With a view to application to thermomechanical coupled two-scale analysis of fiber-reinforced thermoplastics (FRTP), we propose a viscoelastic-viscoplastic combined constitutive modelfor of thermoplastic resins, which iscapable of representing the complex inelastic behaviourwith self-heating effect. The generalized Maxwell model is employedto characterize the viscoelastic behaviourat small or moderate strain regime, while a finite strain viscoplastic model is employed to represent transient creep deformations due to frictional resistance of molecular chainsalong withthe hardening due to orientation of molecular chains. Within theframework of de-coupled computational homogenization[1]for FRTP, we are concerned with the effect of self-heating behaviour due to large strains distributed locally in periodic microstructures(unit cells)on the macroscopic thermomechanical behaviour that inevitably become extremely complex.

The thermodynamics-based formulation adopted here enables us to naturally derive a set of coupled governing equations for heat conduction, thermo-mechanics and self-heating phenomena. As the self-heating plays a role of heat sources in the microstructureof FRTP, the unsteady heat conduction problem has to be solved at a micro-scale to obtain the time-variation of temperature distribution that causes the transition from the glassy state to the rubbery one. As a result, the macroscopic self-heating effect is supposed to be delayed according to the unit cell size. In order to strictly consider this kind of temperature effects in homogenization analyses and reflect them in the macroscopic responses, we employ the incremental variational formulation [2]to formulatea coupled thermomechanical problem.

After the fundamental performance of the proposed constitutive model is verified in representing typical material behaviourof typical thermoplastic resins, representative numerical examples are presented to demonstrate the capability of the proposed model in reproducing the stress-softening, non-homogeneous creep, stress-build-upand self-heating phenomenon due to large inelastic deformations as well as the deformation-rate dependency. It is also confirmed that the modelis capable ofproperly representingthe transition between glassy and rubbery states, which may be caused by the self-heating phenomena especially under the condition of relatively high deformation rates. Then, the proposed constitutive model is applied to the numerical material testing (NMT) [2] for unit cells of FRTP to characterize the overall anisotropic inelastic behaviouralong with micro-macro self-heating effects.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.
Date: 5-7 September 2017, Barcelona, Spain.

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[1]K. Terada, J. Kato, N. Hirayama, T. Inugai, K. Yamamoto: A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials. Comput. Mech., Vol. 52(2013), pp 1199–1219.

[2] Q. Yang, L. Stainier and M. Ortiz: A variational formulation of the coupled thermomechanical boundary-value problem for general dissipative solids. J. Mech. Phys. Solids, Vol.54 (2006), pp.401–424.

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Published on 22/10/19

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