Biaxial characterisation of poly(ether-ether-ketone) for thermoforming: A comparison between bulge and in – plane biaxial testing

The biaxial response of extruded PEEK films at conditions relevant to thermoforming has 10 been investigated extensively using a combination of load controlled (bulge test) and displacement 11 controlled (biaxial stretcher) experiments. Results from bulge testing yielded average and 12 maximum strain rate ranges of 2.5 – 5 s-1 and 5 – 18 s-1 respectively, across the forming temperature 13 range. In-plane biaxial characterisation highlighted the anisotropic non-linear viscoelastic 14 behaviour of the films with strong dependence on the yield and strain hardening behaviour on the 15 temperature and strain history at conditions equivalent to the forming process. The combined 16 approach to material characterisation highlights the pros and cons of each test method, the 17 complementary nature of the data generated and the need to use both methods to have a complete 18 data set for developing accurate material models and validated numerical simulations of 19 thermoforming. 20


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Thermoforming is commonplace for the large-scale manufacture of thin-walled, polymeric 24 products due to the repeatability of the process for complex parts, with the advantage of relatively 25 cheap production costs. Although the thermoforming process can differ greatly in scale and 26 complexity according to the eventual application, parts are intrinsically fabricated through the 27 radiative heating of the thermoplastic sheet above its glass transition temperature (Tg), and then 28 forcing it to rapidly deform and take the shape of a pre-defined mould, either through air pressure, 29 mechanical contact or a combination of both. The material is then allowed to cool and then released for Short Fibre Reinforced Composites (SFRC). A number of studies have examined the uniaxial 48 tensile properties over a wide range of strain rates and temperatures. Initial studies by Cebe et al. [5] 49 investigated the temperature dependency of mechanical properties of PEEK samples of differing 50 thermal histories, at temperatures of 125⁰C, 25 ⁰C and -100 ⁰C. This work was further complemented 51 by work by Alberola et al. [6], and more recently by , examining the effect 52 of strain rate on similarly treated samples. Rae et al. [8], although extensively focussing on the 53 compressive properties of PEEK, investigated the initial uniaxial tensile behaviour approaching the 54 Tg of PEEK specimens. Conclusions drawn by all of the aforementioned studies appear to be 55 consistent, with PEEK exhibiting a profound dependence on both temperature and strain rate -the 56 yield stress of specimens seen to decrease with increasing temperature, and the opposite being true 57 for increasing strain rate. Ductility was also seen to have a positive correlation with increasing sample 58 temperature [8].

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Although the above-mentioned literature has provided a comprehensive understanding of the 60 fundamental mechanical behaviour of PEEK in uniaxial tension, to the best of the author's knowledge 61 no studies exist concerning the simultaneous or sequential tensile deformation behaviour in more 62 than one axis. As outlined previously, this mechanical characterisation is of particular concern in 63 order to fully understand the material behaviour during thermoforming processes. Upon knowledge 64 of the biaxial response of PEEK film specimens, there lies potential for a mathematical model to be 65 fitted representative of the observed deformation behaviour, along with possible implementation 66 into a forming simulation capable of the accurate prediction of the final shaped part. A similar 67 modelling approach has been outlined by previous authors through either load-controlled [9][10][11][12] or 68 displacement controlled testing [1,[13][14][15] for a wide array of material types.

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The aforementioned limitations of unidirectional testing for the characterisation of materials for 70 thermoforming / blow moulding applications has led to a number of institutions building specialised 71 biaxial test rigs capable of deforming polymeric films under biaxial conditions [1,16] conditions. Whilst indispensable in understanding material behaviour and dependencies, little 86 consideration for the actual forming history is shown -often limiting the calibration of these models 87 to idealised equal-biaxial (EB) and constant width (CW) deformation modes. This is obviously not 88 the case during the manufacture of complex parts using industrial forming practices where strain 89 rate and mode of deformation will vary arbitrarily depending on the process conditions.

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As outlined previously, biaxial deformation is the dominant mode experienced during 91 thermoforming, when subject to air pressure. A complementary material characterisation method 92 analogous to the forming process, such as the load-controlled bulge test, is vital in outlining 93 appropriate strain rates and mode of deformations to be investigated along with validating any test particularly applicable for investigation into the induced states of stress during the 100 thermoforming process due to their analogous nature. By subjecting the thin polymer film to forming a detailed insight into the deformation behaviour and possible influences of external variables on the polymers for thermoforming processes [19,20]. These studies have identified the analogy between 106 the bulge test and thermoforming although the data produced is yet to be used to characterise and 107 model polymers for FE simulation applications. Other work has directed efforts to using the bulge 108 test to impose a biaxial state of stress onto specimens and then attempt to model this response using 109 constitutive equations. Sasso and Amodio [9] conducted bulge testing on rubber specimens with the experimental data produced used to fit hyperelastic material models within FE simulations of the 111 bulge test. Tonge et al. [12] used the bulge test to characterise the stress-strain response of human 112 skin tissues. Once more, material models of the observed behaviour were validated through FE 113 simulations. Although not directly applicable to this work, these studies demonstrate the potential 114 for biaxial data to be produced using with subsequent material models calibrated to describe the 115 resultant deformation behaviour of this characterisation technique. One limitation of this approach, 116 however, is the lack of knowledge over specific parameters (e.g. temperature and strain rate) in 117 understanding their individual influence on the resultant material behaviour. The combination of 118 several factors acting together creates difficulty in distinguishing the separate effects of these 119 parameters on the stress -strain response, as tests at different temperatures will experience different 120 speeds of deformation. It is here that displacement-controlled testing, with defined uniform strain 121 rate at varying temperatures, has the capability to complement the findings in a load-controlled 122 analysis.

