W.A. Curtin
The strength and reliability of most fiber-reinforced composites depend on the strengths of the fibers, which are brittle materials and must thus be described statistically. Composite performance then depends on the statistical distribution of fiber- strengths and the manner in which load is transferred from broken to unbroken fibers as some fibers break under loading. The resulting strength of the composite is also statistical, and depends on the composite volume. Predicting and understanding the evolution of damage in a fiber composite is a important but difficult problem, and only limited analytical progress has been made to date.
Our new research in this area is focused on numerically intensive simulation studies of fiber composite failure. The fiber composite is mapped onto a discrete anisotropic lattice of elastic elements which represent the elastic fibers and the slip between fibers and matrix; each fiber element is assigned a strength selected from the desired strength distribution, and the anisotropy of the lattice controls the load transfer. The inhomogeneous distribution of stresses throughout the composite is calculated numerically using the 3D Green Functions appropriate to the anisotropic elastic lattice. This requires the inversion of a matrix which is on the order of the composite volume. However, one inversion must be made for each damage state of the system as the fiber damage evolves, until failure occurs, which then represents one single composite strength value at the selected composite size, fiber distribution, and load transfer. The entire procedure must be repeated many times to generate statistical distributions, and on increasingly larger system sizes to garner information on size scaling. Since laboratory composites typically contain 100,000 fibers in a cross-section, and actual components are many times larger, volume scaling is a critical issue and requires simulations on systems as conceivable. Visualization of these results are also an important where 3D visualization tools have already been developed in GL to aid in the interpretation of simulation results. Visualization of results will be developed first on workstations and where particulary complex 3D structures are involved our reserach can benefit from access to CAVE resources.
The numerical intensity requires the use of advanced work stations for program development and initial studies. Current work is being carried out on a SGI Indigo 2. Individual runs on composites containing only 100 fibers required about 1 hour of CPU time. For larger systems, 2500 fibers, tile time per run increases rapidly, as does the required memory. Access to multiple machines of the same type through a transparent network could allow for some parallel operation, which would increase speed by factors of 20-40. Access to larger machines will permit larger system sizes to be investigated far more systematically then presently.