A multi‐mode approach to finite, three‐dimensional, nonlinear viscoelastic behavior of polymer glasses

Abstract

SynopsisIn this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three-dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the ͑elastic͒ hydrostatic and ͑viscoelastic͒ deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of parameters, the multi-mode Leonov model is capable of describing realistic constant strain rate experiments, including the strain rate dependent yield behavior. It is also capable of giving a quantitative description of nonlinear stress-relaxation experiments.

Deformation-induced accelerated dynamics in polymer glasses

“…It is most often assumed that mechanical stress lowers the activation barriers to molecular mobility, thereby allowing the solid to yield and flow. This simple idea, first proposed by Eyring in 1936 [1], remains the central tenet of several models of plasticity in amorphous solids [2,3]. Other control variables have also been proposed to explain the increased molecular mobility under deformation.…”

Quantitative assessment and prediction of contact area development during spherical tip indentation of glassy polymers

“…The first one is to use a so-called multimode approach to describe the complete pre-yield viscoelastic behaviour. In previous work we showed that the behaviour can be accurately captured by a parallel arrangement of eighteen modes [15]. Unfortunately, this solution increases tremendously the computation time and will therefore not be used.…”

“…In the last 20 years, considerable effort has been made to model the post yield behaviour of glassy polymers and a number of 3D numerical models were developed and validated, by Boyce et al at MIT [9][10][11], Paul Buckley et al in Oxford [12][13][14] and our own group in Eindhoven [15][16][17]. Common factors of these models are the application of a stress dependent viscosity to capture the deformation kinetics and the use of rubber elasticity to model strain hardening.…”

“…In previous work we developed an 3D elasto-viscoplastic constitutive equation that accurately captures the deformation characteristics of polymer glasses [15,16,20,21]. The basis of this constitutive model is the division of the total stress into two contributions, first proposed by Howard and Thackray [22]:…”

“…The so-called driving stress s in equation (4) accounts for the rate-dependent plastic flow response, attributed to intermolecular interactions on a segmental scale [15,21] and is represented by a compressible Leonov model [20,24]:…”