PSI - Issue 32

S.A. Bochkareva et al. / Procedia Structural Integrity 32 (2021) 334–339 Author name / Structural Integrity Procedia 00 (2019) 000–000

335

2

1. Introduction Laminated composites based on thermoplastic polymers Mallick (2020) reinforced with continuous fibers possess much higher mechanical properties as compared with dispersed fiber reinforce в ones Dhand et. al. (2015). In doing so, the fiber layout Morioka et. al. (2000) as well as adhesion between a binder and enforcement are the main factors that determine their deformation–strength properties. Numerical modeling of composites makes it possible to predict the effect of fiber layout pattern as well as adhesion level on key mechanical properties. The relevant literature mostly focuses on constitutive and structural models based on finite element method Guo et. al. (2021), Garg et. al. (2020), Luccioni (2006). Multilevel approaches are also developed LLorca (2012). In this paper, to determine strength properties of layered composites, models are proposed that take into account interfacial delamination and fracture under different stress states. The effect of interfacial adhesion and contact imperfection between carbon fibers and PEEK matrix on the mechanical properties of composites was analyzed. 2. Problem statement To determine the parameters of the stress-strain state of composites the plane problem of the elasticity theory was solved with the use of finite element method (FEM). The paper deals with investigation of mechanical properties of laminated composites reinforced with continuous carbon fibers. As a rule, commercially available unidirectional carbon fiber tapes as well as carbon fabric are used for their manufacturing. The fiber layers were impregnated with a PEEK binder. Carbon fibers were laid out in various directions that determined the strength of composites. The carbon fibers within each layer were bundles with an average diameter of 160 μm ; the layer thickness was assumed to be the same (hereinafter, carbon fiber means a bundle of fibers). The number of such monolayers (with carbon fibers) in the specimen was 11. The strength of the carbon fibers was 4.9 GPa, the modulus of elasticity was 240 GPa. According to the technical specification for industrially produced CF tapes the percentage of fibers in one direction should be equal to 80%. In doing so, the ratio of polymer and CF bundles in one layer of unidirectional fabric was: 20 ÷ 80 vol. %, while for the biaxil fabric (bidirectional) it was equal to 40 ÷ 60 vol. % (since its surface density by a specification is 2.2 times less than that of unidirectional fabric). Thus, it was assumed that in one monolayer with 20 % carbon fibers (in the case of fabric it was 40 %) there was free space between the fibers. It might be filled with a polymer. 2.1. Effective characteristics of a monolayer The calculation of the effective mechanical properties of one CF layer impregnated with a polymer (monolayer) was carried out by modeling the plane stress-strain state (SSS) in a computational domain. Fig. 1 illustrates data for stretching i) along the fiber direction, ii) across it and iii) under shear. The size of the computational area was 3.5 × 3.5 mm. Carbon fibers are located at the lower and upper boundaries of the computational domain. The PEEK’s elastic modulus was equal to 3750 MPa. The nonlinear pattern of the stress-strain diagram was taken into account under PEEK tension (Fig. 2). Carbon fibers were elastically deformed. The imperfect contact between the carbon fibers and the binder was considered when the materials did not contact over the entire surface area. However, imperfect contact was introduced partially in several locations. It was taken into account through the number of contacting nodes between carbon fibers and the matrix, as well as the level of separation stresses between these nodes. In practical sense, these parameters do determine the level of adhesion. The contacting nodes were distributed evenly along the fiber length (Fig. 1). The stretching of the finite element mesh without breaking of nodes is shown in the figure 1 in order to clarify its location. The calculations were carried out using the author's homemade program based on the FEM. To ensure the bonding between fibers and matrix in the contacting nodes, the conditions of displacement equality were set. The appropriate changes were made to the stiffness matrix described in Bochkareva et. al. (2020). At each loading step, the elastic modulus of the polymer was corrected for each finite element (fig. 1), while the failure criteria were checked. For the latter, reaching of limiting values (equal to the yield stress - criterion of maximum stresses) for one of the stress tensor