DMA test results of particulate nanocomposites

DMA tests on particulate nanocomposites with varying frequencies are presented in Fig 4.11. Each curve plotted in Fig 4.5 was obtained from a curve fitting procedure in terms of 10 data points (0.1, 1, 10, 50, 75, 100, 125, 150, 175, and 200 Hz). The purpose of DMA test is to validate damping properties of the nanocomposites measured in the vibration tests.

In order to compare the loss factors obtained from the DMA tests with those in the vibration tests, the data points corresponding to the frequency of 25 Hz were selected from Fig 4.11 to represent the loss factor of the samples determined in DMA tests and the results are illustrated in Table 4.7. It is found that the loss factors determined from the vibration tests have a good agreement with those in DMA tests. Subsequently, the loss factor measured from the DMA tests at 150 Hz was presented in Table 4.8 and the associated results were plotted in Fig 4.6.

Comparison of Figs 4.2 with 4.6 indicates that the loss factors obtained from DMA tests and vibration tests are close to each other. As a result, after the confirmation of DMA tests, the

current vibration technique can be used effective to determine the damping properties of nanocomposites.

4.1.3 Vibration test results of sandwich nanocomposite structure

In addition to the damping properties of nanocomposites, the damping responses of sandwich structures embedded with the nanocomposites as core material were also investigated by means of the vibration tests. The natural frequency and loss factor of the sandwich structure embedded with different nanocomposites are illustrated in Table 4.9. The averaged values and the associated increment with respective to the base materials were also presented in Tables 4.10 and plotted in Fig 4.7. It demonstrates that the damping property of sandwich structure with particulate nanocomposite core is better than that with the pure epoxy core at frequencies of 150-160 Hz. It is found that the loss factor of sandwich structure with 30 wt% CTBN nanocomposite embedded still has the best damping properties.

Furthermore, sandwich structure embedded with silica-CTBN hybrid inclusions nanocomposite also show good damping property with 18.12% increment. Therefore, based on the above observation, it was found that the damping property of stiffer structure can be promoted with the particulate nanocomposite as core material interleaved.

Subsequently, in order to understand the flexural stiffness of sandwich structure embedded with a nanocomposite core material, the effective flexural modulus determined from the first mode experimental data are illustrated in Table 4.11. It can be seen that the variations of effective flexural modulus of different sandwich structures are not significant.

Even though the sandwich structure is interleaved with 30 wt% CTBN/epoxy nanocomposite, the variation of the effective flexural modulus is just less than 5% compared to that with the pure epoxy. However, this is not a surprising result, since the stiffness of the sandwich structure is governed by the graphite/epoxy face sheet. Therefore, the variation of the stiffness in the nanocomposite core basically has no apparent influence on the entire effective

flexural modulus. As a result, the sandwich structure with 30 wt% CTBN/epoxy nanocomposite interleaved can indicate excellent damping properties than other cases.

4.2 Micromechanical model

In order to understand the effect of the ingredients on the dynamic properties of nanocomposites, a micromechanical model [26] in conjunction with the viscoelastic correspondence principle [37] was employed in the following analysis. This research basically follows the procedure given in [26, 36]. It is noted, the inclusion in the analysis is the spherical shape rather than the oblate-spheroids present in the literature [26].

The volume fraction of the matrix and spherical inclusion are and , and thus the σm is the average stress of matrix, σ ^p is the average stress of spherical inclusion, and , in which and are the composite storage and loss constitutive matrix.

It was assumed that silica was randomly and uniformly distributed and perfectly bonded to the surrounding matrix. With these assumptions, the composite complex modulus is given as [26]

1

where and are the complex constitutive matrix of spherical inclusions and epoxy matrix, respectively, I is the identity tensor, and is the complex dilute strain concentration tensor of the inclusions. Thus, the complex in Eq. (4.4) can be divided into two parts, i.e., real part and imaginary part. The real part is so called the storage modulus and the imaginary part indicates loss modulus. In addition, the complex dilute strain-concentration tensor in Eq. (4.4) is expressed as [26]

*

where is the complex Poisson’s ratio of the matrix. The loss factor (tanδ) could be defined as the ratio of the loss modulus to the storage modulus. In addition, the source code of the micromechanical model is shown in Appendix B.

