*Proceedings of the 5th World Congress on Computational
Mechanics (WCCM-V)*
(Eds. H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner),
paper # 80869, 2002

### 3D FINITE ELEMENT UNIT CELL STUDY OF PARTICLE FAILURE IN
BRITTLE PARTICLE REINFORCED DUCTILE MATRIX COMPOSITES

A. Eckschlager and H.J. Böhm

CDL Functionally Oriented Materials Design,

Institute of Lightweight Structures and Aerospace
Engineering,

TU Wien,
Vienna, Austria

**Abstract** -
The aim of the present contribution is the modeling of the brittle failure of
particles embedded in a ductile matrix subjected to global uniaxial loading.
The study is based on three-dimensional multi-particle unit cells and uses the
Finite Element method.
Appropriate microgeometries are generated by randomly arranging a number of
spherical particles within the unit cell, a variant of the Random Sequential
Adsorption (RSA) method modified for compatibility with periodic boundary
conditions being employed.
Elastic material properties are used for the particles and the matrix is
described by J2 plasticity.
Predefined fracture surfaces, which are assumed to be perpendicularly oriented
with respect to the overall uniaxial load, are provided for within the
reinforcements.
Brittle failure of the reinforcements, which is modeled as an instantaneous
cleavage at these surfaces, is implemented by a node release technique.
Failure in a given particle is controlled by Weibull-type fracture
probabilities in combination with a Monte Carlo algorithm.
The fracture probabilities are evaluated for the whole particle on the basis
of the current stress distribution.

Within the modeling assumptions used, which include neglecting other local
failure mechanisms such as ductile damage of the matrix and decohesion at the
interface between the constituents, successive particle cleavage and the
resulting stress redistribution effects are simulated.
Results are presented in terms of predictions for the overall stress vs.~strain
behavior and for damage relevant fields at the microscale.

(hjb,020523)