Low-velocity impact response of nanotube-reinforced composite cylindrical shells

23 May 2016
Mohammad R. Bayat, M. Mosavi Mashhadi, and Omid Rahmani
A two-step perturbation method is used to study the nonlinear behavior of functionally graded carbon-nanotube-reinforced composite cylindrical shells with different filler distributions.

Compared with traditional carbon fibers, carbon nanotubes (CNTs) have remarkable mechanical properties.1 For this reason, there has been a considerable amount of attention paid to the use of CNTs as reinforcements for polymer composites, and to thus obtain lightweight structural materials with improved thermomechanical characteristics.2, 3 Damage to such materials from impacts, however, can be a critical issue. This is especially the case for the fabrication of aircraft structural components. Studying the response of thin laminates that are subjected to low-velocity impacts is therefore a significant area of ongoing research.4

In a previous study, the nonlinear low-velocity impact response of CNT-reinforced composite (CNTRC) single-layer and sandwich plates in a thermal environment have been analyzed.5 Such CNTRC structures are often used in aerospace and automobile applications because of their favorable properties. In the previous study, the effects of various parameters on the impact response of the plate structures were explored. These parameters included the material property gradient, volume fraction distribution, temperature change, initial stress, initial velocity of the impactor, and core-to-face sheet-thickness ratio. To the best of our knowledge, however, there has not yet been an investigation into the low-velocity impact response of functionally graded (FG) CNTRC cylindrical shells.

In this work,6 we have thus considered two different types of CNT distribution (i.e., uniformly distributed and FG-distributed reinforcements) in CNTRC cylindrical shells. The geometry and coordinate system of the cylindrical shells is illustrated in Figure 1(a). The CNT distributions for our different configurations of FG (in the thickness dimension) cylindrical shells are presented in Figure 1(b). In the uniformly distributed (UD) sample, the CNT volume fraction (V*CN) is constant across the shell's thickness. In contrast, for the two FG-distributed samples (‘type Λ’ and ‘type X’), V*CN varies across the thickness of the shell. To estimate the material properties of our samples, we used micromechanical models. The equations of motion that we employed were based on higher-order shear deformation theory, and we used a two-step perturbation technique to solve these equations. Furthermore, we assumed that the material properties of the CNTRC shells were temperature-dependent.

(a) The geometry and coordinate system of a carbon-nanotube-reinforced composite (CNTRC) cylindrical shell that is being subjected to a low-velocity impact. V0: Initial impactor velocity. L, R, and h represent the shell length, radius, and thickness, respectively. X, Y, and Z: Coordinate axes. (b) The variation in CNT volume distribution (V*CN) across the shell thickness (t) for the uniformly distributed (UD) and functionally graded (FG) CNTRC shells. Two different distributions—type Λand type X—of FG shells were obtained.

To verify the accuracy of our micromechanical model calculations, we conducted a series of measurements on our CNTRC samples as part of a low-velocity impact study. For this study—as in previous experiments by other groups7–10—we used a simply supported isotropic square plate. We resolved this plate by letting the radius of the cylinder reach infinity. The histories of impact displacement and contact force that we measured in our experiments are presented in Figure 2. We find a good agreement between our results and those of previous studies that are available in the literature, which shows that our model is accurate. The small differences between our results and the previous data may arise because of the different methodologies, i.e., we use higher-order shear deformation theory and a nonlinear contact law, whereas classical plate theory and a linearized contact law were used in the earlier work. We also measured the impact response of our two types of FG-CNTRC shells (i.e., type Λ and type X), as well as that of the UD shell (see Figure 3). We found that the type X FG-CNTRC shell had the lowest deflection from the impact, with the shortest contact duration. In addition, the type Λ FG-CNTRC shell had the lowest contact force among the three samples because of its low transverse Young's modulus value.

The (a) impactor displacement and (b) contact force histories of an isotropic plate that was subjected to a low-velocity impact. Results from this study (present) are compared with previously published data.7–10

(a) Central deflection and (b) contact force measurements of the impact response for the three types of CNTRC cylindrical shells.

In addition, we have studied how the V*CN affects the impact response of our FG-CNTRC cylindrical shells. For these tests, we used V*CN values of 0.12, 0.17, and 0.28. Our results—see Figure 4(a) and (b)—indicate that with an increased CNT volume fraction, both the central deflection and the contact duration decrease. In contrast, we find that contact force increases as a function of V*CN because of the increase in the transverse Young's modulus of the surface.

