Department of Mechanical and Materials Engineering, **Machine** VP

University of Western Australia

**Three Dimensional Modelling of Metal Matrix Composites**

The mechanical properties of aluminium/silicon carbide composites are investigated using a fully three dimensional elastoplastic boundary element code. The matrix is allowed to deform plastically, while the ceramic reinforcement is assumed to be elastic. The three dimensional code allows the simulation of any reinforcement shape and position, in contrast to the commonly used axisymmetric or planar models. The simulations show that the geometry and orientation of the reinforcement particles can significantly alter the behaviour of the composites. Clustering of particles is also seen to have a significant effect, since the particles in a cluster are effectively joined together by small volumes of highly strain-hardened matrix material.

**What are the basic questions addressed?**

(i) Previous work of this sort has made use of simple two-dimensional models. This reduces the computational cost, but also imposes significant constraints on the reinforcement shape and distribution. This project has been directed at determining what further information can be obtained from a full three-dimensional analysis.

(ii) It has been observed experimentally that differential contraction of the matrix and reinforcement during cooling after heat treatment can cause significant plastic deformation. A three dimensional cooling model has been implemented to assess the importance of this effect.

**What are the results to date and the future of the work?**

(i) The three-dimensional analysis has allowed us to produce much more
realistic models of the physical system. As described in the outline, we have
found that the detailed particle shape is important. This information can only
come from the three-dimensional model. The model indicates that particle shape
and alignment do not greatly affect the elastic properties unless the volume
fraction exceeds approximately 20%. On the other hand, the particle shape is
important after the material yields, even at small volume fractions, since the
stress field around the particle determines the strain-hardening behaviour.
(ii) The model confirms that localised plastic deformation can be severe during
cooling from about 50^{0}C to room temperature. This effectively
pre-loads the particle and therefore has an effect on the properties of the
composite when subjected to subsequent loading. We have found that this
`residual strain' does greatly affect the properties of the material. In
particular, particle shape becomes important for both the elastic and plastic
(post-yield) properties. The residual strain tends to enhance the
strain-hardening of the composite.

Future work will focus on detailed modelling of actual materials by incorporation of experimentally determined characterisation data for the matrix and reinforcement materials.

**What computational techniques are used and why is a supercomputer
required?**

The boundary element method has been utilised due to its superior convergence characteristics. The three-dimensional analysis, however, implies a great deal of temporary data storage. This would normally be stored on disk, which considerably slows the calculation. The available memory of the supercomputer has allowed this data to be stored in core, thereby permitting large, realistic simulations to be performed.

**Publications**

*Three dimensional elastoplastic modelling of ceramic reinforced metal
matrix composites using the boundary element method*, A A Mammoli and M B
Bush, CADCOMP#94, International Conference on Computer Aided Design in
Composite Materials Technology, Southampton, July 1994.

*Numerical modelling of microstructural interactions in particulate
reinforced aluminium alloys (INVITED)*, A A Mammoli and M B Bush,
Australia-Korea Joint Seminar on Advanced Light Alloys, Taejon, Korea, October,
1994.

*The effects of reinforcement geometry on the elastic and plastic properties
of metal matrix composites*, A A Mammoli and M B Bush, Acta. Metall. Mater.,
in press.