Skip to main content
Log in

Estimation of Tensile Modulus for Cross-Linked Polyethylene/Clay Shape Memory Nanocomposites

  • Published:
Physical Mesomechanics Aims and scope Submit manuscript

Abstract

Many models are used for the analysis of tensile modulus in cross-linked polyethylene/clay shape memory polymer nanocomposites. The conventional models such as modified rule of mixtures, Guth, Paul, Counto, Kerner–Nielsen, etc. underestimate the modulus exhibiting that the reinforcing effect of nanofiller should be considered for the estimation of tensile modulus in the shape memory nanocomposites. In addition, the appropriate parameters in some models are indicated for proper prediction of tensile modulus. Several models such as Halpin–Tsai for fillers with random 3D distribution and Hui–Shia offer the average aspect ratio of 56 for nanoclay layers. The results obtained by the Takayanagi model are not fitted to the experimental results demonstrating the important effect of the interphase between polymer matrix and nanoclay. Some models such as Guth, Halpin–Tsai and Kerner–Nielsen are modified for better adjustment to tensile modulus of cross-linked polyethylene/clay shape memory nanocomposites.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

Similar content being viewed by others

REFERENCES

  1. Panahi-Sarmad, M., Abrisham, M., Noroozi, M., Amirkiai, A., Dehghan, P., Goodarzi, V., and Zahiri, B., Deep Focusing on the Role of Microstructures in Shape Memory Properties of Polymer Composites: A Critical Review, Eur. Polymer J., 2019, vol. 117, pp. 280–303.

    Article  Google Scholar 

  2. Wu, G., Gu, Y., Hou, X., Li, R., Ke, H., and Xiao, X., Hybrid Nanocomposites of Cellulose/Carbon-Nanotubes/Polyurethane with Rapidly Water Sensitive Shape Memory Effect and Strain Sensing Performance, Polymers, 2019, vol. 11, p. 1586.

    Article  Google Scholar 

  3. Liu, Y., Zhang, F., Leng, J., Wang, L., Cotton, C., Sun, B., and Chou, T.-W., Synergistic Effect Enhanced Shape Recovery Behavior of Metal-4D Printed Shape Memory Polymer Hybrid Composites, Composites. B. Eng., 2019, vol. 179, p. 107536.

    Article  Google Scholar 

  4. Zaeem, M.A., Zhang, N., and Mamivand, M., A Review of Computational Modeling Techniques in Study and Design of Shape Memory Ceramics, Comput. Mater. Sci., 2019, vol. 160, pp. 120–136.

    Article  Google Scholar 

  5. Cho, J.W. and Lee, S.H., Influence of Silica on Shape Memory Effect and Mechanical Properties of Polyurethane–Silica Hybrids, Eur. Polymer J., 2004, vol. 40, pp. 1343–1348.

    Article  Google Scholar 

  6. Rezanejad, S. and Kokabi, M., Shape Memory and Mechanical Properties of Cross-Linked Polyethylene/Clay Nanocomposites, Eur. Polymer J., 2007, vol. 43, pp. 2856–2865.

    Article  Google Scholar 

  7. Hassanzadeh-Aghdam, M., Ansari, R., and Darvizeh, A., Thermal Expanding Behavior of Carbon Nanotube-Shape Memory Polymer Nanocomposites, Mech. Adv. Mater. Struct., 2018, pp. 1–12.

  8. Hassanzadeh-Aghdam, M., Mahmoodi, M., Ansari, R., and Darvizeh, A., Interphase Influences on the Mechanical Behavior of Carbon Nanotube–Shape Memory Polymer Nanocomposites: A Micromechanical Approach, J. Intelligent Mater. Syst. Struct., 2018. https://doi.org/10.1177/1045389X18812704

  9. Liu, Y., Gall, K., Dunn, M.L., and McCluskey, P., Thermomechanics of Shape Memory Polymer Nanocomposites, Mech. Mater., 2004, vol. 36, pp. 929–940.

    Article  Google Scholar 

  10. Di Prima, M., Gall, K., McDowell, D., Guldberg, R., Lin, A., Sanderson, T., Campbell, D., and Arzberger, S., Cyclic Compression Behavior of Epoxy Shape Memory Polymer Foam, Mech. Mater., 2010, vol. 42, pp. 405–416.

    Article  Google Scholar 

  11. Ohki, T., Ni, Q.-Q., Ohsako, N., and Iwamoto, M., Mechanical and Shape Memory Behavior of Composites with Shape Memory Polymer, Composites. A. Appl. Sci. Manufactur., 2004, vol. 35, pp. 1065–1073.

