Calculation of the stress-strain state of layers of cross-ply laminate based on an experimental stress-strain curves under uniaxial tension

Abstract

A method for calculating the stress-strain state of layers of cross-ply laminate based on an experimental deformation diagram under uniaxial tension is proposed. The essence of the method consists in solving a system of two equations describing the experimental curves σx = f(εx) and σx = f(εy), which allows determination of two unknown parameters related to the secant elastic characteristics of the material layers. The law of change in the remaining unknown parameters is set by assumptions regarding deformation of the polymer matrix composite and its layers during loading. To carry out the calculation, it is necessary to set the initial values of the elastic properties of the unidirectional material of the layers, which should be well consistent with the initial values of the elastic properties of the structure under study determined from the experiment. According to the developed algorithm, calculated dependences between average stresses, deformations and secant elastic properties of the layers of the structure are obtained (0°/90°/90°/0°) made of fiberglass E-Glass/MY750 using experimental data from the literature. Calculations carried out for three sets of initial values of the elastic properties of the material under study showed qualitatively identical results. The transverse tensile stress in the 90° layer reaches a maximum in the first half of the stress-strain diagram, and then decreases to zero. A similar stress in the 0° layer reaches a maximum at the failure point of the structure under study. It is revealed that the maximum calculated values of transverse stresses acting in layers 0° and 90° noticeably exceed the transverse tensile strength of the material specified in the literature. The longitudinal tensile stress in the 0° layer reaches a maximum at the failure point and corresponds to 95% of the value of the longitudinal tensile strength of the material. The longitudinal compressive stress in the 90° layer is at a low level throughout the deformation process of the structure under study. The results of this study can be recommended for developing models of the behavior of layers with cracks in the matrix when loading a polymer matrix composite.