夹FGM金属/陶瓷复合板变物性稳态热力行为研究
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摘要
功能梯度材料(Functionally Graded Material,简称FGM)是指一种组分、结构和性能都在空间上呈梯度变化的非均匀复合材料。这种材料是航天航空领域研发的产物。由于FGM具备良好的耐高温、耐腐蚀和耐磨损等性能,研发该材料就显得尤为重要。目前FGM的主要研究方向之一为热应力分析。因为有限单元法是计算机和数值分析相结合的方法并且能解决具有复杂边界条件的问题,所以有限单元法是解决热应力分析问题的有效方法。
本文以夹FGM金属/陶瓷复合板和金属/陶瓷复合板为主要研究对象。为了研究夹FGM金属/陶瓷复合板的稳态热力行为,主要进行了以下研究工作。
⑴首先建立以上两种复合板的计算模型,其次通过热传导问题的泛函推导出夹FGM金属/陶瓷复合板的一维有限元基本方程,利用Fortran语言编写了一维热传导问题的有限元计算程序。
⑵利用Fortran语言编写物性系数子程序和辛普生数值积分法子程序。结合有限元基本方程和编写完成的物性系数子程序求出物性系数,再代入辛普生数值积分法程序来求出复合板的稳态热应力。
⑶通过和已有的文献对比,检验了本文采用的数值方法的正确性。
⑷通过数值计算,结果表明:
(a)改变复合板中的FGM层的厚度对板中部变、常物性加热稳态温度分布和ECBC、ECBF复合板内的热应力分布有影响,随着FGM层的厚度增加,温度分布和热应力分布变化趋于平缓,更为合理。(b) FGM层材料组分的分布形状系数M的变化对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板内的热应力影响显著。M=1时曲线最为理想,不像M=0.1和M=10时那样出现明显的转折点和起伏。
(c) FGM层的孔隙率对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板的热应力影响显著。(d)有无FGM层对变、常物性加热稳态温度场的温度分布曲线和ECBC、
ECBF复合板的热应力影响显著。很明显,有FGM层的情况大大优于无FGM层的情况。
(e)上下表面温度Ta和Tb对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板内的热应力影响显著。
Functionally graded material (It is called FGM for short) is a kind of non-homogeneous material, whose composition structure and performance is gradient in space. This material is the product of aerospace research. Because of high temperature, corrosion and wear resistant properties, FGM is worth researching. So far, thermal stress analysis is one of the research interests. The finite element method is effective to solve thermal stress analysis, because it is a combination of computer and numerical analysis and able to solve problems with complicated boundary conditions.
This paper selects ceramics/metal FGM and ceramics/metal composite plates as research object. In order to study ceramics/metal FGM composite plate, some studies have been done as follows.
(1) Firstly, the calculation models of the two kinds of composite plates have been established. Then one-dimensional finite element equation of the composite plates has been derived by analyzing the functional of the heat conduction problem. One-dimensional finite element program was written by Fortran language.
(2) Using Fortran language the subroutines of material properties and Simpson numerical integration were written. Combining subroutine of material properties and finite element equation the values of material properties were obtained, then the results were put into subroutine of Simpson numerical integration to obtain steady thermal stress of composite plates.
(3) By comparing with the existing literature, he numerical integration method applied by this paper has been proved to be correct.
(4) From numerical calculation, the results are as follows.
(a) The variation of FGM layer thickness will induce the variations of the steady heating temperature fields and the thermal stress fields of the middle part in the ECBC and ECBF composite plate with constant and variable material properties. The FGM layer is thicker, the temperature and thermal stress distributions in the plate tend to gentle and are more reasonable.
(b) Changing the material composition M strongly influence on temperature distribution curves in variable ,steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates. When M=1, unlike M=0.1 and M=10 shows apparent turning point, the curve is the most reasonable.
(c) Porosity influence much on temperature distribution curves in variable, steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates.
(d) The existence of FGM layer influence much on temperature distribution curves in variable ,steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates. Apparently, the composite plate with FGM layer are much better than that without.