    Article  Google Scholar 

  12. Panin, V.E., Surikova, N.S., Panin, S.V., Shugurov, A.R., and Vlasov, I.V., Effect of Nanoscale Mesoscopic Structural States Associated with Lattice Curvature on the Mechanical Behavior of Fe–Cr–Mn Austenitic Steel, Phys. Mesomech., 2019, vol. 22, no. 5, pp. 382–391. https://doi.org/10.1134/S1029959919050059

    Article  Google Scholar 

  13. Golovnev, I.F., Golovneva, E.I., and Utkin, A.V., Effect of the Nanorod Size on Energy Absorption at the Microlevel under Cyclic Loading, Phys. Mesomech., 2019, vol. 22, no. 5, pp. 420–431. https://doi.org/10.1134/S1029959919050084

    Article  Google Scholar 

  14. Bochkarev, A.O. and Grekov, M.A., Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem, Phys. Mesomech., 2019, vol. 22, no. 3, pp. 209–223. https://doi.org/10.1134/S1029959919030068

    Article  Google Scholar 

  15. Golovnev, I.F. and Golovneva, E.I., Numerical Study of the Kinetic Aspects of Fracture of Metal Nanocrystals, Phys. Mesomech., 2019, vol. 22, no. 3, pp. 195–202. https://doi.org/10.1134/S1029959919030044

    Article  Google Scholar 

  16. Korotaev, A.D., Litovchenko, I.Yu., and Ovchinnikov, S.V., Structural-Phase State, Elastic Stress, and Functional Properties of Nanocomposite Coatings Based on Amorphous Carbon, Phys. Mesomech., 2019, vol. 22, no. 6, pp. 488–495. https://doi.org/10.1134/S1029959919060055

    Article  Google Scholar 

  17. Zare, Y., Rhee, K.Y., and Park, S.J., Simple Model for Hydrolytic Degradation of Poly (Lactic Acid)/Poly (Ethylene Oxide)/Carbon Nanotubes Nanobiosensor in Neutral Phosphate-Buffered Saline Solution, J. Biomed. Mater. Res. A, 2019, vol. 107, pp. 2706–2717.

    Article  Google Scholar 

  18. Zare, Y. and Rhee, K.Y., Prediction of Loss Factor (tan δ) for Polymer Nanocomposites as a Function of Yield Tress, Relaxation Time and the Width of Transition Region between Newtonian and Power-Law Behaviors, J. Mech. Behav. Biomed. Mater., 2019, vol. 96, pp. 136–143.

    Article  Google Scholar 

  19. Zare, Y. and Rhee, K.Y., Significances of Interphase Conductivity and Tunneling Resistance on the Conductivity of Carbon Nanotubes Nanocomposites, Polymer Composites, 2020, vol. 41, pp. 748–756.

    Article  Google Scholar 

  20. Li, Z., Xu, K., and Pan, Y., Recent Development of Supercapacitor Electrode Based on Carbon Materials, Nanotechnology Rev., 2019, vol. 8, pp. 35–49.

    Article  Google Scholar 

  21. Ventrapragada, L.K., Creager, S.E., Rao, A.M., and Podila, R., Carbon Nanotubes Coated Paper as Current Collectors for Secondary Li-Ion Batteries, Nanotechnology Rev., 2019, vol. 8, pp. 18–23.

    Article  Google Scholar 

  22. Cherepanov, G.P., Theory of Superplasticity and Fatigue of Polycrystalline Materials Based on Nanomechanics of Fracturing and Failure, Phys. Mesomech., 2019, vol. 22, no. 1, pp. 52–64. https://doi.org/10.1134/S1029959919010090

    Article  Google Scholar 

  23. Beznosyuk, S.A., Maslova, O.A., and Zhukovsky, M.S., Quantum Infrastructure of Attosecond Sensors and Actuators of Nonequilibrium Physical Media in Smart Materials, Phys. Mesomech., 2019, vol. 22, no. 5, pp. 432–438. https://doi.org/10.1134/S1029959919050096

    Article  Google Scholar 

  24. Le, J.-L. and Xu, Z., A Simplified Probabilistic Model for Nanocrack Propagation and its Implications for Tail Distribution of Structural Strength, Phys. Mesomech., 2019, vol. 22, no. 2, pp. 85–95. https://doi.org/10.1134/S1029959919020012

    Article  Google Scholar 

  25. Ditenberg, I.A., Tyumentsev, A.N., Smirnov, I.V., Grinyaev, K.V., and Chernov, V.M., Thermal Stability of Nanostructured Internally Oxidized Vanadium Alloy with Combined Dispersion and Substructural Hardening, Phys. Mesomech., 2019, vol. 22, no. 6, pp. 496–503. https://doi.org/10.1134/S1029959919060067

    Article  Google Scholar 

  26. Tabatabaeian, A. and Ghasemi, A.R., Curvature Changes and Weight Loss of Polymeric Nano-Composite Plates with Consideration of the Thermal Cycle Fatigue Effects and Different Resin Types: An Experimental Approach, Mech. Mater., 2019, vol. 131, pp. 69–77.

