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Equivalent and Simplification of Nickel-Based Superalloy Plates with Close-Packed Film Cooling Holes

  • Y. M. Zhang (a1), Z. X. Wen (a1), H. Q. Pei (a1), W. Y. Gan (a1) and Z. F. Yue (a1)...


The mechanical properties of thin-walled plate with close-packed film cooling holes are studied based on the equivalent solid material concept. The equivalent principals of the method of equivalent strain energy, homogenization theory and uniform static deformation are considered. A simplification method of square penetration pattern for pitch and diagonal direction loading is presented. The goodness of fit is calculated to determine the optimal method. The tensile deformation, bending deflection, rotation displacement and maximum Mises equivalent stress of simplification plate models are in good agreement with plate models with close-packed film cooling holes. For square penetration pattern for pitch direction loading, the equivalent errors of Mises equivalent stress are all less than 10% when the ligament efficiency is more than 0.6.


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1.Wen, Z. X., Zhang, D. X., Li, S. W., Yue, Z. F. and Gao, J. Y., “Anisotropic Creep Damage and Fracture Mechanism of Nickel-Base Single Crystal Superal-loy under Multiaxial Stress,” Journal of Alloys and Compounds, 692, pp. 301312 (2017).
2.Zhu, Z., Basoalto, H., Warnken, N. and Reed, R. C., “A Model for the Creep Deformation Behaviour of Nickel-Based Single Crystal Superalloys,” Acta Materialia, 60, pp. 48884900 (2012).
3.Jiao, Z., Fu, S., Kawakubo, T., Ohuchida, S. and Tamaki, H., “Analysis of a Rotating Disk System with Axial Cooling Air,” Journal of Mechanics, pp. 113 (2017).
4.Wen, Z. X., Pei, H. Q., Yang, H., Wu, Y. W. and Yue, Z. F., “A Combined CP Theory and TCD for Predicting Fatigue Lifetime in Single-Crystal Super-alloy Plates with Film Cooling Holes,” International Journal of Fatigue (2018).
5.Wen, Z. X., Li, Z. W., Zhang, Y. M., Wen, S. F. and Yue, Z. F., “Surface Slip Deformation Characteristics for Perforated Ni-Based Single Crystal Thin Plates with Square and Triangular Penetration Patterns,” Materials Science & Engineering A, 723, pp. 5669 (2018).
6.Pei, H. Q., Wen, Z. X. and Yue, Z. F., “Long-Term Oxidation Behavior and Mechanism of DD6 Ni-Based Single Crystal Superalloy at 1050°C and 1100°C in Air,” Journal of Alloys and Compounds, 704, pp. 218226 (2017).
7.Hassani, B. and Hinton, E., “A Review of Homoge-nization and Topology Optimization I-Homogenization Theory for Media with Periodic Structure,” Computers & Structures, 69, pp. 707717 (1998).
8.Hassani, B. and Hinton, E., “A Review of Homoge-nization and Topology Optimization II-Analytical and Numerical Solution of Homogenization Equations,” Computers & Structures, 69, pp. 719738 (1998).
9.Zhang, W., Dai, G., Wang, F., Sun, S. and Bassir, H., “Using Strain Energy-Based Prediction of Effective Elastic Properties in Topology Optimization of Material Microstructures,” Chinese Journal of Theoretical and Applied Mechanics, 23, pp. 7789 (2007).
10.Dai, G. and Zhang, W. H., “Size Effects of Effective Young’s Modulus for Periodic Cellular Materials,”Science in China, 52, pp. 12621270 (2009).
11.Webb, D. C., Kormi, K. amd AL-Hassani, S. T. S., “Use of FEM in Performance Assessment of Perforated Plates Subject to General Loading Conditions,” International Journal of Pressure Vessels and Piping, 64, pp. 137152 (1995).
12.O’Donnell, W. J., “Effective Elastic Constants for the Bending of Thin Perforated Plates with Triangular and Square Penetration Patterns,” Journal of Engineering for Industry, 95, pp. 121128 (1973).
13.Gibson, L. J. and Ashby, M. F., “Cellular Solids: Structure and Properties,” Cambridge University Press, 33, pp. 487488 (2014).
14.Gibson, L. J., Ashby, M. F. and Schajer, G. S., “The Mechanics of Two-Dimensional Cellular Materials,” Proceedings of the Royal Society of London, 382, pp. 2542 (1982).
15.Gibson, L. J., “Modelling the Mechanical Behavior of Cellular Materials,” Materials Science and Engineering A, 110A, pp. 136 (1989).
16.Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, 3rd Edition, McGraw-Hill Book Company, New York (1970).
17.Sanchez-Palencia, E., “Comportements Local et Macroscopique d’un Type de Milieux Physiques Heterogenes,” International Journal of Engineering Science, 12, pp. 331351 (1974).
18.Bensoussan, A., Lions, J. L. and Papanicolaou, G., “Asymptotic Analysis for Periodic Structures,” Encyclopedia of Mathematics & Its Applications, 20, pp. 307309 (1991).
19.Bakhvalov, N. and Panasenko, G., “Mathematics of Boundary-Layer Theory in Composite Materials,” Homogenisation: Averaging Processes in Periodic Media Springer Netherlands, pp. 312345 (1989).
20.Bendsøe, M. P. and Kikuchi, N., “Generating Optimal Topologies in Structural Design Using a Homoge-nization Method,” Computer Methods in Applied Mechanics and Engineering, 71, pp. 197224 (1988).
21.Zhuang, X., Wang, Q. and Zhu, H., “A 3D Computational Homogenization Model for Porous Material and Parameters Identification,” Computational Materials Science, 96, pp. 536548 (2015).
22.Mercier, S., Molinari, A., Berbenni, S. and Berveiller, M., “Comparison of Different Homogenization Approaches for Elastic-Viscoplastic Materials,” Modelling and Simulation in Materials Science and Engineering, 20, pp. 373379 (2012).
23.Miehe, C., “Strain-Driven Homogenization of Inelastic Microstructures and Composites Based on An Incremental Variational Formulation,” International Journal for Numerical Methods in Engineering, 55, pp. 12851322 (2002).
24.Myers, K., Juhasz, M., Cortes, P. and Conner, B., “Mechanical Modeling Based on Numerical Ho-mogenization of An Al2O3/Al Composite Manufactured via Binder Jet Printing,” Computational Materials Science, 108, pp. 128135 (2015).
25.Liu, Q., “The Application of Elastic Modulus of Steel Fiber Reinforced Concrete by Homogenization Method,” M. S. Thesis, College of Civil Engineering and Mechanics, Xiangtan University, Hunan, China (2014).
26.Slot, T., “Theoretical and Experimental Analysis of a Thermal Stress Problem in Tube-Sheet Design,” Proceedings First International Conference on Pressure Vessel Technology, Delft, New York (1969).
27.Hu, Z., Lu, W., Thouless, M. D. and Barber, J. R., ”Simulation of Wear Evolution Using Fictitious Eigenstrains,” Tribology International, 82, pp. 191194 (2015).
28.Zhang, S. Q., “Approach on the Fitting Optimization Index of Curve Regression,” Chinese Journal of Health Statistics, 19, pp. 911 (2002).



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