(e) The upper and lower surface temperatures Ta and Tb influence much on temperature distribution curves in variable, steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates.
本文以夹FGM金属/陶瓷复合板和金属/陶瓷复合板为主要研究对象。为了研究夹FGM金属/陶瓷复合板的稳态热力行为,主要进行了以下研究工作。
⑴首先建立以上两种复合板的计算模型,其次通过热传导问题的泛函推导出夹FGM金属/陶瓷复合板的一维有限元基本方程,利用Fortran语言编写了一维热传导问题的有限元计算程序。
⑵利用Fortran语言编写物性系数子程序和辛普生数值积分法子程序。结合有限元基本方程和编写完成的物性系数子程序求出物性系数,再代入辛普生数值积分法程序来求出复合板的稳态热应力。
⑶通过和已有的文献对比,检验了本文采用的数值方法的正确性。
⑷通过数值计算,结果表明:
(a)改变复合板中的FGM层的厚度对板中部变、常物性加热稳态温度分布和ECBC、ECBF复合板内的热应力分布有影响,随着FGM层的厚度增加,温度分布和热应力分布变化趋于平缓,更为合理。(b) FGM层材料组分的分布形状系数M的变化对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板内的热应力影响显著。M=1时曲线最为理想,不像M=0.1和M=10时那样出现明显的转折点和起伏。
(c) FGM层的孔隙率对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板的热应力影响显著。(d)有无FGM层对变、常物性加热稳态温度场的温度分布曲线和ECBC、
ECBF复合板的热应力影响显著。很明显,有FGM层的情况大大优于无FGM层的情况。
(e)上下表面温度Ta和Tb对变、常物性加热稳态温度场的温度分布曲线和ECBC、ECBF复合板内的热应力影响显著。
Functionally graded material (It is called FGM for short) is a kind of non-homogeneous material, whose composition structure and performance is gradient in space. This material is the product of aerospace research. Because of high temperature, corrosion and wear resistant properties, FGM is worth researching. So far, thermal stress analysis is one of the research interests. The finite element method is effective to solve thermal stress analysis, because it is a combination of computer and numerical analysis and able to solve problems with complicated boundary conditions.
This paper selects ceramics/metal FGM and ceramics/metal composite plates as research object. In order to study ceramics/metal FGM composite plate, some studies have been done as follows.
(1) Firstly, the calculation models of the two kinds of composite plates have been established. Then one-dimensional finite element equation of the composite plates has been derived by analyzing the functional of the heat conduction problem. One-dimensional finite element program was written by Fortran language.
(2) Using Fortran language the subroutines of material properties and Simpson numerical integration were written. Combining subroutine of material properties and finite element equation the values of material properties were obtained, then the results were put into subroutine of Simpson numerical integration to obtain steady thermal stress of composite plates.
(3) By comparing with the existing literature, he numerical integration method applied by this paper has been proved to be correct.
(4) From numerical calculation, the results are as follows.
(a) The variation of FGM layer thickness will induce the variations of the steady heating temperature fields and the thermal stress fields of the middle part in the ECBC and ECBF composite plate with constant and variable material properties. The FGM layer is thicker, the temperature and thermal stress distributions in the plate tend to gentle and are more reasonable.
(b) Changing the material composition M strongly influence on temperature distribution curves in variable ,steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates. When M=1, unlike M=0.1 and M=10 shows apparent turning point, the curve is the most reasonable.
(c) Porosity influence much on temperature distribution curves in variable, steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates.
(d) The existence of FGM layer influence much on temperature distribution curves in variable ,steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates. Apparently, the composite plate with FGM layer are much better than that without.
(e) The upper and lower surface temperatures Ta and Tb influence much on temperature distribution curves in variable, steady heating temperature field and the thermal stresses of ECBC、ECBF composite plates.
