https://doi.org/10.1140/epje/i2017-11606-5
Regular Article
Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition
1
CNRS UPMC ESPCI ParisTech PSL Res Univ, Lab. SIMM, UMR 7615, F-75231, Paris, France
2
MINES ParisTech, PSL-Research University, MAT - Centre des Matériaux, CNRS UMR 7633, BP 87, 91003, Evry, France
* e-mail: helene.montes@espci.fr
Received:
16
October
2017
Accepted:
4
December
2017
Published online:
27
December
2017
In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.
Key words: Soft Matter: Polymers and Polyelectrolytes
© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2017