SSNEMS Internal Report

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1 E.3. Nanotube Reinforced Piezoelectric Polymeric Composites Subjected to Electro-Thermo- Mechanical Loadings Understanding the stress transfer between nanotube reinforcements and surrounding matrix is an important factor in determining the overall mechanical properties of nanotube-reinforced composites. An efficient load transfer from the polymer matrix to the nanotube through interface is required to take the advantage of very high Young s modulus and strength of carbon nanotubes (CNTs) in the composites. On the other hand, considerable energy dissipation can be obtained by interfacial slippage in the interface of nanotube and matrix which is beneficial in term of structural damping. In order to obtain a composite structure with tunable properties ranging from stiffer structure to better damper, we propose a semi-active control approach in which applied electrical loading to piezoelectric polymeric matrix such as Polyvinylidene Fluoride (PVDF) and reinforced with nanomaterials results in radial displacement of piezoelectric polymer corresponding to the direction and magnitude of electrical load. This leads to control of restriction effect of nanotube on the polymer segments, and consequently results in tunable interfacial adhesion between piezoelectric polymer and nanomaterials with faster response time. For this porous, a shear lag model is obtained for a nanotube reinforced piezoelectric polymer under electrothermo-mechanical loadings. As the adhesion in CNT composite is universally present in the form of van der Waals (vdw) interaction, the shear stress and the axial displacement of nanotube and matrix differ in the interface zone and are not the same. This makes modeling of interface region more challenging and involved. To remedy this complexity, we propose to obtain the relative axial displacement between nanotube and polymer in the interface according to the Lennard-Jones potential. Results indicate that as the electrical load increases, the relative displacement between nanotube and polymer increases which mean the possibility for slippage increases. Furthermore, results indicate that stiffer structures have more potential to show more switched stiffness capability for semi-active vibration control implementation. Figure 2 (a-c) shows the distribution of average axial normal stress in the nanotube along the nanotube length for three different applied electrical loads and different values of A (A is a constant smaller than one which depends on the strength of interaction). It can be seen that the increase of applied electrical load leads to the decrease of the average axial normal stress in the nanotube. This indicates that lower loads can be transferred from matrix to the nanotube as the interfacial distance between nanotube and PVDF increases. In this situation, nanotube has small contribution on the overall properties of the composite. Also, results indicate that the maximum axial normal stress is achieved in the middle of nanotube, whereas the minimum values are at its two ends. As the applied electrical load increases, the distribution of axial stress along the nanotube length becomes more uniform. Moreover, Figure 2(a-c) shows that the intensity of interaction between nanotube and matrix directly affects the role of nanotube in the composite structure. Results indicate that for the similar mechanical and electrical loading, higher mechanical load can be carried by nanotube at higher interaction between naotube and matrix. The opposite trends are seen for the average axial normal stress of matrix (Figure 2(a-c)). As the applied electrical load increases, the axial stress of matrix increases. Comparing the results for different values of A demonstrates that fabrication methods of composites and chemical interaction in the interphase zone play an important role regarding to the properties of structure. The better interaction results in stiffer composite structure. Moreover, these figures demonstrate that the stiffer structures have more potential to show switched stiffness capability for future semi-active vibration control implementation. The variations of shear stress in the outer layer of nanotube are shown in Figure 22(a-c). The shear stress shows the maximum values are at nanotube ends, while the middle of nanotube is shear stress free. With the increase of applied electrical load, the shear stress along the length of nanotube decreases, while the shear stress in the inner layer of matrix shows the opposite trends. On the other hand, if the applied electrical load increases the shear stress increases in the inner layer of matrix as depicted in Figure 23(ac). The reason is that with the increase of electrical loads, the role of nanotube as reinforcement decreases, and the matrix has to carry more shear force. Moreover, results show that differences between the shear stress of nanotube and matrix increases as the applied electrical load increases.

