A Finite Element Study of Crack Behavior for Carbon Nanotube Reinforced Bone Cement

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