Modelling & Simulation


Simulation of an extrinsic self-healing polymer based on the micro-encapsulation approach using the theory of porous media

Joachim Bluhm, University of Duisburg-Essen, Essen, Germany
Steffen Specht, University of Duisburg-Essen, Essen, Germany
Jörg Schröder, University of Duisburg-Essen, Essen, Germany

In modern technical applications, e.g. in the fields of aerospace or energy generation, like wind turbine blades, the construction of strong but light structural parts is required. For that purpose polymers and polymeric composites are very useful. But they can lose a high rate of strength and stiffness due to damages which are initiated by micro-cracks or delamination. In order to prevent such micro-damages, materials with self healing ability can be used. For instance, materials where micro-capsules filled with a monomer, and catalysts are dispersed in the polymeric matrix. If a micro-crack propagates and ruptures such a capsule, the monomer flows into the crack, polymerizes due to reaction with the catalysts and closes the crack [1].

For the numerical simulation of such a multiphase material model, the Theory of Porous Media (TPM) is used [2, 3]. TPM is a continuum mechanical homogenization approach where internal interactions, like mass or temperature transfer, can be taken into consideration as well. Here, a thermodynamically consistent five phase model was developed, which consists of the solid matrix material, liquid healing agents, solid healed material, catalysts and gas representing the air in the cracks. For the description of damage (for the virgin as well as for the healed material) the well known (1-D)-approach is incorporated, with respect to the constitutive relations, for the stresses of both solid phases. Furthermore, the healing is described by a mass transition between the liquid like healing agents and the solid-like healed material.

The applicability of the model will be shown by comparison of a numerical simulation with an experimental result from [4].

[1] S.R. White, N.R. Sottos, P.H. Geubelle, J.S. Moore, M.R. Kessler, S.R. Sriram, E.N. Brown, and S. Viswanathan. Autonomic healing of polymer composites. Nature, 409:794--797, 2001.
[2] R. de Boer. Theory of porous media. Springer, 2000.
[3] W. Ehlers and J. Bluhm, editors. Porous media. Springer, 2002.
[4] E.N. Brown, N.R. Sottos, and S.R. White. Fracture testing of a self-healing polymer composite. Experimental Mechanics, 42:372--379, 2002.

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