Rauter, Natalie

Indentation tests are widely used to characterize the material properties of heterogeneous materials. So far there is no explicit analysis of the spatially distributed material properties for short fiber-reinforced composites on the mesoscale as well as a determination of the effective cross-section that is characterized by the obtained measurement results. Hence, the primary objective of this study is the characterization of short fiber-reinforced composites on the mesoscale. Furthermore, it is of interest to determine the corresponding area for which the obtained material parameters are valid. For the experimental investigation of local material properties of short fiber-reinforced composites, the Young’s modulus is obtained by indentation tests. The measured values of the Young’s modulus are compared to results gained by numerical simulation. The numerical model represents an actual microstructure derived from a micrograph of the used material. The analysis of the short fiber-reinforced material by indentation tests reveals the layered structure of the specimen induced by the injection molding process and the oriented material properties of the reinforced material are observed. In addition, the experimentally obtained values for Young’s modulus meet the results of a corresponding numerical analysis. Finally, it is shown, that the area characterized by the indentation test is 25 times larger than the actual projected area of the indentation tip. This leads to the conclusion that indentation tests are an appropriate tool to characterize short fiber-reinforced material on the mesoscale.

The present work provides a profound analytical and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.

In recent research on Structural Health Monitoring (SHM) guided waves, especially nonlinear Lamb waves, turned out to be a suitable means for monitoring material deterioration in thin-walled structures. In the corresponding numerical simulations on wave propagation the nonlinear elastic theory by Murnaghan is often implemented, which requires 14 material parameters for transversely isotropic materials. Enhancing an existing linear strain energy potential, a new nonlinear hyperelastic transversely isotropic material model is introduced which reduces the number of independent material parameters to six. In order to verify the applicability of the presented material model with respect to the simulation of nonlinear wave propagation in composite structures, and the generation of higher harmonic wave modes, the existence of a power flux from the fundamental to the higher harmonic mode is investigated analytically and numerically. Analytical considerations show that this power flux exists like in Murnaghan's theory. For the numerical validation the S0–S0 mode pair in the low frequency range is used. Therefore, the amplitude of the second harmonic wave mode is oscillating with increasing propagation distance. This behavior is in excellent agreement with the theoretical prediction. It is shown further, that even for an oscillating behavior the amplitude of the second harmonic mode can be approximated by a linear curve fit over a considerably propagation distance and hence shows a quasi cumulative behavior. Therefore, the introduced material model is an advantageous alternative to Murnaghan's theory to simulate the second harmonic Lamb wave generation due to in composite structures. © 2017 Elsevier Ltd