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Size effects of effective Young's modulus for periodic cellular materials

Science China(Physics,Mechanics & Astronomy) 2009年第8期52卷 1262-1270页

作者： DAI GaoMing ZHANG WeiHong Engineering Simulation and Aerospace Computing Key Laboratory of Contemporary Design&Integrated Manufacturing TechnologyNorthwestern Polytechnical UniversityXi’an 710072China

With the wide demands of cellular materials applications in aerospace and civil engineering,research effort sacrificed for this type of materials attains nowadays a higher level than ever before.This paper is focused on the prediction methods of effective Young's modulus for periodical cellular materials.Based on comprehensive studies of the existing homogenization method(HM),the G-A meso-mechanics method(G-A MMM) and the stretching energy method(SEM) that are unable to reflect the size effect,we propose the bending energy method(BEM) for the first time,and a comparative study of these four methods is further made to show the generality and the capability of capturing the size effect of the BEM method.Meanwhile,the underlying characteristics of each method and their relations are clarified.To do this,the detailed finite element computing and existing experimental results of hexagonal honeycombs from the literature are adopted as the standard of comparison for the above four methods.Stretch and bending models of periodical cellular materials are taken into account,respectively for the comparison of stretch and flexural displacements resulting from the above methods.We conclude that the BEM has the strong ability of both predicting the effective Young's modulus and revealing the size effect.Such a method is also able to predict well the variations of structural displacements in terms of the cell size under stretching and bending loads including the non-monotonous variations for the hexagonal cell.On the contrary,other three methods can only predict the limited results whenever the cell size tends to be infinitely small.

关键词： periodic cellular materials effective Young’s modulus size effect bending energy method homogenization method G-A mesomechanics method stretching energy method

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A new method of estimating the equivalent elastic modulus of RCCD

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Science China(Technological Sciences) 2007年第Z1期50卷 136-143页

作者： GU ChongShi1,2?, WU Yuan1, SU HuaiZhi1,2 & TANG LiHui1 1 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China 2 National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Nanjing 210098, China College of Water Conservancy and Hydropower Engineering Hohai University Nanjing China National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety Nanjing China

Based on the composite material mechanic theory, the analysis method for the equivalent elastic moduli which are parallel and vertical to the construction interface of RCCD is studied in this paper. The differences between the equivalent elastic moduli which are vertical to the construction interface of RCCD gotten from different methods are discussed in detail. The variation range of the equivalent elastic modulus which is vertical to the construction interface of RCCD is studied based on the principle of minimum complementary energy and the principle of minimum potential energy. The effect of the related influential factors on the equivalent elastic modulus is analyzed. The estimation formula of the equivalent modulus which is vertical to the construction interface of RCCD is proposed. The feasibility of the approach proposed in this paper is analyzed through an example.

关键词： RCCD equivalent elastic modulus variation range estimation method

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The critical behavior of shear modulus in solid-liquid mixing phase

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Science China(Physics,Mechanics & Astronomy) 2007年第6期50卷 742-746页

作者： RAN XianWen1,2,TANG WenHui1,TAN Hua2 & DAI ChengDa2 1 Institute of Technological Physics,College of Science,National University of Defense Technology,Changsha 410073,China 2 Laboratory for Shock Wave and Detonation Physics Research,Institute of Fluid Physics,Chinese Academy of Engineering Physics (CAEP),Mianyang 621900,China Institute of Technological Physics College of Science National University of Defense Technology Changsha China Laboratory for Shock Wave and Detonation Physics Research Institute of Fluid Physics Chinese Academy of Engineering Physics (CAEP) Mianyang China

The behavior of shear modulus in solid-liquid mixing phase has been discussed and analyzed. The result was concluded that shear modulus went to zero as the melting mass ratio attained a critical value. The percolation theory model we pro-posed showed that this value was about 0.68742. The melting-induced destabilizing factor of material proposed by us can represent phenomenologically the change of shear modulus in melting process.

