Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling

A sensitivity analysis (SA) has been conducted to examine the influence of uncertain input parameters on the fracture toughness of polymeric clay nanocomposites (PNCs). In order to predict the macroscopic properties of the composite, a phase-field approach has been employed considering six input parameters. For computationally efficiency, the SA is performed based on a surrogate model. Screening methods of the Standardized Regression Coefficients and the Regionalized Sensitivity Analysis are applied first. Then, quantitative methods, i.e. Sobol', EFAST, and PAWN are employed. Moreover, we have presented an improvement to the PAWN method that reduces the computational cost. The efficiency, robustness, and repeatability are compared and evaluated comprehensively of the five SA methods. The convergence of the sensitivity indices is achieved through the bootstrapping technique. The matrix Young's modulus is the most important input parameter affecting the macroscopic fracture toughness, whereas the volume fraction of the clay and the fracture energy of the matrix have a moderate importance. On the other hand, the aspect ratio, the radius of curvature, and the Young's modulus of the clay have negligible effects. Finally, fixing the uncertainties in the important input parameters reduces the coefficient of variation (COV) from 16.82% to 1.97%.