Abstract
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.
Highlights
IntroductionA semi-crystalline polymer belonging to the family of poly-aryl-ether-ketones, poly(ether-ether-ketone)(PEEK) is an emerging polymer gaining popularity for implementation into a wide range of applications in bulk form and as a matrix material for Short Fibre Reinforced Composites (SFRC) as a result of its superior mechanical qualities combined with high thermal stability and chemical resistance.The anticipated suitability of PEEK for the application of thin walled, thermoformed products is governed by its characteristically large stiffness to mass ratio (2.571 MNm/kg), or specific stiffness, Polymers 2019, 11, 1042; doi:10.3390/polym11061042 www.mdpi.com/journal/polymersPolymers 2019, 11, 1042 when compared to similar thermoplastics in this field such as poly(ethylene terephthalate) (PET) and polypropylene (PP)—exhibiting stiffness to mass ratios of 1.206 and 1.935 MNm/kg respectively.The industrial practice of thermoforming is widely used for the large-scale manufacture of lightweight, thin-walled polymeric parts with the advantage of producing repeatable, complex products, along with relatively cheap production costs
Trial and error approaches in the hopes of optimising the formed part is often time consuming, causing authors to take a more systematic methodology. This is predominantly achieved through the use of a mathematical material model to represent the deformation behaviour subject to characteristic loading experienced during forming processes. In order for this mathematical model to be accurate in its predictions of the mechanical behaviour of the polymeric material, characterisation at conditions comparable to those experienced during the forming process is encouraged [2,3,4]—allowing the constitutive model to be calibrated and implemented into a process simulation [5,6,7] with the ultimate aim of optimising the forming conditions and/or the formed part
The biaxial deformation behaviour can be predicted by the modified Buckley material model by employing the above characterised constants under differing combinations of experimental variables typical to those observed within the processing window
Summary
A semi-crystalline polymer belonging to the family of poly-aryl-ether-ketones, poly(ether-ether-ketone)(PEEK) is an emerging polymer gaining popularity for implementation into a wide range of applications in bulk form and as a matrix material for Short Fibre Reinforced Composites (SFRC) as a result of its superior mechanical qualities combined with high thermal stability and chemical resistance.The anticipated suitability of PEEK for the application of thin walled, thermoformed products is governed by its characteristically large stiffness to mass ratio (2.571 MNm/kg), or specific stiffness, Polymers 2019, 11, 1042; doi:10.3390/polym11061042 www.mdpi.com/journal/polymersPolymers 2019, 11, 1042 when compared to similar thermoplastics in this field such as poly(ethylene terephthalate) (PET) and polypropylene (PP)—exhibiting stiffness to mass ratios of 1.206 and 1.935 MNm/kg respectively.The industrial practice of thermoforming is widely used for the large-scale manufacture of lightweight, thin-walled polymeric parts with the advantage of producing repeatable, complex products, along with relatively cheap production costs. Trial and error approaches in the hopes of optimising the formed part is often time consuming, causing authors to take a more systematic methodology This is predominantly achieved through the use of a mathematical material model to represent the deformation behaviour subject to characteristic loading experienced during forming processes. In order for this mathematical model to be accurate in its predictions of the mechanical behaviour of the polymeric material, characterisation at conditions comparable to those experienced during the forming process is encouraged [2,3,4]—allowing the constitutive model to be calibrated and implemented into a process simulation [5,6,7] with the ultimate aim of optimising the forming conditions and/or the formed part
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