关键词： solid-liquid mixing phase, critical behavior, shear modulus, destabilizing factor The behavior of shear modulus in solid-liquid mixing phase has been discussed and analyzed. The result was concluded that shear modulus went to zero as the melting mass ratio attained a critical value. The percolation theory model we proposed showed that this value was about 0.68742. The melting-induced destabilizing factor of material proposed by us can represent phenomenologically the change of shear modulus in melting process.……

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Fractal analysis of polyethylene catalysts surface morphologies based on wavelet transform modulus maxima method

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Science China Chemistry 2007年第3期50卷 372-378页

作者： CEN Wei YANG ShiFeng XUE Rong XU RiWei YU DingSheng College of Material Science and Engineering Beijing University of Chemical TechnologyBeijing 100029China Sinopec Catalyst Company Beijing 100011China

Surface morphologies of supported polyethylene (PE) catalysts are investigated by an approach combining fractal with wavelet. The multiscale edge (detail) pictures of catalyst surface are extracted by wavelet transform modulus maxima (WTMM) method. And, the distribution of edge points on the edge image at every scale is studied with fractal and multifractal method. Furthermore, the singularity intensity distribution of edge points in the PE catalyst is analyzed by multifractal spectrum based on WTMM. The results reveal that the fractal dimension values and multifractal spectrums of edge images at small scales have a good relation with the activity and surface morphology of PE catalyst. Meanwhile the catalyst exhibiting the higher activity shows the wider singular strength span of multifractal spectrum based on WTMM, as well as the more edge points with the higher singular intensity. The research on catalyst surface morphology with hybrid fractal and wavelet method exerts the superiorities of wavelet and fractal theories and offers a thought for studying solid surfaces morphologies.

关键词： wavelet transform modulus maxima (WTMM) edge image fractal multifractal polyethylene catalyst surface morphology

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Experimental Study on Young′s modulus of Concrete

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Journal of Central South University 2000年第1期12卷 43-45页

作者： Wen, SY Li, XB Cent S Univ Technol Coll Resources Environm & Civil Engn Changsha 410083 Peoples R China

Young′s modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young′s modulus and dynamic Young′s modulus when dynamic Poisson ratio μ d varies nearby 0.20.P wave velocity and elastic modulus have the same varying tendency as letter N. μ,μ d decrease with the increase of loading rate and μ d has a great effect on the parameters E d and E D.

关键词： concrete static Young′s modulus dynamic Young′s modulus P wave velocity

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In-situ measurement of elastic modulus for ceramic top-coat at high temperature

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Journal of Central South University 2008年第S2期15卷 372-376页

作者：齐红宇周立柱马海全杨晓光李旭 School of Jet Propulsion Beihang University Beijing Branch China Eastern Airlines Co. Ltd. China Academy of Space Technology

The ceramic thermal barrier coatings (TBCs) play an increasingly important in advanced gas turbine engines because of their ability to further increase the engine operating temperature and reduce the cooling, thus help achieve future engine low emission, high efficiency and improve the reliability goals. Currently, there are two different processes such as the plasma spraying (PS) and the electron beam-physical vapor deposition (EB-PVD) techniques. The PS coating was selected to test the elastic modulus. Using the nanoindentation and resonant frequency method, the mechanical properties of ceramic top-coat were measured in-situ. According to the theory of the resonant frequency and composite beam, the testing system was set up including the hardware and software. The results show that the accurate characterization of the elastic properties of TBCs is important for stress-strain analysis and failure prediction. The TBCs systems are multi-layer material system. It is difficult to measure the elastic modulus of top-coat by tensile method. The testing data is scatter by nanoindentation method because of the microstructure of the ceramic top-coat. The elastic modulus of the top-coat between 20?1 150 ℃ is obtained. The elastic modulus is from 2 to 70 GPa at room temperature. The elastic modulus changes from 62.5 GPa to 18.6 GPa when the temperature increases from 20 ℃ to 1 150 ℃.

