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Karel Matous



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Damage evolution in particulate composite materials


K. Matous

Department of Mechanical Aerospace & Nuclear Engineering
Rensselaer Polytechnic Institute
110 8th Street, Troy, NY 12180

Abstract


Damage evolution in heterogeneous solids is modeled using transformation field analysis and imperfect interface model. Stress changes caused by local debonding are simulated by residual stresses generated by equivalent transformation strains or eigenstrains. Decohesion and both overall and local stress and strain rates are derived from thermodynamics of irreversible processes, which provide excellent framework for the development of constitutive equations. Both tangent and unloading secant stiffness tensors are found along any prescribed mechanical loading path. Numerical simulation of debonding evolution in glass/elastomer composites is compared with experimental data and provides good agreement between the model and experiments.

Conclusion


The proposed mathematical model based on Dvorak's transformation field analysis together with thermodynamics of irreversible processes and the internal state variables theory, which induces sufficient constraints against a set of possibilities that is too large, is shown to describe successfully the damage evolution in particularly reinforced elastomers. Stress changes caused by local debonding are simulated by residual stresses generated by equivalent transformation strains or eigenstrains, which are derived from Hashin's imperfect interface spring-layer model. The energy release rate is derived from the free energy function, and both the total and incremental strain-based formulations including loading tangent and unloading secant stiffness tensors are found for any loading path. The current numerical approach is limited to small deformations; however, good agreement between the model and experiments for the uniaxial tension test performed by Vratsanos and Farris was obtained for several densities of reinforcement. The material completely raptures before decohesion of all particles, especially for high reinforcement densities and thus much stiffer and brittle material. However, for low densities almost all particles debond before rupture, so that the material becomes porous and the fracture is very similar to ductile. Based on such observations, the material constraint condition for the percolation threshold of a closely packed reinforcement is proposed and limits the total decohesion. Further study is required to extend the model to cover the nonlinear deformation of matrix. Moreover, implementation of theory into a finite element code is necessary for the solution of complex geometry and/or boundary and loading conditions.

Acknowledgment


I wish to thank Professor G.J. Dvorak for helpful discussions.
2009 Notre Dame and Dr. Karel Matous