A Finite Element Study of Crack Behavior for Carbon Na-notube Reinforced Bone Cement

Author(s)
Kaveh PourAkbar Saffar^{*},
Ahmad Raeisi Najafi^{*},
Manssour H. Moeinzadeh,
Leszek J. Sudak

Affiliation(s)

Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Canada.

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, USA.

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, USA.

Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Canada.

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, USA.

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, USA.

ABSTRACT

Polymethylmethacrylate (PMMA) bone cement is a polymeric material that is widely used as a structural orthopedic material. However, it is not an ideal material for bone grafting due to its fragility. Carbon nanotubes (CNTs) have been introduced in order to reinforce PMMA resulting in a composite material which exhibits improved tensile properties, increased fatigue resistance and fracture toughness. This improvement is potentially due to bridging and arresting cracks as well as absorption of energy. In this study, a two-dimensional finite element model is presented for the fracture analysis of PMMA-CNT composite material. Instead of the classical single fiber model, the present work considers an ensemble of CNTs interacting with a pre-existing crack. Casca is used to produce a two dimensional mesh and the fracture analysis is performed using Franc 2D. The model is subjected to uni-axial loading in the transverse plane and the interaction between the crack and CNTs is evaluated by determining the stress intensity factor in the vicinity of the crack tips. The effects of geometric parameters of the CNTs and the material structural heterogeneity on crack propagation trajectory are investigated. Furthermore, the effects of CNT diameter, wall thickness and elastic mismatch between the matrix and the nanotubes on crack growth are studied. The results illustrate that the CNTs repel cracks during loading as they act as barriers to crack growth. As a result, the incorporation of CNTs into PMMA reduces crack growth but more importantly increases the fracture resistance of bone cement.

Cite this paper

K. Saffar, A. Najafi, M. Moeinzadeh and L. Sudak, "A Finite Element Study of Crack Behavior for Carbon Na-notube Reinforced Bone Cement,"*World Journal of Mechanics*, Vol. 3 No. 5, 2013, pp. 13-21. doi: 10.4236/wjm.2013.35A003.

K. Saffar, A. Najafi, M. Moeinzadeh and L. Sudak, "A Finite Element Study of Crack Behavior for Carbon Na-notube Reinforced Bone Cement,"

References

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[22] B. Marrs, R. Andrews, T. Rantell and D. Pienkowski, “Augmentation of Acrylic Bone Cement with Multiwall Carbon Nanotubes,” Journal of Biomedical Materials Research Part A, Vol. 77, No. 2, 2006, pp. 269-276. doi:10.1002/jbm.a.30651

[23] A. A. Gawandi, J. M. Whitney, R. B. Brockman and G. P. Tandon, “Interaction between a Nanofiber and an Arbitrarily Oriented Crack,” Journal of Composite Materials, Vol. 42, No. 1, 2008, pp. 45-68.

[24] A. A. Gawandi, J. M. Whitney, G. P. Tandon and R. B. Brockman, “Three-Dimensional Analysis of the Interaction between a Matrix Crack and Nanofiber,” Composites Part B: Engineering, Vol. 40, No. 8, 2009, pp. 698-704. doi:10.1016/j.compositesb.2009.04.001

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[30] A. Raeisi Najafi, A. R. Arshi, K. PourAkbar Saffar, M. R. Eslami, S. Fariborz and M. H. Moeinzadeh, “A Fiber-Ceramic Matrix Composite Material Model for Osteonal Cortical Bone Micromechanics Fracture: General Solution of Microcracks Interaction,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 2, No. 3, 2009, pp. 217-223. doi:10.1016/j.jmbbm.2008.06.003

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[1] G. Lewis and Y. Li, “Dependence of in Vitro Fatigue Properties of PMMA Bone Cement on the Polydispersity Index of Its Powder,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 3, No. 1, 2010, pp. 94-101. doi:10.1016/j.jmbbm.2009.05.003

[2] M. Nakai, M. Niinomi, T. Akahori, H. Tsutsumi, S. Itsuno, N. Haraguchi, Y. Itoh, T. Ogasawara, T. Onishi and T. Shindoh, “Development of Biomedical Porous Titanium Filled with Medical Polymer by in-Situ Polymerization of Monomer Solution Infiltrated into Pores,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 3, No. 1, 2010, pp. 41-50. doi:10.1016/j.jmbbm.2009.03.003

