Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta, Canada.
J Biomed Mater Res A. 2010 Aug;94(2):594-602. doi: 10.1002/jbm.a.32737.
Carbon nanotubes (CNTs) provide a suitable environment for growth and proliferation of bone cells. The elastic properties exhibited by CNTs can enhance mechanical characteristics of bone mineral phase, hydroxyapatite (HAp), precipitated on such a scaffold. In this article, a simplified model for estimating the axial Young's modulus of a representative volume element (RVE) of CNT-HAp composite is presented. The model is based on the idea of HAp formation on functionalized sites on CNTs as cross-links between HAp matrix and CNT. Modeling results show that the reinforcement role contributed by CNT in the RVE causes a significant increase in the Young's modulus of the composite material which is a direct consequence of transferring stresses from the HAp matrix to the CNT through the cross-links. Similar conclusions may be suggested regarding the improvement of overall mechanical properties of the material. The prediction made by the model lies reasonably well within the limits proposed by conventional Rule-of-Mixtures, and sliding below Voigt's model. The Young's modulus predicted by the model lies adjacent to the Hashin-Shtrikman upper bound as a function of the RVE length (or equivalently CNT aspect ratio). The model simulation indicates that an increase in the CNT aspect ratio and/or number of cross-links in the RVE, results in the prediction to move closer to the estimation made by Voigt as the assumption of perfect bonding between composite phases is approached.
碳纳米管（CNTs）为骨细胞的生长和增殖提供了适宜的环境。CNTs 表现出的弹性特性可以增强沉淀在这种支架上的羟磷灰石（HAp）的矿物质相的机械特性。本文提出了一种估算 CNT-HAp 复合材料代表性体积元（RVE）轴向杨氏模量的简化模型。该模型基于 HAp 在 CNT 功能化位点上形成的概念，作为 HAp 基质与 CNT 之间的交联。建模结果表明，CNT 在 RVE 中的增强作用导致复合材料杨氏模量的显著增加，这是由于通过交联将应力从 HAp 基质传递到 CNT 的直接结果。对于材料整体力学性能的提高，也可能得出类似的结论。该模型的预测与传统混合规则提出的范围相当吻合，低于 Voigt 模型。作为 RVE 长度（或等效 CNT 纵横比）的函数，模型预测的杨氏模量接近 Hashin-Shtrikman 上限。模型模拟表明，随着复合材料相之间完美结合假设的接近，增加 RVE 中的 CNT 纵横比和/或交联数量，预测结果将更接近 Voigt 的估计。
