Elastic modulus formulation of cementitious materials incorporating carbon nanotubes: Probabilistic approach

Abstract

Carbon nanotube (CNT) is one of the most promising nanomaterials to increase the elastic modulus of cementitious composites. However, CNT characteristics, dispersion procedure, and matrix composition/hydration are critical and correlated with a high degree of uncertainty in achieving a desirable performance. This paper proposes a mechanics-based model to predict the elastic modulus of CNT reinforced cementitious materials based on the Halpin-Tsai equation. The current study employs a probabilistic approach to consider the influences of multiple experimental variables and various sources of uncertainty associated with them. To this end, first, a Bayesian methodology is adopted to perform the model validation, evaluation, and selection procedures using extensive literature test data. Then, the optimum ranges of variables are found to maximize the chance of achieving a certain target modulus (herein, 50% more than control) using a reliability analysis. The proposed model suggests that the highest elastic modulus is achieved when using CNT aspect ratio ranges from 400 to 800 and concentration between 0.08 and 0.18 c-wt%. Also, the experimentally observed elastic modulus and the proposed probabilistic model exhibit a similar trend. For example, the importance of hydration age increases as CNT concentration increases. Finally, the proposed model can be used to reliably predict the elastic modulus, guiding future researchers to design more efficiently.