Journal articles: 'Halpin-tsai model'

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Lei, Yongpeng, Ling Luo, Zhenhang Kang, Jifeng Zhang, and Boming Zhang. "Modified Halpin–Tsai equation for predicting interfacial effect in water diffusion process." Science and Engineering of Composite Materials 28, no. 1 (January 1, 2021): 180–89. http://dx.doi.org/10.1515/secm-2021-0017.

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Abstract Interfacial degradation is the main reason for deterioration of mechanical properties of composites in hydrothermal environments. In this study, the effect of the interphase on water diffusion in two types of unidirectional continuous carbon fiber-reinforced polyamide 6 (CF/PA6) composites is investigated through experimental measurements, theoretical analysis, and numerical simulation. The moisture diffusion coefficient of composite at different environmental temperatures is characterized by water immersion tests for analyzing the barrier and accelerating effects of the interphase layer. Based on the experimental results, the three-phase Halpin–Tsai model is derived and validated, and then the critical diffusivity is obtained to quantify the interfacial effect during the diffusion process. To further validate the present three-phase Halpin–Tsai model, the stable and transient finite element models of moisture diffusion are developed. It is found that the critical diffusivity coefficient of the interphase for the CF/PA6 composite system is 7.31 times higher than that of the matrix.

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Islam, M. A., and K. Begum. "Prediction Models for the Elastic Modulus of Fiber-reinforced Polymer Composites: An Analysis." Journal of Scientific Research 3, no. 2 (April 28, 2011): 225–38. http://dx.doi.org/10.3329/jsr.v3i2.6881.

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An analysis has been done on the existing models for the prediction of the elastic modulus of fiber-reinforced polymer composites (FRPC). The experimental data reported in different specialized research journals have been fitted to the models. It is found the theoretical models such as the Parallel, Series and Halpin-Tsai model, by no means, predict the modulus within an acceptable deviation factor of 0.1. The semi-empirical models such as modified Halpin-Tsai and Bowyer-Bader model, which have one adjustable parameter, and are expressed in terms of volume fraction describe the modulus satisfactorily. In this paper, a mass fraction based model with one adjustable parameter is proposed, which also describe the modulus successfully. The proposed model, being mass fraction-based, is more convenient to work with than any volume-fraction based model, and unlike all other models (theoretical and semi-empirical), it has the potentials to have practical applications in structural material design.Keywords: Fibers; Polymer-matrix composites (PMCs); Short-fiber composites; Mechanical properties; Prediction model.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.6881 J. Sci. Res. 3 (2), 225-238 (2011)

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Georgantzinos, Stelios K., Panagiotis A. Antoniou, Georgios I. Giannopoulos, Antonios Fatsis, and Stylianos I. Markolefas. "Design of Laminated Composite Plates with Carbon Nanotube Inclusions against Buckling: Waviness and Agglomeration Effects." Nanomaterials 11, no. 9 (August 31, 2021): 2261. http://dx.doi.org/10.3390/nano11092261.

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In the present study, a buckling analysis of laminated composite rectangular plates reinforced with multiwalled carbon nanotube (MWCNT) inclusions is carried out using the finite element method (FEM). The rule of mixtures and the Halpin–Tsai model are employed to calculate the elastic modulus of the nanocomposite matrix. The effects of three critical factors, including random dispersion, waviness, and agglomeration of MWCNTs in the polymer matrix, on the material properties of the nanocomposite are analyzed. Then, the critical buckling loads of the composite plates are numerically determined for different design parameters, such as plate side-to-thickness ratio, elastic modulus ratio, boundary conditions, layup schemes, and fiber orientation angles. The influence of carbon nanotube fillers on the critical buckling load of a nanocomposite rectangular plate, considering the modified Halpin–Tsai micromechanical model, is demonstrated. The results are in good agreement with experimental and other theoretical data available in the open literature.

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Mansor, M. R., S. M. Sapuan, E. S. Zainudin, A. A. Nuraini, and A. Hambali. "Rigidity Analysis of Kenaf Thermoplastic Composites Using Halpin-Tsai Equation." Applied Mechanics and Materials 548-549 (April 2014): 29–33. http://dx.doi.org/10.4028/www.scientific.net/amm.548-549.29.

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In this paper, the stiffness mechanical property of natural fiber reinforced thermoplastic composites is analyzed using composite micromechanical model. Kenaf natural fiber is selected as the reinforcement material in the composites construction while three types of commonly used automotive grade thermoplastic matrices, namely polypropylene, acrylonitrile butadiene styrene and polyamide 6 were selected to be reinforced with kenaf fibers. Their stiffness property was later analyzed using Halpin-Tsai micromechanical model at varying fiber content and fiber aspect ratio conditions. In all cases, theoretical results show that the kenaf reinforced thermoplastic composites stiffness increased linearly as the fiber contents were increased. Apart from that, results also show that the stiffness property also increases as the fiber aspect ratio was increased. Higher final composites stiffness property was also observed as stiffness matrix material is utilized in the composites formulation. The prediction results also provided valuable and quick insight as well as cost effective alternative to composite designers in assessing the stiffness performance of natural fiber composites especially those which are reinforced with thermoplastic matrices compared to conventional experimental technique for automotive product development purposes in addition to identifying the optimal parameter to be put into focus in their composites design to achieve the intended design performance specifications.

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Goyal, R. K., A. N. Tiwari, and Y. S. Negi. "Microhardness of PEEK/ceramic micro- and nanocomposites: Correlation with Halpin–Tsai model." Materials Science and Engineering: A 491, no. 1-2 (September 2008): 230–36. http://dx.doi.org/10.1016/j.msea.2008.01.091.

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Kucukyildirim, Bedri Onur, and Aysegul Akdogan Eker. "Fabrication of carbon nanotube reinforced aluminum alloy composites by vacuum-assisted infiltration technique." Journal of Composite Materials 55, no. 16 (January 14, 2021): 2225–35. http://dx.doi.org/10.1177/0021998320988320.

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Carbon nanotube (CNT) reinforced 6063 aluminum (Al) matrix composites were fabricated by vacuum-assisted infiltration of molten 6063 Al alloy into a CNT preform to enhance compressive mechanical properties. Preforms were produced with different amounts of chemically functionalized CNTs to obtain three different CNT reinforcement ratios (0.25, 0.50, and 0.75 wt.%). In addition to the investigation of properties throughout all stages of the preparation of the CNTs, CNT preforms and fabricated composites by various methods of analysis, all steps of the composite fabrication process, as well as the compressive mechanical test results of CNT/6063 Al composites are all discussed. Approximately 250% and 280% increases in the yield and ultimate compressive strength, respectively, are achieved with low-purity CNT addition. Consequently, it is confirmed from the micrographs that the mechanical enhancements of the composites are mainly interrelated with the successful bridging of CNTs in the matrix material. Meanwhile, it is observed that both the modified Halpin-Tsai model and the modified Halpin-Tsai model developed with a dispersion-based prediction model results match with experimental results. Overall results can be accepted as developmental stages of significant progress in the CNT preform reinforced metal matrix composites field.

