ABSTRACT
The cube in cube approach was used by Paul and Ishai-Cohen to model and derive formulas for filler content dependent Young's moduli of particle filled composites assuming perfect filler matrix adhesion. Their formulas were chosen because of their simplicity, and recalculated using an elementary volume approach which transforms spherical inclusions to cubic inclusions. The EV approach led to expression of the composites moduli that allows introducing an adhesion factor kadh ranging from 0 and 1 to take into account reduced filler matrix adhesion. This adhesion factor scales the edge length of the cubic inclusions, thus reducing the stress transfer area between matrix and filler. Fitting the experimental data with the modified Paul model provides reasonable kadh for PA66, PBT, PP, PE-LD and BR which are in line with their surface energies. Further analysis showed that stiffening only occurs if kadh exceeds [Formula: see text] and depends on the ratio of matrix modulus and filler modulus. The modified model allows for a quick calculation of any particle filled composites for known matrix modulus EM, filler modulus EF, filler volume content vF and adhesion factor kadh. Thus, finite element analysis (FEA) simulations of any particle filled polymer parts as well as materials selection are significantly eased. FEA of cubic and hexagonal EV arrangements show that stress distributions within the EV exhibit more shear stresses if one deviates from the cubic arrangement. At high filler contents the assumption that the property of the EV is representative for the whole composite, holds only for filler volume contents up to 15 or 20% (corresponding to 30 to 40 weight %). Thus, for vast majority of commercially available particulate composites, the modified model can be applied. Furthermore, this indicates that the cube in cube approach reaches two limits: (i) the occurrence of increasing shear stresses at filler contents above 20% due to deviations of EV arrangements or spatial filler distribution from cubic arrangements (singular), and (ii) increasing interaction between particles with the formation of particle network within the matrix violating the EV assumption of their homogeneous dispersion.
ABSTRACT
This study investigates the effects of four multifunctional chain-extending cross-linkers (CECL) on the processability, mechanical performance, and structure of polybutylene adipate terephthalate (PBAT) and polylactic acid (PLA) blends produced using film blowing technology. The newly developed reference compound (M·VERA® B5029) and the CECL modified blends are characterized with respect to the initial properties and the corresponding properties after aging at 50 °C for 1 and 2 months. The tensile strength, seal strength, and melt volume rate (MVR) are markedly changed after thermal aging, whereas the storage modulus, elongation at the break, and tear resistance remain constant. The degradation of the polymer chains and crosslinking with increased and decreased MVR, respectively, is examined thoroughly with differential scanning calorimetry (DSC), with the results indicating that the CECL-modified blends do not generally endure thermo-oxidation over time. Further, DSC measurements of 25 µm and 100 µm films reveal that film blowing pronouncedly changes the structures of the compounds. These findings are also confirmed by dynamic mechanical analysis, with the conclusion that tris(2,4-di-tert-butylphenyl)phosphite barely affects the glass transition temperature, while with the other changes in CECL are seen. Cross-linking is found for aromatic polycarbodiimide and poly(4,4-dicyclohexylmethanecarbodiimide) CECL after melting of granules and films, although overall the most synergetic effect of the CECL is shown by 1,3-phenylenebisoxazoline.