*

vm

The corresponding ingredient properties used in the simulation were shown in Table 4.12.

The storage and loss moduli of epoxy were calculated based on the natural frequency and loss factor listed in Table 4.4 and the complex Poisson’s ratio was found in the reference [26], while the material properties of silica nanoparticles were obtained from reference [28]. It is noted that the silica nanoparticles was assumed to be inclusion without any damping characteristic. Nanocomposites with 10 wt% and 20 wt% silica nanoparticles loading were selected to as examples in the micromechanical model. Table 4.13 shows the calculated results of storage modulus and loss factor of 10 wt% and 20 wt% silica nanocomposites.

The results indicate that the storage modulus increased with increasing filler loadings of silica.

However, the loss factor is slightly decreased with the introduction of silica nanoparticles, which is not consistent with the experiment results. The possible reason for the discrepancy could be due to the micro-morphology change of the polymer chain caused by the presence of the silica nanoparticles. In addition, the local stress concentration may induce the interfacial debonding taking place and the contact friction during the vibration may be the other mechanism to dissipate the energy. Apparently, the conventional simply micromechanical model may not be able to include all the mechanism and lose the capability in describing the damping behavior of nanocomposites. An analytical model that can account for the polymer morphology effect as well as the condition of the interface is necessary in order to comprehensively predict the damping responses of the nanocomposites. The continuum mechanics concept in conjunction with the molecular simulation, so called multi-scale simulation, may be an effective manner to achieve the above goal.

4.3 Finite element analysis

In light of the forgoing, the nanocomposite beam and sandwich structure was tested in forced vibration for the measurement of the corresponding damping properties. In fact, during the vibration test, the nanocomposites beams basically is subjected to tension and compression loading (extension mode), however, the nanocomposite core within a sandwich

structure may be under combined extension and shear modes depending on the relative thickness of the core material. The energy dissipation capacity for these two modes may not be the same. In order to understand the influence of the vibration modes (i.e., extension mode and shear mode) on the damping properties of nanocomposites, the tested samples were modeled using FEM analysis. The dissipated energy due to shear deformation as well as the dissipated energy in extension mode

Ezx

Δ Exx

Δ was evaluated from FEM analysis and then, the ratio of the two modes was calculated accordingly. Moreover, the finite element method (FEM) static analysis was also employed to simulate the vibration of the nanocomposite in the DMA test. Here, the first bending mode is taken as an example to demonstrate the procedure, how to determine those ratio from FEM analysis. The nodal displacements of the nanocomposite associated with the vibrating in the first mode were evaluated after the modal analysis was conducted. In this research, the FEM analysis was conducted using a commercial code, ANSYS 10.0 with SOLID45 element.

4.3.1 FEM modal analysis of the nanocomposite

Fig 4.9 illustrated the mesh plot of nanocomposite plate with the clamped-free boundary condition, and the associated mode shapes were presented in Fig 4.10. In this study, the pure epoxy was selected as an analysis example; the corresponding material properties are listed respectively in Table 4.14, which were found in reference [28, 39]. The dimensions of the epoxy plate are 180 mm in free length, 15 mm in width, and 3 mm in thickness which are the same as those used in the vibration test. After conducting the modal analysis, the nodal displacements of the nanocomposite associated with the first vibration mode were evaluated.

Those nodal displacements of the nanocomposite were then regarded as a boundary condition of the nanocomposite in a FEM static analysis. Thus, the corresponding strain energy (due to shear deformation), and (due to extension deformation) of the nanocomposite was calculated as

Ezx

Exx

∑

shear strain in the k^th element, and and indicates the normal stress and normal strain in the k^th element. Moreover, the corresponding dissipated energy and

)

of the nanocomposite were computed as the following

zx

where ψ is the specific damping capacity of the nanocomposite in extension, and ψ_shear is the specific damping capacity of the nanocomposite in shear deformation. All the values can be found in [39].

