Computational developments for simulation based design: Multi-scale physics and flow/thermal/cure/stress modeling, analysis, and validation for advanced manufacturing of composites with complex microstructures

Abstract

In the process modeling and manufacturing of large geometrically complex lightweight structural components comprising of fiber-reinforced composite materials with complex microstructures by Resin Transfer Molding (RTM), a polymer resin is injected into a mold cavity filled with porous fibrous preforms. The over-all success of the manufacturing process depends on the complete impregnation of the fiber preform by the polymer resin, prevention of polymer gelation during filling, and subsequent avoidance of dry spots. Since the RTM process involves the injection of a cold resin into a heated mold, the associated multi-physics encompasses a moving boundary value problem in conjunction with the multi-disciplinary and multi-scale study of flow/thermal/cure and the subsequent prediction of residual stresses in side the mold cavity. Although experimental validations are indispensable, routine manufacture of large complex structural geometries can only be enhanced via computational simulations; thus, eliminating costly trial runs and helping designers in the set-up of the manufacturing process. This manuscript describes an in-depth study of the mathematical and computational developments towards formulating an effective simulation-based design methodology using the finite element method. The present methodology is well suited for applications to practical engineering structural components encountered in the manufacture of complex RTM type lightweight composites, and encompasses both thick and thin shell-type composites with the following distinguishing features: (i) an implicit pure finite element computational methodology to track the fluid flow fronts with illustrations first to isothermal situations to overcome the deficiencies of traditional explicit type methods while permitting standard mesh generators to be employed in a straightforward manner: (ii) a methodology for predicting the effective constitutive model thermophysical properties, namely, the permeability tensor of the fiber preform microstructures in both virgin and manufactured states, the conductivity tensor, and the elasticity tensor; (iii) extension of the implicit pure finite element methodology to non-isothermal situations with and without influence of thermal dispersion to accurately capture the physics of the RTM process; (iv) stabilizing features to reduce oscillatory solution behavior typically encountered in the numerical analysis of these classes of problems: and (v) as a first step, preliminary investigations towards the prediction of residual stresses induced in the manufacturing process during post-cure cool-down. The underlying theory and formulations detailing the relevant volume averaging and homogenization techniques are first outlined for the multi-scale problem. Then the implicit pure finite element methodology, followed by the models for permeability prediction, is presented and compared for the case of isothermal mold filling. Applications of the pure finite element method is next extended to non-isothermal situations to accurately capture the flow/thermal/cure effects and the physics of the RTM process. Subsequently, a preliminary attempt is made to integrate the developments with the problem of thermoelasticity for residual stress prediction during post-cure cool-down. Where applicable, extensive validations of numerical results are made with analytical solutions and/or available experimental data. From these comparisons, relevant conclusions are drawn about the effectiveness of the present developments and their subsequent application to large-scale practical analysis of fiber-reinforced composite structures. Finally, some future directions relevant to the present study encompassing the multi-physics and multi-scale aspects of fibrous preforms with complex microstructures for use in lightweight composites are outlined.