拉伸条件下泡沫金属的细观统计分析模型及统计特性研究
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摘要
泡沫金属材料作为一种新型的工程材料,具有质轻、比强度和比刚度高、比表面积大、隔音、吸能性能优异、高效散热与隔热等多种优异的物理特性,已经广泛应用于航空航天、汽车、建筑等领域。本文对开孔泡沫铝材料的拉伸性能进行了实验研究,重点研究了开孔泡沫金属材料细观结构与宏观力学性能之间的关系,深入分析了开孔泡沫金属材料变形的细观力学机制,探讨了材料非均匀性质和单元细观结构特征对材料宏观力学性能的影响,并在此基础上研究材料性能参数与本构关系,其结果及相关方法不仅能加深了解泡沫金属材料的细观破坏机理,而且还有助于促进细观力学的发展。本文的主要研究内容有:
基于开孔泡沫铝试件的准静态拉伸试验,分析了开孔泡沫铝材料的准静态拉伸力学性能,探讨了泡沫金属材料的初始非均匀特性,重点研究了初始相对密度对材料在准静态拉伸过程的破坏特征的影响,观察了材料拉伸破坏的非均匀特征。通过分析各阶段材料等效弹性模量与应变的实验曲线,提出一种较简洁的开孔泡沫铝准静态拉伸经验本构关系。
为了研究泡沫金属材料的非均匀特性对其拉伸力学性能的影响,本文建立了泡沫金属材料的一维拉伸等应变格子单元模型,假设格子单元的弹性模量、屈服应变与破坏应变等独立地满足Weibull分布,结合统计理论分析了单元处于不同拉伸状态下的概率大小,进而导出了准静态拉伸下开孔泡沫金属材料的多参数本构方程,可对材料拉伸破坏曲线进行合理的解释。
对Gibson-Ashby空心立方体模型进行推广,通过综合考虑单元横梁挠曲与立柱拉伸变形的作用,对开孔泡沫金属材料的立方体单元模型进行了变形机制的分析,定义了空心立方体单元模型的拉伸名义屈服应变,使材料单元具有弹性-理想塑性性质,并通过引入塑性铰长度概念,确定了单元的破坏模式,建立了开孔泡沫金属材料单元的拉伸破坏应变公式,使得该模型首次能用于描述泡沫金属的拉伸破坏。
通过假定Gibson-Ashby空心立方体单元模型的单元结构尺寸满足一定概率分布的方式,以表征材料的非均匀性质。进而推导了单元弹性模量、屈服应变和破坏应变的概率分布,运用细观损伤力学的方法成功地推导出适合中高孔隙率开孔泡沫金属材料在准静态拉伸条件下的本构关系。此本构关系能较好地模拟了材料从弹性到破坏的全过程。
对中高孔隙率的开孔泡沫金属材料参数的概率分布函数进行了分析,分析结果表明:只有在高孔隙率下,泡沫金属材料单元的弹性模量、屈服应变、破坏应变等才满足Weibull分布。对于中孔隙率泡沫金属,它们不严格满足Weibull分布,但它们均可以找到比较理想的等效Weibull分布,并首次揭示了这些Weibull分布不是独立的。
根据由细观统计模型导出的泡沫金属本构关系和单元参数的概率分布函数,推导了泡沫金属在拉伸过程中弹性单元、塑性单元和破坏单元的概率及其随泡沫金属拉伸应变的变化规律,该规律支持了我们创新性地提出用应力-应变曲线的极大曲率来定义材料宏观的屈服和破坏点的观点。
As a new kind of engineering materials, metallic foam possesses various excellent physical and mechanical properties including light-weight, high specific strength and stiffness, large surface, well sound insulation, high energy-absorbing capability, and novel thermal properties etc. It has been extensively used in engineering fields such as aircraft, spacecraft, automobile, and architecture and so on. In this dissertation experimental research to investigate the tensile performances of open-celled metal form was carried out , which focusing on the relation between the meso-structures and the macro mechanical performances; The meso-mechanical mechanism of deformations was analyzed; The effects of the material heterogeneous features and the structural characteristics of meso elements on the macro mechanical performances was also researched. Based on the above studies, the relationship between material property parameters and the constitutive relation is exploited. The research results and developed methods can not only realize failure mechanism of metallic foam but also do great help on meso mechanics. The details of the research include:
Based on the quasi-static tensile test, the tensile mechanical performance of open-celled aluminum foams has been analyzed, and heterogeneity of the metal foam material was also studied with a focus on the impact of initial relative density upon the failure characteristics in the process of quasi-static tensile, non-uniformity of the failure in the metal foam was observed. By analyzing the experimental curves of tensile open-celled aluminum foam, this dissertation yielded a concise relation function of the open-celled foam aluminum materials under quasi-static tension.
In order to investigate the heterogeneous characteristics of foam metal materials on their tensile mechanical performances, this dissertation built a one-dimension equivalent-strain grid element model to simulate metal foam, in which assuming that the elastic modulus, the yield strain, and the failure strain all meets the Weibull distribution independently. The probabilities of the elements in each tensile state were analyzed by using the statistical theory. Consequently, the multi-parameter constitutive equation of open-celled metal foam under quasi-static tension was deduced, which can rationally explain the failure curves of the tensile metal foam.
By modifying Gibson-Ashby’s hollow-cubic model and synthetically considering the deformations of deflection of the beam and the tension of the column, an analysis was presented for the deformation mechanism of the cubic element model, and a tensile yield strain of the hollow-cubic element model was defined, which makes the material element possessing an elastic–perfect plastic characteristic. Further by introduced the concept of plastic hinge length, the element failure model and the failure strain were determined, which let the Gibson-Ashby be used for depict the tensile of metal foam firstly.
The internal heterogeneity of the metal foam was charactered by using the element structural dimension in Gibson-Ashby model as a specific statistical distribution. Further, the probability distributions of elastic modulus, yield strain and failure strain were derived. By employing the method of statistical meso-damage mechanics, the appropriate constitute relation of medium and high porosity open-celled metal foams under quasi-static tension was successfully deduced. This constitutive relation can effectively model the whole process from elasticity to material failure.
Analysis is presented for the probability distribution function of medium and high porosity open-celled foam metal materials’parameters. Results showed that, only under a higher porosity do the elastic modulus, yield strain, and the failure strain of metal foam element satisfy the Weibull distribution. For metal foams of medium porosity, though the Weibull distribution did not strictly satisfy, a perfectly equivalent Weibull distribution can always be found, which firstly indicated that and these Weibull distributions are not dependent.
According to the derived constitutive relation and the probability distributions of elementparameters, the probability and its variation against tensile strain of elemet in elasticity, yielding and failure were derived, The variation supports a new view, we recommended firstly, that the yield and failure state can be defined by the maximum curevatures in the stress-strain curve.? ?
基于开孔泡沫铝试件的准静态拉伸试验,分析了开孔泡沫铝材料的准静态拉伸力学性能,探讨了泡沫金属材料的初始非均匀特性,重点研究了初始相对密度对材料在准静态拉伸过程的破坏特征的影响,观察了材料拉伸破坏的非均匀特征。通过分析各阶段材料等效弹性模量与应变的实验曲线,提出一种较简洁的开孔泡沫铝准静态拉伸经验本构关系。
为了研究泡沫金属材料的非均匀特性对其拉伸力学性能的影响,本文建立了泡沫金属材料的一维拉伸等应变格子单元模型,假设格子单元的弹性模量、屈服应变与破坏应变等独立地满足Weibull分布,结合统计理论分析了单元处于不同拉伸状态下的概率大小,进而导出了准静态拉伸下开孔泡沫金属材料的多参数本构方程,可对材料拉伸破坏曲线进行合理的解释。
对Gibson-Ashby空心立方体模型进行推广,通过综合考虑单元横梁挠曲与立柱拉伸变形的作用,对开孔泡沫金属材料的立方体单元模型进行了变形机制的分析,定义了空心立方体单元模型的拉伸名义屈服应变,使材料单元具有弹性-理想塑性性质,并通过引入塑性铰长度概念,确定了单元的破坏模式,建立了开孔泡沫金属材料单元的拉伸破坏应变公式,使得该模型首次能用于描述泡沫金属的拉伸破坏。
通过假定Gibson-Ashby空心立方体单元模型的单元结构尺寸满足一定概率分布的方式,以表征材料的非均匀性质。进而推导了单元弹性模量、屈服应变和破坏应变的概率分布,运用细观损伤力学的方法成功地推导出适合中高孔隙率开孔泡沫金属材料在准静态拉伸条件下的本构关系。此本构关系能较好地模拟了材料从弹性到破坏的全过程。
对中高孔隙率的开孔泡沫金属材料参数的概率分布函数进行了分析,分析结果表明:只有在高孔隙率下,泡沫金属材料单元的弹性模量、屈服应变、破坏应变等才满足Weibull分布。对于中孔隙率泡沫金属,它们不严格满足Weibull分布,但它们均可以找到比较理想的等效Weibull分布,并首次揭示了这些Weibull分布不是独立的。
根据由细观统计模型导出的泡沫金属本构关系和单元参数的概率分布函数,推导了泡沫金属在拉伸过程中弹性单元、塑性单元和破坏单元的概率及其随泡沫金属拉伸应变的变化规律,该规律支持了我们创新性地提出用应力-应变曲线的极大曲率来定义材料宏观的屈服和破坏点的观点。
As a new kind of engineering materials, metallic foam possesses various excellent physical and mechanical properties including light-weight, high specific strength and stiffness, large surface, well sound insulation, high energy-absorbing capability, and novel thermal properties etc. It has been extensively used in engineering fields such as aircraft, spacecraft, automobile, and architecture and so on. In this dissertation experimental research to investigate the tensile performances of open-celled metal form was carried out , which focusing on the relation between the meso-structures and the macro mechanical performances; The meso-mechanical mechanism of deformations was analyzed; The effects of the material heterogeneous features and the structural characteristics of meso elements on the macro mechanical performances was also researched. Based on the above studies, the relationship between material property parameters and the constitutive relation is exploited. The research results and developed methods can not only realize failure mechanism of metallic foam but also do great help on meso mechanics. The details of the research include:
Based on the quasi-static tensile test, the tensile mechanical performance of open-celled aluminum foams has been analyzed, and heterogeneity of the metal foam material was also studied with a focus on the impact of initial relative density upon the failure characteristics in the process of quasi-static tensile, non-uniformity of the failure in the metal foam was observed. By analyzing the experimental curves of tensile open-celled aluminum foam, this dissertation yielded a concise relation function of the open-celled foam aluminum materials under quasi-static tension.
