Stress–strain state and elastic properties of composites with variable reinforcement structure

Abstract

A numerical and analytical investigation of the influence of spatial variation in reinforcement density on the stress–strain state (SSS) and effective elastic characteristics of unidirectional fibrous composites is presented. The importance of this work is due to the fact that in modern engineering applications (aerospace, automotive, and shipbuilding), the reinforcement density often varies along one or several coordinates for components of complex shape or variable thickness. This affects the stress–strain state and the accuracy of analytical estimates based on classical averaged models. The objective of the paper is to formulate and analyze relationships for the effective characteristics of an orthotropic layer with a variable reinforcement coefficient. Based on the rule of mixtures (Voigt and Reuss estimates), refined relationships for the components of the stiffness matrix of the orthotropic layer were derived. These relationships take into account the variable reinforcement coefficient along the height of the cross-section, and a constant coefficient along the width. Verification and comparison of the obtained relationships with simplified averaged formulas and 3D finite element method (FEM) calculations performed in Ansys Workbench were carried out. For the FEM modeling, a representative volume of trapezoidal shape (height 200 mm, bases 30 mm and 90 mm, thickness 30 mm) was considered in the tension problem (one end fixed, the load of 40 kN applied at the other end). Materials: carbon fiber and matrix. Three models were constructed: (1) with geometrically separated components, (2) equivalent orthotropic with refined stiffness matrix components, (3) equivalent orthotropic with simplified formulas. It is shown that taking into account the variability of reinforcement density in two directions reduces the error in determining displacements and moduli. The refined formulas demonstrate a significant reduction in errors in the “quasi-homogeneous” interior region of the sample: the average relative displacement error is about 2% for the refined formulas compared to 5% for the simplified ones. At the ends of the sample, due to edge effects, the errors reach up to 30%. The limits for the correct application of averaged relationships in tension problems were determined (for the given sample, the interval is 75–190 mm), and directions for extrapolation to bending were outlined. This requires a separate sensitivity analysis with respect to shear characteristics.