Abstract
A practical method to utilize carbon nanotubes (CNTs) in structural applications is to fabricate them into buckypapers (BPs), a thin film containing two-dimensional CNT networks, and combine them with a polymer matrix to make BP-polymer (BPP) composites. It has been demonstrated that BPP composites have very good mechanical properties with multi-functional capabilities. However, due to the uncertainties involved in different manufacturing stages, the resulting BPP composites exhibit larger property variations when compared with traditional metal or ceramic materials. As such, there is need for an improved modeling strategy that can provide rapid property predictions and variation quantifications for BPP composites through measurable buckypaper nanostructures and processing conditions. Due to high material costs and long production cycle times, it is nearly impossible to construct a statistical-based model for BPP composites purely from physical experiments. Theoretical (micromechanical) models are more cost effective, but they also have some drawbacks. Namely, they are computationally intensive, deterministic in nature, and have questionable accuracy due to underlying simplified assumptions. Different sources of variations in BPP composite manufacturing also build on the inadequacy of these micromechanical models for providing reasonable predictions without further adjustments.
Therefore, the main objective of this study is to provide a better modeling strategy for the prediction of BPP composite stiffness. By integrating a series of statistical methods with traditional micromechanical models, the variations observed in different stages were quantified, and a better predictive surrogate modeling strategy was constructed as a result. The statistical dispersions of buckypaper nanostructures (nanotube bundle length, diameter, orientation and waviness) were first analyzed and characterized by applying image analysis to microscopic images of buckypaper surface. It was found that the distribution of bundle length and diameter can be reasonably described by a two-parameter Weibull distribution, and the orientation of nanotubes can be represented by a periodic Fourier series. A stochastic based model was then constructed to predict the theoretical dispersions of BPP composite stiffness through experimentally measured nanostructure distributions by combining micromechanics with a Monte-Carlo simulation. It was found that the distribution of BP nanostructures would bias the resultant BPP composite modulus if a non-symmetric nanostructure distribution was present. The degree of nanostructure effects and interactions was analyzed using polynomial modeling and sensitivity analysis. The diameter and waviness of nanotube bundles were found to be the most influential factors for BPP composite modulus in most cases. The intra/inter buckypaper variations were studied using an Analysis of Variance (ANOVA) test. Both variations were tested as insignificant and can thus be statistically combined using the “mean nanostructure distribution” with pooled mean and variance. Lastly, two different sets of BPP composite experiments were used to validate the predictive capability of the constructed model. Preliminary results exhibited a noticeable discrepancy between theoretical predictions and physical observations due to the imperfections of the CNT-polymer interface. Therefore, statistical two-stage sequential modeling was applied to calibrate the original micromechanical model, and the resultant surrogate model was demonstrated to possess improved predictive capabilities. Recently functionalized BPP composite data also showed a very good correspondence to the theoretical predictions after the CNT-polymer interface was improved.
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