[3] R. Ormsby, T. McNally, C. Mitchell and N. Dunne, “Incorporation of Multiwalled Carbon Nanotubes to Acrylic Based Bone Cements: Effects on Mechanical and Thermal Properties,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 3, No. 2, 2010, pp. 136-145. doi:10.1016/j.jmbbm.2009.10.002

[4] R. Ormsby, T. McNally, C. Mitchell and N. Dunne, “Influence of Multiwall Carbon Nanotube Functionality and Loading on Mechanical Properties of PMMA/MWCNT Bone Cements,” Journal of Materials Science: Materials in Medicine, Vol. 21, No. 8, 2010, pp. 2287-2292. doi:10.1007/s10856-009-3960-5

[5] B. Marrs, R. Andrews and D. Pienkowski, “Multiwall Carbon Nanotubes Enhance the Fatigue Performance of Physiologically Maintained Methyl Methacrylate-Styrene Copolymer,” Carbon, Vol. 45, No. 10, 2007, pp. 2098-2104. doi:10.1016/j.carbon.2007.05.013

[6] G. Lewis, “Properties of Acrylic Bone Cement: State of the Art Review,” Journal of Biomedical Materials Research, Vol. 38, No., 1997, pp. 155-182. doi:10.1002/(SICI)1097-4636(199722)38:2<155::AID-JBM10>3.0.CO;2-C

[7] N. Ihaddadene, P. Erani, M. Cotifava, F. Tomei, M. Baleani, M. Viceconti, S. Bouzid and L. Cristofolini, “Fatigue-Fractured Surfaces of Commercial Bone Cements,” Computer Methods in Biomechanics and Biomedical Engineering, Vol. 10, Suppl. 1, 2007, pp. 157-158. doi:10.1080/10255840701479610

[8] J. Jeffers, M. Browne, A. Lennon, P. Prendergast and M. Taylor, “Cement Mantle Fatigue Failure in Total Hip Replacement: Experimental and Computational Testing,” Journal of Biomechanics, Vol. 40, No. 7, 2007, pp. 1523-1533.

[9] B. A. O. McCormack and P. J. Prendergast, “Microdamage Accumulation in the Cement Layer of Hip Replacements under Flexural Loading,” Journal of Biomechanics, Vol. 32, No. 5, 1999, pp. 467-476. doi:10.1016/S0021-9290(99)00018-4

[10] M. Jasty, W. J. Maloney, C. R. Bragdon, D. O. O’Conner, T. Haire and W. H. Harris, “The Initiation of Failure in Cemented Femoral Components of Hip Antroplasties,” Journal of Bone and Joint Surgery, Vol. 73B, No. 4, 1991, pp. 551-558.

[11] R. J. Kane, W. Yue, J. J. Mason and R. K. Roeder, “Improved Fatigue Life of Acrylic Bone Cements Reinforced with Zirconia Fibers,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 3, No. 7, 2010, pp. 504-511. doi:10.1016/j.jmbbm.2010.05.007

[12] K.-T. Lau and D. Hui, “The Revolutionary Creation of New Advanced Materials-Carbon Nanotube Composites,” Composites Part B: Engineering, Vol. 33, No. 4, 2002, pp. 263-277. doi:10.1016/S1359-8368(02)00012-4

[13] K. I. Tserpes, P. Papanikos and S. A. Tsirkas, “A Progressive Fracture Model for Carbon Nanotubes,” Composites: Part B: Engineering, Vol. 37, No. 7-8, 2006, pp. 662-669. doi:10.1016/j.compositesb.2006.02.024

[14] V. A. Buryachenko and A. Roy, “Effective Elastic Moduli of Nanocomposites with Prescribed Random Orientation of Nanofibers,” Composites Part B: Engineering, Vol. 36, No. 5, 2005, pp. 405-416. doi:10.1016/j.compositesb.2005.01.003

