Numerical Simulation of Composite Materials

Composite materials bring together the individual properties of physically different phases or components with the aim of creating a material which shows new and superior properties compared to the individual components. An important class of engineering materials is short fiber composites, which typically consist of a polymer matrix reinforced by glass or carbon fibers with an average length of several hundred microns. The presence of the fibers in the polymer matrix increases the stiffness, strength, toughness and dimensional stability. Polymeric short fiber composites can be processed by conventional polymer manufacturing techniques, such as injection molding, compression molding, extrusion, etc. Advanced engineering properties and easy processing have already considerably increased the fraction of polymeric short fiber composites in the automotive and the sports equipment industry.

In order to maximize the usage of this class of materials it is necessary that reliable and accurate simulation techniques are available in order to predict the behavior of short fiber composites in operation. In the Institute of Polymers at ETH Zürich a generic finite element simulation technique has been developed.[1,2] This approach enables one to generate realistic 3D computer models of short fiber composite microstructures and to construct periodic morphology-adaptive finite element meshes with a sophisticated meshing algorithm. The finite element mesh is then used to calculate the overall, effective properties of the composite numerically, based on the properties of the fiber and matrix phases. In collaboration with the University of Leeds (UK), the numerical methodology has been validated against experimentally measured properties.[3] This study revealed that this new simulation technique is highly accurate, thus being valuable in practice in order to reliably predict the effective properties of short fiber reinforced plastic parts.

Figure 1. Left: Computer model comprising 150 fibers of aspect ratio 37 at a concentration of 8 vol%. Periodic boundary conditions are applied at the boundaries of the cubic unit cell. Right: Cut through the periodic unstructured morphology-adaptive finite-element mesh which consisted of several million tetrahedrons.

If one looks at the microstructure of complex injection molded parts one can see that locally, the degree of fiber alignment varies due to different local velocity fields during injection molding. There already exists commercial software (Moldflow, Sigmasoft, etc.) which enables the simulation of the mold filling process and the prediction of the distinct local fiber orientation states in an injection molded part. If one were able to assign the appropriate material properties to each section with a particular fiber orientation state this would permit simulation with a structural finite element software (for example Ansys, Abaqus, etc.). Consequently one could then predict and explore the part’s behavior under a variety of expected operation stress states and hence significantly simplify the design process.

Figure 2. Injection molded short fiber reinforced part whose local fiber orientation states were calculated by Sigmasoft.[4] The arrows show the preferred fiber orientation and the colors the degree of fiber alignment (blue: low, white: high).

To bridge this gap between mold filling simulations and structural finite element calculations the numerical approach of Gusev is highly suitable because it can provide accurate elastic, thermal, electrical and transport properties for any local fiber orientation state. It is clear that it would be very time consuming to numerically calculate the effective properties for every single fiber orientation state in an injection molded part. It has been shown, however, that the orientation averaging scheme, which is basically a weighted average of unidirectional composite properties, is appropriate to accurately predict the properties of any fiber orientation state.[5] The only prerequisite is reliable properties for unidirectional short fiber composites which can be readily calculated by the finite element approach.[6]

In our publications we have demonstrated that accurate property predictions for short fiber composites with complex morphologies can be made. Clearly in future the demand for reliable simulation techniques, which enable the development of high-quality industrial goods in a shorter time of period, will grow. With our research we intend to enhance this progression towards high-quality and environmentally efficient industrial goods as well as helping to reduce development time and promote cost-intensive product developments.[7]

Authors

Hans Rudolf Lusti, Andrei Gusev
Department of Materials Science, Institute of Polymers

References

1. A.A. Gusev, J. Mech. Phys. Solids 1997, 45, 1449-1459.
2. A.A. Gusev, Macromolecules 2001, 34, 3081-3093.
3. H.R. Lusti, P.J. Hine, A.A. Gusev, Comp. Sci. Tech. 2002, 62, 1927-1934.
4. L.H. Kallien, 18. CAD-FEM User’s Meeting, Friedrichshafen, September 20-22, 2000.
5. A.A. Gusev, H.R. Lusti, P.J. Hine, Adv. Eng. Mater. 2002, 4, 927-931.
6. A.A. Gusev, M. Heggli, H.R. Lusti, P.J. Hine, Adv. Eng. Mater. 2002, 4, 931-933.
7. Palmyra. Materials Simulation GmbH, Zürich, Switzerland, http://www.matsim.ch.