Numerical Homogenization Calculation of Effective Stiffness of Fused Deposition Modeling Printing Carbon Fiber Reinforced Polylactic Acid Composites

The varied material and the inherent complex microstructure make predicting the effective stiffness of fused deposition modeling (FDM) printed polylactic acid (PLA)/carbon fiber (CF) composite a troublesome problem. This article proposes a microstructure scanning electron microscope (SEM) mapping modeling and numerical mean procedure to calculate the effective stiffness of FDM printing PLA/CF laminates. The printed PLA/CF parts were modeled as a continuum of 3D uniform linear elasticity with orthotropic anisotropy, and their elastic behavior was characterized by orthotropic constitutive relations. Micromechanical models of two typical deposition configurations, 0° unidirectional aligned configuration and 0°/90° angle-ply configuration of the printed parts were established based on the periodic representative volume element (RVE) technique. The elastic constants of the RVE models were estimated by volume average method in the finite element stress analysis, and the effects of deposition configurations, CF length, and content on the effective stiffness were also investigated. The results show that the effective stiffness of FDM printing PLA/CF composite is closely related to CF length, content, and the deposition configuration. With the increase of CF length and content, the Young's modulus and shear modulus of printed PLA/CF parts increase, whereas Poisson's ratio decreases. The printed PLA/CF parts with 0° unidirectional aligned configuration exhibits orthotropic characteristics, and the maximum Young's modulus appears along the first axis. The 0°/90° angle-ply FDM PLA/CF composite exhibits transverse isotropic characteristics and the lowest Young's modulus is found along the thickness direction.