A Constitutive Model for Carbon Fiber Reinforced Epoxy Resin Laminate under Compression Load: Considering the Initial Non-linearity

At present, constitutive models considering the initial non-linearity of fiber reinforced composites under compression are rare. However, due to the inevitable manufacturing and processing defects, different material properties and inter-layer interface characteristics, the fiber reinforced composites show an initial non-linearity in engineering applications, which makes the stress path obtained by finite element analysis (FEA) inconsistent with the actual condition. To prove the existence of the initial non-linearity, the in-plane and out-of-plane compression experiments were conducted for carbon fiber reinforced epoxy resin (CFRP) laminate. According to the microscopic morphology from the scanning electron microscope (SEM) and experimental results, reasons for the initial non-linearity were discussed. Further, the initial nonlinear factor was introduced to develop a nonlinear constitutive model on the basis of orthotropic constitutive model. Combining Hashin failure criteria, inter-layer constitutive model and damage evolution law, the complete compression behaviors of CFRP laminate were obtained by user subroutine material VUMAT. The experimental results show that the initial non-linearity originates partly from the microscopic defects of material itself, such as the pores of matrix, the micro-cracks and interface dislocation. The slopes (i.e., elastic modulus) of stress–strain curves with linear and nonlinear models are consistent after the initial nonlinear stage. The CFRP calculation results by nonlinear VUMAT have an agreement well with the actual stress path. As a conclusion, the strain lag will occur when the initial non-linearity is considered. The contribution of this paper is to restore the practical problems encountered in engineering and provide the basis for engineering prediction.