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A potential use of both load-controlled bulge testing and displacement-controlled planar biaxial

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Although not within the field of thermoforming, Yan et al. [22] investigated the potential use of 132 a free stretch blow (FSB) test to be used in combination with in-plane biaxial testing to characterise

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In the present work, we propose two methods of applying a biaxial state of stress on PEEK 140 samples: a load controlled bulge test and a displacement controlled in-plane biaxial test. The ultimate 141 aim of this work is to use both characterisation methods to determine the constitutive response of 142 PEEK films subject to multiaxial stress. Firstly, the bulge test is adopted to generate stress -strain 143 data observed at the pole of the deformed specimen, along with identifying typical strain rates 144 observed during the thermoforming process. In-plane biaxial testing is subsequently used to 145 characterise the stress -strain response of PEEK films as a function of strain rate and temperature, 146 with replication of the loading paths observed in the bulge test used to compare and conclusively 147 validate the observed material behaviour.

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Fastcam SA1.1) were placed in plane with the custom rig to track the bulging displacement of 175 specimens synchronously, dictated by a random speckle pattern applied manually using a paint 176 marker. Vic-3D 7 software was used for the DIC analysis, with the options adopted in the correlation 177 step shown in Table 1. Due to the transparent nature of the specimens, the background of the lower 178 die was spray painted white in order to create sufficient contrast of the pattern to be recognised by 179 the cameras. A targeted light source was also employed to improve the recorded images. One 180 phenomenon particularly apparent however whilst using targeted lighting on smoothly curved 181 surfaces is that of a highly concentrated area of reflection -known as specular reflection. These polar 182 reflections appear as a spot of highly saturated pixels, and due to the ever-evolving nature of the 183 bulge, can be seen to travel throughout the analysis from the perimeter to the pole. This can be 184 particularly troublesome when conducting DIC analysis as the travelling reflection misleads the 185 analysis into thinking the specimen is deforming locally during incremental correlation, even causing 186 the path of the reflection to be erased during conventional correlation. In order to mitigate this, the 187 technique of cross polarization [25] was adopted using a series of perpendicular linear polarizers 188 placed between the light source and the camera lens. This method obstructs the orthogonally 189 polarised specular reflection from reaching the camera aperture allowing only diffuse lighting to where σ is the biaxial stress in both directions, R is the radius of curvature, and t the actual thickness 202 at the pole of the bulge. Recent work by Min et al. [26] had accounted for potential anisotropic 203 deformation in bulging specimens, in the calculation of principal stresses at the specimen pole (Eq.

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(2): 205 206 replicating temperature, complex deformation modes, and rapid deformation speeds similar to those 212 seen in thermoforming and blow moulding processes. The square specimens, of maximum allowable 213 thickness of 2mm, are held in place by 24 nitrogen-driven pneumatic clamps as shown in Figure 2(a).

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Once secured, the sample is heated to the desired temperature by two convection heaters, one above 215 and below the sample. Temperature control is provided by thermocouples placed in close proximity 223 224 where F is the force as measured by the force transducer, A0 is the original cross-section area and εeng 225 is the engineering strain in the specimen. Figure 2

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The evolution of strain rate was probed for each temperature and is displayed in Table 2. It is 275 apparent that increasing specimen temperature induces an increase in average and maximum 276 deformation rate observed in both directions, again due to the increasingly softer material behaviour.

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Similarity in this deformation behaviour is apparent with that observed in calculated bulge test stress 302 curves shown in Figure 6.

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With increasing specimen temperature the yield stress in both directions is observed to decrease, 304 similar to that observed in uniaxial tensile experiments [8]. A prominent increase in the strain at    conditions. The load-controlled bulge test is invaluable in understanding the influence of process 364 conditions on the resultant deformation of the material as it provides valuable data on typical strain 365 rates experienced by the material along with its response when subjected to nonlinear loading paths.

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The test also enables a good experimental idealisation of the thermoforming process and thus 367 provides valuable data that can be used for validating forming simulations. However, the apparent 368 weakness of this characterisation technique is the ambiguity concerning the individual contributions 369 of strain rate and temperature on the material deformation behaviour, as highlighted between 370 temperatures of 150 ⁰C and 155 ⁰C in Figure 6.

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The displacement controlled biaxial stretching experiments however clearly separate the 372 effects of temperature and strain rate, as shown in Figure 7 - Figure 9. This displacement controlled 373 data is essential for material model development, where the effects of strain rate and temperature 374 need to be accurately quantified and captured.

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In this work, the biaxial deformation behaviour of commercially sourced PEEK was quantified 377 at temperatures and strain rates relevant to the thermoforming process. DIC measurements focussing 378 on the bulge pole reported an initial disparity between strains achieved in principal directions due to