For the first two bending modes, the ratio of strain energy ratio, i.e. and dissipated energy ratio were listed in Table 4.15. It can be seen that dissipated energy ratio are much less than 1, and thus the energy dissipation mechanism of the epoxy plate in the vibration motion is dominated by the extension mode.

xx

4.3.2 Simulation of the nanocomposite in the DMA test by FEM analysis

In the same manner, the dissipated energy ratio ΔE_zx/ΔE_xx in the DMA test was evaluated from FEM analysis. The maximum deformation of the nanocomposite with

fixed-fixed boundary condition under a sinusoidal oscillation in the middle section was considered in the FEM model. A mesh diagram of the nanocomposite rod with applied displacement boundary condition 0.05 mm is illustrated in Fig 4.11. The material properties for the DMA simulation were also found in Table 4.14, and the dimensions of the epoxy rod are 40 mm in length, 5 mm in width, and 3 mm in thickness which is the same as the test specimen employed in the DMA test.

Fig 4.12 presented deformation shape of the epoxy rod under both end fixed boundary condition through the FEM static analysis. The ratio of the energy dissipation is shown in Table 4.16. It can be seen that, the energy dissipation mechanism of the epoxy rod in the DMA simulation is still dominated by the extension mode.

4.3.3 FEM modal analysis of the sandwich structure

A schematic of the sandwich structure with the cantilever-type boundary condition was shown in Fig 4.13. The stacking sequence of the sandwich structure is [03/d/03], where d is the epoxy core, and the material properties of the sandwich structure were shown respectively in Tables 4.14 and 4.17, which were found in the reference [28, 39-40]. The dimensions of the sandwich laminates are 145 mm in length, 10 mm in width. The thickness of the unidirectional composite face sheet is 0.36 mm. It is known that the energy dissipated mechanisms of the core material were affected by the core thickness; therefore, the influence of the core thickness on the dominant damping mode of the core materials was examined by adjusting core thicknesses, i.e. 0.09, 0.18, 0.36, 0.72, 1.44, and 1.55 mm. For the sake of simplicity, the thickness of the core is defined as Dc and the thickness of the face sheet is denoted as Df. Thus, the ratio of the core thickness to face sheet thickness is expressed as

f cD D .

In Table 4.18, the natural frequencies of the sandwich structure and the ratio of dissipated

energy of nanocomposite core, i.e. ΔE_zx/ΔE_xx , with different thickness ratio are demonstrated. It is apparent that as the core thickness decrease, the energy dissipation is mainly controlled by the shear mode. Once the thickness of core material increases, the energy dissipation mechanism of the core materials would become mixed mode (including extension and shear mode). It should be noted that the

f cD

D value for our current sandwich samples is equal to 4.30. Thus, it can be seen that the energy dissipation mechanism of the epoxy core is mixed mode. Although the energy dissipation mode is mixed mode, it can be seen from Fig 4.7 that the nanocomposites with 30wt% CTBN nanoparticles still exhibit better damping capacity in the sandwich structures.

Chapter 5 Conclusion

The damping responses of the nanocomposites with different nano-inclusions were conducted by using the forced vibration technique. The damping performances of the sandwich structure embedded with particulate nanocomposites as core materials were also characterized in the study. The conventional micromechanical model was employed to predict the damping responses of the nanocomposites. The dominant energy dissipation mechanism during the vibration tests were characterized through FEM analysis. Based on the forgoing investigation, several conclusions were addressed.

1. Apparently, the rubber particles can dramatically improve the damping responses of the nanocomposites as well as the corresponding sandwich structures. However, the flexural stiffness of the nanocomposites can be deduced by the inclusion of the rubber particles. It is interesting to mention that the damping properties can be improved by the silica nanoparticles, which is not quite coincided with the prediction from the micromechanical model. The mechanism resulting in the enhancement of the damping property of silica nanoparticles need to be further studied. In addition, it was found that the hybrid inclusion system (10wt%

silica nanoparticles and 10wt% CTBN rubber particles) can demonstrate good damping properties without scarifying its flexural stiffness. The hybrid concept can be employed in the future design of composite materials.

2. Based on the FEM analysis, the dominant energy dissipation mechanism for cantilever-type nanocomposites samples is extension mode. However, once the nanocomposites were embedded as core materials in the sandwich structures, the dominant energy dissipation mode is becoming mixed mode (including the extension and shear modes).