引文
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[23] Zuiker J R. Functionally graded material: choice of micromechanics model and limitations in property variation[J]. Composites Science and Technology, 1995, 5(7): 807~819
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[2]边祖光.功能梯度材料板壳结构的耦合问题研究[D].博士论文,杭州:浙江大学,2005
[3]程继贵,雷纯鹏,邓丽萍.梯度功能材料的制备及其应用研究的新进展[J].金属功能材料,2003,10(1):29~30
[4]杨久俊,贾晓林,谭伟等.水泥基梯度复合功能材料物理力学性能的初步研究[J].新型建筑材料,2001,18(1):101~104
[5]杨久俊,董延玲,海然,等.骨料表面化学预处理对界面区的组分梯度分布和混凝土力学性能的影响(I:骨料化学预处理对其表面特性与界面过渡区结构的影响)[J].混凝土与水泥制品,2003,12(6):1~5
[6]杨久俊,海然,秦东方.界面组分梯度分布对水泥基材料力学性能的影响[C].2002年材料科学与工程新进展(下)---2002年中国材料研讨会论文集.2002,24~28
[7]杨久俊,董延玲,林伦等.连续相组分梯度分布对水泥基材料力学性能的影响[J].硅酸盐学报,2004,32(10):225~228
[8] Maalej M, Ahmed S F U, Paramasivam P. Corrosion Durability and Structural Response of Functionally-Graded concrete beam[J]. Journal of Advance Concrete Technology, 2003, 1(3): 307~316
[9]徐智谋.功能梯度材料和低温制备研究现状及展望[J].表面技术,2000,29(2):1~5
[10] Hiran T, Sasaki. Vapor-deposited functionally material[J]. Japan Society of Mechanical Engineers International Journal series I-fluids and thermal engineering, 1991, 34(3): 123~124
[11] Kazuhiko Yamanouchi, Masaki Oba. New air-gas-type piezoelectric resonator supported by thin film from surface[J]. Electronics and Communication in Japan(Part II), 2007, 73(3): 21~29
[12] Ding X, Guo X, Hschner B, et al. Preparation of BaTiO3 film by CVD[J]. Proceeding 2nd Int. Symptoms on FGMs. USA San Francisco. 1992,30(3):286~290
[13] Williams B. Powder metallurgy in Japan[J]. Journal of Japan Society of Powder & Powder Metal, 1981, 36(4): 157~158
[14] Subrehamanyam J, Vijayakumar M, Ranganath S. Combusition-assisted synthesis of Ti-Tic composite via the casting route[J].Materials Science and Engineering, 1992, 149(2): 253~257
[15]李云铠,王勇,钟家湘.功能梯度材料[J].材料导报,2002,16(10): 9~11
[16]郑昌琼,冉均国.新型无机材料[M].北京:科学出版社,2003,15(3):385~387
[17] Wakashima K, Hirano T, Niino M, et al. An improvement in design accuracy of functionally gradient material for space plane applications[C]. International Symposium on Space Technology and Science, 1990, 501~506
[18] Watanabe R, Kawasaki A. Recent development of functionally gradient materials for special application to Space plan[C]. Proceedings of the First International Symposium on Functionally Gradient Materials’90, Sendai, Japan, 1990, 107~113
[19] Kawasaki A, Watanabe R. Finite element analysis of thermal stress of the metal/ceramic multilayer composites with controlled compositional gradient[J]. Journal of Japan Institute of Metals, 1987, 57(6): 525~532
[20] Markworth A J, Ramesh K S, Parks W P Jr. Modelling studies applied to functionally graded materials[J]. Journal of Materials Science, 1995, 30(9): 2183~2193
[21] Tanaka K, Tanaka Y, Watanabe H, et al. An improved solution to thermoelastic material design in functionally gradient materials: Scheme to reduce thermal stresses[J].Computer Methods in Applied Mechanics and Engineering, 1993, 109(5): 377~389
[22] Torquato S. Another way to estimate properties of heterogeneous media[J]. Applied Mechanics Review, 1991, 44(2): 37~45
[23] Zuiker J R. Functionally graded material: choice of micromechanics model and limitations in property variation[J]. Composites Science and Technology, 1995, 5(7): 807~819
[24] Miller D P, Lannutti J J. Fabrication and properties of functionally graded NiAl/Al2O3 Composite[J]. Journal of Materials Research Society, 1993, 8(8): 2004~2013
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