Constitutive modeling of large inelastic deformation of amorphous polymers: Free volume and shear transformation zone dynamics

Abstract

Due to the lack of the long-range order in their molecular structure, amorphous polymers possess a considerable free volume content in their inter-molecular space. During finite deformation, these free volume holes serve as the potential sites for localized permanent plastic deformation inclusions which are called shear transformation zones (STZs). While the free volume content has been experimentally shown to increase during the course of plastic straining in glassy polymers, thermal analysis of stored energy due to the deformation shows that the STZ nucleation energy decreases at large plastic strains. The evolution of the free volume, and the STZs number density and nucleation energy during the finite straining are formulated in this paper in order to investigate the uniaxial post-yield softening-hardening behavior of the glassy polymers. This study shows that the reduction of the STZ nucleation energy, which is correlated with the free volume increase, brings about the post-yield primary softening of the amorphous polymers up to the steady-state strain value; and the secondary hardening is a result of the increased number density of the STZs, which is required for large plastic strains, while their nucleation energy is stabilized beyond the steady-state strain. The evolutions of the free volume content and STZ nucleation energy are also used to demonstrate the effect of the strain rate, temperature, and thermal history of the sample on its post-yield behavior. The obtained results from the model are compared with the experimental observations on poly(methyl methacrylate) which show a satisfactory consonance.

Variation of the strain rate during CSM nanoindentation of glassy polymers and its implication on indentation size effect

“…Since the yield behavior of the rate dependent materials like polymers is highly dependent on the applied strain (loading) rate, one expects the higher value of hardness (which is proportional to yield stress) at shallow indentation depths where the strain rate is higher. Figure shows the variation of the hardness during the nanoindentation of PC and PMMA at three different set values.…”

“…) in the current study could also correspond to the elevated values of T g at the surface layer within this tip travel distance compared to the bulk. On the other hand, using the shear transformation theory, Voyiadjis and Samadi‐Dooki have established a model for yielding and plasticity of glassy polymers which shows the relation between the yield stress (which is proportional to hardness through Tabor's relation), and an activation energy, which itself is function of the rigidity of the polymer (see eqs 11 and 13 of ref. ).…”

“…The versatility of polymers has allowed them to be used extensively in nanoscale and microscale structures over the past decades; therefore, the deep knowledge of their mechanical properties in small scales is essential for design and development of components and structures fabricated from these materials. While these properties are well known in millimeter or larger size scales with well‐established testing procedures and constitutive models, in submicron size scales there are still many obscurities about the behavior and mechanism of deformation in polymers. In order to obtain accurate quantitative information, instrumented‐indentation testing can be employed for the purpose of probing the mechanical properties including hardness and elastic modulus of very small volumes of materials including polymers .…”

Phenomenological multi-mechanisms constitutive modelling for thermoplastic polymers, implicit implementation and experimental validation

“…Other works (Arruda et al, 1995) have introduced conformational rearrangement as mechanisms behind yielding and plasticity of glassy polymers. More recent studies (Voyiadjis and Samadi-Dooki, 2016) consider the deformation of glassy polymers through the evolution of the free volume and shear transformation zones during the generation of plastic strain. Despite their efficiency, the latter type of constitutive models requires physical data that can be difficult to measure experimentally or to control during the manufacturing process.…”

Interrelation between mechanical response, strain field, and local free volume evolution in glassy polymers: Seeking the atomistic origin of post-yield softening

“…Note that there is a definite difference in free volume content of annealed and quenched samples. Several decades ago, the free volume concept became popularized as a means to explain the physical origin, and to quantify, the changes of dynamic and mechanical properties, particularly viscosity, relaxation time, and physical aging in polymeric materials [14][15][16][17]. Despite its importance, the correlation between free volume and plastic deformation in solid polymers is unclear and under debate.…”