When the thickness ratio of the core to the face sheet is decreasing, the energy dissipation is mostly controlled by the shear mode. In our current design of sandwich structure, both extension and shear modes occur. Although the dominant modes in cantilever-type sample and sandwich structures is different, experimental results demonstrate that the hybrid

nanocomposites still exhibit superior damping responses than other cases.

Reference:

[1] Chen C, Justice RS, Schaefer DW, Baur JW. Highly dispersed nanosilica-epoxy resins with enhanced mechanical properties. Polymer 2008;49:3805-3815.

[2] Zhang H, Zhang Z, Friedrich K, Eger C. Property improvements of in situ epoxy nanocomposites with reduced interparticle distance at high nanosilica content.

Acta Materialia 2006;54:1833-1842.

[3] Sengupta R, Bandyopadhyay A, Sabharwal S, Chaki TK, Bhowmick AK.

Polyamide-6,6/in situ silica hybrid nanocomposites by sol-gel technique:

synthesis, characterization and properties. Polymer 2005;46:3343-3354.

[4] Lu SR, Wei C, Yu JH, Yang XW, Jiang YM. Preparation and characterization of epoxy nanocomposites by using PEO-grafted silica particles as modifier. Journal of Material Science 2007;42:6708-6715.

[5] Goertzen WK, Kessler MR. Dynamic mechanical analysis of fumed silica/cyanate ester nanocomposites. Composite: Part A 2008;39:761-768.

[6] Peng Z, Kong LX, Li SD. Dynamic mechanical analysis of polyvinyl alcohol/silica nanocomposite. Synthetic Metals 2005;152:25-28.

[7] Zheng Y, Chonung K, Wang G, Wei P, Jiang P. Epoxy/Nano-Silica Composites:

Curing Kinetics, Glass Transition Temperature, Dielectric, and Thermal-Mechanical Performances. Journal of Applied Polymer Science 2009;111:917-927.

[8] Lu S, Zhang H, Zhao C, Wang X. New Epoxy/Silica-Titania Hybrid Materials Prepared by the Sol-Gel Process. Journal of Materials Science 2006;101:1075-1081.

[9] Omrani A, Simon LC, Rostami AA. The effects of alumina nanoparticle on the properties of an epoxy resin system. Materialrs Chemistry and Physica 2009;114:145-150.

[10] Vassileva E, Friedrich K. Epoxy/alumina nanoparticle composites. I. Dynamic mechanical behavior. Journal of Applied Polymer Science 2003;89:3774-3785.

[11] Zhao XY, Xiang P, Tian M, Fong H, Jin R, Zhang LQ. Nitrile butadiene rubber/hindered phenol nanocomposites with improved strength and high damping performance. Polymer 2007;48:6056-6063.

[12] Kishi H, Nagao A, Kobayashi Y, Matsuda S, Asami T, Murakami A.

Carboxyl-terminated butadiene acrylonitrile rubber epoxy polymer alloys as damping adhesives and energy absorbable resins. Journal of Applied Polymer Science 2007;105:1817-1824.

[13] Nigam V, Setua DK, Mathur GN. Characterization of Rubber Epoxy Blends by Thermal Analysis. Journal of Thermal Analysis and Calorimetry 2001;64:521-527.

[14] Cheng WC. Morphologies and properties of the IPN-structured epoxy resin and vulcanized CTBN nanocomposites through sequential and simultaneous processes.

Master thesis, Department of Polymer Engineering, National Taiwan University of Science and Technology, 2008.

[15] Fang Z, Shi H, Gu A, Fang Y. Effect of bentonite on the structure and mechanical properties of CE/CTBN system. Journal of Materials Science 2007;42:4603-4608.

[16] Cheng YX. Nanoclay Reinforced Liquid Rubber/Epoxy. Master thesis, Graduate Institute of Textile Engineering, Feng Chia University, 2004.

[17] Aktas L, Dharmavaram S, Hamidi YK, Altan MC. Filtration and Breakdown of Clay Clusters during Resin Transfer Molding of Nanoclay/Glass/Epoxy Composites. Journal of Composite Materials 2008;42:2209-2229.

[18] Huang PH, Effect of Nanoparticles on Mechanical Performance of Composites.