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Mittal, Vikas. "Modeling of Tensile Modulus of Polyolefin-Layered Silicate Nanocomposites: Modified Halpin Tsai Models." Advanced Composites Letters 21, no. 5 (September 2012): 096369351202100. http://dx.doi.org/10.1177/096369351202100501.

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The modified forms of Halpin Tsai model for the prediction of tensile modulus of polyolefin-layered silicate nanocomposites are discussed. The assumptions used in the conventional model like perfect alignment of the particulate filler, uniform shape and size of the filler particles as well as interfacial adhesion between the polymer and filler surface do not hold true in the case of polymer nanocomposites especially using polyolefinic matrices. The modulus reduction factors suggested for polar nanocomposites are also dependent on the polymer nature as well as filler morphology in the composite, thus, are not applicable directly to the polyolefin composites. A master curve could be generated for polyolefin nanocomposites which provided more accurate modulus reduction factor value based on the average aspect ratio of the filler. Incorporation of the effects of incomplete exfoliation as well as filler misalignment though improved the prediction capabilities of the model, however, it still did not match the predictions generated from finite element analysis or TEM analysis. The effect of absence of adhesion forces at the interface was incorporated by suggesting simple modification to the modified Halpin Tsai model equation. Master curves could be generated which predicted the relative tensile modulus of the composites accurately if the value of average aspect ratio was known.

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Mittal, Vikas. "Modeling of tensile modulus of polyolefin-layered silicate nanocomposites: modified micro-mechanical and statistical methods." Journal of Polymer Engineering 32, no. 8-9 (December 1, 2012): 519–29. http://dx.doi.org/10.1515/polyeng-2012-0059.

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Abstract Applicability and subsequent modification of various composite models for the prediction of the relative tensile modulus of polyolefin nanocomposites has been studied. A number of models, such as the modified Halpin-Tsai, Guth, Mori-Tanaka, Hui and Shia and Takayanagi models, as well as factorial and mixture designs, were considered. Various assumptions in the models, such as uniform shape and size of filler (i.e., complete exfoliation), alignment, as well as interfacial bonding between the components, restrict their application for the prediction of the nanocomposite modulus. The modified Guth model and Halpin-Tsai model, with the ∅m concept, were developed further to incorporate the modulus reduction factors for polyolefin nanocomposites. This allowed the generation of master curves of the modulus reduction factor as a function of the aspect ratio of the filler in the composite. It was observed that the Mori Tanaka model, modified by constructing models of various representative volume elements (RVEs) of the underlying structure of the nanoclay filled polymers, matched the experimental values of the tensile modulus of polyolefin nanocomposites. The modified Hui and Shia model, incorporating the non-bonding interfacial effects, as well as the three component modified Takayanagi model, were also able to predict the tensile modulus of polyolefin nanocomposites efficiently. Factorial and mixture designs did not require the conventionally used assumptions and satisfactorily reflected the material behavior, and were specific to the particular components used to generate nanocomposites. These models were also helpful in predicting the aspect ratio of the filler in the composites, when synergistically combined with other modified models.

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Merinska, Dagmar, Jaroslav Mikula, Hana Kubisova, and Petr Svoboda. "PP/MMT Nanocomposite: Mathematic Modelling of Layered Nanofiller." Journal of Nanomaterials 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/860371.

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The comparison of calculated data from proposed mathematic model and experimentally obtained data of PP/clay nanocomposites was done with the focus on the layered shape of MMT platelets. Based on the well-known Kerner's model and the Halpin-Tsai' equation with the use of some described presumption, the mathematic model for PP/clay nanocomposite was proposed. Data from the measurement of prepared PP/clay samples were taken and compared with the calculated ones from the proposed model. The good agreement was found.

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Zare, Yasser. "Development of Halpin-Tsai model for polymer nanocomposites assuming interphase properties and nanofiller size." Polymer Testing 51 (May 2016): 69–73. http://dx.doi.org/10.1016/j.polymertesting.2016.02.010.

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Yung, K. C., J. Wang, and T. M. Yue. "Modeling Young's Modulus of Polymer-layered Silicate Nanocomposites Using a Modified Halpin—Tsai Micromechanical Model." Journal of Reinforced Plastics and Composites 25, no. 8 (May 2006): 847–61. http://dx.doi.org/10.1177/0731684406065135.

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Ebrahimi, Farzad, and Ali Dabbagh. "Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model." Composites Part B: Engineering 173 (September 2019): 106955. http://dx.doi.org/10.1016/j.compositesb.2019.106955.

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Li, Yuanji, Yu Zhao, Yanhua Cui, Zheyi Zou, Da Wang, and Siqi Shi. "Screening polyethylene oxide-based composite polymer electrolytes via combining effective medium theory and Halpin-Tsai model." Computational Materials Science 144 (March 2018): 338–44. http://dx.doi.org/10.1016/j.commatsci.2017.12.014.

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Duzzi, Matteo, Mirco Zaccariotto, and Ugo Galvanetto. "Application of Peridynamic Theory to Nanocomposite Materials." Advanced Materials Research 1016 (August 2014): 44–48. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.44.

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The purpose of this paper is to describe the computational procedure developed to apply the Bond-based Peridynamic Theory to nanocomposite materials. The goal is to predict the Young’s modulus as a function of the filling fraction of different nanocomposite materials with an accuracy better than that of other methods (like Halpin-Tsai, Mori-Tanaka, FEA models). A displacement control method is adopted here in order to simulate the incremental application of an external load. The constitutive law considered is linear and thus the problem can be seen as a static-linear problem. A description of the model and of the “multiscale approach” is given, supported by a comparison between experimental data and simulation results for different nanocomposites.

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Hadi, Agung Efriyo, Mohammad Hazim Mohamad Hamdan, Januar Parlaungan Siregar, Ramli Junid, Cionita Tezara, Agustinus Purna Irawan, Deni Fajar Fitriyana, and Teuku Rihayat. "Application of Micromechanical Modelling for the Evaluation of Elastic Moduli of Hybrid Woven Jute–Ramie Reinforced Unsaturated Polyester Composites." Polymers 13, no. 15 (August 1, 2021): 2572. http://dx.doi.org/10.3390/polym13152572.

