Multiscale Damage Modeling of Solid Propellants: Theory and
Computational Framework
K. Matous1,2, H.M Inglis1,
X. Gu1, D. Rypl3, T.L
Jackson1 and P.H. Geubelle1,2
1Center for Simulation of Advanced Rockets
2Department of Aerospace Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.
3Department of Structural Mechanics
Czech Technical University in Prague
Prague, 160 00 P6, Czech Republic
Abstract
The present work provides a theoretical and computational framework
for modeling the macroscopic/microscopic behavior and interfacial
decohesion of grains during propellant loading. The micro-scale is
characterized by a unit cell, which contains micro-constituents
(grains) dispersed in a polymeric blend. We have used a packing
algorithm, treating the ammonium perchlorate (AP) as spheres or discs,
which enables us to generate packs which match the size distribution
and volume fraction of actual propellants. Then a novel technique to
characterize the pack geometry suitable for meshing is described and
a powerful mesh generator is employed to obtain high quality periodic
meshes with refinement zones in the regions of interest. The proposed
numerical multiscale framework, based on the mathematical theory of
homogenization, is capable of predicting non-homogeneous
micro-fields and damage nucleation and propagation along the particle
matrix interface, as well as the macroscopic response and mechanical
properties of the damaged continuum. Examples are considered involving
simple unit cells in order to illustrate the multiscale algorithm and
demonstrate the complexity of the underlying physical processes.
Conclusions
A fully automated mathematical/numerical framework for multiscale
modeling of heterogeneous propellants from particle packing up to
grain failure has been proposed. The microscale description is based
on a periodic unit cell consisting of particles dispersed in a blend
and incorporates the local non-homogeneous stress and deformation
fields present in the unit cell during the failure of the
particle/matrix interfaces. A packing algorithm, treating the ammonium
perchlorate particles as spheres or discs, is used to generate packs
which match the size distribution and volume fraction of actual
propellants. Moreover, a sophisticated preprocessing tool is developed
to generate a geometric model based on Bezier curves and/or surfaces,
shrink particles in contact and compute nonuniform mesh density
parameter. This geometric model is then used in $T3d$, a powerful
meshing tool, to create high quality periodic meshes. Since the
identical meshing of the mirrored/periodic entities using the
advancing front technique seems not to be viable, a different
approach, based on mapping, has been adopted. Next, the mathematical
theory of homogenization based on the asymptotic expansion of the
displacement, strain and stress fields has been derived and used in
modeling debonding (or dewetting) damage evolution in reinforced
elastomers subject.
Various examples involving 2D unit cells and macroscopic deformation
histories of an idealized solid propellant have been considered to
study the link between the failure process taking place at the
particle scale and its effect on the macroscopic stress-strain curves
and the evolution of void volume.
The emphasis of this work has been to develop a design tool from
particle packing to grain failure. Further research will
involve a more complex, rate dependent description of the matrix and
matrix tearing model needed to capture the initiation and propagation
of matrix cracks between the voids. Also the three dimensional
parallel solver based on our recent work is currently under
development. Such parallel solver will allow us, together with the
packing/preprocessing/meshing tool proposed here, to provide more
reliable predictive results on larger more representative assembly of
particles, possibly of different sizes.
Acknowledgment
The work of K. Matous, H.M. Inglis, X. Gu, T.L. Jackson and
P.H. Geubelle was supported by the Center for Simulation of Advanced
Rockets (CSAR) under contract number B341494 by the U.S. Department of
Energy as a part of its Advanced Simulation and Computing program
(ASCI). The work of Dr. Rypl was supported by the Grant Agency of the
Czech Republic under contract number GACR 103/05/2315.
© 2006 UIUC and Dr. Karel
Matous