## Multi-scale modeling of heterogeneous adhesives: Effect of
particle decohesion

M.G. Kulkarni^{1}, P.H. Geubelle^{1} and K. Matous^{1,2}^{}

^{1}Department of Aerospace Engineering

^{2}Computational Science and Engineering

University of Illinois at Urbana-Champaign

Urbana, IL 61801, USA.

#### Abstract

We examine the microscopic toughening mechanisms and their effect on
the macroscopic failure response of heterogeneous adhesives made of
stiff particles embedded in a more compliant matrix. The analysis
relies on a multi-scale cohesive framework first described in Matouš et
al. [Matouš, K., Kulkarni, M., Geubelle, P., 2008. Multiscale cohesive
failure modeling of heterogeneous adhesives. Journal of the Mechanics
and Physics of Solids 56, 1511–1533]. Two microscopic constitutive
failure models are incorporated: an isotropic damage model to capture
the fracture response of the matrix and a cohesive law to model the
inclusion-matrix interfacial debonding. A detailed study of the RVE
size is presented followed by a set of examples that illustrate the
effect of filler size, volume fraction and particle–matrix interface
properties on the macroscopic effective traction-separation law of
heterogeneous adhesives.

#### Conclusions

A multi-scale cohesive scheme has been used to study the failure
processes occurring at the micro-scale in heterogeneous adhesives and
their effect on the macroscopic cohesive response. A study of the RVE
size has shown that the microscopic domain width has to be about 2 or 3
times the layer thickness for the macroscopic response to be
representative for the loading histories considered. The effect of
particle size, volume fraction and particle–matrix interfacial
parameters on the failure response and effective macroscopic properties
has been analyzed. In contrast to the perfect particle–matrix interface
case, where the failure is of adhesive–cohesive nature, a weak
interface between the constituents generally results in a cohesive type
of failure. The presented response curves (Figs. 5(b), 10(b), 11(b),
and 12(b)) could be used as design diagrams to yield a potentially new
heterogeneous adhesive with desired macroscopic properties.

#### Acknowledgment

The authors gratefully acknowledge the support from the National
Science Foundation for this work under Grant No. CMS 0527965. The
authors also acknowledge the support from the Center for Simulation of
Advanced Rockets (CSAR) at the University of Illinois,
Urbana-Champaign. Research at CSAR is funded by the US Department of
Energy as a part of its Advanced Simulation and Computing (ASC) program
under Contract No. B523819.

© 2009 UIUC and Dr. Karel
Matous