Computational Analysis of the Micromechanical Stress Field in Undamaged and Damaged Unidirectional Fiber-Reinforced Plastics Using a Modified Principal Component Analysis

This study investigated the internal stress distribution of unidirectional fiber-reinforced plastics (UD-FRP) at the micro level using principal component analysis (PCA). The composite material was simulated using a representative volume element model together with the embedded cell approach. Two fundamental quasi-static load cases, transverse and longitudinal tensile deformation, were considered. The experimental results show that mechanical failure occurred at 2.15 ± 0.06% transverse tensile strain and at 1.52 ± 0.07% longitudinal tensile strain. Furthermore, the undamaged state and a combination of matrix and interface damage, as well as fiber breakage, were simulated. From the simulations, the octahedral shear stress and octahedral normal stress were computed at the integration points of the matrix elements, constituting what is known as the octahedral stress field. A modification on the PCA to obtain mesh-independent eigenvalues is presented and was used to investigate the effects of damage events on the octahedral stress field. The results indicate that each damage mechanism had a distinct signature in the redistribution of the stress field, characterized by specific changes in the eigenvalues and orientation of the principal component (θ₁). Furthermore, the PCA suggests that the accumulation of matrix damage began to be relevant at the 1% strain, while fiber breakage began at an average longitudinal strain of 0.98 ± 0.12%. Additionally, it is shown that the first principal component served as an indicator of the predominant stress state of the stress field. This investigation suggests that the PCA can provide valuable insights regarding the complex damage mechanisms of UD-FRP that may not be captured by conventional mechanical analysis.