[15] W. Wei, A. Sethuraman, C. Jin, N. A. Monteiro-Riviere and R. J. Narayan, “Biological Properties of Carbon Nanotubes,” Journal of Nanoscience and Nanotechnology, Vol. 7, No. 4-5, 2007, pp. 1284-1297. doi:10.1166/jnn.2007.655

[16] S. K. Smart, A. I. Cassady, G. Q. Lu and D. J. Martin, “The Biocompatibility of Carbon Nanotubes,” Carbon, Vol. 44, No. 6, 2006, pp. 1034-1047. doi:10.1016/j.carbon.2005.10.011

[17] L. P. Zanello, B. Zhao, H. Hu and R. C. Haddon, “Bone Cell Proliferation on Carbon Nanotubes,” Nano Letters, Vol. 6, No. 3, 2006, pp. 562-567. doi:10.1021/nl051861e

[18] B. Zhao, H. Hu, S. K. Mandal and R. C. Haddon, “A Bone Mimic Based on the Self-Assembly Of Hydroxyapatite on Chemically Functionalized Single-Walled Carbon Nanotubes,” Chemical Materials, Vol. 17, No. 12, 2005, pp. 3235-3241. doi:10.1021/cm0500399

[19] K. PourAkbar Saffar, A. R. Arshi, N. Jamilpour, A. Raeisi Najafi, G. Rouhi and L. Sudak, “A Cross-Linking Model for Estimating Young’s Modulus of Artificial Bone Tissue Grown on Carbon Nanotube Scaffold,” Journal of Biomedical Materials Research Part A, Vol. 94A, No. 2, 2010, pp. 594-602. doi:10.1002/jbm.a.32737

[20] A. A. White, S. M. Best and I. A. Kinloch, “Hydroxyapatite-Carbon Nanotube Composites for Biomedical Applications: A Review,” International Journal of Applied Ceramic Technology, Vol. 4, No. 1, 2007, pp. 1-13. doi:10.1111/j.1744-7402.2007.02113.x

[21] Y. Chen, Y. Q. Zhang, T. H. Zhang, C. H. Gan, C. Y. Zheng and G. Yu, “Carbon Nanotube Reinforced Hydroxyapatite Composite Coatings Produced through Laser Surface Alloying,” Carbon, Vol. 44, No. 1, 2006, pp. 37-45. doi:10.1016/j.carbon.2005.07.011

[22] B. Marrs, R. Andrews, T. Rantell and D. Pienkowski, “Augmentation of Acrylic Bone Cement with Multiwall Carbon Nanotubes,” Journal of Biomedical Materials Research Part A, Vol. 77, No. 2, 2006, pp. 269-276. doi:10.1002/jbm.a.30651

[23] A. A. Gawandi, J. M. Whitney, R. B. Brockman and G. P. Tandon, “Interaction between a Nanofiber and an Arbitrarily Oriented Crack,” Journal of Composite Materials, Vol. 42, No. 1, 2008, pp. 45-68.

[24] A. A. Gawandi, J. M. Whitney, G. P. Tandon and R. B. Brockman, “Three-Dimensional Analysis of the Interaction between a Matrix Crack and Nanofiber,” Composites Part B: Engineering, Vol. 40, No. 8, 2009, pp. 698-704. doi:10.1016/j.compositesb.2009.04.001

[25] C. Atkinson, “On the Stress Intensity Factors Associated with the Cracks Interacting with an Interface between Two Elastic Media,” International Journal of Engineering Science, Vol. 13, No. 5, 1975, pp. 487-504. doi:10.1016/0020-7225(75)90018-X

[26] A. Romeo and R. A. Ballarini, “A Crack Very Close to a Bimaterial Interface,” ASME Journal of Applied Mechanics, Vol. 62, No. 3, 1995, pp. 614-619. doi:10.1115/1.2895990

[27] Z. Li and L. Yang, “The Near-Tip Stress Intensity Factor for a Crack Partially Penetrating an Inclusion,” Journal of Applied Mechanics, Vol. 71, No. 4, 2002, pp. 465-469. doi:10.1115/1.1651539