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Woven laminated composite has gained researchers’ and industry’s interest over time due to its impressive mechanical performance compared to unidirectional composites. Nevertheless, the mechanical properties of the woven laminated composite are hard to predict. There are many micromechanical models based on unidirectional composite but limited to the woven laminated composite. The current research work was conducted to evaluate elastic moduli of hybrid jute–ramie woven reinforced unsaturated polyester composites using micromechanical effectiveness unidirectional models, such as ROM, IROM, Halpin–Tsai, and Hirsch, which are based on stiffness. The hybrid jute–ramie laminated composite was fabricated with different layering sizes, and the stacking sequence was completed via hand lay-up with the compression machine. Tensile modulus values for hybrid composites are between those for single jute and single ramie. Obtained p-values less than 0.05 prove the relationship between layering size and tensile modulus. This study showed that several micromechanical models, such as Halpin–Tsai’s predicted value of homogenized mechanical properties, were in good agreement with the experimental result. In the case of the hybrid composite, the micromechanical model deviates from the experimental result. Several modifications are required to improve the current existing model. A correlation function was calculated based on the differences between the elastic modulus values determined experimentally and those derived from each micromechanical model calculation.

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Zare, Yasser, Kyong Yop Rhee, and Soo-Jin Park. "A developed equation for electrical conductivity of polymer carbon nanotubes (CNT) nanocomposites based on Halpin-Tsai model." Results in Physics 14 (September 2019): 102406. http://dx.doi.org/10.1016/j.rinp.2019.102406.

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Karimiasl, Mahsa, Farzad Ebrahimi, and Mahesh Vinyas. "Nonlinear vibration analysis of multiscale doubly curved piezoelectric composite shell in hygrothermal environment." Journal of Intelligent Material Systems and Structures 30, no. 10 (April 22, 2019): 1594–609. http://dx.doi.org/10.1177/1045389x19835956.

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This research studied large amplitude vibration behaviors of multiscale composites doubly curved shells with piezoelectric layer. By using Reddy’s third-order shear deformation theory, the strains and stresses are obtained. According to the Halpin–Tsai model three-phase composites layers are considered. The governing equations of the multiscale doubly curved shell are derived by implementing the Hamilton’s principle and are solved via homotopy perturbation method. For investigating correctness and accuracy, this article is validated by other previous studies. Finally, the influence of different parameters such as temperature rise, various distributions pattern, applied voltage, magnetic potential, and aspect and curvature ratio are observed in this article. It is found that these parameters have significant influence on nonlinear frequencies.

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Mekala, Narasimha Rao, Rüdiger Schmidt, and Kai Uwe Schröder. "Modelling and Analysis of Piezolaminated Functionally Graded Polymer Composite Structures Reinforced with Graphene Nanoplatelets under Strong Electroelastic Fields." Applied Mechanics and Materials 875 (January 2018): 3–8. http://dx.doi.org/10.4028/www.scientific.net/amm.875.3.

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This paper focuses on the electromechanical modelling and analysis of piezolaminated functionally graded polymer composites reinforced with graphene nanoplatelets considering strong electric field nonlinearities. Non-uniform distribution of reinforcement of graphene nanoplatelets is assumed along the thickness direction in multilayer polymer nanocomposites, whereas uniform dispersion GPLs in each layer is assumed. Modified Halpin-Tsai micromechanics is used to determine the effective Young’s modulus of GPLs considering the effects of geometry and dimension changes. Electro-elastic nonlinear constitutive relations are used to model the piezoelectric layers under strong applied electric fields. Through variational formulation, a finite element is derived to model and analyse the layered GPL/polymer composite structures. Various simulations are performed to study the effects of several parameters like distribution pattern and size of GPLs by applying actuation voltages to piezoelectric layers.

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Meng, Qing Chang, Hai Bo Feng, De Chang Jia, and Yu Zhou. "Young’s Modulus of In Situ TiB Whiskers in Ti Metal Matrix Composites." Key Engineering Materials 353-358 (September 2007): 365–68. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.365.

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The TiB/Ti metal matrix composites (MMCs) with different volume fractions of in situ TiB reinforcements were spark plasma sintered at 1000 °C with a pressure of 20 MPa for 5 minutes in vacuum. The in situ synthesized TiB is whisker shape with a hexagonal transverse section and distributes uniformly and randomly in the Ti matrix. The Young’s modulus of TiB was back-calculated from the elastic properties of the composites using the Halpin-Tsai model. The Young’s moduli of all the composites were found to increase with the increase of TiB volume fraction. The calculated value of TiB Young’s modulus is about 489±83GPa. Values of Young’s moduli of TiB whisker obtained according to different methods were compared and discussed.

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Tran, Trung Thanh, Van Ke Tran, Pham Binh Le, Van Minh Phung, Van Thom Do, and Hoang Nam Nguyen. "Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method." Advances in Civil Engineering 2020 (January 3, 2020): 1–17. http://dx.doi.org/10.1155/2020/1471037.

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This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

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Zhao, Zhen, Yiwen Ni, Shengbo Zhu, Zhenzhen Tong, Junlin Zhang, Zhenhuan Zhou, C. W. Lim, and Xinsheng Xu. "Thermo-Electro-Mechanical Size-Dependent Buckling Response for Functionally Graded Graphene Platelet Reinforced Piezoelectric Cylindrical Nanoshells." International Journal of Structural Stability and Dynamics 20, no. 09 (August 2020): 2050100. http://dx.doi.org/10.1142/s021945542050100x.

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An accurate buckling response analysis for functionally graded graphene platelet (GPL) reinforced piezoelectric cylindrical nanoshells subject to thermo-electro-mechanical loadings is presented by a rigorous symplectic expansion approach. Three types of GPL reinforced patterns are considered, and the modified Halpin–Tsai model is employed to determine their effective material properties. By using Eringen’s nonlocal stress theory and Reissner’s shell theory, new governing equations are established in the Hamiltonian form. Exact solutions are expanded into symplectic series and three possible forms are derived. A comparison with the existing study is presented to validate the solution and very good agreement is observed. The effects of material and geometrical properties of GPLs, electric voltage and temperature rise on critical buckling stresses are investigated and discussed in detail.

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Townsend Valencia, Patrick. "Isotropic Modeling of a Composite Panel of the Stern of a Fiberglass Boat Propelled by an Outboard Motor." Ciencia y tecnología de buques 7, no. 14 (January 26, 2014): 9. http://dx.doi.org/10.25043/19098642.90.

