Effect of 3D Printing Parameters on the Viscoelastic Behavior of Acrylonitrile Butadiene Styrene: Fractional Calculus Modeling and Statistical Optimization

This study addresses the challenge of optimizing the viscoelastic performance of acrylonitrile butadiene styrene (ABS) parts manufactured by fused deposition modeling (FDM), where printing parameters strongly influence mechanical properties. The objective was to systematically evaluate the effects of four key factors-infill pattern, build orientation, layer height, and filament color-on storage modulus, damping factor, and glass transition temperature. A combined experimental design approach was employed: Taguchi's L9 orthogonal array efficiently screened parameter effects, while response surface methodology (RSM) enabled detailed analysis of interaction effects and multiresponse optimization. Results revealed that build orientation and layer height had the greatest impact, increasing instantaneous stiffness (Eu) by up to 81%, equilibrium modulus (E0) by 128%, and glass transition temperature (Tg) by 1.46%, while decreasing the damping factor (tan δ) by 3.4% between optimized and suboptimal conditions. To complement the statistical optimization, the fractional Zener model (FZM) was applied to characterize the viscoelastic response of two representative samples optimized for either high stiffness or high flexibility. The flexible sample exhibited a higher fractional order (α=0.24), indicating enhanced elastic mobility, while the stiff sample showed a higher activation energy (Ea=0.52 eV), consistent with restricted molecular motion. This integrated approach provides a robust and generalizable framework for improving material performance in polymer additive manufacturing.