In order to investigate the heterogeneous characteristics of foam metal materials on their tensile mechanical performances, this dissertation built a one-dimension equivalent-strain grid element model to simulate metal foam, in which assuming that the elastic modulus, the yield strain, and the failure strain all meets the Weibull distribution independently. The probabilities of the elements in each tensile state were analyzed by using the statistical theory. Consequently, the multi-parameter constitutive equation of open-celled metal foam under quasi-static tension was deduced, which can rationally explain the failure curves of the tensile metal foam.
By modifying Gibson-Ashby’s hollow-cubic model and synthetically considering the deformations of deflection of the beam and the tension of the column, an analysis was presented for the deformation mechanism of the cubic element model, and a tensile yield strain of the hollow-cubic element model was defined, which makes the material element possessing an elastic–perfect plastic characteristic. Further by introduced the concept of plastic hinge length, the element failure model and the failure strain were determined, which let the Gibson-Ashby be used for depict the tensile of metal foam firstly.
The internal heterogeneity of the metal foam was charactered by using the element structural dimension in Gibson-Ashby model as a specific statistical distribution. Further, the probability distributions of elastic modulus, yield strain and failure strain were derived. By employing the method of statistical meso-damage mechanics, the appropriate constitute relation of medium and high porosity open-celled metal foams under quasi-static tension was successfully deduced. This constitutive relation can effectively model the whole process from elasticity to material failure.
Analysis is presented for the probability distribution function of medium and high porosity open-celled foam metal materials’parameters. Results showed that, only under a higher porosity do the elastic modulus, yield strain, and the failure strain of metal foam element satisfy the Weibull distribution. For metal foams of medium porosity, though the Weibull distribution did not strictly satisfy, a perfectly equivalent Weibull distribution can always be found, which firstly indicated that and these Weibull distributions are not dependent.
According to the derived constitutive relation and the probability distributions of elementparameters, the probability and its variation against tensile strain of elemet in elasticity, yielding and failure were derived, The variation supports a new view, we recommended firstly, that the yield and failure state can be defined by the maximum curevatures in the stress-strain curve.? ?
引文
[1] Gibson L.J, Ashby M.F. Cellular Solids: Structure and properties [M]. 2nd edition .Cambridge: Cambridge University Press, 1997
[2] Mukai T, Miyoshi T, Nakano S, et al. Compressive response of a closed-cell aluminum foam at high strain rate [J]. SeriPta Materialia 2006, 54:533-537.
[3] Wallash J.C, Gibson L.J. Defect sensitivity of a 3D truss material [J]. SeiriPta Materialia 2001, 45:639-644.
[4] Crowson A. Materials issues in imPact engineering, Impact response of materials and structures [A], Proc. 3rd int. Symp. On impact engineering, eds. V.P.W.shim, S.Tanimuar and C.T.Lim, Oxford, Oxford Univ. Press,1999,15-25.
[5] Abstract book, 20th International congress of theoretical and applied mechanics [C]. Technical report No.950, ISSN 0073-5264.
[6] Degischer H.P., Kristy B.多孔泡沫金属[M].北京:化学工业出版社,2005.5
[7]鲁彥平.汽车保险杠用泡沫铝的能量吸收特性[J].汽车技术,1999, 12:32-33
[8]宋宏伟,虞钢,范子杰等.多孔材料填充壁结构能量吸收的相互作用效应[J].力学学报,2005, 37(6):697-703
[9]赵桂平,卢天健.多孔金属夹层板在冲击载荷作用下的动态响应[J].力学学报, 2008, 40(2):194-206
[10] Cheng H.F., Hunag X.M., Wei J.N., et al. Damping capacitr and compressive characteristic in some aluminum foams [J]. Trans. Nnof. Met. Soc. China, 2003, 13(5):1046-1050.
[11]程和法.泡沫铝合金阻尼性能的研究[J].材料科学与工程学报, 2003, 21(4):521-523
[12]王月,王政红.新型船用吸声材料泡沫铝[J].中国造船,2002,43(4):63-68
[13]于英华,陈宗桢.泡沫铝阻尼塞在齿轮传动中的减振降噪特性的研究[J].组合机床与自动化加工技术,2007(10):35-37
[14]于英华,梁冰,张建华.泡沫铝基高分子复合材料制备及其性能[J].辽宁工程技术大学学报:自然科学版,2005,24(6):903-905
[15]许光鹏,张丽,伍薇.新型多功能材料泡沫铝的结构性能及前景展望[J].重庆科技学院学报:自然科学版, 2006, 8(2):51-53
[16]刘长松,朱震刚,韩福生.泡沫铝的低频内耗[J].材料研究学报, 1997, 11(2):153-157
[17]余兴泉,何德坪.泡沫金属机械阻尼性能研究[J].机械工程材料,1994, 18(2):26-28
[18] Jaezynski J. Sound and Vibration Damping With Polymers [A]. Rabert D.ACS Symposium series[C]. Wasington, DC :American Chemical Society, 1990:167-171
[19] Banhart J., Baumeister J., Weber M. Damping properties of aluminium foam [J]. Materials Science and Engineering, 1996, A205:221-225
[20]荒木庸夫著,赵清译.电子设备的屏蔽设计[M].北京:国防工业出版社, 1975
[21] Davies G.J., Shu Z. Review Metallic Foams:their production、properties and application [J]. Journal of Materials Science, 1983, 18:1899-1911
[22]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(1)[J].轻合金加工技术, 1999, 27(10):5-8
[23]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(2)[J].轻合金加工技术, 1999, 27(12):1-6
[24]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(3)[J].轻合金加工技术, 1999, 27(12):1-5
[25] Smith H.B., Bastawros A.F., Mumm D.R., et al. Compressive defomation and yielding mechanisms in cellular aluminum alloys using x-ray tomography and surface strain mapping [J]. Acta Mater, 1998, 46(10):3583-3592
[26] Satosa S., Wierzbicki T. On the modeling of crush behavior of a closed-cell aluminum foam structure [J]. Journal of Mehcanics and Physics in Solids, 1998, 46(4):645-669
[27] Andrews E. W., Gibson L. J. The influence of crack-like defects on the influence of crack-like defects on the tensile strength of an open-cell aluminum foam [J]. Scripta Materialia, 2001, 44: 1005-1010
[28] Olurin O. B., Fleck N. A., Ashby M. F. Deformation and fracture of aluminum Foams [J]. Materials Science and Engineering, 2000, 291(A):136-146
[29] Lu T. J., One J. M. Characterization of close-celled cellular aluminum alloys [J]. Journal of Materials Science, 2001, 36: 2773-2786
[30] Banhart J., Baumeister M.W. Powder metallurgical technology for the production of metallic foams [A]. Proceedings of the Powder Metallurgy European Congress Euro PM95[C]. 1995: 201-208
[31] Meguid S.A., Cheon S.S., Abbasi N.E. FE Modeling deformation localization in mstallic foams [J]. Finite Elements in Analrsis and Design, 2002, 38:631-643
