Multi-Objective Optimization of Mechanical Properties for FDM-Printed PLA/TPU Blends via Box–Behnken Design and Entropy Weight Method

Abstract

Polylactic acid (PLA) is widely used in fused deposition modeling (FDM) due to its excellent mechanical properties and processability. However, its inherent brittleness significantly restricts its application in load-bearing and high-toughness scenarios. To address this limitation, this study establishes a multi-objective optimization framework that integrates single-factor experiments, Box–Behnken design (BBD), response surface methodology (RSM), and entropy weight-based objective weighting to simultaneously enhance the tensile strength, elongation at break, and flexural strength of FDM-printed PLA/thermoplastic polyurethane (TPU) blends. Through single-factor experiments, the optimal PLA/TPU blend ratio was determined as 80:20, achieving a tensile strength of 38.93 MPa, an elongation at break of 14.12%, and a flexural strength of 42.33 MPa—representing improvements of 39.4%, 15.7%, and 31.6%, respectively, over the 70:30 blend. Multi-scale characterization via FTIR, XRD, and SEM reveals that this enhanced performance arises from strong interfacial hydrogen bonding, a well-retained crystalline PLA framework, and the uniform dispersion of fine TPU domains. Subsequently, a four-factor, three-level BBD was employed to investigate the effects of printing speed, nozzle temperature, raster angle, and layer height on the mechanical properties. The entropy weight method assigned objective weights of 0.4924, 0.0901, and 0.4805 to the three properties, yielding a comprehensive score as the evaluation index. Unlike conventional approaches that rely solely on software-recommended optima from RSM models, this study critically compares two decision routes: secondary RSM modeling followed by continuous optimization versus direct ranking of BBD experimental data. Direct ranking identified the optimal parameter set (90 mm/s, 200 °C, 0° raster angle, 0.2 mm layer height) with a comprehensive score of 0.9614, surpassing the RSM-recommended route (70 mm/s, 200 °C, 0° raster angle, 0.2 mm layer height; score 0.7366) by 30.5%. This comparison demonstrates that, in strongly nonlinear FDM processes, software-based continuous optimization may converge to mathematically conservative suboptimal regions, whereas direct ranking of discrete experimental data preserves full physical responses and captures higher-order synergistic effects that the RSM model fails to account for. ANOVA results further confirm that raster angle is the most influential factor affecting the comprehensive score. Overall, this work bridges material formulation and printing parameter optimization for PLA/TPU blends, offering a validated strategy for high-performance FDM manufacturing.