Central deflection (a) and (c), and contact force (b) and (d) measurements that illustrate how changing V*CN (left) and the initial impactor velocity (right) affects the impact response of the FG-X CNTRC cylindrical shell.

Similarly, we examined the effect of the impactor's initial velocity (V0) on the impact response of the type X FG-CNTRC cylindrical shell. For these measurements, we considered three different initial velocities for the impactor (i.e., V0 of 3, 6, and 9m/s). Our data—see Figure 4(c) and (d)—obviously shows that as the initial velocity increases, both the central deflection and the contact force increase. We also find, akin to the impact response of fiber-reinforced polymer honeycomb composite sandwich beams,11 that the maximal contact force approximately doubles as the initial velocity increases from 3 to 6m/s, and that it increases by about a factor of 1.5 as the velocity increases from 6 to 9m/s.

In the final part of our study, we examined the influence of temperature change on the impact response of the type X FG CNTRC cylindrical shell. We obtained data at temperatures of 300, 400, 500, and 700K for these measurements (see Figure 5). Our results clearly reveal that as the temperature increases, the curves of central deflection increase, whereas the measured contact force decreases.

The impact response of the FG-X CNTRC cylindrical shell, in terms of the (a) central deflection and (b) contact force, under four different thermal conditions.

In summary, we have presented the nonlinear low-velocity impact response of carbon-nanotube-reinforced composite cylindrical shells that have different CNT distributions. We have examined the effect of a variety of parameters (i.e., CNT volume fraction, initial impactor velocity, and temperature) on the impact response of our functionally graded shells. Our results show that the linear FG-CNT reinforcement has a significant effect on the nonlinear impact response of CNTRC cylindrical shells. In addition, our parametric numerical results illustrate that the initial velocity of the impact and the initial CNT load (as well as the CNT volume fraction, temperature, and shell dimensions) have a substantial influence on the impact behavior. Our methodology and results are also validated with existing data available in the literature. This kind of analysis is useful for the design and optimization of CNTRC structures that are subjected to impacts in thermal environments. In our future work we plan to add a damage model to our calculations.


Mohammad R. Bayat
Department of Mechanical Engineering, University of Tehran

Mohammad Bayat received his BSc from the University of Zanjan, Iran, in 2013 and his MSc in mechanical engineering from the University of Tehran in 2015. He is currently a PhD student under the supervision of Mostafa Baghani.

M. Mosavi Mashhadi
Department of Mechanical Engineering, University of Tehran

Omid Rahmani
Department of Mechanical Engineering, University of Zanjan


  1. C. H. Sun, F. Li, H. M. Cheng and G. Q. Lu, Axial Young's modulus prediction of single-walled carbon nanotube arrays with diameters from nanometer to meter scales, Appl. Phys. Lett. 87, pp. 193101, 2005.

  2. M.-F. Yu, B. S. Files, S. Arepalli and R. S. Ruoff, Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties, Phys. Rev. Lett. 84, pp. 5552, 2000.

  3. J. Hone, Carbon nanotubes: thermal properties, Dekker Encyclopedia of Nanoscience and Nanotechnology, pp. 603-610, CRC Press, 2004.

  4. S. Abrate, Impact on Composite Structures, pp. 289, Cambridge University Press, 2005.

  5. Z. X. Wang, J. Xu and P. Qiao, Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates, Compos. Struct. 108, pp. 423-434, 2014.

  6. M. R. Bayat, O. Rahmani and M. M. Mashhadi, Nonlinear low-velocity impact analysis of functionally graded nanotube-reinforced composite cylindrical shells in thermal environments, Polym. Compos., 2016. First published online: 4 April. doi:10.1002/pc.23990

  7. K. Karas, Platten unter seitlichem Stoß, Ingenieur-Archiv 10, pp. 237-250, 1939.

  8. H.-Y. T. Wu and C. Fu-Kuo, Transient dynamic analysis of laminated composite plates subjected to transverse impact, Comput. Struct. 31, pp. 453-466, 1989.

  9. S. M. R. Khalili, K. Malekzadeh and A. V. Gorgabad, Low velocity transverse impact response of functionally graded plates with temperature dependent properties, Compos. Struct. 96, pp. 64-74, 2013.

  10. H.-Y. T. Wu and G. S. Springer, Impact induced stresses, strains, and delaminations in composite plates, J. Compos. Mater. 22, pp. 533-560, 1988.

  11. P. Qiao and M. Yang, Impact analysis of fiber reinforced polymer honeycomb composite sandwich beams, Compos. Part B Eng. 38, pp. 739-750, 2007.

DOI:  10.2417/spepro.006487

Footer Links (2nd Row)