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We performed a theoretical and experimental study to define the best way to model the finite element sandwich structure aft of a fiberglass boat less than 15 meters in length, using an isotropic linear mathematical model that fits anisotropic material conditions. This is done by defining the properties of the ship’s fiberglass resin structure, which is representative of the influence of the forces acting during the glide on the geometry of the entire vessel. Formulation of the Finite Elements Method is presented, which works on the mathematical model to define the limitations of the results obtained. Isotropic material adjustment is calculated using Halpin-Tsai laws, developing its mathematical formulation for restrictions of modulus data entered as the finite element program experimentally calculated for each of the sandwich materials. The best-fit mathematical presentation to the modulus of the composite tool justifies the calculation thereof.

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Lee, Sang-Youl, and Gyu-Dong Kim. "Micromechanical damage identification of vibrating laminated composites using bivariate Gaussian function-based genetic algorithms." Journal of Composite Materials 52, no. 20 (January 25, 2018): 2829–44. http://dx.doi.org/10.1177/0021998318754997.

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This study deals with a micromechanical detection of stiffness degradation occurred by the fiber damage in vibrating laminated composite plates. Five unknown parameters are considered to determine the fiber or matrix damage distribution, which is a modified form of the bivariate Gaussian distribution function. The proposed approach is more feasible than the conventional element-based damage detection method from the computational efficiency because it is independent on the number of divided elements. The micromechanical model is embedded in the reconstruction algorithm using the modified Halpin–Tsai formulation. The numerical examples show that the proposed technique is a feasible and practical method, which can prove the location of a damaged region as well as inspect the distribution of deteriorated stiffness of composites for different fiber angles and layup sequences.

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Mousa, Mohanad, and Yu Dong. "Towards Sophisticated 3D Interphase Modelling of Advanced Bionanocomposites via Atomic Force Microscopy." Journal of Nanomaterials 2020 (August 4, 2020): 1–22. http://dx.doi.org/10.1155/2020/4526108.

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Nanomechanical properties and interphase dimensions of PVA bionanocomposites reinforced with halloysite nanotubes (HNTs) and Cloisite 30B montmorillonite (MMT) were evaluated by means of peak force quantitative nanomechanical mapping (PFQNM). A three-phase theoretical composite model was established based on hard-core–soft-shell structures consisting of hard mono-/polydispersed anisotropic particles and soft interphase and matrices. Halpin-Tsai model and Mori-Tanaka model were employed to predict experimentally determined tensile moduli of PVA bionanocomposites where effective volume fraction of randomly oriented nanoparticles resulted from the inclusion of interphase properties and volume fractions. Overall, it was suggested that the estimation of elastic modulus according to effective volume fraction of nanoparticles revealed better agreement with experimental data as opposed to that based upon their nominal volume fraction. In particular, the use of polydispersed HNTs and Cloisite 30B MMT clays with Fuller particulate gradation was proven to yield the best prediction when compared with experimental data among all proposed theoretical models. This study overcomes the neglected real interphase characteristics in modelling nanocomposite materials with much more accurate estimation of their mechanical properties.

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Safarpour, Mehran, Alireza Rahimi, Omid Noormohammadi Arani, and Timon Rabczuk. "Frequency Characteristics of Multiscale Hybrid Nanocomposite Annular Plate Based on a Halpin–Tsai Homogenization Model with the Aid of GDQM." Applied Sciences 10, no. 4 (February 19, 2020): 1412. http://dx.doi.org/10.3390/app10041412.

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In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin–Tsai model to predict the effective properties of the MHCAP. Hamilton’s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency.

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Luo, Zirong, Xin Li, Jianzhong Shang, Hong Zhu, and Delei Fang. "Modified rule of mixtures and Halpin–Tsai model for prediction of tensile strength of micron-sized reinforced composites and Young’s modulus of multiscale reinforced composites for direct extrusion fabrication." Advances in Mechanical Engineering 10, no. 7 (July 2018): 168781401878528. http://dx.doi.org/10.1177/1687814018785286.

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A modified rule of mixtures is required to account for the experimentally observed nonlinear variation of tensile strength. A modified Halpin–Tsai model was presented to predict the Young’s modulus of multiscale reinforced composites with both micron-sized and nano-sized reinforcements. In the composites, both micron-sized fillers—carbon fibers—and nano-sized fillers—rubber nanoparticles and carbon nanotubes—are added into the epoxy resin matrix. Carbon fibers can help epoxy resins increase both the tensile strength and Young’s modulus, while rubber nanoparticles and carbon nanotubes can improve the toughness without sacrificing other properties. Mechanical experiments and scanning electron microscopy observations were used to study the effects of the micron-sized and nano-sized reinforcements and their combination on tensile and toughness properties of the composites. The results showed that the combined use of multiscale reinforcements had synergetic effects on both the strength and the toughness of the composites.

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Phan, Duc-Huynh. "Isogeometric Analysis of Functionally-Graded Graphene Platelets Reinforced Porous Nanocomposite Plates Using a Refined Plate Theory." International Journal of Structural Stability and Dynamics 20, no. 07 (June 10, 2020): 2050076. http://dx.doi.org/10.1142/s0219455420500765.

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In this study, we propose a novel and effective computational approach for free and forced vibration analyses of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement under various loads. To this end, the outstanding features of isogeometric analysis (IGA) are first combined with the four-variable refined plate theory (RPT). The non-uniform rational B-splines (NURBS) are adopted to obtain the [Formula: see text]-continuity essential to the RPT model. The various distributions of internal pores as well as GPLs with uniform or non-uniform properties along the plate’s thickness are investigated. The effective elastic properties of the material models are obtained by the Halpin–Tsai micromechanics model for Young’s modulus, the rule of mixture for Poisson’s ratio and mass density. The Newmark’s time integration scheme is implemented to obtain the solutions of the forced vibration problems. Numerical examples are carried out to investigate the effects of various key parameters such as porosity coefficient, GPL weight fraction, porosity distribution, as well as GPL dispersion pattern, on the behaviors of the plate structure.

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Liu, Dongying, Jing Sun, and Linhua Lan. "Elasticity Solutions for In-Plane Free Vibration of FG-GPLRC Circular Arches with Various End Conditions." Applied Sciences 10, no. 14 (July 8, 2020): 4695. http://dx.doi.org/10.3390/app10144695.

