Constitutive modelling of polymer glasses : finite, nonlinear viscoelastic behaviour of polycarbonate

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Thermodynamic considerations on nonisothermal finite anisotropic elasto- viscoplasticity

A class of dynamic models to describe finite anisotropic elasto-viscoplastic behavior in an Eulerian setting are examined from the perspective of non-equilibrium thermodynamics. A proper description of anisotropic elastic behavior, using the deformation gradient as an internal variable, serves as a starting point. A general model for elasto-viscoplastic deformation is then formulated by allowing isochoric relaxation of the total deformation gradient, giving rise to an elastic deformation gradient and a plastic strain rate. Thermodynamic restrictions on specific forms of the plastic strain rate for anisotropic materials, using the representation theorem for tensor functions, are discussed. In addition, the thermodynamic admissibility of a multi-mode formulation of the elasto-viscoplastic model is demonstrated. Finally, the model is applied to describe rate-dependent inelastic deformation of an amorphous polymer glass, and anisotropic strain-rate dependent crystalline slip as found in metal plasticity

Continuum damage mechanics; combining thermodynamics with a thoughtful characterization of the microstructure

We formulate a macroscopic description of the mechanics of damaged materials. To represent the microstructure, the distribution of crack sizes is captured by way of the Minkowski functionals, or so-called quermass integrals, while a second-rank tensor is used to describe the average orientation of the cracks. A two phase-type approach is adopted to distinguish elastically strained material from unstrained regions in the wake of the cracks. Using nonequilibrium thermodynamic techniques, the driving force for the growth of the microcracks is naturally identified. In particular, Griffiths law is generalized to assemblies of polydisperse crack sizes. Due to the detailed characterization of the microstructure, we are also able to account for the plastic zones at the rims of the cracks that are known to hamper the crack growth, and to discuss possible forms of the damage parameter. The presented approach separates in a transparent fashion the incorporation of fundamental thermodynamic and mechanic principles on one hand, from the specification of the material and details of the crack formation and growth on the other hand

Statistical-mechanics based modeling of anisotropic viscoplastic deformation

Statistical mechanics-based coarse graining is used for constitutive modeling of finite elasto-viscoplastic deformation behavior of transversely isotropic materials, without relying on the associated flow rule or classical yield criteria. It was shown previously (Hütter and Tervoort, 2008c) that a detailed expression for the plastic velocity gradient can be obtained in terms of correlations of the fluctuations of the elastic deformation gradient. In this paper, we demonstrate that it is crucial to include cross-correlations between fluctuations of different components of the elastic deformation gradient in order to describe materials with strong plastic anisotropy. Subsequently, the expression for the equivalent stress is obtained from a steady-state analysis during plastic deformation, and is shown to coincide with the Hill equivalent stress in the limit of small elastic deformations. In this case, only two material parameters describe in a self-consistent manner the anisotropic structure of both the plastic velocity gradient and the equivalent stress. Finally, the new constitutive viscoplastic description is successfully applied to describe experimental yield data of oriented isotactic polypropylene, specifically the influence of anisotropy and deformation rate on yielding. Particularly, a step-by-step procedure is given to identify all model parameters

Strain-hardening behavior of polycarbonate in the glassy state

This paper presents an experimental characterization of the three-dimensionalstrain-hardening response of polycarbonate in the glassy state. Using a specialmechanical conditioning technique large homogeneous deformations were ob-tained in tension compression and shear. The experimental results are comparedto a number of existing network models. It was found that the state-of deforma-tiondependence of the strain-hardening response was adequately described byneo-Hookean behavior with a shear modulus G =26 MPa. Up to thedeforma-tionsapplied in this study no sign of a finite extensibility of the entanglementnetwork was observed

Coarse graining in elasto-viscoplasticity : bridging the gap from microscopic fluctuations to dissipation

The interrelation between the elasto-viscoplastic behavior of anisotropic solids on the macroscopic scale and the microscopic dynamics of their constituent atoms and molecules is examined. To that end, we employ a scheme for coarse graining as used in the context of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework. First, the framework is introduced and illustrated with several examples that are self-contained on a single level of description, that is, that do not establish any links to other levels of description. Second, as a prototype example of applying the coarse graining scheme, the derivation of the evolution equations for nonisothermal hydrodynamics based on the microscopic Hamiltonian point mechanics is illustrated, leading to the well-known Navier-Stokes equation and the balance equations for mass and energy. Third, in the main part, we elaborate in detail on the application of the same methodology of coarse graining to elasto-viscoplastic solids. On the macroscopic scale, the elastic part of the deformation gradient is used as an internal variable to describe the state of deformation. Viscoplasticity then follows from relaxation of the elastic deformation gradient and is conveniently expressed in terms of so-called plastic velocity gradient tensor. Typically, constitutive relations for the plastic velocity gradient tensor rely on phenomenological macroscopic arguments, resulting in a large number of material constants. In this work, we illustrate a procedure to relate the plastic velocity gradient tensor to the rapid microscopic fluctuations of the elastic deformation gradient. In this way, we are able to use microscopic information about anisotropic solids to restrict the tensorial structure of the plastic velocity gradient tensor, thereby drastically reducing the number of material parameters. The antisymmetric part of the plastic velocity gradient tensor, the so-called plastic spin, naturally arises in our treatment and does not require any special constitutive assumptions

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

In 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 (elastic) hydrostatic and (viscoelastic) 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