[32] Kanahashi H., Mukai T., Yamada Y., et al. Dynamic compression of an ultra-low density aluminum foam [J]. Materials Science and Engineering, 2000, 280(A): 349-353
[33] Han F.S., Zhu Z.G., Gao J.C. Characteristic of foamed compressive deformation and energy absorbing aluminum [J]. Metallurgical and Transactions A. 1998(29A)2497-2502
[34]何其健,宋宏伟,黄晨光.基于分形的泡沫金属细观结构与尺寸效应研究[J].力学学报,2009, 41(3):370-375
[35] Yu J.L., Wang E.H., Li J.R. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression [A]. In: Advances in Heterogeneous Material Mechanics 2008, eds. J.H. Fan, H.B. Chen, DE Stech Publications, Lancaster[C]. 2008, p. 879-882
[36] Yu J.L., Liu Y.D., Zheng Z.J, et al. Influences of inertia and material property on the dynamic behavior of cellular metals [A]. In: IUTAM Symposium on Mechanical Properties of Cellular Materials, eds H. Zhao and N.A. Fleck, Springer 2009, p.149-157
[37] Xiao D.W., Li Y.L., Hu S.S., et al. Compression deformation behavior of pure zirconium [J]. Rare Met Mater Eng 2008, 37(12): 2122-2124
[38] Qin K., Yang L.M., Hu S.S. Strain rate sensitivities of face-centred-cubic metals using molecular dynamics simulation [J]. Chinese Phys Let, 2008, 25(7): 581-2584
[39] Zhu J., Hu S.S., Wang L.L. An analysis of stress uniformity for concrete-like specimens during SHPB tests [J]. Int J Impact Eng, 2009, 36(1): 61-72
[40]刘培生,梁开明,顾守仁等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855
[41] Karagiozova D., Yu T.X., Gao Z.Y. Modelling of MHS cellular solid in large strains [J]. Interational Journal of Mechanical Sciences, 2006, 48(11):1273-1286
[42]孙士勇,陈浩然,胡晓智.基于连续本构模型的泡沫铝弹塑性断裂问题无网格法分析[J].大连理工大学学报,2009, 49(1):8-12
[43] Hu L.L., Huang X.Q., Tang L.Q.,et.al. Study on the plastic constitution and the energy-absorbing characteristics of aluminum foam [J]. Key Eng. Mater., 2004, 274-276:235-240
[44] Zhang X.Q., Huang X.Q.,Tang L.Q. Dynamic mechanical behaviors of aluminium foam filled circular tubes under transverse compressive load [J]. Key Eng. Mater., 2007, 340-341:397-402
[45]张红,黄小清,汤立群等.泡沫铝细观结构及其分布特性的数字图像分析[J].华南理工大学学报, 2004, 32(1):9-13
[46]黄小清,刘逸平,汤立群等.基于相对即时密度的泡沫铝材料力学性能研究[J].实验力学, 2004, 19(2):170-177
[47] Hu L.L., Huang X.Q., Tang L.Q. Constitutive relation of open-celled metal foams based on the mesoscopic behavior of random cells [J]. Key Eng. Mater., 2007, 340-341:403-408
[48]刘宇.泡沫铝用AIPO_4/TiH_2包覆工艺研究[D].大连:大连理工大学, 2006
[49] Yan J. Cheng G.D. Comparison of and Scale effects on prediction of equivalent elastic property and the shape optimization of truss material with Periodic microstructure [J]. International Journal of Mechanical Science, 2006,48,400-413.
[50]吕艳凤.开孔泡沫铝若干物理性能的研究[D].合肥:合肥工业大学, 2006
[51]王松林.碳化硅增强泡沫铝层合圆管的制备及其力学性能研究[D].合肥:合肥工业大学,2006
[52]郑明军,何德坪,陈锋.多孔铝合金的压缩应力-应变特征及能量吸收性能[J].中国有色金属学报, 2001, 11 (S2): 81-85
[53]王斌,何德坪,舒广冀.泡沫AI合金的压缩性能及其能量吸收[J].金属学报, 2000, 136(10): 1037-1039
[54]王志华.泡沫铝合金动态力学性能及其吸能机理的研究[D].太原:太原理工大学应用力学研究所, 2005
[55]曹晓卿.泡沫铝材料动力学特性的实验研究与理论分析[D].太原:太原理工大学应力研究所,2005
[56] Cao X.Q., Ma H.W., Zhao L.M., et al. Effects of heat treatment on dynamic compressive properties and energy absorption characteristics of open-cell aluminum alloy foams [J]. Transactions of Nonferrous Metals Society of Chian, 2006, 16(1):159-163
[57] Zhang J.Y., Zhang P., Gan Q.L., Guo X.G. The temperature-dependence of open-cell nickel foams properties [J]. Mater. Sci. Letter, 2003, 22(23):1701-1703.
[58]康颖安.开孔与闭孔泡沫铝力学性能的实验研究[D].湘潭:湘潭大学, 2006
[59]刘培生.多孔材料引论[M].清华大学出版社,2004.
[60] Konrer C., Robert F. Singer, Porcessing of metal fomas-challenges and opportunities [J]. Advanced engineering materials, 2000, 2(4):159-165
[61] Baumgartner F., Duarte I., Banhart J. Industrialization of powder compact foaming process [J]. Advanced engineering materials, 2000, 2(4):168-174
[62] Gergely V., Clyne B.,The FORMGRIP Process: Foaming of reinforced metals by gas release in precursors [J], Advanced engineering materials, 2000, 2(4):175-178
[63] Yamada Y., Shimojima K., Sakaguehi Y., et al. Processing of cellular magnesium materials [J]. Advanced engineering materials, 2000, 2(4):184-187
[64] Banhart J. Manufacture、Characterisation and application of cellular metals and metal foams [J]. Progress in Materials Science, 2001,46:559-632
[65]Degischer H.P., Kriiszt B.主编,左孝青,周芸译.多孔泡沫金属[M].化学工业出版社工业装备与信息工程出版中心, 2005.
[66]吴照金,王艳名,何德坪[J].铝熔体泡沫化制备胞状铝的研究进展.铸造, 1999(4):1-6
[67] Akiyama S., Imagawa K., Kitahara A. Foamed metal and method for producing the same [P]. European Patent, 1986, EP0210803AI
[68] Degischer H.p., KrisZt B. Handbook of cellular metals [M], Production, Processing Applica -tions.Wiley-VCH 2002.
[69]王录才,王芳,游晓红等.渗流法泡沫Al板材的研制[J].太原重型机械学院学报, 2002, 23 (3): 251-259
[70] Wagner L., Hintz C., Sahm P.R. Metal matrix composites and metallic foams [M]. proe. Euromat 99, Munieh, Germany, Clyne T.W., Simaneik F. (eds), DGM/wiley-VCH, Weinheim, 2000, 40
[71] San Marehi C., Mortensen A. Deformation of open-cell aluminum foam [J]. Acta Materialia 200l, 49(19):3959-3969
[72] DesPois J.F., Mueller R., Mortensen A. Uniaxial deformation of microcellular metals [J]. Acta Materialia. 2006, 54:4129
[73] Despois J.F., Mortensen A. Permeability of open-pore microcellular materials[J]. Acta Materialia, 2005, 53:1381
[74]王录才,陈新,柴跃生等.熔模铸造法通孔泡沫铝制备工艺研究[J],铸造, 1999, (1):8-10
[75] Thompson A.C., Llacer J. Computed tomography using synchrotron radition [J]. Nuclear Instruments and Methods in Physics Research, 1984, 222:319-323
[76] Takeda T.,Yu Q., et al. Iodine imaging in ihyroid by fluorescent X-ray CT with 0.05mm spatial resolution [J]. Nuclear Instruments and Methods in Physics Research A, 2001, 467-468:1318-1321
[77] Lopes R.T., Rocha H.S., et al. X-Ray transmission microtomography using synchrotron radiation [J]. Nuclear Instruments and Methods in Physics Research A, 2003,505:604-607
[78] Sakamoto K., Suzuki Y., et al. Improvement of spatial resolution of monochromatic X-Ray CT using synchrotron radiation [J]. Japanese Journal of Applied Physics, 1988,27(1):127-132
[79]汪敏,胡小方,将锐等.应用SXR-CT技术研究闭孔泡沫铝微结构演化及变形分析[J].材料科学与工程学报, 2006, 24(2):171-174
[80]张俊彦多孔材料的力学性能及破坏机理[D].湘潭,湘潭大学,2003
[81]卢子兴,石上路.低密度开孔泡沫材料力学模型的理论研究进展[J].力学与实践,2005,7(5):13-20
[82] Marchi S.C., Mortensen A. Deformation of open-cell aluminum foam [J]. Acta Materialia 2001, 49:3959-3969
[83] Kou D.P., Li J.R., Yu J.L., Cheng HF. Mechanical behavior of open-cell metallic foams with dual-size cellular structure [J]. Scripta Materialia 2008, 59(5):483-486.