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In-plane free vibration of functionally graded graphene platelets reinforced nanocomposites (FG-GPLRCs) circular arches is investigated by using the two-dimensional theory of elasticity. The graphene platelets (GPLs) are dispersed along the thickness direction non-uniformly, and the material properties of the nanocomposites are evaluated by the modified Halpin-Tsai multi-scaled model and the rule of mixtures. A state-space method combined with differential quadrature technique is employed to derive the governing equation for in-plane free vibration of FG-GPLRCs circular arch, the semi-analytical solutions are obtained for various end conditions. An exact solution of FG-GPLRCs circular arch with simply-supported ends is also presented as a benchmark to valid the present numerical method. Numerical examples are performed to study the effects of GPL distribution patterns, weight fraction and dimensions, geometric parameters and boundary conditions of the circular arch on the natural frequency in details.

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Tahouneh, Vahid. "An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes." Periodica Polytechnica Mechanical Engineering 61, no. 4 (September 20, 2017): 309. http://dx.doi.org/10.3311/ppme.11254.

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In the present work, vibration characteristics of functionally graded (FG) sandwich rectangular plates reinforced by multiwalled carbon nanotubes (MWCNTs) resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation is used to evaluate the Young’s modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The mass density and Poisson’s ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. The proposed sandwich rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the sandwich plates are investigated.

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Zhao, Tianyu, Yu Ma, Jiannan Zhou, and Yanming Fu. "Wave Propagation in Rotating Functionally Graded Microbeams Reinforced by Graphene Nanoplatelets." Molecules 26, no. 17 (August 25, 2021): 5150. http://dx.doi.org/10.3390/molecules26175150.

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This paper presents a study on wave propagation in rotating functionally graded (FG) microbeams reinforced by graphene nanoplatelets (GPLs). The graphene nanoplatelets (GPLs) are considered to distribute in the diameter direction of the micro-beam in a gradient pattern, which leads to the functionally graded structure. By using the Halpin-Tsai micromechanics model and the rule of mixture, the effective material properties of the microbeam are determined. According to the Euler-Bernoulli beam theory and nonlocal elasticity theory, the rotating microbeams are modeled. A comprehensive parametric study is conducted to examine the effects of rotating speed, GPL distribution pattern, GPL length-to-thickness ratio, GPL length-to-width ratio, and nonlocal scale on the wavenumber, phase speed and group speed of the microbeam. The research findings can play an important role on the design of rotating graphene nanoplatelet (GPL) reinforced microbeams for better structural performance.

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Cai, Yi, Zi-Feng Liu, Tian-Yu Zhao, and Jie Yang. "Parameter Interval Uncertainty Analysis of Internal Resonance of Rotating Porous Shaft–Disk–Blade Assemblies Reinforced by Graphene Nanoplatelets." Materials 14, no. 17 (September 3, 2021): 5033. http://dx.doi.org/10.3390/ma14175033.

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This paper conducts a parameter interval uncertainty analysis of the internal resonance of a rotating porous shaft–disk–blade assembly reinforced by graphene nanoplatelets (GPLs). The nanocomposite rotating assembly is considered to be composed of a porous metal matrix and graphene nanoplatelet (GPL) reinforcement material. Effective material properties are obtained by using the rule of mixture and the Halpin–Tsai micromechanical model. The modeling and internal resonance analysis of a rotating shaft–disk–blade assembly are carried out based on the finite element method. Moreover, based on the Chebyshev polynomial approximation method, the parameter interval uncertainty analysis of the rotating assembly is conducted. The effects of the uncertainties of the GPL length-to-width ratio, porosity coefficient and GPL length-to-thickness ratio are investigated in detail. The present analysis procedure can give an interval estimation of the vibration behavior of porous shaft–disk–blade rotors reinforced with graphene nanoplatelets (GPLs).

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Gao, Jian Hong, Xiao Xiang Yang, and Li Hong Huang. "Application of Embedded Element in the Short Fiber Reinforced Composite." Key Engineering Materials 774 (August 2018): 241–46. http://dx.doi.org/10.4028/www.scientific.net/kem.774.241.

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The finite element analysis (FEA) is a numerical method for predicting the mechanical property of short fiber reinforced composite usefully. However, as we know, there is always a “jamming” limit when generating fiber architecture expecially in the cases of high volume fraction and high aspect ratio of short fiber. Even if the volume fraction and aspect ratio in finite element model meet the practical requirements, the problem of mesh deformity will always occur which would lead to unconverge of numerical computation. In this work, embedded element technique which will help to reduce the probability of the above two problems is employed to establish the finite element model of short fiber reinforced composite. The effect of edge size, thickness and mesh density of FE models on the elastic modulus were investigated. Numerical results show that the value of elastic modulus mainly depend on the edge size and fiber amount of FE model while the effect of thickness can be neglected. The elastic modulus takes to converge for high element number. An inverse method is proposed to calculate volume fraction of short fibers, by which numerical results agree well with the calculation results of empirical formula based on Halpin-Tsai equation.

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Yerramalli, Chandra S., and Anthony M. Waas. "In Situ Matrix Shear Response Using Torsional Test Data of Fiber Reinforced Unidirectional Polymer Composites." Journal of Engineering Materials and Technology 124, no. 2 (March 26, 2002): 152–59. http://dx.doi.org/10.1115/1.1446471.

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The in situ shear response of the matrix in polymer matrix composites (PMC) has been studied. Torsion tests were performed on solid cylinders of unidirectional glass fiber reinforced/vinylester and unidirectional carbon fiber reinforced/vinylester composites. The composite specimens were subjected to a uniform rate of twist. From the composite stress-strain curve, a plot of tangent shear modulus vs shear strain was derived. Then, using the Halpin-Tsai equations, the in situ matrix shear modulus was determined. The in situ matrix properties obtained from glass/vinylester and carbon/vinylester composites were found to be different. In addition, the properties of the in situ matrix were found to be a function of fiber volume fraction and the elastic properties of the reinforcing fiber. The behavior of the in situ matrix as a function of the fiber volume fraction was explained by using a three cylinder interphase model. The validity of the interphase model in predicting the composite shear modulus was studied by comparison of results against a conventional 2 cylinder model.

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Gaska, Karolina, Georgia C. Manika, Thomas Gkourmpis, Davide Tranchida, Antonis Gitsas, and Roland Kádár. "Mechanical Behavior of Melt-Mixed 3D Hierarchical Graphene/Polypropylene Nanocomposites." Polymers 12, no. 6 (June 8, 2020): 1309. http://dx.doi.org/10.3390/polym12061309.

