Multiphase constitutive modeling for interphase-driven mechanics in polymer blends: Application to PE/PS and PP/PS systems processed by solid-state and melt mixing

Abstract

In polymer blends, the mechanical response is governed not only by the intrinsic properties of each constituent polymer but also by the morphology and mechanical role of the interphase regions formed at their interfaces. These interphases mediate stress transfer, accommodate molecular mobility, and influence local deformation mechanisms – making them especially influential in immiscible systems where interfacial adhesion is inherently weak. This study presents a multiphase continuum-based constitutive model that explicitly incorporates the interphase as a mechanically active domain. The model distinguishes between crystalline, amorphous, and interphase contributions, and extends existing crystalline-amorphous constitutive formulations – based on intermolecular elasto-viscoplasticity and molecular network viscohyperelasticity – by embedding interphase-specific deformation mechanisms. Its aim is twofold: to improve macroscopic stress–strain estimates and to shed light on the underlying phase interactions that control the mechanical behavior of polymer blends. The model is applied to two representative immiscible polymer systems, each combining a semi-crystalline polyolefin – polyethylene (PE) or polypropylene (PP) – with a glassy amorphous polymer, polystyrene (PS). Its development is guided and supported by a comprehensive experimental campaign that includes uniaxial tensile testing, SEM, DSC, solid-state NMR, and DMTA. Constitutive parameters are identified through inverse fitting, supplemented by literature-based values for the crystalline phases of PE and PP. The PE/PS and PP/PS blends are processed using both conventional melt mixing and high-pressure torsion (HPT) – a solid-state processing method that reduces domain sizes to the nanoscale and promotes enhanced interfacial connectivity. Results demonstrate that explicitly incorporating the interphase as a mechanically active domain significantly improves the accuracy of stress–strain estimates, particularly in HPT-processed blends. In these systems, the model captures key experimental features such as enhanced stiffness and distinct failure modes driven by interfacial cohesion. The proposed framework offers a physically grounded approach to elucidate the underlying deformation mechanisms in complex multiphase systems. It highlights the central role of the interphase – not only in enabling efficient stress transfer, but also in controlling the degree of mechanical coupling between otherwise immiscible polymer phases.