Probabilistic Determination of Thermal Conductivity and Cyclic Behavior of Nanocomposites via Multi-Phase Homogenization

A novel multiscale approach is introduced for determining the thermal conductivity of polymer nanocomposites (PNCs) reinforced with single-walled carbon nanotubes (SWCNTs), which accounts for their intrinsic uncertainties associated with dispersion, distribution, and morphology. Heterogeneities in PNCs on nanoscale are identified and quantified in a statistical sense, for the calculation of effective local properties. A finite element method computes the overall macroscale properties of PNCs in conjunction with the Monte Carlo simulations. This Monte Carlo Finite Element Approach (MCFEA) allows for acquiring the randomness in spatial distribution of the nanotubes throughout the composite. Furthermore, the proposed MCFEA utilizes the nanotube content, orientation, aspect ratio and diameter inferred from their statistical information. Local SWCNT volume or weight fractions are assigned to the finite elements (FEs), based on various spatial probability distributions. Multi-phase homogenization techniques are applied to each FE to calculate the local thermal conductivities. Then, the Monte Carlo simulations provide the statistics on the overall thermal conductivity of the PNCs. Subsequently, dispersion characteristics of the nanotubes are assessed by incorporating nanotube agglomerates. In this regard, a multi-phase homogenization method is developed for enhanced accuracy and effectiveness. The effect of the nanotube orientation in a polymer is studied for the cases where the SWCNTs are randomly oriented as well as longitudinally aligned. The influence of voids existing in the polymer is investigated on the thermal conductivity, to capture the uncertainties in PNCs more extensively. Further, a unique damage evaluation model is proposed to assess the degradation of PNCs when subjected to thermal cycling. The growth in void content is represented with a Weibull-based equation, to quantify the deterioration of the thermal and mechanical properties of PNCs under thermal fatigue. In addition, the MCFEA considers the interface resistance of the carbon nanotubes as one of the key factors in the thermal conductivity of nanocomposites. Parametric studies are performed comprehensively. The numerical results obtained are compared with available analytical techniques at hand and with the data from pertinent independent experimental studies. It is found that the proposed MCFEA is capable of estimating the thermal conductivity with good accuracy