2 E.4. Boron Nitride Nanotube Reinforced Piezoelectric Polymeric Composites Subjected to Electro- Thermo-Mechanical Loadings Unlike widely-used carbon nanotubes, boron nitride nanotubes (BNNTs) have shown to possess stable semiconducting behavior and strong piezoelectricity. Such properties along with their outstanding mechanical properties and thermal conductivity, make BNNTs promising candidate reinforcement materials for a verity of applications especially nanoelectronic and nanophotonic devices. Motivated by these abilities, we aimed to study the buckling behavior of BNNT-reinforced piezoelectric polymeric composites when subjected to combined electro-thermo-mechanical loadings. For this, the multi-walled structure of BNNT is considered as elastic media and a set of concentric cylindrical shell with van der Waals interaction between them. Using three-dimensional equilibrium equations, Donnell shell theory is utilized to show that the axially compressive resistance of BNNT varies with applying thermal and electrical loads. Also, a new equivalent spring constant model of piezoelectric matrix under electrothermo-mechanical loadings is developed according to the concept of Whitney-Riley model. Results indicate that the support of piezoelectric matrix significantly enhances the buckling resistance of BNNT. Alternatively, the effect of BNNT piezoelectric property on the buckling behavior of the composites is demonstrated. Furthermore, it is demonstrated that the supporting effect of elastic medium depends on the direction of applied voltage and thermal flow. More specifically, it is shown that applying direct and reverse voltages to BNNT changes the buckling loads for any axial and circumferential wavenumbers. Such capability could be uniquely utilized when designing BNNT-reinforced composites. Figure 24a shows the result of buckling load as a function of wavenumbers (m,n) under mechanical loading. It can be seen that the critical buckling loads are not unique and depend on wavenumbers. From Figure 24b it can be seen that applying reverse voltage to BNNT increases the critical buckling load for any given wavenumbers. The reason is that applying reverse voltage results in polarization of BNNT in the longitudinal direction, and leads to its contraction. This makes the structure of BNNT more compact and strong in loading direction. Furthermore, this leads to smaller length of BNNT as a shell, and consequently more resistance to compressive load. Similar results were obtained as the temperature of BNNT reduces (Figure 24c). However, the response of BNNT to electric field is much faster than thermal field, and hence using electrical field is more efficient and more effective than using thermal load. Moreover, for some applications where there is a restriction in terms of temperature, applying electrical field to piezoelectric materials such as BNNT would be more beneficial. Figures 24(d-e) depicts the results of critical buckling load using direct voltage and increasing the temperature of structure. As expected, the critical buckling load decreases compared to normal situation, and results can be explained using the similar concept as mentioned in the pervious condition. The difference between buckling load of normal situation and buckling load under electric field presents the equivalent force due to piezoelectric property of BNNT. From Figures 24(a,b and d), it can be seen that the absolute values of this force is very small. This means that BNNT is sensitive even to very small external or internal force. This property of BNNTs makes them a promising candidate for use as actuators and sensors. Finally, Figure 24(f-g) indicates the buckling load of BNNT under thermo-electromechanical loadings. Results show that the compressive resistance of BNNTs can be changed in the range of.48 to.7 N/m, with tuning percentage of 2%. Figure 2(a-d) shows the buckling load as a function of wavenumbers for PVDF+BNNTs structure.. 2

3 a _ f z b _ f z c _ f z Figure 2. Average axial normal stress in the nanotube along the nanotube length for different applied electrical loads and for (a) A=, (b) A=.7, and (c) A=.4. 3

4 m z a m z b m z c Figure 2. Average axial normal stress in the matrix for different applied electrical loads and for (a) A=, (b) A=.7, and (c) A=.4. 4

5 τ f rz a τ f rz b τ f rz c Figure 22. Variations of shear stress in the outer layer of nanotube for different applied electrical loads and for (a) A=, (b) A=.7, and (c) A=.4.

6 τ m rz a τ m rz b τ m rz c Figure 23. Variations of shear stress in the inner layer of matrix for different applied electrical loads and for (a) A=, (b) A=.7, and (c) A=.4. 6

7 n= n=..47 (a) n= n= n= n= (b).47.7 (c) n= n= The load buckling (N/m) n= n=...47 (d).47 (e) 7

8 n= n= n= n=...47 (f).47 Figure 24. The buckling load vs. axial half wavenumber m for; (a) axial compressive, (b) axial load and negative electrical load, (c) axial and negative thermal load, (d) axial and positive electrical load, (e) axial load and thermal (g) (a) (b) (c) Figure 2. The buckling load vs. axial half wavenumber m at different ratios of G total /c for; (a), (b) 4, (c) n=3, and (d) 8. (d) 8

9 This subtask has resulted in the following publications during this report period.. Salehi-Khojin, A. and Jalili, N., A Comprehensive Model for Load Transfer in Nanotube Reinforced Piezoelectric Polymeric Composites subjected to Electro-Thermo-Mechanical Loadings, isubmitted to Journal of Composites Part B: Engineering (March 27). 2. Salehi-Khojin, A. and Jalili, N., Buckling of Boron Nitride Nanotube Reinforced Piezoelectric Polymeric Composites subject to Combined Electro-Thermo-Mechanical Loadings, in print, Composites Science and Technology (27). 3. Salehi-Khojin, A. and Jalili, N., A New Modeling Framework for Piezoresponse Force Microscopy, Proceedings of 27 ASME International Mechanical Engineering Congress & Exposition, Seattle, WA (November 27). 4. Salehi-Khojin, A. and Jalili, N., An Analytical Modeling Framework for Boron Nitride Nanotube based Microcantilever Actuators with Thermal Effects Consideration, Proceedings of 27 ASME International Mechanical Engineering Congress & Exposition, Seattle, WA (November 27).. Salehi-Khojin, A. and Jalili, N., A Shear-Lag Model for Nanotube Reinforced Piezoelectric Polymeric Composites subjected to Electro-Thermo-Mechanical Loadings, Proceedings of ASME 27 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Las Vegas, NV (September 4-7, 27). 6. Salehi-Khojin, A. and Jalili, N., Axially Compressed Buckling of an Embedded Boron Nitride Nanotube subjected to Thermo-electro-mechanical Loadings, Proceedings of SPIE 4 th Annual Symposium on Smart Structures and Materials, Behavior and Mechanics of Multifunctional and Composite Materials, San Diego, CA (March 27). 7. Salehi-Kojin, A. and Jalili, N., A Shear lag Model for Nano-Reinforced Composite Systems under Transient Heat Transfer, Proceedings of 26 ASME International Conference on Multifunctional Nano-composites, Hawai (September 26). 9