Theory of Plasticity and Strain Hardening of Glassy Polymers

Abstract

We extend a theory for the deformation of glassy polymers based on the heterogeneous nature of the dynamics up to the strain-hardening regime. We attribute the latter to the increase of free-energy barriers for α-relaxation as a consequence of local orientation of monomers. The free-energy barriers are set on a scale ξ ≈ 5 nm or of about N c ∼ 1000 monomers which are involved in the α-relaxation mechanism. The variation of the local free-energy barriers is given by the expression , where ΔF 0 is the free-energy barrier per monomer in the glassy state, typically ∼40–45k B T g for an aged polymer, is the local order parameter (nematic in nature) whose distribution is computed during the course of deformation, is the local stress, and G 0′ is the bulk glassy modulus. is an energy scale of the typical order of 0.2–0.3k B T g. The second term is negative and is responsible for yielding and the onset of plastic flow. The third one is positive and becomes important after a large deformation has significantly oriented the chains on the scale of the monomers. It may overcompensate the decrease of the free-energy barriers due to the increasing stress and is responsible for strain hardening. Since the contribution of the stress to the reduction of the free-energy barrier between stress softening and the deformation λ ∼ 2 is of the order of −5k B T g, the contribution which leads to strain hardening, , is found to be of the order of 10 k B T g, which corresponds to an increase of the order of 0.01k B T g per monomer. This order of magnitude is compatible with the calculated values of the order parameter q ∼ 0.3 in the direction of tension during our simulations as well as that measured by Vogt et al. (1990) by NMR. We calculate the evolution dynamics of the order parameter . Its dynamics is controlled by a driving force due to the local stress and a relaxation process due to rotational diffusion. The latter is entropic in nature and may be very slow in glassy polymers. We compare the predictions of our model to recent experimental results regarding the evolution of both the dominant relaxation time under applied strain and the width of the relaxation times distribution up to a large deformation amplitude, and more specifically their non-monotonic behavior.

Quantitative Insight into the Compressive Strain Rate Sensitivity of Polylactic Acid, Acrylonitrile Butadiene Styrene, Polyamide 12, and Polypropylene in Material Extrusion Additive Manufacturing

“…The temperature was kept constant throughout the experiments, as mentioned above. At low strain rates strain hardening phenomena in polymers exist but are barely present [78]. However, polymeric chains can potentially undergo some deformation shapes were consistent across the replicates in each loading scenario studied.…”

What Determines Yield Stress in Semicrystalline Polymers within Lamellar Stack Dimensions: Competition between the Yield Behaviors of Crystalline and Glassy Amorphous Phases

“…However, the physical meaning of the activation volume ν in this model is vague. Recently, Long et al , have extended this model, which attributes yield of glassy amorphous polymers to their evolution and distribution of dynamical heterogeneities (ζ = 3–5 nm at length scale). In this new model, the stress is assumed to not only bias the molecular motion as described by the Eyring model but also lower the free energy barrier Δ F 0 for a local change of configuration.…”

Mapping the Nanoscale Heterogeneous Responses in the Dynamic Acceleration of Deformed Polymer Glasses

“…Disordered glasses are generally formed upon cooling liquids through the glass transition temperature ( T g ) without an obvious change in the structural behavior of the molecules. , However, such a transition is commonly associated with a substantial slowing of the segmental dynamics of the materials. Despite the extremely slow dynamics, many kinds of amorphous glasses, such as polymer and metallic glasses, can undergo plastic flow rather than brittle fracture under large compressive or tensile stress. − It has been recognized that this toughness mechanism is largely related to the fact that many glasses can effectively dissipate large amounts of energy during the plastic deformation, which is supposed to be governed by the relationship between external applied stress and molecular dynamics in the glassy state. − Consequently, the influence of mechanical stress on the molecular mobility of amorphous glasses has received great attention in both fundamental and practical studies over the past decades. − In theoretical studies, the applied stress is commonly modeled to lower the effective energy barrier that restricts the molecular motions, leading to the increase of molecular mobility of the glass in a similar manner to the effect of increased temperature. − , Thus, the acceleration of molecular mobility in deformed glasses is expected to be a universal phenomenon regardless of how the materials are deformed. − This scenario is indeed strongly supported by several simulation results. ,,, For example, Riggleman et al have proved the similarity in the stress-induced acceleration of the segmental dynamics of a polymer glass under both tension and compression by using double-bridging Monte Carlo and molecular dynamics simulations …”