A computational modeling approach based on random fields for short fiber-reinforced composites with experimental verification by nanoindentation and tensile tests

Abstract

In this study a modeling approach for short fiber-reinforced composites is presented which allows one to consider information from the microstructure of the compound while modeling on the component level. The proposed technique is based on the determination of correlation functions by the moving window method. Using these correlation functions random fields are generated by the Karhunen–Loève expansion. Linear elastic numerical simulations are conducted on the mesoscale and component level based on the probabilistic characteristics of the microstructure derived from a two-dimensional micrograph. The experimental validation by nanoindentation on the mesoscale shows good conformity with the numerical simulations. For the numerical modeling on the component level the comparison of experimentally obtained Young’s modulus by tensile tests with numerical simulations indicate that the presented approach requires three-dimensional information of the probabilistic characteristics of the microstructure. Using this information not only the overall material properties are approximated sufficiently, but also the local distribution of the material properties shows the same trend as the results of conducted tensile tests.

Experimental Characterization of Short Fiber-Reinforced Composites on the Mesoscale by Indentation Tests

“…In the center of the cross-section, the obtained Young's modulus is significantly higher in comparison to the remaining cross-section. This also meets the results of the microstructural analysis of the cross-section presented in [35]. However, this characteristic of the cross-section is not detected by the results shown in Fig.…”

“…5 for the indentation test in the x-direction. At first, this contradicts the results of the measurement in the z-direction as well as the findings regarding the cross-section layout due to an injection molding process as described in [37][38][39][40][41] and the results of the cross-section analysis in [35]. This is resolved by analyzing the obtained values more in detail.…”

“…6 Fiber orientation scheme consisting of five different layers due to injection molding process, compare [41] characteristic in melt flow direction whereas the fibers in the core layer are mostly orientated perpendicular to the melt front. However, the orientation characteristics are not identical when transforming one by 90 • [35]. Because of the different fiber mass fraction and slightly different fiber orientation in these layers, the mean value for the shell layer in a fiber direction of 0 • and the corresponding value of the core layer differ significantly.…”

“…The results are provided in Table 4. Furthermore, the corresponding fiber mass fraction taken from the microstructural analysis in [35] is given. First of all, again the mean values of the measurement results at 500mN and 1500mN match very well for each layer, which meets the results presented in [29].…”

“…7. The generation of the numerical model is described in detail in [35] and will, therefore, only discussed briefly here. To be able to analyze the overall material properties of the micrograph by numerical simulation the obtained image is transferred to an array that holds a zero or one for each pixel of the image, indicating whether the pixel represents matrix or fiber material.…”