Investigations into the applicability of rubber elastic analogy to hardening in glassy polymers
DK Mahajan and S Basu, MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, 18, 025001 (2010).
In this paper we attempt to understand the origins of strain hardening response in glassy polymers at large strains through well-designed molecular dynamics (MD) simulations on an atomistic model of a glassy polymer. In the existing constitutive theories of glassy polymers, strain hardening is assumed to be the result of affine orientation of an underlying entanglement network with stretch. This model is inspired by theories of rubber elasticity. However, in the glassy state the length scale of the network is uncertain although satisfactory fits to experimental stress-strain curves can be obtained using rubber elasticity-inspired constitutive theories. In this work we probe whether the network of entangled macromolecules in the glassy state is capable of deforming affinely obeying Langevin or Gaussian statistics. We also investigate the thermodynamics of the deformation process and try to ascertain if the free energy description of deformation in rubbery materials can be used to model irreversible plastic deformation of glassy polymers. We observe in particular that the 'locked in energy', which is the part of the energy dissipated during deformation that is not converted to heat, shows remarkably different behavior in MD simulations as compared with rubber elasticity based continuum models.
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