A simple and systematic scheme implemented in explicit FEM solver for surface tension effects in powder injection moulding process
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In order to simulate more accurately the powder injection moulding process, the explicit finite element method solver is extended with the surface tension effect. The evaluation of surface tension takes the notion of pressure boundary method, while a simple and systematic scheme is proposed to fit the finite element method solver for the Laplacian operator. Because of the difference in dimension for filling function and velocity function, the integration of filling function in second derivative is not suitable to be transformed into the boundary integration and the integration of function in lower order derivative. To evaluate conveniently the curvature of filling front, hence the force of surface tension, a simple and systematic scheme is suggested and implemented into the finite element method solver. This specific scheme includes only the vectorial operations in low cost, and is completely systematic without piecemeal operations. Fitness of the proposed method is proved by the numerical examples of filling flow in a small-scaled channel. It shows the considerable effect of surface tension for the problems in micro-scale of sub-millimeter sizes, in which the boundary conditions at front surface are not negligible in powder injection moulding process. The surface tension effect becomes the dominating role for governing the trace and shape of filling front, which can no longer be neglected.
KeywordsSurface tension Injection moulding Solution scheme Explicit solver
This work is financially supported by the National Natural Science Foundation of China (Grant No. 11502219) and Doctoral Research Foundation of Southwest University of Science and Technology (Grant No. 14zx7139).
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We confirm that this work is original and has not been published elsewhere nor is it currently under consideration for publication elsewhere.
We confirm with have no conflict of interest and their research proposal to publication in line with best practices and codes of conduct of relevant.
- 1.Sha B, Dimov S, Griffiths C, Packianather MS (2007) Investigation of micro-injection moulding: factors affecting the replication quality. J Mater Process Technol 183(2-3):284–296Google Scholar
- 2.Foudzi FM, Muhamad N, Sulong AB, Zakaria H (2013) Yttria stabilized zirconia formed by micro ceramic injection molding: rheological properties and debinding effects on the sintered part. Ceram Int 39(3):2665–2674Google Scholar
- 3.Cheng ZQ, Barriere T, Liu BS, Gelin JC (2009) A new explicit simulation for injection molding and its validation. Polym Eng Sci 49(6):1243–1252Google Scholar
- 4.Cao W, Hassanger O, Wang Y (2008) Surface tension effect on micro-injection molding. Proceedings of the polymer processing society, 24th annual meeting, PPS 24, June 15–19. Salerno (Italy)Google Scholar
- 5.Kim DS, Lee K, Kwon TH, Lee SS (2002) Micro-channel filling flow considering surface tension effect. J Micromech Microeng 12:3Google Scholar
- 8.Eyiyurekli M, Breen D (2010) Interactive free-form level-set surface-editing operators. Comput Graph 34(5):621–638Google Scholar
- 9.Moelans N, Blanpain B, Wollants P (2008) An introduction to phase-field modeling of microstructure evolution. Calphad 32(2):268–294Google Scholar
- 10.Pianet G, Vincent S, Leboi J, Caltagirone JP, Anderhuber M (2010) Simulating compressible gas bubbles with a smooth volume tracking 1-fluid method. Int J Multiphase Flow 36(4):273–283Google Scholar
- 11.Bourlioux AA (1995) A coupled level set volume of fluid algorithm for tracking material interfaces. In: Dwyer HA (ed) Proceedings of the sixth international symposium on computational fluid dynamics, Lake Tahoe, p 15–22Google Scholar
- 13.Son G, Hur N (2002) A couple level set and volume-of-fluid method for the buoyancy-driven motion of fluid particles. Numer Heat Transf B Fund 42(6):523–542Google Scholar
- 14.Ménard T, Tanguy S, Berlemont A (2007) Coupling level set/VOF/ghost fluid methods: validation and application to 3D simulation of the primary break-up of a liquid jet. Int J Multiphase Flow 33(5):510–524Google Scholar
- 35.Li CT, Lai FC (2010) Visualization of the surface tension and gravitational effects on flow injection in center-gated disks. Int Commun Heat Mass Transfer 37(3):230–233Google Scholar