[84]李剑荣,寇东鹏,虞吉林.具有双重尺寸孔结构的开孔泡沫金属的优化设计[J].中国力学学会学术大会2005(CCTAM2005)
[85] Kwon Y.W., Cooke R.E., Park C. Representative unite-cell models for open-cell metal foams with or without elastic filler [J]. Material Science and Engineering A,2003,343:63-70
[86] Zhu H.X., Mills N.J., Knott J.F. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells [J]. Journal of Mechanics and Physics of Solids, 1997, 45(3):319-343
[87] Zhu H.X., Mills N.J., Knott J.F. Analysis of the high strain compression of open-cell foams [J]. Journal of Mechanics and Physics of Solids, 1997, 45:1875-1904
[88] Mills N.J. The high strain mechanical response of the wet Kelvin model for open-cell foams [J]. International Journal of Solids and Structures, 2007, 44:51-65
[89] Warren W.E., Kraynik A.M. The linear elastic properties of open-cell foams [J]. Journal of Applied Mechanics, 1998, 55:341-346
[90] Li K., Gao X.L., Roy A.K. Micromechanics model for three dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano’s second theorem [J]. Composites Science and Technology, 2003, 3:1769-1781
[91] Laroussi M., Sab K., Alaoui A. Foam mechanics: nonlinear response of an elastic 3D-Peiodic microstructure [J]. International Journal of Solids and Structures, 2002, 39:3599-3623
[92] Shulmeister V., vander Burg M.M.D., vander Burg E.R.M. A numerical study of large deformations of low-density elastomeric open cell foams [J]. Mech. Mater., 1998, 30:125-140
[93]刘培生.关于多孔材料的新模型[J].材料研究学报, 2006, 20(1):64-68
[94]刘培生.泡沫金属双向承载的力学模型[J].中国有色金属学报, 2006, 16(4):567-574
[95]刘培生,付超,李铁藩.高孔率金属材料的抗拉强度[J].稀有金属材料与工程, 2000, 29(2):94-100
[96]苏华冰,黄小清,汤立群等.基于统计孔径的泡沫铝小变形压缩的有限元模拟分析[J].科学技术与工程,2009(23):6991-6996
[97]王展光,尚金堂,何思渊,等.球形孔泡沫铝合金压缩性能与理论模型[J].材料热处理学报,2006,27(6):129-133
[98]曹晓卿,王志华,马宏伟,等.微孔结构对多孔材料细观力学特性的影响[J].太原理工大学学报, 2006, 37(1):1-8
[99] Gan Y.X., Chen C., Shen Y.P. Three dimensional modeling of the mechanical property of elastomeric open cell foams [J]. Int. J. Solids Struct., 2005, 42:6628-6624
[100] Yu J.L., Wang E.H., Guo L.W. A theoretical and experimental study on the constitutive model of aluminium foams[R]. Invited and to be presented at THERMEC’2009, Berlin, Germany, 2009.
[101] Yu J.L., Wang E.H., Li J.R. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression [A]. In: Advances in Heterogeneous Material Mechanics 2008, eds. J.H. Fan, H.B. Chen, DEStech Publications, Lancaster [C], 2008, p. 879-882.
[102]胡孔刚,杜大明,魏健宁等.二元孔结构对开孔泡沫铝力学性能的影响[J].热加工工艺,2009(20):57-60
[103]刘荣佩,张国强,张钱珍等.泡沫铝孔单元结构模型及压缩特性研究[J].材料导报2007,21(11):133-135
[104] Suh K.W., Skochdopole R.E. Encyclopedia of chemical technology [M]. 3rd Edition. Kirk-Othmer, 1980, 2
[105] Chen C.,Lu T.J.,Fleek N.A. Effect of imperfections on the yielding of two-dimensional foams[J].Jonrnal of the Mechanics and Physics of solids, 1999, 47(11):2235-2272
[106] Zhu H.X., Hobdell J.R., Windle A.H. Effects of cell irregularity on the elastic properties of open-cell foams [J]. Acta Materialia, 2000, 48(20):4893-4900
[107] Zhu H.X., Hobdell J.R., Windle A.H. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs [J]. Jonrnal of the Mechanics and Physics of solids, 2001, 49:857-870
[108]袁应龙,卢子兴.利用随机模型计算低密度开孔泡沫材料的弹性模量[J].材料热处理学报,.2004,.25(2):130-132
[109] Gan Y.X., Chen C., Shen Y.P. Three-dimensional modeling of the mehanical property of linearly elastic open cell foams [J]. International Journal of Solids and Structures, 2005, 42:6628-6642
[110] Silva M.J., Hayes W.C.,Gibson L.J. The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids [J]. International Journal of Mechanical Sciences, 1995, 37(11):1161-1177
[111] Silva M.J., Gibson L.J. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids [J]. International Journal of Mechanical Sciences, 1997, 39(5):549-563
[112] van der Burg M.M.D., Shulmeister V., van der Burg E.R.M. On the linear elastic properties of regular and random open cell foam models [J]. Cell Plast,1997, 33:31-54
[113] Li K., Gao, X.L. Subhash G. Effects of cell shape and strut cross-sectiomal area variations on the elastic properties of three-dimensional open-cell foams [J]. Jourmal of the Mechanics and Physics of Solids, 2006, 54:783-906
[114] Roberts A.P., Garboczi E.J. Elastic properties of model random three-dimensional open-cell solids [J]. Journal of the Mechanics and Physics of Solids, 2002, 50(1):33-35
[115] Shulmeister V., van der Burg M.M.D., van der Burg E.R.M.A numerical study of large deformations of low-density elastomeric open cell foams [J]. Mech. Mater.,1998, 30:125-140
[116] Zhu H.X., Windle A.H. Effects of cell irregularity on the high strain compression of open-cell foams [J]. Acta Materialia, 2002, 50:1041-1105
[117]张俊彦,张平,陈锐林.多孔材料的格构模型[J].工程力学, 2003, 20:408-411
[118]张俊彦,张平,肖映雄等.多孔材料代表单元的性质[J].工程力学, 2004, 21(2):12-128
[119]张俊彦.多孔材料的力学性能及破坏机理[D].湘潭:湘潭大学,2003
[120]刘耀东,虞吉林,郑志军.惯性对多孔金属材料动态力学行为的影响[J].高压物理学报, 2008, 22(2):118-124
[121]程和法,黄笑梅,王强,等.通孔泡沫铝的动态压缩行为[J].爆炸与冲击,2006,26(2):169-173
[122] Calladine C.R., English R.W. Strain and intertia effects in the collapse of two types of energy-absorbing structure [J]. International Journal of Mechanical Science, 1984(11/12):689-701.
[123]潘艺,胡时胜,蒋家桥等.泡沫铝泡孔动态变形特性研究[J].爆炸与冲击,2004, 24(5): 407-412
[124] Terzaghi K. Erdbaumechanik auf bodenphysikalisher Grundlage [A]. Franz Deuticke, Leipzig, Wien, 1982.15-21
[125] Biot M.A. Theory of elasticity and consolidation for a porous anisotropic solid [J]. Appl. Phy., 1955, 26:182-185
[126] Biot M.A. General theory of three-dimensional consolidation [J]. Appl. Phy., 1941,12:155-164
[127] Gent A.N., Thomas A.G. The Deformation of Foamed Elastic Materials[J]. Appl. Polym. Sci., 1959, 1:107-113
[128] Rusch K.C. Load-Compression Behavior of Flexible Foam [J]. Appl. Polym. Sci., 1969, 13: 2297-2311
[129] Throne J.L., Progelhof R.C. Closed-cell foam behavior under dynamic loading-I: stress-strain behavior of low-density foams[J]. Cell Plast, 1984, 20: 437-442
[130] Triantafillou T.C., Gibson L.J. Constitutive modeling of elastic-plastic open-cell foams [J]. Journal of Engineering Mechanics.1990,116:2772-2778
[131]周光全,程经毅.金属材料的热粘塑性本构理论及其应用[A].王礼立,余同希,李永池.冲击动力学进展[C].合肥:中国科学技术大学出版社, 1992:58-86
[132]卢子兴,王仁.高孔隙度泡沫塑料的一种近似非线性本构关系[J].高分子科学与工程, 1996, 12(5):6-11
[133] Progelhof R.C., Throne J.L. Young’s Modulus of Uniform Density Thermoplastic Foam [J]. Polym. Eng. Sci., 1979, 19: 493-499
[134] hsnddsni B., Hinton E.A. review of homogenisation and to pology optimisation I homopenization theory for media with periodic structure [J]. Computers and Structures, 1998, 69:707~717.
[135]庄守兵,吴长春,冯淼林,等.基于均匀化方法的多孔材料细观力学特性数值研究[J].材料科学与工程, 2001, 19(4):9~13
[136]王飞,庄守兵,虞吉林.用均匀化理论分析蜂窝结构的等效弹性参数[J].力学学报,2002, 34(6):914~923
[137]王仁,熊祝华,黄文彬.塑性力学基础[D].科学出版社, 1982
[138] Kanahashi H., Mukai T., Yamada Y., et al. Dynamic compression of an ultra-low density aluminum foam [J]. Materals Science and Engineering, 2000(A280):349-353
[139]程和法,黄笑梅,许玲.泡沫铝镁合金的压缩与吸能性的研究[J].兵器材料科学与工程,2002, 25(6):12-14.
