Numerical analysis and optimal design of composite thermoforming process.

Abstract

The primary goals of this research are to analyze the thermoforming process of continuous fiber reinforced thermoplastic composites by the finite element method, and to optimally design this composite forming process using the numerical optimization algorithm with design sensitivity analysis. For the forming stage of this process, the flow rheology of continuous fibrous composites was characterized by the homogenization method, assuming that the matrix is a viscous fluid and the fibers are instantaneously rigid solids suspended in this fluid during processing. For the consequent cooling stage, the materials were assumed to behave elastically. Based on these assumptions, the homogenization method can decouple the processing governing equations into the macroscopic and microscopic relations for the forming and cooling problems. The global-local finite element method was then developed that enables us to solve the microscopic equations for the homogenized properties using the local FEM, and to simulate this process using the global FEM. For the forming stage, this global FEM analysis consists of the shaping and heat transfer simulations, taking into account large deformation and contact conditions. The fiber orientation of the microstructures was predicted using a kinematic model to keep track of the microstructure change due to large deformation. For the cooling stage, this global FEM analysis was implemented to calculate residual stresses and warpage, taking into account the temperature and crystallinity dependency of the elastic properties. Thus, this global-local FEM analysis with the localization of the homogenization method is capable of predicting global and local deformation mechanics during processing. For process optimization, the design objective was to achieve a uniform final thickness distribution by designing the preheated composite temperature field. The finite difference approximation was utilized to evaluate the design sensitivities. Using the FEM developed in the first part as the analysis tool, the optimization scheme can allow process designers to optimally design this process. Finally, a number of numerical examples have been performed to demonstrate the combined analysis and optimization algorithm.