Mechanics of Materials 109 (2017) 51–66 Contents lists available at ScienceDirect Mechanics of Materials journal homepage: www.elsevier.com/locate/mechmat A two-phase integrated flow-stress process model for composites with application to highly compressible phases Sina Amini Niaki, Alireza Forghani, Reza Vaziri ∗ , Anoush Poursartip Composites Research Network (CRN), Departments of Civil Engineering and Materials Engineering, The University of British Columbia, Vancouver, B.C., V6T 1Z4, Canada a r t i c l e i n f o Article history: Received 9 September 2016 Revised 25 March 2017 Available online 28 March 2017 Keywords: Thermoset matrix composites Resin flow Compressibility Residual stress Integrated flow-stress process model a b s t r a c t A new methodology is presented to integrate the simulation of flow and stress development into a uni- fied computational modelling framework for processing of two-phase composite materials. The governing equations are developed for the general case of a composite material system that, as a consequence of curing, undergoes a transition from a fluid-like state into an elastic solid. The constitutive equations em- ployed are such that they provide a continuous representation of the evolving material behaviour while maintaining consistency with the formulations that are typically used to represent the material at each of the two extremes. The formulation is capable of handling highly compressible phases, which is an im- portant consideration when extending the model to a three-phase model that includes gas as a distinct phase. The model is implemented in a 2D plane strain u-v-P finite element code developed in MATLAB. Numerical examples are presented to demonstrate the capability of the integrated flow-stress model to predict the flow-compaction and stress development throughout the curing process of thermoset com- posite materials. The interactive effects of resin flow and stress development under various representa- tive boundary conditions are investigated and comparisons are made with the predicted results obtained from the application of the stress model alone. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction Processing of fibre-reinforced polymeric composite materials is complex due to multitude of physical and chemical processes that occur at multiple scales during the manufacturing event. As the resin cures, it undergoes very diverse behavioural regimes such as viscous, rubber-like, and glassy behaviour at different stages of processing (Johnston et al., 1996; Hubert et al., 1999). This complex process involves various aspects such as flow of resin through the fibre-bed, thermochemical changes, heat transfer, and stress development. These phenomena are usually simulated by researchers and engineers in a so-called “integrated sub-model” based framework first applied to composite processing by Loos and Springer (Loos and Springer, 1983) and later by Bogetti and Gille- spie (1991, 1992), White and Hahn (1992), and other more recent work (Johnston et al., 1996; Hubert et al., 1999; Johnston et al., 2001; Arafath, 2007). In this approach, process modelling is car- ried out in several independent sub-models implemented in differ- ent software modules. Hubert et al. (1999) focused on the flow module for process- ing of composite materials with constituents that were assumed ∗ Corresponding author. E-mail address: reza.vaziri@ubc.ca (R. Vaziri). to be incompressible. They used Darcy’s equation for flow of resin along with Terzaghi’s effective stress theory (Terzaghi, 1943) for load sharing between the resin and the fibre-bed, which does not account for the deformability of the solid grains within the porous medium. In order to take into account the compressibil- ity of the phases, the flow model developed by Biot et al. (Biot, 1941; Biot and Willis, 1957) and its extension by Zienkiewicz and Shiomi (1984) can be considered. Biot et al. (Biot, 1941; Biot and Willis, 1957) developed equations to model consolidation of the porous media taking into account the compressibility of the phases through the introduction of some physical constants for the porous media. Zienkiewicz and Shiomi (1984) presented an alternative form of Biot’s model to be extended for dynamic behaviour of sat- urated porous media. They demonstrated the effectiveness of the model for slow compaction as well as shock excitation scenarios. The work by Gutowski et al. (1987) can be considered as one of the pioneering studies that applied such theories to consolidation of composite materials during curing. Celle et al. (2008 a, b) pro- posed a model for non-isothermal flow of fluid through porous media for resin infusion processes. Their model took into account deformation of the porous media as a result of applied pressure and temperature. Gigliotti (Gigliotti et al., 2007) used a thermo- chemically-elastic model in a finite element framework to predict residual stresses developed after the gel point during processing http://dx.doi.org/10.1016/j.mechmat.2017.03.016 0167-6636/© 2017 Elsevier Ltd. All rights reserved.