    Article  Google Scholar 

  27. Hassanzadeh-Aghdam, M. and Ansari, R., Thermal Conductivity Of Shape Memory Polymer Nanocomposites Containing Carbon Nanotubes: A Micromechanical Approach, Composites. B. Eng., 2019, vol. 162, pp. 167–177.

    Article  Google Scholar 

  28. Hassanzadeh-Aghdam, M.K., Ansari, R., Mahmoodi, M.J., Thermo-Mechanical Properties of Shape Memory Polymer Nanocomposites Reinforced by Carbon Nanotubes, Mech. Mater., 2019, vol. 129, pp. 80–98.

    Article  Google Scholar 

  29. Koerner, H., Price, G., Pearce, N.A., Alexander, M., Vaia, R.A., Remotely Actuated Polymer Nanocomposites—Stress-Recovery of Carbon-Nanotube-Filled Thermoplastic Elastomers, Nature Mater., 2004, vol. 3, pp. 115–120.

    Article  ADS  Google Scholar 

  30. Zare, Y. and Rhee, K.Y., A Core–Shell Structure for Interphase Regions Surrounding Nanoparticles to Predict the Shear, Bulk and Young’s Polymer Moduli of Particulate Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 1, pp. 89–96. https://doi.org/10.1134/S1029959920010099

    Article  Google Scholar 

  31. Zare, Y. and Rhee, K.Y., A Modeling Approach for Young’s Modulus of Interphase Layers in Polymer Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 2, pp. 176–181. https://doi.org/10.1134/S1029959920020095

    Article  Google Scholar 

  32. Zare, Y., Rhee, K.Y., and Park, S.-J., Simple Models for Interphase Characteristics in Polypropylene/Montmorillonite/CaCo3 Nanocomposites, Phys. Mesomech., 2020, vol. 23, no. 2, pp. 182–188. https://doi.org/10.1134/S1029959920020101

    Article  Google Scholar 

  33. Hassanzadeh-Aghdam, M.K., Mahmoodi, M.J., Ansari, R., and Mehdipour, H., Effects of Adding CNTs on the Thermo-Mechanical Characteristics of Hybrid Titanium Nanocomposites, Mech. Mater., 2019, vol. 131, pp. 121–135.

    Article  Google Scholar 

  34. Hasanzadeh, M., Ansari, R., and Hassanzadeh-Aghdam, M., Evaluation of Effective Properties of Piezoelectric Hybrid Composites Containing Carbon Nanotubes, Mech. Mater., 2019, vol. 129, pp. 63–79.

    Article  Google Scholar 

  35. Haghighat, M., Zadhoush, A., and Khorasani, S.N., Physicomechanical Properties of α-Cellulose—Filled Styrene–Butadiene Rubber Composites, J. Appl. Polymer Sci., 2005, vol. 96, pp. 2203–2211.

    Article  Google Scholar 

  36. Cox, H., The Elasticity and Strength of Paper and Other Fibrous Materials, British J. Appl. Phys., 1952, vol. 3, p. 72.

    Article  ADS  Google Scholar 

  37. Dong, Y. and Bhattacharyya, D., Mapping the Real Micro/Nanostructures for the Prediction of Elastic Moduli of Polypropylene/Clay Nanocomposites, Polymer, 2010, vol. 51, pp. 816–824.

    Article  Google Scholar 

  38. Verbeek, C., The Influence of Interfacial Adhesion, Particle Size and Size Distribution on the Predicted Mechanical Properties of Particulate Thermoplastic Composites, Mater. Lett., 2003, vol. 57, pp. 1919–1924.

    Article  Google Scholar 

  39. McGeary, R., Mechanical Packing of Spherical Particles, J. Am. Ceram. Soc., 1961, vol. 44, pp. 513–522.

    Article  Google Scholar 

  40. Kalaprasad, G., Joseph, K., Thomas, S., and Pavithran, C., Theoretical Modelling of Tensile Properties of Short Sisal Fibre-Reinforced Low-Density Polyethylene Composites, J. Mater. Sci., 1997, vol. 32, pp. 4261–4267.

