Viscoelastic effects and shrinkage as accompanying phenomena of the curing of polymers. Single‐ and multiscale effects

Abstract

The contribution deals with the modeling of two phenomena that are characteristic of the curing of polymers, namely the increasing viscosity and the volume decrease known as autogeneous shrinkage. Both of these processes are caused by the crosslinking of polymer chains during polymerization. In order to model the viscoelastic effects, the free energy consisting of an equilibrium and a non-equilibrium part is proposed. The former is related to the elastic processes and depends on total deformations. The latter is caused by the viscoelastic effects and only depends on the elastic part of deformations. In order to avoid volume locking effects typical of isochoric materials, both parts of the free energy density are furthermore split into a volumetric and a deviatoric part. A multifield description depending on the displacements, volume change and hydrostatic pressure is introduced as well. Different from the viscous process, the modeling of shrinkage effects does not require a new assumption for the free energy but a split of the total deformation gradient into a shrinkage and a mechanical part. The model suitable for simulating both of the mentioned phenomena is implemented in the single-and multiscale FE program. Mechanical modeling of viscoelastic and shrinkage effectsThe curing of polymers is a complex process accompanied by the change of material properties such as stiffness, viscosity or opacity. Within this contribution, the emphasis will first be placed on the viscous effects for the modeling of which the free energy density is decomposed into an equilibrium and a non-equilibrium partIn addition, a decomposition into a volumetric and deviatoric part is introduced since the polymers commonly show an isochoric material behaviorWithin the proposed formulation, Ψ denotes the strain energy density, u the displacement field, θ the volume change, p is the hydrostatic pressure, J = det F is the Jacobian related to the deformation gradient F, C is the right Cauchy-Green deformation tensor, the index "e" denotes the elastic quantities and the notation "iso" represents the isochoric part of the deformations. The remaining notation is self-explanatory. The multiplicative decomposition of the deformation gradient F = F e · F i is introduced to define the relationships between the elastic and inelastic deformations. In order to complete the model, the equilibrium energy parts are assumed in the form of convolution integrals, which is substantiated by their dependence on the time-sensitive material parameters [1]Here, C and K are deviatoric and volumetric stiffnesses. Different from the equilibrium part, the non-equilibrium part depends on the time-insensitive material parameters such that it can directly be equalized with the non-equilibrium strain energy density Φ neq = Ψ neq . The evolution of the elastic deformations is controlled through the evolution of the viscous deformations determined by the approach of Reese andwhere T denotes the relaxation time [2]. Apart from the viscous effects, the behavior of curing poly...