[140] Cheng H.f., Huang X.M., Xue G.X., et al. Shock wave compression behavior of aluminum foam [J]. Journal of Central South University of Technology, 2003, 10(4):333-337
[141]程和法,胡孔刚,薛国宪.泡沫铝合金显微组织和压缩力学性能的研究[J].材料热处理学报, 2005, 26(4):60-64.
[142]张章,程和法,黄笑梅,等.开孔泡沫铝压坑力学行为研究[J].兵器材料科学与工程,2007, 30(4):37-40
[143]赵桂平,卢天健.多孔金属夹层板在冲击载荷作用下的动态响应[J].力学学报,2008, 40(2):194-206
[144]康颖安,张俊彦,赵荣国.泡沫铝结构对其拉伸力学性能的影响[J].机械工程材料, 2006, 30(9): 51-53
[145] Andrews E., Sanders W., Gibson L.J. Compressive and tensile behaviour of aluminum foams [J]. Materials Science and Engineering A, 1999, 2(270):113-124
[146] Ková?ik J. The tensile behaviour of porous metals made by GASAR process [J]. Acta Materialia , 1998, 15(46):5413-5422
[147] Liu P.S., Chao F.u., Tiefan L.i., et al. Relationship between tensile strength and porosity for high porosity metals [J]. Science in China Series E: Technological Sciences, 1999, 1(42):100~107
[148] Liu P.S Mechanical behaviors of porous metals under biaxial tensile loads[J].Materials Science and Engineering A,2006,1-2(422):176-183
[149]刘培生,梁开明,顾守仁,等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855
[150]刘培生.泡沫金属在单、双向载荷作用下的拉伸破坏行为初探[J].稀有金属材料与工程, 2006, 35(5):770-773
[151] Badiche X., Forest S., Guibert T., et al. Mechanical properties and non-homogeneous deformation of open-cell nickel foams: application of the mechanics of cellular solids and of porous materials [J]. Materials Science and Engineering A , 2000, 1-2(289):276-288
[152]项苹,开孔泡沫铝物理及力学性能的研究[D].合肥:合肥工业大学, 2008
[153] Tang C.A., Fu Y.F., Kou S.Q., et al. Numerical simulation of loading inhomogeneous rocks[J]. Int. J. Rock. Mech. Min. Sci., 1998, 35(7):1001~1007
[154] Tang C.A., Kaiser P.K. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure—PartⅠ: Fundamentals [J]. Int. J. Rock. Mech. Min. Sci., 1998, 35(2):113~121
[155] Kaiser P.K., Tang C.A. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure—PartⅡ: Rib pillar collapse [J]. Int J Rock Mech Min Sci, 1998, 35(2):123~134
[156] Blair S.C., Cook N.G. Analysis of compressive fracture in rock using statistical techniques: Part I. a non-linear rule-based model [J]. Iternational Journal of Rock Mechanics and Mining Sciences, 1998, 35(7):837~845
[157] Blair S.C., Cook N.G. Analysis of compressive fracture in rock using statistical techniques: Part II. Effect of microscale heterogeneity on macroscopic deformation [J]. Iternational Journal of Rock Mechanics and Mining Sciences,1998,35(7):49~861
[158] Schlangen E., van Mier J.G.M. Simple lattice model for numerical simulation of fracture of concrete materials and structures[J]. Materials and Structures, 1992, 25:534~542
[159] McCullough K.Y.G., Fleck N.A., Ashby M.F. Uniaxial stress-strain behaviour of aluminium alloy foams [J]. Acta Materialia, 1999, 47(8):2323-2330
[160] Blazy J.S., Marie-Louose A. Forest S., et al. Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading : statistical analysis and size effect [J]. International Journal of Mechanical Sciences, 2004, 46:217-244
[161]陈永强,郑小平,姚振汉,等.应用格形模型和统计方法分析两相材料宏观等效力学性质[J].固体力学学报,2001,22(4):394~402
[162]陈永强,姚振汉,郑小平.三维非均匀固体材料等效性质和破坏过程数值模拟[J].北京:“力学2000”会议论文集, 2000, 577-579
[163]陈永强,姚振汉,郑小平.非均匀脆性材料本构关系统计解析解[J].清华大学学报(自然科学版),2002,42(12):1515~1518
[164] Weibull W. A statistical distribution function of wide applicability [J]. ASME Trans. J. Appl. Mech., 1995, 293-297
[165] Stronge W.J., Yu T.X. Dynamic models for structural plasticity [M]. 1nd ed. Springer Verlag Press, 1993.
[166] Jones N. Structural Impact [M]. 1nd ed. Cambridge:Cambridge Universty Press, 1989.
[167] Jones N. On the dynamic inelastic failure of beams [M]. Structural failure,(eds T.wierzbicki and N.Jones)John wiley, 1989, 133-159
[168] Shu D. Structural arrangement and geometric effects on plastic deformation in collisions[D]. Ph.D.thesis, Chap.4, Cambrige University, U.K. 1990.
[169] Gan Y.X., Chen C., Shen Y.P. Three dimensional modeling of the mechanical property of elastomeric open cell foams [J]. Int. J. Solids Struct., 2005, 42:6628-6624
[170] Yu J.L., Wang E.H., Guo L.W. A theoretical and experimental study on the constitutive model of aluminium foams [C]. Invited and to be presented at THERMEC’2009, August 25-29, 2009, Berlin, Germany.
[171] Gibson L.J., Ashby M.F., Schajer G.S., et al.The mechanics of two dimensional cellular materials [C]. Proceedings of the Royal Society of Londom, Series A:Mathematical and Physical Sciences, 1982, 382(1782):25-42.
[172] Gibson L.J., Ashby M.F. The mechanics of three-dimensional cellular materials, Proceedings of the Royal Society of Londom [C]. Series A: Mathematical and Physical Sciences, 1982, 382: (1782) 43-59.
[173] Miller K.J. A historical perspective of the important parameters of metal fatigue,and problems for the next century [A]. Proc. Of 7th Int. Fatigue Congress[C]. Beijing:Higher Education Press, 1999:15-40
[174]夏蒙棼,韩闻生,柯孚久.等.统计细观损伤力学和损伤演化诱致突变(I)[J].力学进展, 1995, 25(1):1-23
[2] Mukai T, Miyoshi T, Nakano S, et al. Compressive response of a closed-cell aluminum foam at high strain rate [J]. SeriPta Materialia 2006, 54:533-537.
[3] Wallash J.C, Gibson L.J. Defect sensitivity of a 3D truss material [J]. SeiriPta Materialia 2001, 45:639-644.
[4] Crowson A. Materials issues in imPact engineering, Impact response of materials and structures [A], Proc. 3rd int. Symp. On impact engineering, eds. V.P.W.shim, S.Tanimuar and C.T.Lim, Oxford, Oxford Univ. Press,1999,15-25.
[5] Abstract book, 20th International congress of theoretical and applied mechanics [C]. Technical report No.950, ISSN 0073-5264.
[6] Degischer H.P., Kristy B.多孔泡沫金属[M].北京:化学工业出版社,2005.5
[7]鲁彥平.汽车保险杠用泡沫铝的能量吸收特性[J].汽车技术,1999, 12:32-33
[8]宋宏伟,虞钢,范子杰等.多孔材料填充壁结构能量吸收的相互作用效应[J].力学学报,2005, 37(6):697-703
[9]赵桂平,卢天健.多孔金属夹层板在冲击载荷作用下的动态响应[J].力学学报, 2008, 40(2):194-206
[10] Cheng H.F., Hunag X.M., Wei J.N., et al. Damping capacitr and compressive characteristic in some aluminum foams [J]. Trans. Nnof. Met. Soc. China, 2003, 13(5):1046-1050.
