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Research Papers

# An Orthotropic Integrated Flow-Stress Model for Process Simulation of Composite Materials—Part I: Two-Phase Systems

[+] Author and Article Information
Sina Amini Niaki, Anoush Poursartip

Composites Research Network (CRN),
Departments of Civil Engineering and Materials
Engineering,
The University of British Columbia,

Alireza Forghani

Convergent Manufacturing Technologies Inc.,

Reza Vaziri

Composites Research Network (CRN),
Departments of Civil Engineering and Materials
Engineering,
The University of British Columbia,
e-mail: reza.vaziri@ubc.ca

1Corresponding author.

Manuscript received June 5, 2018; final manuscript received October 25, 2018; published online January 25, 2019. Assoc. Editor: Martine Dubé.

J. Manuf. Sci. Eng 141(3), 031010 (Jan 25, 2019) (15 pages) Paper No: MANU-18-1391; doi: 10.1115/1.4041861 History: Received June 05, 2018; Revised October 25, 2018

## Abstract

An integrated flow-stress (IFS) model provides a seamless and mechanistic connection between the two distinct regimes during the manufacturing process of composite materials, namely, fluid flow in the pregelation stage of the thermoset resin and stress development in the composite when it acts as a solid material. In this two-part paper, the two- and three-phase isotropic IFS models previously developed by the authors are extended to the general case of composite materials with orthotropic constituents. Part I presents the two-phase, fluid-solid, orthotropic model formulation for the case where the fluid phase solidifies during the course of curing. Part II extends the orthotropic formulation to a three-phase model that includes a gas phase as the third constituent of the composite material system. A broader definition of material properties in poroelasticity formulation is adopted in the development of the general orthotropic formulation. The model is implemented in a two-dimensional (2D) plane strain $u$-$v$-$P$ finite element (FE) code and its capability in predicting the flow-compaction behavior and stress development is demonstrated through application to a case study involving an L-shaped unidirectional laminate undergoing curing on a conforming convex tool. Comparison of the results with those obtained from sole modeling of the stress development reveals the importance of capturing the simultaneous and interactive effect of the mechanisms involved during the entire process cycle using an IFS modeling approach presented in this paper.

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## Figures

Fig. 1

A schematic representation of the two-phase unidirectional composite system and its constituents considered in this study

Fig. 2

A schematic showing the evolution of the properties of the solid/solid-skeleton and fluid phases with increasing solidity of the fluid phase during processing

Fig. 3

Algorithm for the FE implementation of the two-phase IFS model

Fig. 4

Geometry and boundary conditions for the single element orthotropic sample undergoing curing in Example 1

Fig. 5

Time-histories of (a) applied temperature and predicted viscosity and (b) predicted degree of cure (χ) and solidification factor of material (λ) for Example 1

Fig. 6

Final deformed shape of the sample corresponding to example 1 shown in Fig. 4 for the different fiber orientations: (a) =0 deg, (b) β=45 deg, and (c) β=90 deg

Fig. 7

Predicted time-histories of the (a) resin velocity through the right boundary, (b) resin velocity through the top boundary, (c) normal strain for β=0 deg and β=90 deg, (d) shear strain for β=45 deg, (e) normal stress for β=45 deg, and (f) shear stress for β=45 deg in Example 1

Fig. 8

Half-geometry and boundary conditions for a unidirectional L-shaped laminate processed on a convex tool; location of key points A, B, and C used for interrogation of the process model in Example 2. Dashed lines show the mid-plane of the laminate.

Fig. 9

Time histories of autoclave and part temperatures (a) and predicted evolution of state variables and material properties including resin viscosity (a) degree of cure and solidification factor (b), and resin bulk and shear moduli (c) corresponding to Example 2

Fig. 10

Different FE meshes used in the analysis of the L-shaped laminate (shown in Fig. 8) for investigating convergence of the numerical solutions

Fig. 11

(a) Predicted deformed shape of the laminate (deformations are scaled up by a factor of 2 for better visualization), (b) normal (through-thickness) displacement of critical points A, B, and C through the curing process, and (c) tangential (longitudinal) displacement of the laminate's edge at different times during processing of the laminate shown in Fig. 8 (Example 2)

Fig. 12

Fringe plots showing the predicted spatial distribution of the fiber volume fraction, φf, at different instants of time during processing of the L-shaped laminate shown in Fig. 8 (Example 2)

Fig. 13

Distribution of the resultant axial force (a) and the resultant bending moment (b) along the mid-plane of the laminate at three different times during the processing of the L-shaped laminate in Example 2 showing the comparison between the predictions of the stress model and the current IFS model

## Errata

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