关键词： thermal barrier coatings plasma spraying resonant frequency elastic modulus

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Cold Resistant Properties of High modulus Polyurethane

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Journal of Wuhan University of Technology(Materials Science) 2009年第5期24卷 805-809页

作者：章于川 Key Laboratory of Enviroment-friendly Polymer materials of Anhui Province School of Chemistry and Chemical Engineering Anhui University

Six kinds of polyurethane （PU） elastomers were prepared based on different polyesters, polyethers and chain extenders. The structure, mechanical properties and cold resistant properties of PU were systematically investigated by FTIR, XRD, DMTA,universal testing machine and flex ductility machine. The results show that Tg of soft segment is the main factor of the cold resistant properties of polyurethane elastomer. Compared with the same relative molecular mass of the polyester and the polyether, the polyether flexibility is better, the glass transition temperature （Tg） is lower and the cold resistant properties is remarkable, for example the cold resistant properties of PU based on poly （tetramethylene glycol）, 1, 4-BG and MDI achieves the fifth level. The physics performances of polyurethane elastomers, such as breakdown strength, Young＇s modulus and the cold resistant properties, are all superior.

关键词： polyurethane elastomer soft segment glass transitition temperature cold resis-tant properties modulus

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ELASTICITY modulus OF RANDOM COMPOSITE AND ELASTIC PERCOLATION FAILURE OF SOLIDS

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Chinese Physics Letters 1990年第10期7卷 457-460页

作者： ZHENG Maosheng ZHENG xiulin Department of Physics Xian University of Electronic Science and TechnologyXian 710071 Department of Materials Science and Engineering Northwestern Polytechnical UniversityXian 710072

The elasticity modulus of random composite is obtained in 2 and 3 dimensional spaces,based on the solutions of over-matching problems in elastic mechanics.A system with 2 components is also considered,and the calculated results are in good agreement with available references.Further,taking the voids and defects in materials as the second phase with zero modulus,one can easily obtain the expressions for predicting modulus and threshold of the elastic percolation failure of materials containing voids,and the results agree excellently with those in available literatures.

关键词： modulus elasticity matching

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Modification of Longitudinal modulus of 3D Full Five Directional Braided Composite Materials Base on Energy Theory

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Journal of Beijing Institute of Technology 2019年第3期28卷 651-658页

作者： Apeng Dong Shu Li Wenguo Zhu Jing Pu School of Aeronautic Science and Engineering Beihang UniversityBeijing 100191China Faculty of Engineering University of NottinghamNottingham NG7 2RDUnited Kingdom

The aim of this paper is to investigate the longitudinal modulus of three dimensional full five directional (3Df5d) braided composite. First, the analytical model of the internal unit cell is established based on its topological structure. Then, according to the intrinsic relation of different cells, the axial moduli of internal, surface and corner cells are systematically deduced, and the influence of corner-cell periodic discontinuity on the moduli is also analyzed. Finally, considering the actual shape of axial yarns after consolidation, the longitudinal moduli of the different cells are modified based on energy theory. The technology factor λ is also proposed in this modification. The results show that the axial mechanical properties of this material can be strongly designable. The straightness of the axial yarns greatly affects the longitudinal modulus. Technology factor λ is between 1 to 2, corresponding to the minimum and the maximum modulus, respectively.

关键词： braided composites braiding parameters elastic modulus strain energy technology factor

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Fractal Properties of the Weibull modulus and the Strength of Rock

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Chinese Science Bulletin 1993年第19期38卷 1636-1640页

作者：高峰谢和平赵鹏 Department of Mathematics and Mechanics China University of Mining and Technology Xuzhou 221008 PRC

As everyone knows, the fracture strength of rock materials shows-statistical character. Although test conditions can be controlled strictly, the results still exhibit a large scatter. This phenomenon certainly results from the stochastic distribution and growth of defects of a variety of scales in the structure of material and should be handled by probabilistic and indefinite methods. As early as 1939, Weibull gave the fundamental work for

关键词： the weakest link principle the Weibull modulus fractal dimension.

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