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Open AccessArticle

Modelling the Temperature Dependent Biaxial Response of Poly(ether-ether-ketone) Above and Below the Glass Transition for Thermoforming Applications

School of Mechanical and Aerospace Engineering, Queen’s University, Belfast BT9 5AH, UK
Author to whom correspondence should be addressed.
Polymers 2019, 11(6), 1042;
Received: 15 May 2019 / Revised: 4 June 2019 / Accepted: 8 June 2019 / Published: 12 June 2019
(This article belongs to the Special Issue Mechanical Behavior of Polymers)


Desire to accurately predict the deformation behaviour throughout industrial forming processes, such as thermoforming and stretch blow moulding, has led to the development of mathematical models of material behaviour, with the ultimate aim of embedding into forming simulations enabling process and product optimization. Through the use of modern material characterisation techniques, biaxial data obtained at conditions comparable to the thermoforming process was used to calibrate the Buckley material model to the observed non-linear viscoelastic stress/strain behaviour. The material model was modified to account for the inherent anisotropy observed between the principal directions through the inclusion of a Holazapfel–Gasser–Ogden hyperelastic element. Variations in the post-yield drop in stress values associated with deformation rate and specimen temperature below the glass transition were observable, and facilitated in the modified model through time-temperature superposition creating a linear relationship capable of accurately modelling this change in yield stress behaviour. The modelling of the region of observed flow stress noted when above the glass transition temperature was also facilitated through adoption of the same principal. Comparison of the material model prediction was in excellent agreement with experiments at strain rates and temperatures of 1–16 s−1 and 130–155 °C respectively, for equal-biaxial mode of deformation. Temperature dependency of the material model was well replicated with across the broad temperature range in principal directions, at the reference strain rate of 1 s−1. When concerning larger rates of deformation, minimum and maximum average error levels of 6.20% and 10.77% were noted. The formulation, and appropriate characterization, of the modified Buckley material model allows for a stable basis in which future implementation into representative forming simulations of poly-aryl-ether-ketones, poly(ether-ether-ketone) (PEEK) and many other post-yield anisotropic polymers. View Full-Text
Keywords: PEEK; constitutive model; anisotropy; simulation; thermoforming PEEK; constitutive model; anisotropy; simulation; thermoforming

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Turner, J.A.; Menary, G.H.; Martin, P.J.; Yan, S. Modelling the Temperature Dependent Biaxial Response of Poly(ether-ether-ketone) Above and Below the Glass Transition for Thermoforming Applications. Polymers 2019, 11, 1042.

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