Closed-form solution for process-induced stresses and deformation of a composite part cured on a solid tool: Part I – Flat geometries

Dimensional control can be a major concern in the processing of composite structures. Numerical models based on the finite element method are increasingly being used to predict process-induced deformations. However, finite element analyses are costly to set up and run, and often do not lead to any insight into the physics of the problem, thus making the interpretation of their results difficult. In this work, a closed-form analytical model based on the theory of elasticity is developed to analyse the process-induced stresses and deformations that develop during the curing process of a composite flat part laid up on a solid tool. Specifically, analytical expressions are derived for the through-thickness variation of axial stresses in flat composite parts subjected to a temperature history, taking into account the evolution of material properties with advancement in cure. Despite many simplifying assumptions that are made in the course of the analytical development, the successful comparisons between the closed-form and the finite element solutions show the effectiveness of the current analytical model in capturing the underlying mechanisms that are involved in the processing of flat composite structures. In a companion paper, the current analytical methodology is extended to treat curved geometries.