Evolution of strain localization in glassy polymers: A numerical study

Abstract

a b s t r a c tAn explicit numerical implementation is described, for a constitutive model of glassy polymers, previously proposed and validated. Then it is exploited within a Finite Element continuum model, to simulate spontaneous strain localization (necking) occurring during extension of a prismatic bar of a typical glassy polymer. Material parameters for atactic polystyrene are employed. The material model is physically based and highly non-linearly viscoelastic. Three of its principal features are critical in simulations of strain localization: rate-dependence of plastic flow stress; strain-induced structural rejuvenation, represented by increase of Tool's fictive temperature and leading to pronounced post-yield strain softening; and molecular alignment during extension, giving rise to strain-hardening. In all simulations there is a peak in nominal stress, satisfying the condition for localization to occur. Nevertheless, the simulations show that the process of strain localization varies considerably, depending on details of the extension sequence and on assumed values for certain material parameters. A characteristic feature observed is that strain localization in such a material occurs in two stages. There is an initial spurt associated with strainsoftening, followed by a slower growth of localization that eventually subsides, ultimately giving way to uniform extension of the neck. But the details of evolution of the strain distribution vary greatly. The rapidity and severity of localization are increased by decreased temperature, increased strain-rate or greater structural rejuvenation. A simple one-dimensional stability analysis is successful in explaining the results.

Deformation behavior of thermoplastic elastomer specimens: Observation of the strain behavior in a wide range of tensile speeds

“…Figure shows the NDRs of Samples A and B. In both samples, the NDR increased with the tensile speed.…”

“…In particular, studies on high tensile speed are insufficient. However, it is difficult to perform strain measurements over a wide range of deformation rates .…”

In situ multiscale study of deformation heterogeneities in polylactide‐based materials upon drawing: Influence of initial crystallinity and plasticization

“…In the case of glassy amorphous polymers, the onset of plastic deformation when the yield point is reached engenders a change of the local molecular packing resulting in a strain‐softening phenomenon, as noted in Figure (a). As a consequence, strain localization occurs and manifests as necking . Generally, strain localization is noted at the center of a tensile specimen, but in the case of glassy amorphous polymers, the presence of specimen edge defects induced by the cutting locally promote plastic deformation and can explain why strain localization on PLA and aPLA specimen follows diagonal lines [Fig.…”

Strain hardening and its relation to Bauschinger effects in oriented polymers

“…In its original form, the strain hardening contribution in the BPA model was captured by the “three‐chain” model of Wang and Guth11, 12; later, this was replaced with the more realistic “eight‐chain” model 13. Other 3‐D models using different hyperelastic strain hardening approaches followed, for example, the Oxford Glass‐Rubber (OGR) model,14, 15 incorporating the crosslink sliplink model of Edwards and Vilgis,16 and the Eindhoven Glassy Polymer (EGP) model,17, 18 which uses a neo‐Hookean model, equivalent to the application of the Gaussian network theory of rubber elasticity. In this theory, the polymer strands between entanglements never reach a fully stretched conformation, and the elastic stress in uniaxial loading is represented by the following: where G r is the strain hardening modulus and λ is the draw ratio.…”