3D micromechanics assisted finite element approach for bending analysis of straight/wavy CNT-reinforced multi-scale hybrid composite plate

This study examines the micromechanical and structural behavior of straight and wavy carbon nanotube (CNT) reinforced multi-scale fiber-reinforced hybrid composite (MFRHC) plates. An important feature of MFRHC is the incorporation of nano-scale CNTs into two-phase carbon fiber-reinforced composites (CFRC), enhancing their micromechanical and macroscopic properties, particularly the bending and stress behaviors. In CNT fiber-reinforced composites, the fiber waviness can arise from manufacturing imperfections which demands in-depth analysis of MFRHC plates reinforced with both straight or wavy CNTs to characterize their relative influences. In this work, the CNTs are assumed to be continuous and distributed uniformly within the CFRC, and the waviness is considered to be sinusoidal spanning both longitudinal and transverse planes. A mathematical formulation is devised, based on a three-dimensional mechanics of materials (MOM) model, to analyze the micromechanical behavior of the hybrid composite and the model's accuracy are compared with the multi-inclusion Mori-Tanaka method and the Voigt/Reuss rule of mixtures. The MOM model indicates that the waviness pattern of the CNTs significantly influences the effective stiffness properties of MFRHC in comparison to that of the straight CNTs. Following this, a finite element model is constructed to investigate the bending deflection and stress properties of a simply-supported symmetric cross-ply (0/90/0) MFRHC laminate under sinusoidal transverse loading, utilizing first-order shear deformation theory (FSDT). The results suggest that the bending deflection decreases for the MFRHC laminate when the waviness factor (Psi) is <= 0.05, but increases when Psi>0.05. Finally, the bending stress behavior is examined for both straight and wavy CNT-reinforced MFRHC laminates considering their geometrical parameters (a/h, z/h), and the CNTs' waviness factor (Psi), respectively.