[11]程和法.泡沫铝合金阻尼性能的研究[J].材料科学与工程学报, 2003, 21(4):521-523
[12]王月,王政红.新型船用吸声材料泡沫铝[J].中国造船,2002,43(4):63-68
[13]于英华,陈宗桢.泡沫铝阻尼塞在齿轮传动中的减振降噪特性的研究[J].组合机床与自动化加工技术,2007(10):35-37
[14]于英华,梁冰,张建华.泡沫铝基高分子复合材料制备及其性能[J].辽宁工程技术大学学报:自然科学版,2005,24(6):903-905
[15]许光鹏,张丽,伍薇.新型多功能材料泡沫铝的结构性能及前景展望[J].重庆科技学院学报:自然科学版, 2006, 8(2):51-53
[16]刘长松,朱震刚,韩福生.泡沫铝的低频内耗[J].材料研究学报, 1997, 11(2):153-157
[17]余兴泉,何德坪.泡沫金属机械阻尼性能研究[J].机械工程材料,1994, 18(2):26-28
[18] Jaezynski J. Sound and Vibration Damping With Polymers [A]. Rabert D.ACS Symposium series[C]. Wasington, DC :American Chemical Society, 1990:167-171
[19] Banhart J., Baumeister J., Weber M. Damping properties of aluminium foam [J]. Materials Science and Engineering, 1996, A205:221-225
[20]荒木庸夫著,赵清译.电子设备的屏蔽设计[M].北京:国防工业出版社, 1975
[21] Davies G.J., Shu Z. Review Metallic Foams:their production、properties and application [J]. Journal of Materials Science, 1983, 18:1899-1911
[22]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(1)[J].轻合金加工技术, 1999, 27(10):5-8
[23]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(2)[J].轻合金加工技术, 1999, 27(12):1-6
[24]王祝堂.泡沫铝材:生产工艺、组织性能及应用市场(3)[J].轻合金加工技术, 1999, 27(12):1-5
[25] Smith H.B., Bastawros A.F., Mumm D.R., et al. Compressive defomation and yielding mechanisms in cellular aluminum alloys using x-ray tomography and surface strain mapping [J]. Acta Mater, 1998, 46(10):3583-3592
[26] Satosa S., Wierzbicki T. On the modeling of crush behavior of a closed-cell aluminum foam structure [J]. Journal of Mehcanics and Physics in Solids, 1998, 46(4):645-669
[27] Andrews E. W., Gibson L. J. The influence of crack-like defects on the influence of crack-like defects on the tensile strength of an open-cell aluminum foam [J]. Scripta Materialia, 2001, 44: 1005-1010
[28] Olurin O. B., Fleck N. A., Ashby M. F. Deformation and fracture of aluminum Foams [J]. Materials Science and Engineering, 2000, 291(A):136-146
[29] Lu T. J., One J. M. Characterization of close-celled cellular aluminum alloys [J]. Journal of Materials Science, 2001, 36: 2773-2786
[30] Banhart J., Baumeister M.W. Powder metallurgical technology for the production of metallic foams [A]. Proceedings of the Powder Metallurgy European Congress Euro PM95[C]. 1995: 201-208
[31] Meguid S.A., Cheon S.S., Abbasi N.E. FE Modeling deformation localization in mstallic foams [J]. Finite Elements in Analrsis and Design, 2002, 38:631-643
[32] Kanahashi H., Mukai T., Yamada Y., et al. Dynamic compression of an ultra-low density aluminum foam [J]. Materials Science and Engineering, 2000, 280(A): 349-353
[33] Han F.S., Zhu Z.G., Gao J.C. Characteristic of foamed compressive deformation and energy absorbing aluminum [J]. Metallurgical and Transactions A. 1998(29A)2497-2502
[34]何其健,宋宏伟,黄晨光.基于分形的泡沫金属细观结构与尺寸效应研究[J].力学学报,2009, 41(3):370-375
[35] Yu J.L., Wang E.H., Li J.R. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression [A]. In: Advances in Heterogeneous Material Mechanics 2008, eds. J.H. Fan, H.B. Chen, DE Stech Publications, Lancaster[C]. 2008, p. 879-882
[36] Yu J.L., Liu Y.D., Zheng Z.J, et al. Influences of inertia and material property on the dynamic behavior of cellular metals [A]. In: IUTAM Symposium on Mechanical Properties of Cellular Materials, eds H. Zhao and N.A. Fleck, Springer 2009, p.149-157
[37] Xiao D.W., Li Y.L., Hu S.S., et al. Compression deformation behavior of pure zirconium [J]. Rare Met Mater Eng 2008, 37(12): 2122-2124
[38] Qin K., Yang L.M., Hu S.S. Strain rate sensitivities of face-centred-cubic metals using molecular dynamics simulation [J]. Chinese Phys Let, 2008, 25(7): 581-2584
[39] Zhu J., Hu S.S., Wang L.L. An analysis of stress uniformity for concrete-like specimens during SHPB tests [J]. Int J Impact Eng, 2009, 36(1): 61-72
[40]刘培生,梁开明,顾守仁等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855
[41] Karagiozova D., Yu T.X., Gao Z.Y. Modelling of MHS cellular solid in large strains [J]. Interational Journal of Mechanical Sciences, 2006, 48(11):1273-1286
[42]孙士勇,陈浩然,胡晓智.基于连续本构模型的泡沫铝弹塑性断裂问题无网格法分析[J].大连理工大学学报,2009, 49(1):8-12
[43] Hu L.L., Huang X.Q., Tang L.Q.,et.al. Study on the plastic constitution and the energy-absorbing characteristics of aluminum foam [J]. Key Eng. Mater., 2004, 274-276:235-240
[44] Zhang X.Q., Huang X.Q.,Tang L.Q. Dynamic mechanical behaviors of aluminium foam filled circular tubes under transverse compressive load [J]. Key Eng. Mater., 2007, 340-341:397-402
[45]张红,黄小清,汤立群等.泡沫铝细观结构及其分布特性的数字图像分析[J].华南理工大学学报, 2004, 32(1):9-13
[46]黄小清,刘逸平,汤立群等.基于相对即时密度的泡沫铝材料力学性能研究[J].实验力学, 2004, 19(2):170-177
[47] Hu L.L., Huang X.Q., Tang L.Q. Constitutive relation of open-celled metal foams based on the mesoscopic behavior of random cells [J]. Key Eng. Mater., 2007, 340-341:403-408
[48]刘宇.泡沫铝用AIPO_4/TiH_2包覆工艺研究[D].大连:大连理工大学, 2006
[49] Yan J. Cheng G.D. Comparison of and Scale effects on prediction of equivalent elastic property and the shape optimization of truss material with Periodic microstructure [J]. International Journal of Mechanical Science, 2006,48,400-413.
[50]吕艳凤.开孔泡沫铝若干物理性能的研究[D].合肥:合肥工业大学, 2006
[51]王松林.碳化硅增强泡沫铝层合圆管的制备及其力学性能研究[D].合肥:合肥工业大学,2006
[52]郑明军,何德坪,陈锋.多孔铝合金的压缩应力-应变特征及能量吸收性能[J].中国有色金属学报, 2001, 11 (S2): 81-85
[53]王斌,何德坪,舒广冀.泡沫AI合金的压缩性能及其能量吸收[J].金属学报, 2000, 136(10): 1037-1039
[54]王志华.泡沫铝合金动态力学性能及其吸能机理的研究[D].太原:太原理工大学应用力学研究所, 2005
[55]曹晓卿.泡沫铝材料动力学特性的实验研究与理论分析[D].太原:太原理工大学应力研究所,2005
[56] Cao X.Q., Ma H.W., Zhao L.M., et al. Effects of heat treatment on dynamic compressive properties and energy absorption characteristics of open-cell aluminum alloy foams [J]. Transactions of Nonferrous Metals Society of Chian, 2006, 16(1):159-163
[57] Zhang J.Y., Zhang P., Gan Q.L., Guo X.G. The temperature-dependence of open-cell nickel foams properties [J]. Mater. Sci. Letter, 2003, 22(23):1701-1703.
[58]康颖安.开孔与闭孔泡沫铝力学性能的实验研究[D].湘潭:湘潭大学, 2006
[59]刘培生.多孔材料引论[M].清华大学出版社,2004.
[60] Konrer C., Robert F. Singer, Porcessing of metal fomas-challenges and opportunities [J]. Advanced engineering materials, 2000, 2(4):159-165
[61] Baumgartner F., Duarte I., Banhart J. Industrialization of powder compact foaming process [J]. Advanced engineering materials, 2000, 2(4):168-174
[62] Gergely V., Clyne B.,The FORMGRIP Process: Foaming of reinforced metals by gas release in precursors [J], Advanced engineering materials, 2000, 2(4):175-178
[63] Yamada Y., Shimojima K., Sakaguehi Y., et al. Processing of cellular magnesium materials [J]. Advanced engineering materials, 2000, 2(4):184-187
[64] Banhart J. Manufacture、Characterisation and application of cellular metals and metal foams [J]. Progress in Materials Science, 2001,46:559-632
[65]Degischer H.P., Kriiszt B.主编,左孝青,周芸译.多孔泡沫金属[M].化学工业出版社工业装备与信息工程出版中心, 2005.
[66]吴照金,王艳名,何德坪[J].铝熔体泡沫化制备胞状铝的研究进展.铸造, 1999(4):1-6
[67] Akiyama S., Imagawa K., Kitahara A. Foamed metal and method for producing the same [P]. European Patent, 1986, EP0210803AI
[68] Degischer H.p., KrisZt B. Handbook of cellular metals [M], Production, Processing Applica -tions.Wiley-VCH 2002.
