ABSTRACT of the Doctoral Thesis
The present thesis is concerned with the computational simulation of Metal Matrix Composites (MMCs), a material where particulate reinforcements are embedded in a metal phase, and which bears the potential to be tailored to particular applications. The objective of this work is to improve computational predictions, on the one hand, of the thermo-mechanical behavior in frictional contact and, on the other hand, of the elasto-plastic properties of MMCs undergoing finite strains. Both topics follow a hierarchical approach employing micromechanical methods within the continuum mechanics approach.
The first executive chapter deals with computational predictions of the tribological behavior of MMCs. The influence of particle volume fraction and clustering of particles is investigated at different length scales. Finite Element simulations are performed employing periodic unit cells based on homogeneous, randomly distributed inclusions in a matrix phase with 30% particle volume fraction. In addition, the present work introduces modified unit cells with 10% particle volume fraction, with both homogeneous random and clustered distributions. These modifications are derived from the original cell by either randomly removing inclusions in the former case, or from a predefined area in the latter case. Based on these experiences, numerical simulations employing the Finite Element Method (FEM) of the frictional behavior of a MMC material, including heat conduction in the steady state, are performed. Experiments and analytical calculations serve to determine certain unknown process parameters by employing a simplified model by means of homogenizing the material. Within the scope of this model, heat transfer and conduction are described. In the FEM simulations, the inhomogeneous body is considered. Limitations of the thermo-elastic FEM predictions are related to frictionally excited thermo-elastic instability, the stability limit is estimated analytically using two different approaches from the literature and compared to the simulation findings. The limited number of experimental tests does not allow for quantitatively reliable results but the analytical and the FEM simulations' predictions are qualitatively compared. The practical consequences of thermoelastic instability are discussed.
The second executive chapter deals with computational simulations of elasto-plastic properties of a particulate metal matrix composite (MMC) undergoing finite strains. Two different procedures are utilized for homogenization and localization; an analytical constitutive material law based on a mechanics of materials approach, and a periodic unit cell method. Investigations are performed on different length scales -- the macroscale of the component, the mesoscale where the MMC is regarded as homogenized material, and the microscale corresponding to the particle size. The FEM is employed to predict the macroscopic response of a MMC component. Its constitutive material law has been implemented into the employed FEM package, based on the incremental Mori Tanaka (IMT) approach and extended to the finite strain regime. This approach gives access to the meso-scale fields as well as to approximations for the micro-scale fields in the individual MMC phases. Selected locations within the macroscopic model are chosen to extract general loading histories. These deformation and temperature histories are applied to unit cells using the periodic microfield approach (PMA). As a result, mesoscopic responses as well as highly resolved microfields in the matrix and the particles are available. A Gleeble-type experiment employing an MMC with 20%vol of particles is investigated as an example. Comparisons of the IMT and the PMA are performed on the macro-, meso-, and microlevels to investigate if the IMT is a tool capable of predicting the behavior of an entire MMC component in the first place, and to assess its limits.
The two constitutive laws, Incremental Mori-Tanaka and J2-plasticity, are compared to determine how large an error is made (on the mesoscopic level) if the behavior of the inhomogeneous material is described by a homogeneous, isotropic material model employing the uniaxial stress-strain curve of the MMC and adopting J2-plasticity for the post-yield regime. Furthermore, a method to address mesoscopic strain concentration of periodic unit cells under certain circumstances is presented.