[28] P. S. Steif, “A Semi-Infinite Crack Partially Penetrating a Circular Inclusion,” Journal of Applied Mechanics, Vol. 54, No. 1, 1987, pp. 87-92. doi:10.1115/1.3172999

[29] A. Raeisi Najafi, A. R. Arshi, M. R. Eslami, S. Fariborz and M. H. Moeinzadeh, “Haversian Cortical Bone Model with Many Radial Microcracks: An Elastic Analytic Solution,” Medical Engineering and Physics, Vol. 29, No. 6, 2007, pp. 708-717. doi:10.1016/j.medengphy.2006.08.001

[30] A. Raeisi Najafi, A. R. Arshi, K. PourAkbar Saffar, M. R. Eslami, S. Fariborz and M. H. Moeinzadeh, “A Fiber-Ceramic Matrix Composite Material Model for Osteonal Cortical Bone Micromechanics Fracture: General Solution of Microcracks Interaction,” Journal of the Mechanical Behavior of Biomedical Materials, Vol. 2, No. 3, 2009, pp. 217-223. doi:10.1016/j.jmbbm.2008.06.003

[31] N. A. Noda, Y. Takase and T. Hamashima, “Generalized Stress Intensity Factors in the Interaction within a Rectangular Array of Rectangular Inclusions,” Archive of Applied Mechanics, Vol. 73, No. 5-6, 2003, pp. 311-322. doi:10.1007/s00419-002-0249-2

[32] Y. Qiao, X. Kong and E. Pan, “Fracture Toughness of Thermoset Composites Reinforced by Perfectly Bonded Impenetrable Short Fiber,” Engineering Fracture Mechanics, Vol. 71, No. 18, 2004, pp. 2621-2633. doi:10.1016/j.engfracmech.2004.02.007

[33] M. B. Bush, “The interaction between a Crack and a Particle Cluster,” International Journal of Fracture, Vol. 88, No. 3, 1997, pp. 215-232. doi:10.1023/A:1007469631883

[34] K. Kim and L. J. Sudak, “Interaction between a Radial Matrix Crack and a Three-Phase Circular Inclusion with Imperfect Interface in Plane Elasticity,” International Journal of Fracture, Vol. 131, No. 2, 2005, pp. 155-172. doi:10.1007/s10704-004-3636-6

[35] P. G. Park and L. J. Sudak, “Stress Intensity Factor for an Interphase Crack Interacting with Two Imperfect Interfaces,” Mathematics and Mechanics of Solids, Vol. 15, No. 3, 2010, pp. 353-367. doi:10.1177/1081286508101512

[36] G. D. Seidel and D. C. Lagoudas, “Micromechanical Analysis of the Effective Elastic Properties of Carbon Nanotube Reinforced Composites,” Mechanics of Materials, Vol. 38, No. 8-10, 2006, pp. 884-907. doi:10.1016/j.mechmat.2005.06.029

[37] J. P. Lu, “Elastic Properties of Carbon Nanotubes and Nanoropes,” Physical Review Letters, Vol. 79, No. 7, 1997, pp. 1297-1300. doi:10.1103/PhysRevLett.79.1297

[38] D. Swenson, M. James and B. Hardeman, “CASCA: A Simple 2-D Mesh Generator, Version 1. 4 User’s Guide,” Kansas State University, Manhattan, Kansas, 1997.

[39] P. Wawrzynek and A. Ingraffea, “FRANC2D: A Two-Dimensional Crack Propagation Simulator,” Version 2. 7 User’s Guide, NASA CR 4572, 1994.

[40] X.-L. Xie, Y.-W. Mai and X.-P. Zhou, “Dispersion and Alignment of Carbon Nanotubes in Polymer Matrix: A Review,” Materials Science and Engineering: R: Reports, Vol. 49, No. 4, 2005, pp. 89-112. doi:10.1016/j.mser.2005.04.002

[41] Y. Liu, C. Q. Ru, P. Schiavone and A. Mioduchowski, “New Phenomena Concerning the Effect of Imperfect Bonding on Radial Matrix Cracking in Fiber Composites,” International Journal of Engineering Science, Vol. 39, No. 18, 2001, pp. 2033-2050. doi:10.1016/S0020-7225(01)00049-0.