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.
Highlights
Polymethylmethacrylate (PMMA) bone cement is a polymeric material that shows good compatibility with living tissues
The results illustrate that the Carbon nanotubes (CNTs) repel cracks during loading as they act as barriers to crack growth
The crack location is considered as the normalized distance of the crack from the single CNT shown in Figure 4(a) (corresponding to Figure 9(a)), and the normalized distance of the crack from the CNT at left of the cross arrangement as shown in Figure 4(b) (corresponding to Figure 9(b))
Summary
Polymethylmethacrylate (PMMA) bone cement is a polymeric material that shows good compatibility with living tissues. Gawandi and colleagues addressed the problem of a single nano-fiber interacting with a crack [23,24] These works are limited because the atomistic structure of the nanotube has been neglected in the formulation of the finite element model. In the present work we develop a two dimensional finite element model incorporating an array of CNTs as the reinforcing phase in PMMA bone cement where the atomistic structure of CNTs are taken into account. It is observed that the incorporation of CNTs into PMMA reduces crack growth but more importantly increases the fracture resistance of bone cement
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