the scanning direction than those along the other two perpendicular directions, and the von Mises stress reaches the maximum value in the last scanning track. KEYWORDS: Additive manufacturing; Selective laser melting; Thermo-mechanical model; Residual stress field INTRODUCTION Selective laser melting (SLM) is one of the most promising additive manufacturing technologies, and can be used to manufacture complex and high-density products efficiently. With the increasing demands of customized and low-cost products, SLM has attracted extensive attentions in various industrial applications such as aerospace, automobile and biomedicine (Liu, Stevens, Yang, Chmielus, & To, 2017; Yuan, Zheng, Chua, Yan, & Zhou, 2018). However, the products fabricated by SLM suffer from disadvantages such as poor surface finish, thermal distortion and unsatisfactory mechanical strength (Calignano, 2018; Wu, et al., 2017; Yang, Wei, & Lin, 2017). Among these defects, the thermal residual stress, resulting from the high temperature gradient and solid phase transformation in the layer-by-layer process, adversely affects the mechanical performance of SLM-printed products. To improve the product reliability, plenty of efforts have been done to have a comprehensive understanding of the thermal stress evolution in the printing process (Li, et al., 2018; Salmi & Atzeni, 2017; Sillars, et al., 2018; Yadroitsev & Yadroitsava, 2015). In this work, the process modeling of SLM was carried out using a three-dimensional (3D) thermo-mechanical coupling approach which considered the powder melting, vaporization, solidification, cooling and shrinkage processes. The temperature and stress fields of the SLM-built products were predicted by solving the heat conduction and stress equilibrium equations. THERMO-MECHANICAL COUPLING MODEL The laser melting process includes three heat transfer modes: heat conduction, heat convection and radiation. In the instantaneous interaction of the laser and powders, the heat conduction is the main way to diffuse the heat. Hence, the thermal analysis is based on the heat conduction equations. The
A THERMO-MECHANICAL COUPLING MODEL FOR PREDICTING TEMPERATURE AND RESIDUAL STRESS FIELDS IN SELECTIVE
LASER MELTING
PENGFEI TAN, FEI SHEN, KUN ZHOU
Singapore Centre for 3D Printing, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, 639798, Singapore
mechanical model is composed of the stress equilibrium equations and temperature-dependent mechanical properties. The total strain considers the elastic strain, plastic strain and thermal strain. Heat conduction equations The 3D transient heat conduction equation with temperature-dependent material properties is expressed by
, (1)
where T(x, y, z, t) is the temperature, (T) is the density, c(T) is the specific heat capacity, k(T) is the thermal conductivity, and U(x, y, z) is the internal heat source. The natural convection and radiation boundary conditions are applied. Due to the porosity among powder articles, the laser radiation can penetrate the powder layer and be absorbed by powders and the substrate. Based on the interaction model of laser and powder (Gusarov, Yadroitsev, Bertrand, & Smurov, 2009), the volumetric heat source due to the radiation absorption is expressed as
, (2)
where is the extinction coefficient, Q0 is the surface distribution of the laser energy, dimensionless variable = z, and q denotes the normalized laser irradiance in the thickness direction:
, (3)
, (4)
where is the hemispherical reflectivity of the powder, a = , and the optical thickness = L with being the thickness of powder layer.
Stress equilibrium equations The total strain increment is given as the sum of elastic strain increment e, plastic strain increment p, and thermal strain increment t:
, (5) According to the elastic relation, the stress is obtained as
, (6)
( )( )0
( , , , )( ) ( ) ( ) ( , , , ) ( , , ), 0
( , , , ) , 0
T x y z tT c T k T T x y z t U x y z tt
T x y z t T t
= + >
= =
0dQ dqU Qdz d
= =
2 2 2 2 2 ( )
22 ( )
{(1 ) [(1 ) (1 ) ] (3 ) {[1 (1 )](4 3)
3(1 )( )[1 (1 )] }}4 3
a a a
a
aq e a e a e e a a eD
e ea a e
= + + + × +
+ +
2 2(1 )[1 (1 )] (1 )[1 (1 )]a aD a a a e a a a e= + + +
e p t= + +
( )p t= D
Proc. Of the 3rd Intl. Conf. on Progress in Additive Manufacturing
565
Chee Kai Chua, Wai Yee Yeong, Ming Jen Tan, Erjia Liu and Shu Beng Tor (Eds.)