    Article  ADS  Google Scholar 

  41. Ahmed, S. and Jones, F., A Review of Particulate Reinforcement Theories for Polymer Composites, J. Mater. Sci., 1990, vol. 25, pp. 4933–4942.

    Article  ADS  Google Scholar 

  42. Nunez, A.J., Sturm, P.C., Kenny, J.M., Aranguren, M.I., Marcovich, N.E., and Reboredo, M.M., Mechanical Characterization of Polypropylene–Wood Flour Composites, J. Appl. Polymer Sci., 2003, vol. 88, pp. 1420–1428.

    Article  Google Scholar 

  43. Guth, E., On the Hydrodynamical Theory of the Viscosity of Suspensions, Phys. Rev., 1938, vol. 53, pp. 322–325.

    Google Scholar 

  44. Wu, Y.-P., Jia, Q.-X., Yu, D.-S., and Zhang, L.-Q., Modeling Young’s Modulus of Rubber–Clay Nanocomposites Using Composite Theories, Polymer Test., 2004, vol. 23, pp. 903–909.

    Article  Google Scholar 

  45. Davies, W., The Theory of Elastic Composite Materials, J. Phys. D. Appl. Phys., 1971, vol. 4, p. 1325.

    Article  ADS  Google Scholar 

  46. Halpin, J.C. and Kardos, J., The Halpin–Tsai Equations: A Review, Polymer Eng. Sci., 1976, vol. 16, pp. 344–352.

    Article  Google Scholar 

  47. Landel, R.F. and Nielsen, L.E., Mechanical Properties of Polymers and Composites, CRC Press, 1993.

  48. Lewis, T.B. and Nielsen, L.E., Dynamic Mechanical Properties of Particulate-Filled Composites, J. Appl. Polymer Sci., 1970, vol. 14, pp. 1449–1471.

    Article  Google Scholar 

  49. Kerner, E., The Elastic and Thermo-Elastic Properties of Composite Media, Proc. Phys. Soc. B, 1956, vol. 69, p. 808.

    Article  ADS  Google Scholar 

  50. Hui, C. and Shia, D., Simple Formulae for the Effective Moduli of Unidirectional Aligned Composites, Polymer Eng. Sci., 1998, vol. 38, pp. 774–782.

    Article  Google Scholar 

  51. Ji, X.L., Jiao, K.J., Jiang, W., and Jiang, B.Z., Tensile Modulus of Polymer Nanocomposites, Polymer Eng. Sci., 2002, vol. 42, p. 983.

    Article  Google Scholar 

  52. Cauvin, L., Kondo, D., Brieu, M., and Bhatnagar, N., Mechanical Properties of Polypropylene Layered Silicate Nanocomposites: Characterization and Micro–Macro Modelling, Polymer Test., 2010, vol. 29, pp. 245–250.

    Article  Google Scholar 

  53. Sato, Y. and Furukawa, J., A Molecular Theory of Filler Reinforcement Based upon the Conception of Internal Deformation (a Rough Approximation of the Internal Deformation), Rubber Chem. Technol., 1963, vol. 36, pp. 1081–1106.

    Article  Google Scholar 

  54. Sisakht Mohsen, R., Saied, N.K., Ali, Z., Hosein, E.M., and Hasan, P., Theoretical and Experimental Determination of Tensile Properties of Nanosized and Micron-Sized CaCO3/PA66 Composites, Polymer Composites, 2009, vol. 30, pp. 274–280.

    Article  Google Scholar 

  55. Coleman, J.N., Khan, U., and Gun’ko, Y.K., Mechanical Reinforcement of Polymers Using Carbon Nanotubes, Adv. Mater., 2006, vol. 18, pp. 689–706.

    Article  Google Scholar 

  56. Shaffer, M.S. and Windle, A.H., Fabrication and Characterization of Carbon Nanotube/Poly (Vinyl Alcohol) Composites, Adv. Mater., 1999, vol. 11, pp. 937–941.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to K. Y. Rhee.

Additional information

Translated from in Fizicheskaya Mezomekhanika, 2020, Vol. 23, No. 4, pp. 90–98.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zare, Y., Rhee, K.Y. Estimation of Tensile Modulus for Cross-Linked Polyethylene/Clay Shape Memory Nanocomposites. Phys Mesomech 24, 211–218 (2021). https://doi.org/10.1134/S1029959921020119

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1029959921020119

Keywords:

Navigation