Master thesis, Department of Mechanical Engineering, National Chiao Tung University, 2008.

[19] Cheng YL. Investigating SiO2 nanoparticle effect on the mechanical behaviors of glass/epoxy composites. Master thesis, Department of Mechanical Engineering, National Chiao Tung University, 2008.

[20] Biggerstaff JM, Kosmatka JB. Damping Performance of Cocured Graphite and Epoxy Composite Laminates with Embedded Damping Materials. Journal of Composite Materials 1999;33:1457-1469.

[21] Pan L, Zhang B. A new method for the determination of damping in cocured composite laminates with embedded viscoelastic layer. Journal of Sound and Vibration 2009;319:822-831.

[22] Russo A, Zuccarello B. Experimental and numerical evaluation of the mechanical behaviour of GFRP sandwich panels. Composite Structure 2007;81:575-586.

[23] Kishi H, Kuwata M, Matsuda S, Asami T, Murakami A. Damping properities of

thermoplastic-elastomer interleaved carbon fiber-reinforced epoxy composites.

Composites Science and technology 2004;64:2517-2523.

[24] Fujimoto J, Tamura T. Development of CFRP and damping-material laminates.

Advanced Composite Materials 1998;7:365-376.

[25] Yeh MK, Hsieh TH. Dynamic properties of sandwich beams with MWNT/polymer nanocomposites as core materials. Composites Science and Technology 2008;68:2930-2936.

[26] Odegard GM, Gates TS. Modeling and Testing of the Viscoelastic Properties of a Graphite Nanoplatelet/Epoxy Composite. Journal of Intelligent Materials Systems and Structures (JIMSS) 2006;17(3):239-246.

[27]

http://www.emeraldmaterials.com/epm/specpoly/micms_doc_admin.display?p_cu stomer=FISSPECPOLY&p_name=HYPRO+1300X8+AND+1300X8F.PDF

Department of Mechanical Engineering, National Chiao Tung University, 2007.

artment of Mechanical Engineering, National Chiao Tung University, 2008.

[30] http://www.ometron.com/

[28] Shiao H. Effect of Silica Nano Particle on Mechanical Behaviors of Nanocomposites. Master thesis,

[29] Huang PH, Effect of Nanoparticles on Mechanical Performance of Composites.

Master thesis, Dep

[31] l Review 1984-1 Dual Channel FFT Analysis (Part I). Brüel & Kjær, 1984.

[32] Rao SS, Mechanical Vibration, Fourth edition. Prentice-Hall, New Jersey, 2004.

[33] ples of Composite Material Mechanical. McGraw-Hill, Inc., New York 1994.

[34] McConnell KG, Vibration Testing-Theory and Practice. Wiley, New York, 1995.

[35] alysis: A Practical Introduction, Fourth

edition. CRC Press, New York, 1999.

[36] of Materials with

Misfitting Inclusion, Acta Metallurgica 1973: 21(5):571-574.

Technica

Gibson RF, Princi

Menard KP, Dynamic Mechanical An

Mori T, Tanaka K. Average Stress in Matrix and Average Energy

[37] Brinson LC, Lin WS. Comparison of micromechanics methods for effective properties of multiphase viscoelastic composites. Composite Structure 1998;

41:353-367.

[38] Mura T. Micromechanics of defects in solids, Second, revised edition. Kluwer Academic Publishers, Boston, 1987.

[39] Yim JH, Cho SY, Seo YJ, Jang BZ. A study on material damping of 0° laminated composite sandwich cantilever beams with a viscoelastic layer. Composite Structure 2003; 60:367-374.

[40] Chen CW. Predicting Tensile Strength of Fiber Composite With/Without Crack.

Master thesis, Department of Mechanical Engineering, National Chiao Tung University, 2007.

Appendix A: Stoichiometric Calculation

Silica/epoxy nanocomposite: Stoichiometric calculation & manufacturing processes

DGEBA，EEW = 187(g/equiv)… x F400 + DGEBA

F400，EEW = 295 (g/equiv) (40%SiO2)… y H-100，AHEW = 45 (g/equiv)… u

F400，EEW = 295 (g/equiv) (40%SiO2)… y H-100，AHEW = 45 (g/equiv)… u