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The mechanical properties of novel low percolation melt-mixed 3D hierarchical graphene/polypropylene nanocomposites are analyzed in this study. The analysis spans a broad range of techniques and time scales, from impact to tensile, dynamic mechanical behavior, and creep. The applicability of the time–temperature superposition principle and its limitations in the construction of the master curve for the isotactic polypropylene (iPP)-based graphene nanocomposites has been verified and presented. The Williams–Landel–Ferry method has been used to evaluate the dynamics and also Cole–Cole curves were presented to verify the thermorheological character of the nanocomposites. Short term (quasi-static) tensile tests, creep, and impact strength measurements were used to evaluate the load transfer efficiency. A significant increase of Young’s modulus with increasing filler content indicates reasonably good dispersion and adhesion between the iPP and the filler. The Young’s modulus results were compared with predicted modulus values using Halpin–Tsai model. An increase in brittleness resulting in lower impact strength values has also been recorded.

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Liu, Dongying. "Free Vibration of Functionally Graded Graphene Platelets Reinforced Magnetic Nanocomposite Beams Resting on Elastic Foundation." Nanomaterials 10, no. 11 (November 3, 2020): 2193. http://dx.doi.org/10.3390/nano10112193.

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The vibrational characteristics of multilayer magnetic nanocomposite beams reinforced by graphene nanoplatelets (GPLs) are analytically investigated in this paper. The effects of an elastic foundation are also studied. The material properties of piece-wise GPL-reinforced nanocomposites (GPLRCs) are assumed to be graded in the thickness direction of the beams and can be estimated by using the modified Halpin–Tsai model and rules of mixtures. The two-dimensional elasticity theory is adopted to derive the governing equation combined with the state space method, and the analytical frequency equations for simply supported beams are obtained. In addition, the effects of a magnetic field are involved via Maxwell’s equation, and the corresponding Lorentz forces are considered in this work. Numerical examples are carried out to examine the effects of magnetic fields in various directions, the GPL distribution pattern, the scale parameter and weight function of GPLs, as well as an elastic foundation, on the vibration behaviors of functionally graded (FG)-GPLRC beams.

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Wilkes, T. E., J. Y. Pastor, J. Llorca, and K. T. Faber. "Mechanical properties of wood-derived silicon carbide aluminum-alloy composites as a function of temperature." Journal of Materials Research 23, no. 6 (June 2008): 1732–43. http://dx.doi.org/10.1557/jmr.2008.0197.

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The mechanical behavior [i.e., stiffness, strength, and toughness (KIC)] of SiC Al–Si–Mg metal–ceramic composites (50:50 by volume) was studied at temperatures ranging from 25 to 500 °C. The SiC phase was derived from wood precursors, which resulted in an interconnected anisotropic ceramic that constrained the pressure melt-infiltrated aluminum alloy. The composites were made using SiC derived from two woods (sapele and beech) and were studied in three orthogonal orientations. The mechanical properties and corresponding deformation micromechanisms were different in the longitudinal (LO) and transverse directions, but the influence of the precursor wood was small. The LO behavior was controlled by the rigid SiC preform and the load transfer from the metal to the ceramic. Moduli in this orientation were lower than the Halpin–Tsai predictions due to the nonlinear and nonparallel nature of the Al-filled pores. The LO KIC agreed with the Ashby model for the KIC contribution of ductile inclusions in a brittle ceramic.

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Rodríguez-Tembleque, Luis, Felipe García-Sánchez, and Andrés Sáez. "Crack Surface Frictional Contact Modeling in Fractured Fiber-Reinforced Composites." Journal of Multiscale Modelling 10, no. 01 (March 2019): 1841005. http://dx.doi.org/10.1142/s1756973718410056.

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A robust boundary element numerical scheme is presented to study crack-face frictional contact in cracked fiber reinforced composite materials. The dual boundary element method is considered for modeling fracture mechanics on these materials. The formulation is based on contact operators over the augmented Lagrangian to enforce contact constraints on the crack surface. Moreover, it considers a Halpin–Tsai macro model for fiber reinforced composite materials which makes it possible to take into account the influence of micromechanical aspects such as: the fibers’ orientation, the fiber’s aspect ratio or the fiber’s volume fraction, estimating the mechanical properties of these composite materials from the known values of the fiber and the matrix. After solving a crack face frictional contact benchmark problem, the capabilities of this methodology are illustrated by studying the influence of not only these micromechanical aspects but also crack face frictional contact conditions on a fractured carbon fiber-reinforced polymer under compression.

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Wang, Yan Qing, Yun Fei Liu, and Jean W. Zu. "Size-Dependent Vibration of Circular Cylindrical Polymeric Microshells Reinforced with Graphene Platelets." International Journal of Applied Mechanics 11, no. 04 (May 2019): 1950036. http://dx.doi.org/10.1142/s1758825119500364.

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This paper investigates size-dependent vibration of graphene platelet (GPL) reinforced circular cylindrical polymeric microshells. The microshells are composed of multilayers with GPL fillers uniformly dispersed in each individual layer, but GPL weight fraction changes layer-by-layer along the thickness direction. The effective Young’s modulus is predicted by the modified Halpin–Tsai model, while effective Poisson’s ratio and mass density are determined by the rule of mixture. Four different patterns of GPL dispersion are considered to achieve the functionally graded property of the microshells. Based on Love’s thin shell theory and the modified couple stress theory, the governing equations are derived by using Hamilton’s principle. Then, the Navier and Galerkin methods are utilized to solve natural frequencies of GPL reinforced polymeric (GPLRP) microshells. A parametric study is conducted, with a particular focus on the effects of the GPL distribution pattern, the weight fraction, the geometries of the GPL and the microshells, as well as the total number of layers of the microshells.

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39

Georgantzinos, Stelios K., Panagiotis A. Antoniou, and Stylianos I. Markolefas. "A Multi-Scale Method for Designing Hybrid Fiber-Reinforced Composite Drive Shafts with Carbon Nanotube Inclusions." Journal of Composites Science 5, no. 6 (June 10, 2021): 157. http://dx.doi.org/10.3390/jcs5060157.

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In this paper, the modal and linear buckling analysis of a laminated composite drive shaft reinforced by 11 multi-walled carbon nanotubes (MWCNTs) was carried out using an analytical approach, as well as the finite element method (FEM). The theoretical model is based on classical laminated theory (CLT). The fundamental frequency and the critical buckling torque were determined for different fiber orientation angles. The Halpin–Tsai model was employed to calculate the elastic modulus of composites having randomly oriented nanotubes. The effect of various carbon nanotube (CNT) volume fractions in the epoxy resin matrix on the material properties of unidirectional composite laminas was also analyzed. The fundamental frequency and the critical buckling torque obtained by the finite element analysis and the analytical method for different fiber orientation angles were in good agreement with each other. The results were verified with data available in the open literature, where possible. For the first time in the literature, the influence of CNT fillers on various composite drive shaft design parameters such as the fundamental frequency, critical speed, and critical buckling torque of a hybrid fiber-reinforced composite drive shaft is finally predicted.