[69]王录才,王芳,游晓红等.渗流法泡沫Al板材的研制[J].太原重型机械学院学报, 2002, 23 (3): 251-259
[70] Wagner L., Hintz C., Sahm P.R. Metal matrix composites and metallic foams [M]. proe. Euromat 99, Munieh, Germany, Clyne T.W., Simaneik F. (eds), DGM/wiley-VCH, Weinheim, 2000, 40
[71] San Marehi C., Mortensen A. Deformation of open-cell aluminum foam [J]. Acta Materialia 200l, 49(19):3959-3969
[72] DesPois J.F., Mueller R., Mortensen A. Uniaxial deformation of microcellular metals [J]. Acta Materialia. 2006, 54:4129
[73] Despois J.F., Mortensen A. Permeability of open-pore microcellular materials[J]. Acta Materialia, 2005, 53:1381
[74]王录才,陈新,柴跃生等.熔模铸造法通孔泡沫铝制备工艺研究[J],铸造, 1999, (1):8-10
[75] Thompson A.C., Llacer J. Computed tomography using synchrotron radition [J]. Nuclear Instruments and Methods in Physics Research, 1984, 222:319-323
[76] Takeda T.,Yu Q., et al. Iodine imaging in ihyroid by fluorescent X-ray CT with 0.05mm spatial resolution [J]. Nuclear Instruments and Methods in Physics Research A, 2001, 467-468:1318-1321
[77] Lopes R.T., Rocha H.S., et al. X-Ray transmission microtomography using synchrotron radiation [J]. Nuclear Instruments and Methods in Physics Research A, 2003,505:604-607
[78] Sakamoto K., Suzuki Y., et al. Improvement of spatial resolution of monochromatic X-Ray CT using synchrotron radiation [J]. Japanese Journal of Applied Physics, 1988,27(1):127-132
[79]汪敏,胡小方,将锐等.应用SXR-CT技术研究闭孔泡沫铝微结构演化及变形分析[J].材料科学与工程学报, 2006, 24(2):171-174
[80]张俊彦多孔材料的力学性能及破坏机理[D].湘潭,湘潭大学,2003
[81]卢子兴,石上路.低密度开孔泡沫材料力学模型的理论研究进展[J].力学与实践,2005,7(5):13-20
[82] Marchi S.C., Mortensen A. Deformation of open-cell aluminum foam [J]. Acta Materialia 2001, 49:3959-3969
[83] Kou D.P., Li J.R., Yu J.L., Cheng HF. Mechanical behavior of open-cell metallic foams with dual-size cellular structure [J]. Scripta Materialia 2008, 59(5):483-486.
[84]李剑荣,寇东鹏,虞吉林.具有双重尺寸孔结构的开孔泡沫金属的优化设计[J].中国力学学会学术大会2005(CCTAM2005)
[85] Kwon Y.W., Cooke R.E., Park C. Representative unite-cell models for open-cell metal foams with or without elastic filler [J]. Material Science and Engineering A,2003,343:63-70
[86] Zhu H.X., Mills N.J., Knott J.F. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells [J]. Journal of Mechanics and Physics of Solids, 1997, 45(3):319-343
[87] Zhu H.X., Mills N.J., Knott J.F. Analysis of the high strain compression of open-cell foams [J]. Journal of Mechanics and Physics of Solids, 1997, 45:1875-1904
[88] Mills N.J. The high strain mechanical response of the wet Kelvin model for open-cell foams [J]. International Journal of Solids and Structures, 2007, 44:51-65
[89] Warren W.E., Kraynik A.M. The linear elastic properties of open-cell foams [J]. Journal of Applied Mechanics, 1998, 55:341-346
[90] Li K., Gao X.L., Roy A.K. Micromechanics model for three dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano’s second theorem [J]. Composites Science and Technology, 2003, 3:1769-1781
[91] Laroussi M., Sab K., Alaoui A. Foam mechanics: nonlinear response of an elastic 3D-Peiodic microstructure [J]. International Journal of Solids and Structures, 2002, 39:3599-3623
[92] Shulmeister V., vander Burg M.M.D., vander Burg E.R.M. A numerical study of large deformations of low-density elastomeric open cell foams [J]. Mech. Mater., 1998, 30:125-140
[93]刘培生.关于多孔材料的新模型[J].材料研究学报, 2006, 20(1):64-68
[94]刘培生.泡沫金属双向承载的力学模型[J].中国有色金属学报, 2006, 16(4):567-574
[95]刘培生,付超,李铁藩.高孔率金属材料的抗拉强度[J].稀有金属材料与工程, 2000, 29(2):94-100
[96]苏华冰,黄小清,汤立群等.基于统计孔径的泡沫铝小变形压缩的有限元模拟分析[J].科学技术与工程,2009(23):6991-6996
[97]王展光,尚金堂,何思渊,等.球形孔泡沫铝合金压缩性能与理论模型[J].材料热处理学报,2006,27(6):129-133
[98]曹晓卿,王志华,马宏伟,等.微孔结构对多孔材料细观力学特性的影响[J].太原理工大学学报, 2006, 37(1):1-8
[99] Gan Y.X., Chen C., Shen Y.P. Three dimensional modeling of the mechanical property of elastomeric open cell foams [J]. Int. J. Solids Struct., 2005, 42:6628-6624
[100] Yu J.L., Wang E.H., Guo L.W. A theoretical and experimental study on the constitutive model of aluminium foams[R]. Invited and to be presented at THERMEC’2009, Berlin, Germany, 2009.
[101] Yu J.L., Wang E.H., Li J.R. An experimental study on the quasi-static and dynamic behavior of aluminum foams under multi-axial compression [A]. In: Advances in Heterogeneous Material Mechanics 2008, eds. J.H. Fan, H.B. Chen, DEStech Publications, Lancaster [C], 2008, p. 879-882.
[102]胡孔刚,杜大明,魏健宁等.二元孔结构对开孔泡沫铝力学性能的影响[J].热加工工艺,2009(20):57-60
[103]刘荣佩,张国强,张钱珍等.泡沫铝孔单元结构模型及压缩特性研究[J].材料导报2007,21(11):133-135
[104] Suh K.W., Skochdopole R.E. Encyclopedia of chemical technology [M]. 3rd Edition. Kirk-Othmer, 1980, 2
[105] Chen C.,Lu T.J.,Fleek N.A. Effect of imperfections on the yielding of two-dimensional foams[J].Jonrnal of the Mechanics and Physics of solids, 1999, 47(11):2235-2272
[106] Zhu H.X., Hobdell J.R., Windle A.H. Effects of cell irregularity on the elastic properties of open-cell foams [J]. Acta Materialia, 2000, 48(20):4893-4900
[107] Zhu H.X., Hobdell J.R., Windle A.H. Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs [J]. Jonrnal of the Mechanics and Physics of solids, 2001, 49:857-870
[108]袁应龙,卢子兴.利用随机模型计算低密度开孔泡沫材料的弹性模量[J].材料热处理学报,.2004,.25(2):130-132
[109] Gan Y.X., Chen C., Shen Y.P. Three-dimensional modeling of the mehanical property of linearly elastic open cell foams [J]. International Journal of Solids and Structures, 2005, 42:6628-6642
[110] Silva M.J., Hayes W.C.,Gibson L.J. The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids [J]. International Journal of Mechanical Sciences, 1995, 37(11):1161-1177
[111] Silva M.J., Gibson L.J. The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids [J]. International Journal of Mechanical Sciences, 1997, 39(5):549-563
[112] van der Burg M.M.D., Shulmeister V., van der Burg E.R.M. On the linear elastic properties of regular and random open cell foam models [J]. Cell Plast,1997, 33:31-54
[113] Li K., Gao, X.L. Subhash G. Effects of cell shape and strut cross-sectiomal area variations on the elastic properties of three-dimensional open-cell foams [J]. Jourmal of the Mechanics and Physics of Solids, 2006, 54:783-906
[114] Roberts A.P., Garboczi E.J. Elastic properties of model random three-dimensional open-cell solids [J]. Journal of the Mechanics and Physics of Solids, 2002, 50(1):33-35
[115] Shulmeister V., van der Burg M.M.D., van der Burg E.R.M.A numerical study of large deformations of low-density elastomeric open cell foams [J]. Mech. Mater.,1998, 30:125-140
[116] Zhu H.X., Windle A.H. Effects of cell irregularity on the high strain compression of open-cell foams [J]. Acta Materialia, 2002, 50:1041-1105
[117]张俊彦,张平,陈锐林.多孔材料的格构模型[J].工程力学, 2003, 20:408-411
[118]张俊彦,张平,肖映雄等.多孔材料代表单元的性质[J].工程力学, 2004, 21(2):12-128
[119]张俊彦.多孔材料的力学性能及破坏机理[D].湘潭:湘潭大学,2003
[120]刘耀东,虞吉林,郑志军.惯性对多孔金属材料动态力学行为的影响[J].高压物理学报, 2008, 22(2):118-124
[121]程和法,黄笑梅,王强,等.通孔泡沫铝的动态压缩行为[J].爆炸与冲击,2006,26(2):169-173
[122] Calladine C.R., English R.W. Strain and intertia effects in the collapse of two types of energy-absorbing structure [J]. International Journal of Mechanical Science, 1984(11/12):689-701.
