Micromechanics of toughening in polymeric composites

Abstract

The macroscopic tensile toughness of glassy homo-polymers is often limited due to either localized crazing followed by failure [e.g., polymethyl-methacrylate (PMMA), polystyrene (PS)], or cavitation-induced brittle failure under high triaxiality [e.g., polycarbonate (PC)]. Judicious choice of polymer composites alleviates the above concerns by spreading the inelastic deformation and damage throughout the material, thereby increasing the macroscopic toughness. This thesis focuses on the micro- and macro-mechanics of two polymer composite systems - ductile/brittle PC/PMMA microlaminates and rubber-toughened PS. Ductile/brittle microlaminates are comprised of alternating layers of ductile polymer (e.g., PC) that inelastically deform by shear yielding, and brittle polymer (e.g., SAN, PMMA) that undergo crazing in tension. The layer thicknesses are typically in the sub-micron to tens of micron range. We have modeled the deformation and axial tensile toughness of PC/PMMA micro-laminates. Experiments indicate that the macroscopic ductility of ductile/brittle polymeric laminates depends on several factors such as the thickness of the brittle and ductile layers, the volume fraction of the ductile component, as well as strain rate.

(cont.) The nominally brittle layer can undergo in-elastic deformation by both crazing and shear-yielding, with the relative contribution of these mechanisms being dependent on the laminate morphology and strain rate. In particular, with decreasing brittle layer thickness, the inelastic behavior of the brittle layer is dominated by shear-yielding. We present a micromechanical model for two-phase ductile/brittle laminates that enables us to capture the macroscopic behavior, as well as the underlying micro-mechanisms of deformation and failure, in particular the synergy between crazing and shear yielding. The finite element implementation of our model considers a two-dimensional and three-dimensional representative volume element (RVE), and incorporates continuum-based physics-inspired descriptions of shear yielding and crazing, along with failure criteria for the ductile and brittle layers. The interface, between the ductile and brittle layers, is assumed to be perfectly bonded. The model is used to probe the effect of laminate parameters, such as the absolute and relative layer thicknesses, and material properties on the behavior during tensile loading. In addition, our modeling approach can be generalized to other laminate systems, such as two-phase brittle-1/brittle-2 and three-phase ductile-I/brittle/ductile-2 laminates, as well as to more complex loading conditions.

(cont.) Results from our studies reveal that the 2D RVE does not adequately capture the effect of volume fraction of the constituents on the laminate toughness. However, the 3D RVE captures the effect of volume fraction based on the extent of craze tunneling through the width of the specimen; at high volume fractions of PC, crazes emanating from the surface do not tunnel through the specimen width significantly, while at low volume fractions of PC, the crazes tunnel through the entire specimen width. The 3D RVE captures the strain-rate effect on toughness based on the greater rate-sensitivity of shear yielding compared to craze initiation, thereby increasing the craze density in the laminate at higher rates. The length-scale effect is captured by the 3D RVE, based on decrease in the craze opening rate and damage confinement by the PC layers. It is well-known that the incorporation of a small volume fraction (10-25 %) of micron-order size, compliant and well-dispersed rubbery particles in (brittle and crazeable) polystyrene (PS) yields considerable dividends in tensile toughness at the expense of reduction in stiffness and yield strength. In commercial rubber-toughened PS, the rubbery particles often have a composite "salami" morphology, consisting of 70-80 % volume fraction of sub-micron PS occlusions dispersed in a topologically, continuous polybutadiene (PB) phase.

(cont.) While it is recognized that these composite particles play the dual role of providing multiple sites for craze initiation in the PS matrix and allow the stabilization of the crazing process through cavitation/fibrillation in the PB-phase within the particle, the precise role of particle morphology, as well as the particle-matrix interface are not well understood or quantified. This work probes the micromechanics and macromechanics of uni-axial tensile deformation and failure in rubber-toughened PS through axi-symmetric finite element representative volume element (RVE) models that can guide the development of blends of optimal toughness. The RVE models reveal the effect on craze morphology and toughness by various factors such as particle compliance, particle morphology, particle fibrillation and particle volume fraction. The principal result of our study is that particle compliance and particle heterogeneity alone cannot account for the macroscopic behavior of HIPS, as well as the experimentally observed craze profile. Fibrillation/cavitation of PB domains within the heterogeneous particle provides the basic key ingredient to account for the micro- and macro-mechanics of HIPS.