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Salam, Haipan, and Yu Dong. "Theoretical Modelling Analysis on Tensile Properties of Bioepoxy/Clay Nanocomposites Using Epoxidised Soybean Oils." Journal of Nanomaterials 2019 (December 2, 2019): 1–20. http://dx.doi.org/10.1155/2019/4074869.

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A theoretical modelling framework was proposed to predict tensile moduli and tensile strengths of bioepoxy/clay nanocomposites in terms of clay content and epoxidised soybean oil (ESO) content, which could be influenced by properties of blended matrices in nanocomposites, clay filler type, orientation and dispersion status, clay morphological structures, and filler-matrix interfacial bonding. The random orientation of dispersed clay fillers played a significant role in predicting elastic moduli of bioepoxy/clay nanocomposites at clay contents of 1-8 wt% (ESO content: 20 wt%) according to Hui-Shia (H-S) laminate model and Halpin-Tsai (H-T) laminate model. In addition, when clay content was fixed at 5 wt%, H-S laminate model coincided well with the experimental data of bioepoxy/clay nanocomposites at the ESO contents of 0-40 wt%. Whereas, Hirsch model showed closer estimated values with experimental data at the ESO content of 60 wt%. Finally, Turcsányi-Pukànszky-Tüdõs (T-P-T) model predicted better tensile strengths of bioepoxy/clay nanocomposites at clay contents of 1-5 wt% (ESO content: 20 wt%) and at an ESO content of 20-60 wt% (clay content: 5 wt%).

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41

Lal, Achchhe, and Kanif Markad. "Thermo-Mechanical Post Buckling Analysis of Multiwall Carbon Nanotube-Reinforced Composite Laminated Beam under Elastic Foundation." Curved and Layered Structures 6, no. 1 (January 1, 2019): 212–28. http://dx.doi.org/10.1515/cls-2019-0018.

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AbstractIn present paper, buckling analysis is performed over laminated composite beam incorporating multi walled carbon nanotube (MWCNT) polymer matrix and then reinforced with E-glass fiber in an orthotropic manner under inplane varying thermal and mechanical loads by finite element method (FEM). Aim of the study is to develop a model which accurately perform the buckling deterministic analysis of multi-walled carbon nanotube reinforced composite laminated beam (MWCNTRCLB) with the evaluation of material property by applying Halpin–Tsai model. Combined Higher order shear deformation theory and Pasternak elastic foundation based on von Karman nonlinear kinematics and Winkler cubic nonlinearity respectively, are successfully implemented. Through minimum potential energy principle, generalized static analysis is performed using FEM, based on interactive MATLAB coding. The critical buckling load and critical buckling temperature is presented under the action of inplane variable mechanical and thermal load, with different boundary conditions, beam thickness ratio and MWCNT aspect ratio, variation with MWCNT volume fraction and coefficient of thermal expansion, with and without foundation for linear and nonlinear cases.

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Venkatesan, Ganesh, Maximilian J. Ripepi, and Charles E. Bakis. "Transverse Young's modulus of carbon/glass hybrid fiber composites." Journal of Composite Materials 54, no. 7 (August 26, 2019): 947–60. http://dx.doi.org/10.1177/0021998319871689.

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Hybrid fiber composites offer designers a means of tailoring the stress–strain behavior of lightweight materials used in high-performance structures. While the longitudinal stress–strain behavior of unidirectional hybrid fiber composites has been thoroughly evaluated experimentally and analytically, relatively little information is available on the transverse behavior. The objective of the current investigation is to present data on the transverse modulus of elasticity of unidirectional composites with five different ratios of carbon and glass fiber and to compare the data with predictive and fitted models. The transverse modulus increases monotonically with the proportion of glass fiber in the composite. Finite element analysis was used to evaluate different ways to model voids in the matrix and allowed the unknown transverse properties of the carbon fibers to be backed out using experimental data from the all-carbon composite. The finite element results show that the transverse modulus can be accurately modeled if voids are modeled explicitly in the matrix region and if modulus is calculated based on stress applied along the minimum interfiber distance path between adjacent fibers arranged in a rectangular array. The transverse modulus was under-predicted by the iso-stress model and was well predicted by a modified iso-stress model and a modified Halpin–Tsai model.

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Uyanık, N. "Application of the Experimental Results to the Modified Halpin-Tsai Micromechanical Model to Evaluate the Clay Dispersion in Clay-Reinforced Polyethylene Nanocomposites." International Polymer Processing 29, no. 1 (March 28, 2014): 28–34. http://dx.doi.org/10.3139/217.2797.

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Chen, Hongyu, and Donald Baird. "Prediction of Young’s Modulus for Injection Molded Long Fiber Reinforced Thermoplastics." Journal of Composites Science 2, no. 3 (August 6, 2018): 47. http://dx.doi.org/10.3390/jcs2030047.

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In this article, the elastic properties of long-fiber injection-molded thermoplastics (LFTs) are investigated by micro-mechanical approaches including the Halpin-Tsai (HT) model and the Mori-Tanaka model based on Eshelby’s equivalent inclusion (EMT). In the modeling, the elastic properties are calculated by the fiber content, fiber length, and fiber orientation. Several closure approximations for the fourth-order fiber orientation tensor are evaluated by comparing the as-calculated elastic stiffness with that from the original experimental fourth-order tensor. An empirical model was developed to correct the fibers’ aspect ratio in the computation for the actual as-formed LFTs with fiber bundles under high fiber content. After the correction, the analytical predictions had good agreement with the experimental stiffness values from tensile tests on the LFTs. Our analysis shows that it is essential to incorporate the effect of the presence of fiber bundles to accurately predict the composite properties. This work involved the use of experimental values of fiber orientation and serves as the basis for computing part stiffness as a function of mold filling conditions. The work also explains why the modulus tends to level off with fiber concentration.

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Fan, Yin, Y. Xiang, and Hui-Shen Shen. "Nonlinear Dynamics of Temperature-Dependent FG-GRC Laminated Beams Resting on Visco-Pasternak Foundations." International Journal of Structural Stability and Dynamics 20, no. 01 (November 28, 2019): 2050012. http://dx.doi.org/10.1142/s0219455420500121.

