Open Access

Julian Rech, Esther Ramakers-van Dorp, Patrick Michels, Bernhard Möginger, Berenika Hausnerova

• Cube in cube elementary volume (EV) concept serves to predict a filler-content dependent Young´s moduli of particle filled composites using moduli of a matrix EM and a filler EF. Paul and Ishai-Cohen derived formulas for composites moduli considering different load transfer boundaries in the EV assuming a complete filler-matrix adhesion. In this paper it is confirmed that their models represent the upper and lower bounds, respectively, with the respect to the experimental data. However, in vast majority of composites a filler-matrix adhesion is not complete. Therefore, an adhesion factor kadh gaining values between 0 and 1 was introduced into Paul´s model to consider the reduced adhesion as the reduction of the filler-matrix contact area for glass beads filled in polar and unpolar thermoplastic matrices as well as elastomer. The evaluation of these composite systems provides reasonable adhesion coefficients of PA66 > PBT > PP > PE-LD >> BR. It was also found that stiffening only occurs if kadh exceeds the minimum value adhesion of root square of E(M) divided by E(F). The determined kadh correspond to scanning electron microscopy observations of the composites fracture surfaces. Additionally, finite element analysis of the cubic and hexagonal arrangements of the EV show that the stress distributions are different, but they affect the calculated moduli only for the filler volume contents exceeding 20 %. The introduction of the filler-matrix adhesion provides more reliable predictions of Young´s moduli of particulate composites.