Computational Physics Group

Cohesive Modeling of Dewetting in Particulate Composites: Micromechanics vs. Multiscale Finite Element Analysis

H.M Inglis¹, P.H. Geubelle², K. Matous^2,3, H. Tan¹ and Y. Huang<sup>1

1</sup>Department of Mechanical Engineering
²Department of Aerospace Engineering
³Center for Simulation of Advanced Rockets
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.

Abstract

The effect of damage due to particle debonding on the constitutive response of highly  filled composites is investigated using two multiscale homogenization schemes: one based on a closed-form micromechanics solution, and the other on the  finite element implementation of the mathematical theory of homogenization. In both cases, the particle debonding process is modeled using a bilinear cohesive law which relates cohesive tractions to displacement jumps along the particle matrix interface. A detailed comparative assessment between the two homogenization schemes is presented, with emphasis on the effect of volume fraction, particle size and particle-to-particle interaction.

Conclusions

We have performed a detailed comparative assessment of micromechanics and finite element based homogenization schemes for the problem of debonding damage in a 2-D particulate composite. Special emphasis has been placed on the ability of the two schemes to capture particle-to-particle interactions and
the effect of dissimilar particle sizes.
The 2-D micromechanics model developed by Tan et al. (2005a) is effective at capturing key features of the macroscopic stress-strain response for minimal computational effort. The shortcomings of this model are that it cannot capture the instability inherent in the system or the heterogeneous stress and strain  fields. In a highly filled composite, interactions between particles are a significant contributor to failure through local stress concentrations and the occurrence of localization. The micromechanics model does not capture these interactions during the failure process, and hence ceases to be predictive under high volume fraction, f > 0:5, when stress concentrations begin to play a significant role in the solution, or when the particle distribution is random, resulting in localization. Both models demonstrate that, for large differences in particle diameters, it is unnecessary to model the debonding of smaller particles, but is sufficient to represent their contribution to damage nucleation and to the stiffness of the matrix.
The ability of the MTHFE code to function as a direct numerical simulation for validation of simpler models has been demonstrated. The MTH-based code has an ability to capture a richness of detail about the physical response of the system. The method is capable of solving more complex loading cases, and can be extended to include different material models.

Acknowledgment

This work was supported by the Center for Simulation of Advanced Rockets (CSAR) under contract number B341494 by the U.S. Department of Energy. K. Matous and P. H. Geubelle also acknowledge support from ATK/Thiokol (Program Managers, J. Thompson and Dr. I. L. Davis). H. Tan and Y. Huang acknowledge additional support from ONR Composites for Marine Structures Program (Grant N00014-01-1-0205, Program Manager Dr. Y.D.S. Rajapakse).

© 2009 Notre Dame and Dr. Karel Matous