ABSTRACT of the Doctoral Thesis
Metal matrix composites, although not as widely used as polymer matrix composites, are currently a subject of great interest. Metal matrices provide greater strength and stiffnesses than those provided by polymers. Fracture toughness is superior and MMCs offer less-pronounced anisotropy and greater temperature capability than do their polymeric counterparts. Although most metals and alloys could serve as matrix materials, in practice the choice is limited to light metals (especially aluminum, magnesium, and titanium) because of the benefit in weight.
Over the past 20 years, the MMCs have undergone rapid development, so that they are now available for commercial use. First commercial applications were found in aerospace engineering, whereas today some companies in the automotive industry are about to use them. However, the main point of interest, due to the high cost of fabrication, is restricted to the aerospace/military industry. Besides these applications, MMCs have potential applications in the medical and sports-equipment industry, too.
To make use of the superior behavior of these composites special material models are required. Hence the present thesis is concerned with the inelastic mechanical response of MMC's. Emphasis is put on the macromechanical behavior. However, to take advantage of the high performance it is necessary to introduce some micromechanical assumptions with respect to the internal structure of the composite. The materials considered here are unidirectionally longfiber-reinforced laminates under the assumption of mechanical static or quasistatic loadings. Furthermore, the investigation is extended to account for laminated composites.
First an existing micromechanical model is adopted for use in conjunction with 3/D brick finite elements. Derivation of constitutive equations and implementation into a general purpose finite element code are shown. To reduce computational time and error some remarks on the numerical integration of the material law are given. Results predicted by this model are in good agreement with experimental results. To study localized effects in the two constituents (fiber and matrix) a more detailed micromechanical finite element analysis of a unit cell under the assumption of periodic arrangement of the fibers is carried out. This analysis also studies the influence of the type of packing of the fibers.
The model is extended to account for 3/D degenerated shell finite elements. To derive the elastic-plastic material behavior in terms of stiffnesses directly, as necessary for the displacement type of finite element analysis, a mixed stress-strain-space formulation is used. The derived constitutive equations are then implemented into a shell finite element to incorporate both, material and geometric, nonlinearities. Since the shell finite element formulation is based on a layered approach to account for through-the-thickness plasticity, the element is capable of calculating the inelastic response of laminated MMCs.
With respect to large displacements and rotations but small strains a total Lagrangian formulation is used. The element is capable of solving buckling and post-buckling problems due to the modified Riks-Wempner iteration algorithm used. Furthermore, the supplementary eigenvalue analysis is used to detect stability limits and buckling modes. Several numerical examples including material and geometric nonlinearities are given.