Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition

• Published in: The European physical journal. E, Soft matter and biological physics Vol. 40; no. 12; pp. 116 - 14
• Main Authors: Masurel, R. J., Gelineau, P., Lequeux, F., Cantournet, S., Montes, H.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 27-12-2017; Springer Nature B.V; EDP Sciences: EPJ
• Subjects: Biological and Medical Physics; Biophysics; Complex Fluids and Microfluidics; Complex Systems; Condensed Matter; Condensed matter physics; Edge dislocations; Energy storage; Finite element method; Materials Science; Mathematical analysis; Mechanical properties; Mechanics (physics); Nanotechnology; Nonlinear response; Normal distribution; Physics; Physics and Astronomy; Polymer Sciences; Polymers; Regular Article; Residual stress; Shear bands; Soft and Granular Matter; Strain distribution; Strain rate; Stress concentration; Stress relaxation; Surfaces and Interfaces; Temperature; Thin Films; Viscoelasticity; Soft Matter: Polymers and Polyelectrolytes
• ISSN: 1292-8941; 1292-895X
• DOI: 10.1140/epje/i2017-11606-5

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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.
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