[123]潘艺,胡时胜,蒋家桥等.泡沫铝泡孔动态变形特性研究[J].爆炸与冲击,2004, 24(5): 407-412
[124] Terzaghi K. Erdbaumechanik auf bodenphysikalisher Grundlage [A]. Franz Deuticke, Leipzig, Wien, 1982.15-21
[125] Biot M.A. Theory of elasticity and consolidation for a porous anisotropic solid [J]. Appl. Phy., 1955, 26:182-185
[126] Biot M.A. General theory of three-dimensional consolidation [J]. Appl. Phy., 1941,12:155-164
[127] Gent A.N., Thomas A.G. The Deformation of Foamed Elastic Materials[J]. Appl. Polym. Sci., 1959, 1:107-113
[128] Rusch K.C. Load-Compression Behavior of Flexible Foam [J]. Appl. Polym. Sci., 1969, 13: 2297-2311
[129] Throne J.L., Progelhof R.C. Closed-cell foam behavior under dynamic loading-I: stress-strain behavior of low-density foams[J]. Cell Plast, 1984, 20: 437-442
[130] Triantafillou T.C., Gibson L.J. Constitutive modeling of elastic-plastic open-cell foams [J]. Journal of Engineering Mechanics.1990,116:2772-2778
[131]周光全,程经毅.金属材料的热粘塑性本构理论及其应用[A].王礼立,余同希,李永池.冲击动力学进展[C].合肥:中国科学技术大学出版社, 1992:58-86
[132]卢子兴,王仁.高孔隙度泡沫塑料的一种近似非线性本构关系[J].高分子科学与工程, 1996, 12(5):6-11
[133] Progelhof R.C., Throne J.L. Young’s Modulus of Uniform Density Thermoplastic Foam [J]. Polym. Eng. Sci., 1979, 19: 493-499
[134] hsnddsni B., Hinton E.A. review of homogenisation and to pology optimisation I homopenization theory for media with periodic structure [J]. Computers and Structures, 1998, 69:707~717.
[135]庄守兵,吴长春,冯淼林,等.基于均匀化方法的多孔材料细观力学特性数值研究[J].材料科学与工程, 2001, 19(4):9~13
[136]王飞,庄守兵,虞吉林.用均匀化理论分析蜂窝结构的等效弹性参数[J].力学学报,2002, 34(6):914~923
[137]王仁,熊祝华,黄文彬.塑性力学基础[D].科学出版社, 1982
[138] Kanahashi H., Mukai T., Yamada Y., et al. Dynamic compression of an ultra-low density aluminum foam [J]. Materals Science and Engineering, 2000(A280):349-353
[139]程和法,黄笑梅,许玲.泡沫铝镁合金的压缩与吸能性的研究[J].兵器材料科学与工程,2002, 25(6):12-14.
[140] Cheng H.f., Huang X.M., Xue G.X., et al. Shock wave compression behavior of aluminum foam [J]. Journal of Central South University of Technology, 2003, 10(4):333-337
[141]程和法,胡孔刚,薛国宪.泡沫铝合金显微组织和压缩力学性能的研究[J].材料热处理学报, 2005, 26(4):60-64.
[142]张章,程和法,黄笑梅,等.开孔泡沫铝压坑力学行为研究[J].兵器材料科学与工程,2007, 30(4):37-40
[143]赵桂平,卢天健.多孔金属夹层板在冲击载荷作用下的动态响应[J].力学学报,2008, 40(2):194-206
[144]康颖安,张俊彦,赵荣国.泡沫铝结构对其拉伸力学性能的影响[J].机械工程材料, 2006, 30(9): 51-53
[145] Andrews E., Sanders W., Gibson L.J. Compressive and tensile behaviour of aluminum foams [J]. Materials Science and Engineering A, 1999, 2(270):113-124
[146] Ková?ik J. The tensile behaviour of porous metals made by GASAR process [J]. Acta Materialia , 1998, 15(46):5413-5422
[147] Liu P.S., Chao F.u., Tiefan L.i., et al. Relationship between tensile strength and porosity for high porosity metals [J]. Science in China Series E: Technological Sciences, 1999, 1(42):100~107
[148] Liu P.S Mechanical behaviors of porous metals under biaxial tensile loads[J].Materials Science and Engineering A,2006,1-2(422):176-183
[149]刘培生,梁开明,顾守仁,等.多孔金属抗拉强度公式中的指数项取值[J].力学学报,2001,33(6):853-855
[150]刘培生.泡沫金属在单、双向载荷作用下的拉伸破坏行为初探[J].稀有金属材料与工程, 2006, 35(5):770-773
[151] Badiche X., Forest S., Guibert T., et al. Mechanical properties and non-homogeneous deformation of open-cell nickel foams: application of the mechanics of cellular solids and of porous materials [J]. Materials Science and Engineering A , 2000, 1-2(289):276-288
[152]项苹,开孔泡沫铝物理及力学性能的研究[D].合肥:合肥工业大学, 2008
[153] Tang C.A., Fu Y.F., Kou S.Q., et al. Numerical simulation of loading inhomogeneous rocks[J]. Int. J. Rock. Mech. Min. Sci., 1998, 35(7):1001~1007
[154] Tang C.A., Kaiser P.K. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure—PartⅠ: Fundamentals [J]. Int. J. Rock. Mech. Min. Sci., 1998, 35(2):113~121
[155] Kaiser P.K., Tang C.A. Numerical simulation of cumulative damage and seismic energy release during brittle rock failure—PartⅡ: Rib pillar collapse [J]. Int J Rock Mech Min Sci, 1998, 35(2):123~134
[156] Blair S.C., Cook N.G. Analysis of compressive fracture in rock using statistical techniques: Part I. a non-linear rule-based model [J]. Iternational Journal of Rock Mechanics and Mining Sciences, 1998, 35(7):837~845
[157] Blair S.C., Cook N.G. Analysis of compressive fracture in rock using statistical techniques: Part II. Effect of microscale heterogeneity on macroscopic deformation [J]. Iternational Journal of Rock Mechanics and Mining Sciences,1998,35(7):49~861
[158] Schlangen E., van Mier J.G.M. Simple lattice model for numerical simulation of fracture of concrete materials and structures[J]. Materials and Structures, 1992, 25:534~542
[159] McCullough K.Y.G., Fleck N.A., Ashby M.F. Uniaxial stress-strain behaviour of aluminium alloy foams [J]. Acta Materialia, 1999, 47(8):2323-2330
[160] Blazy J.S., Marie-Louose A. Forest S., et al. Deformation and fracture of aluminium foams under proportional and non proportional multi-axial loading : statistical analysis and size effect [J]. International Journal of Mechanical Sciences, 2004, 46:217-244
[161]陈永强,郑小平,姚振汉,等.应用格形模型和统计方法分析两相材料宏观等效力学性质[J].固体力学学报,2001,22(4):394~402
[162]陈永强,姚振汉,郑小平.三维非均匀固体材料等效性质和破坏过程数值模拟[J].北京:“力学2000”会议论文集, 2000, 577-579
[163]陈永强,姚振汉,郑小平.非均匀脆性材料本构关系统计解析解[J].清华大学学报(自然科学版),2002,42(12):1515~1518
[164] Weibull W. A statistical distribution function of wide applicability [J]. ASME Trans. J. Appl. Mech., 1995, 293-297
[165] Stronge W.J., Yu T.X. Dynamic models for structural plasticity [M]. 1nd ed. Springer Verlag Press, 1993.
[166] Jones N. Structural Impact [M]. 1nd ed. Cambridge:Cambridge Universty Press, 1989.
[167] Jones N. On the dynamic inelastic failure of beams [M]. Structural failure,(eds T.wierzbicki and N.Jones)John wiley, 1989, 133-159
[168] Shu D. Structural arrangement and geometric effects on plastic deformation in collisions[D]. Ph.D.thesis, Chap.4, Cambrige University, U.K. 1990.
[169] Gan Y.X., Chen C., Shen Y.P. Three dimensional modeling of the mechanical property of elastomeric open cell foams [J]. Int. J. Solids Struct., 2005, 42:6628-6624
[170] Yu J.L., Wang E.H., Guo L.W. A theoretical and experimental study on the constitutive model of aluminium foams [C]. Invited and to be presented at THERMEC’2009, August 25-29, 2009, Berlin, Germany.
[171] Gibson L.J., Ashby M.F., Schajer G.S., et al.The mechanics of two dimensional cellular materials [C]. Proceedings of the Royal Society of Londom, Series A:Mathematical and Physical Sciences, 1982, 382(1782):25-42.
[172] Gibson L.J., Ashby M.F. The mechanics of three-dimensional cellular materials, Proceedings of the Royal Society of Londom [C]. Series A: Mathematical and Physical Sciences, 1982, 382: (1782) 43-59.
[173] Miller K.J. A historical perspective of the important parameters of metal fatigue,and problems for the next century [A]. Proc. Of 7th Int. Fatigue Congress[C]. Beijing:Higher Education Press, 1999:15-40
[174]夏蒙棼,韩闻生,柯孚久.等.统计细观损伤力学和损伤演化诱致突变(I)[J].力学进展, 1995, 25(1):1-23