Mechanical performance of polymer systems: The relation between structure and properties

Abstract

A direct relation between molecular characteristics and macroscopic mechanical properties of polymeric materials was subject of a vast number academic and industrial research studies in the past. Motivation was that an answer to this question could, in the end, result in guidelines how to construct tailored materials, either on the molecular level or, in heterogeneous materials, on the micro-scale, that could serve our needs of improved materials without the need of extensive trial and error work. Despite all attempts, no real universally applicable success was reported, and it was only after the introduction of the concept of the polymer's intrinsic deformation behavior that some remarkable progress could be recognized. Thus, it is first important to understand where intrinsic deformation behavior of polymeric materials stands for. Second, it is interesting to understand why this intermediate step is relevant and how it relates to the molecular structure of polymers. Third and, in the end, the most computational-modeling-based question to be answered is how intrinsic behavior relates to the macroscopic response of polymeric materials. This is a multi-scale problem like encountered in many of our present research problems.

Introduction

Bridging the gap between molecular and macroscopic properties, with as extra intermediate step the processing history, see Fig. 1a, is a just as challenging as impossible task. Reason is that the multi-scale problems involved require far too much computational time and computational memory to be resolved via ab initio analyses. Analyses on different scales require averaging the resulting properties from the analysis on the underlying scale, consequently loosing detail. Therefore, alternatives are searched for. A big step forward was made with the development of a video-controlled tensile test by Christian G'Sell at the Ecole des Mines in Nancy [1], [2]. This technique enabled the experimental assessment of the intrinsic deformation behavior: the polymer's stress response measured during homogeneous deformation. More or less simultaneously, Mary Boyce, at MIT, optimized the much more practical uniaxial and plain strain compression tests to obtain similar information in different loading geometries [3], [4]. Reason to be pleased with this intermediate step is twofold. First, our present advanced computational tools and expertise can be successfully used in the relation between the intrinsic behavior and the macroscopic response, the right-hand side of Fig. 1b. Prerequisite for the success of this route was the development of constitutive models that could capture the intrinsic behavior. So let start to focus on this issue. It is known that it took the polymer melt rheology community some half a century to arrive at constitutive equations that are not only valid in simple shear flows but also can deal with extensional flows. The (extended) Pom Pom model quantitatively describes the melt rheology for branched, and even also for linear, polymers, in complex flows and is based on molecular characteristics [5], [6], [7]. Since rheology is based on fluid mechanics, rheologists can be considered as successors of Isaac Newton, thus mathematically educated scientists. Therefore, it is at least remarkable that it took them that much time. The main topics of the rheologist's concern were the quantitative modeling of the deformation rate dependent shear and elongational viscosity and first (and eventually second) normal stress difference, in incompressible homogeneous time dependent start-up flows. Interesting now is that the major problem encountered in the solid state rheology of the same polymers is that they are per definition tested in compressible inhomogeneous start-up flows in extension. Solid state rheologists can be considered as the successors of Robert Hooke. They are practical engineers that have to deal with the impossible interpretation of the most widely used test: the tensile test on a normalized dogbone-shaped sample that, at best, shows only a simple localization behavior, like necking. All relatively recent progress reported in solid state rheology made of course use of the results obtained in the constitutive equations for melts and the good news is that at present the macroscopic response of amorphous polymers to shear and tensile loading can now be quantitatively described. In plain strain 2D, or even in completely 3D computations, in short and in long time loading, in homogeneous and also in heterogeneous systems, once the polymer's intrinsic behavior (and its microstructure in case of heterogeneous systems) is known. Use is made of standard (e.g. Marc, Abaqus) software combined with custom made (Multi-Level-Finite-Element) analyses.

Second, the relation between molecular properties of polymers and their intrinsic behavior, the left-hand side of Fig. 1b, are accessible via well defined experiments that are much easier interpretable than when compared to the results of tensile tests, creep and fatigue tests or Izod impact tests. So let us focus now on the structure of polymers.