566
Proc. Of the 3rd Intl. Conf. on Progress in Additive Manufacturing
567
Chee Kai Chua, Wai Yee Yeong, Ming Jen Tan, Erjia Liu and Shu Beng Tor (Eds.)
568
z direction has the minimum stresses compared to other two stress components. In addition, the level of stress component y is larger than the other two stress components. From the von Mises stress distribution, the stress is larger in four corners than the center region. The maximum von Mises stress occurs at the end of the last track. CONCLUSIONS A 3D thermo-mechanical coupling model with temperature-dependent material properties using FEM for SLM is developed. The model takes into account the powder melting, vaporization, solidification, cooling and shrinkage processes. The temperature and stress fields have been investigated for the multi-track printing process. The modeling results show that the component of the residual stresses is generally larger along the scanning direction than those along the other two perpendicular directions, and the von Mises stress reaches the maximum value in the last scanning track. REFERENCES Calignano, F. (2018). Investigation of the accuracy and roughness in the laser powder bed fusion process. Virtual and Physical Prototyping, 13(2), 1-8. Gusarov, A. V., Yadroitsev, I., Bertrand, P., & Smurov, I. (2009). Model of Radiation and Heat Transfer in Laser-Powder Interaction Zone at Selective Laser Melting. Journal of Heat Transfer, 131, 072101. 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. Materials & Design, 52, 638-47. Li, Y., Zhou, K., Tan, P., Tor, S. B., Chua, C. K., & Leong, K. F. (2018). Modeling temperature and residual stress fields in selective laser melting. International Journal of Mechanical Sciences, 136, 24-35. Liu, J., Stevens, E., Yang, Q., Chmielus, M., & To, A. C. (2017). An analytical model of the melt pool and single track in coaxial laser direct metal deposition (LDMD) additive manufacturing. Journal of Micromechanics and Molecular Physics, 1750013. Mills, K. C. (2002). Recommended values of thermophysical properties for selected commercial alloys, Woodhead Publishing. Rombouts, M., Froyen, L., Gusarov, A. V., Bentefour, E. H., & Glorieux, C. (2005). Photopyroelectric measurement of thermal conductivity of metallic powders. Journal of Applied Physics, 97, 024905. Salmi, A., & Atzeni, E. (2017). History of residual stresses during the production phases of AlSi10Mg parts processed by powder bed additive manufacturing technology. Virtual and Physical Prototyping, 12, 153-60. Sillars, S., Sutcliffe, C., Philo, A., Brown, S., Sienz, J., & Lavery, N. (2018). The three-prong method: a novel assessment of residual stress in laser powder bed fusion. Virtual and Physical Prototyping, 13, 20-25. Wu, H., Ren, J., Huang, Q., Zai, X., Liu, L., Chen, C., Liu, S., Yang, X., & Li, R. (2017). Effect of laser parameters on microstructure, metallurgical defects and property of AlSi10Mg printed by selective laser melting. Journal of Micromechanics and Molecular Physics, 2, 1750017. Yadroitsev, I., & Yadroitsava, I. (2015). Evaluation of residual stress in stainless steel 316L and Ti6Al4V samples produced by selective laser melting. Virtual and Physical Prototyping, 10, 67-76.
Proc. Of the 3rd Intl. Conf. on Progress in Additive Manufacturing
569
Yang, H., Wei, L., & Lin, X. (2017). A cellular automaton simulation of W–Ni alloy solidification in laser solid forming process. Journal of Micromechanics and Molecular Physics, 2, 1750016. Yuan, S., Zheng, Y., Chua, C. K., Yan, Q., & Zhou, K. (2018). Electrical and thermal conductivities of MWCNT/polymer composites fabricated by selective laser sintering. Composites Part A: Applied Science and Manufacturing, 105, 203-13.
Chee Kai Chua, Wai Yee Yeong, Ming Jen Tan, Erjia Liu and Shu Beng Tor (Eds.)