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This paper studies the nonlinear dynamic responses of graphene-reinforced composite (GRC) beams in a thermal environment. It is assumed that a laminated beam rests on a Pasternak foundation with viscosity and consists of GRC layers with various volume fractions of graphene reinforcement to construct a functionally graded (FG) pattern along the transverse direction of the beam. An extended Halpin–Tsai model which is calibrated against the results from molecular dynamics (MD) simulations is used to evaluate the material properties of GRC layers. The mechanical model of the beam is on the establishment of a third-order shear deformation beam theory and includes the von-Kármán nonlinearity effect. The model also considers the foundation support and the temperature variation. The two-step perturbation technique is first applied to solve the beam motion equations and to derive the nonlinear dynamic load–deflection equation of the beam. Then a Runge–Kutta numerical method is applied and the solutions for this nonlinear equation are obtained. The influence of FG patterns, visco-elastic foundation, ambient temperature and applied load on transient response behaviors of simply supported FG-GRC laminated beams is revealed and examined in detail.

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46

Ghorbanpour Arani, A., H. BabaAkbar Zarei, M. Eskandari, and P. Pourmousa. "Vibration behavior of visco-elastically coupled sandwich beams with magnetorheological core and three-phase carbon nanotubes/fiber/polymer composite facesheets subjected to external magnetic field." Journal of Sandwich Structures & Materials 21, no. 7 (November 19, 2017): 2194–218. http://dx.doi.org/10.1177/1099636217743177.

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In the present research, modeling and vibration analysis of the double of sandwich beams which are coupled by visco-Pasternak medium are investigated. Also, this system is rested on Winkler foundation. Sandwich beams consist of magnetorheological core and carbon nanotubes/fiber/polymer composite facesheets. The material properties of magnetorheological core are obtained using the experimental data available in literature. Halpin–Tsai model is utilized to determine the material properties of carbon nanotubes/fiber/polymer composite facesheets. Hamilton principle is used to obtain the equations of motion of this system. Based on Navier’s method, a closed-form solution is presented for free vibration analysis of coupled magnetorheological sandwich beams under simply supported boundary conditions. The effects of various parameters such as core-to-facesheets thickness ratio, length-to-thickness ratio, magnetic field intensity, volume fractions of carbon nanotubes, and fibers and visco-Pasternak coefficients on the natural frequencies and loss factors of coupled system are discussed. The results show that the modal loss factor, unlike natural frequency, decreases by increasing magnetic field intensity. These findings can be used in design and manufacturing of sandwich structures.

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Battegazzore, Daniele, Amir Noori, and Alberto Frache. "Natural wastes as particle filler for poly(lactic acid)-based composites." Journal of Composite Materials 53, no. 6 (August 1, 2018): 783–97. http://dx.doi.org/10.1177/0021998318791316.

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The paper describes the production and the mechanical characteristics of composites made completely of renewable raw materials. Several wastes or by-products from agro-industrial production namely hemp hurd, alfalfa, and grape stem were analyzed with respect to their thermal stability, morphological, and chemical composition in an attempt to validate their use in composites. Such natural particle fillers were used in the range of 10–50 wt% in combination with poly(lactic acid) by melt blending to obtain fully bio-based composites. These fillers were responsible for a noteworthy increase in the storage modulus. Furthermore, two micromechanical models (Voigt and Halpin–Tsai) were used to mathematically fitted the experimental data, and then the unknown moduli were extrapolated and compared with other natural fillers. Finally, the flexural strength of the bio-composites and the adhesion evaluation by exploiting Pukanszky’s model were carried out. As a result, the hemp hurd in the form of chips was the best investigated filler, which showed the highest calculated modulus of 10.5 GPa (Voigt) and the best filler–matrix interaction with “B” (Pukanszky’s coefficient) of 2.10. This information can be useful when comparison and selection of a suitable filler among the natural fillers are required.

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Yang, Zhicheng, Jiamian Xu, Hanwen Lu, Jiangen Lv, Airong Liu, and Jiyang Fu. "Multiple Equilibria and Buckling of Functionally Graded Graphene Nanoplatelet-Reinforced Composite Arches with Pinned-Fixed End." Crystals 10, no. 11 (November 5, 2020): 1003. http://dx.doi.org/10.3390/cryst10111003.

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This paper presents an analytical study on the multiple equilibria and buckling of pinned-fixed functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) arches under central point load. It is assumed that graphene nanoplatelets (GPLs) in each GPLRC layer are uniformly distributed and randomly oriented with its concentration varying layer-wise along the thickness direction. The Halpin–Tsai micromechanics-based model is used to estimate the effective elastic modulus of GPLRC. The non-linear equilibrium path and buckling load of the pinned-fixed FG-GPLRC arch are subsequently derived by employing the principle of virtual work. The effects of GPLs distribution, weight fraction, size and geometry on the buckling load are examined comprehensively. It is found that the buckling performances of FG-GPLRC arches can be significantly improved by using GPLs as reinforcing nanofillers. It is also found that the non-linear equilibrium path of the pinned-fixed FG-GPLRC arch have multiple limit points and non-linear equilibrium branches when the arch is with a special geometric parameter.

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Tam, Meifung, Zhicheng Yang, Shaoyu Zhao, and Jie Yang. "Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks." Materials 12, no. 9 (April 30, 2019): 1412. http://dx.doi.org/10.3390/ma12091412.

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This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young’s modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson’s ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.

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Shen, Hui-Shen, Y. Xiang, and Yin Fan. "Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations." Journal of Vibration and Control 25, no. 9 (January 29, 2019): 1507–20. http://dx.doi.org/10.1177/1077546319825671.

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This paper investigates the small- and large-amplitude vibrations of thermally postbuckled graphene-reinforced composite (GRC) laminated plates resting on elastic foundations. The piecewise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the plate. The anisotropic and temperature-dependent material properties of the FG-GRC layers are estimated through the extended Halpin–Tsai micromechanical model. Based on the Reddy's higher order shear deformation plate theory and the von Kármán strain–displacement relationships, the motion equations of the plates are derived. The foundation support, the thermal effect, and the initial deflection caused by thermal postbuckling are also included in the derivation. A two-step perturbation approach is applied to determine the thermal postbuckling equilibrium paths as well as the nonlinear vibration solutions for the FG-GRC laminated plates. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled FG-GRC laminated plates under a uniform temperature field. The effects of graphene reinforcement distributions and foundation stiffnesses on the vibration responses of FG-GRC laminated plates are examined in detail.

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Journal articles on the topic 'Halpin-tsai model'

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