A Semi-Analytical Model for Thermo-Mechanical Stress Analysis in Composite Laminates

Abstract

Composite materials made up of high modulus carbon fiber and thermoset resin have been used in advanced engineering structures across a range of sectors, such as oil exploration, aerospace, wind energy, among others. However, undesired small deformations occurs during the manufacturing of these materials, in the curing process responsible for perfect adhesion between the fiber and matrix constituents. These deformations result in residual stresses that can lead to geometric distortions in the final part or reduce the material's strength, a characteristic highly valued by designers when adopting composite materials. These residuals stresses originate from effects of different natures, such as thermal, chemical and even hygroscopic, which occur in the composite constituents due to thermal gradients and material characteristics under the conditions of humidity and pressure, interaction of the part with the mold, characteristics of each manufacturing process. The analysis and calculation of these stresses can be found in specialized literature; however, several authors, have developed adapted methodologies to calculate and predict deformations and stresses. The purpose of this study was to develop and implement a computational tool to simulate the effects of thermal residual deformations and stresses. The adopted approach is based on the Principle of Stationary of the Total Potential Energy of the system, allowing the analysis of linear or non-linear systems, considering the internal deformation energy and the potential of the forces applied to the system. The solution to the equilibrium of the system is to minimize the total potential energy, using the Rayleigh-Ritz approximation method to determine the generalized coefficients of the series of functions in the equilibrium equations, using Bardell functions to describe strain-displacement relations. The validation of the methodology is demonstrated through comparison with cases where closed solutions exist for mechanical loading problems, the exact solution for a thermal loading problem, and finite element simulations using the ABAQUS® commercial software, demonstrating the effectiveness of the adopted approach.