Numerical simulation of self heating during stretch blow moulding of PET: viscohyperelastic modelling versus experimental results

Abstract

During the stretch blow moulding (SBM) process of polyethylene terephthalate (PET) bottle, high viscous dissipation generates self heating phenomena. Since the influence of temperature on polymer’s behavior is important, it is necessary to evaluate the self heating values in order to manage accurately the simulation of the process. An anisotropic visco-hyperelastic model has been developed to manage numerical simulations of free blowing. The model takes into account the anisotropy and the effect of the temperature. It has been computed in a user-interface VUMAT implemented in the software ABAQUS/Explicit. The identification of the model is based on experimental data of biaxial tension tests. We identified the characteristics taking into account the self-heating effect by a semi analytical process followed by an adjustment using finite element. For sake of validation, PET preforms have been blown from different initial temperature and followed using a thermal camera. The increase of temperature is measured by comparing initial temperature and final temperature. Comparison between the experimental and numerical simulations is discussed and influence of initial temperature or blowing pressure is highlighted in a large numerical investigation.

Introduction

The ISBM process is widely used in the bottling industry to produce PET bottles. This process is managed at a temperature slightly above the glass transition temperature Tg before stretching and inflating inside a bottle mould. Multiple research groups, industrial or academic, have examine the deformation of PET during the ISBM process. Their goal was to comprehend and to model the procedure using numerical simulation. Therefore, numerous approaches have been developed during the 20 last years [1,2,3,4,5,6,7]. The microstructural morphology of PET strongly affects the thermal behavior of the PET during the process. This in turn affects the distribution of the temperature of final bottle, thickness, crystallinity and orientation. These distributions are responsible for the final products’ mechanical properties [8, 9]. An increase of temperature allows chain mobility and relaxation reduces the extension of macromolecular chains [10]. The effects of temperature and heating conditions that have a fundamental importance during ISBM process are the topic of this study.

Regarding the experimental approach, some experimental methods [11,12,13] were among the first study on the PET sheet where the geometry is less complex than a preform. Through their researches, the thermal parameters of the infrared oven and the interaction between the emitter and the PET sheet can be characterized. Later, for the preform case, Huang et al. [14] investigated the use of thermocouples inserted into the preform thickness. Nevertheless, this method remains highly delicate. Recently, Salomeia et al. [15] and Menary [16] did the temperature measurements of the air blown inside the bottle. Their experimental work provided numerous data for the thermal boundary conditions for the ISBM simulations. Temperature was measured using a thermocouple junction mounted in the metallic stretch rod with a silicon sealant. The evolution of the mean temperature of the blown air blown in the hot preform can then be determined.

Besides, the numerical approach has seen a rapid growth in the last decade. Different models were implemented into commercial finite element code [17, 18]. Others developed their own software [13, 19,20,21] to predict the preform temperature distribution. In previous papers [22, 23], we also, have presented a contribution on the thermal aspects of the ISBM process: the identification procedure of the thermal properties of PET sheets from IR heating tests including the natural air convection effect. More recently, an accurate thermal boundary condition has been provided to perform a 3D thermal finite element simulation of the infrared heating [24]. In the stretch blowing stage, numerous reliable and robust simulations of the ISBM process has been managed in order to produce any desired bottle shape [2, 4, 25,26,27,28,29]. This simulation is generally conducted using some form of finite element solver. The classical viscoelastic models such as the Upper Convected Maxwell model [30, 31] do not adequately demonstrate the strain hardening effect during the ISMN process. Schmidt et al. [25] used a viscoelastic model taking into account the strain hardening effect in ISBM simulation and developed a non-isothermal finite element simulation to embed heat transfer during the deformation process. The prediction of the thickness distribution was not significantly improved and these simulations did not show areal improvement the force evolution exerted by the stretch rod. Later, Menary et al. [26, 29] applied a nonlinear viscoelastic model (Buckley’s model) [32] in the ISBM simulation using the finite element package ABAQUS/standard and showed fine agreement with thickness distribution and bubble evolution. Here, we present a different type of visco-hyperelastic modelling coupled to temperature in order to simulate the self-heating phenomena.

In the first part of this work, we recall some results on an experimental study: we have partially presented, in a previous publication [7], results on free blowing of preforms managed at various initial temperatures and blowing pressures. Infrared camera was used to capture the temperature field and comparing the initial and final values in the same area of the PET preform, we evaluate the increase of temperature due to deformation of the preform. We focus on bubble that have the same inside volume to characterize the self-heating phenomenon.

In the second section, a numerical study of the free blow case is performed. We identified the properties of the visco-hyperelastic model previously presented in its orthotropic version in [33]. It has been extended here, to be coupled with the thermal equation and is used to characterize the PET behavior. It has been done from experimental data issued from biaxial tension tests and taking into account the self-heating effect. We have computed and implemented our model via a user-interface VUMAT, into the software ABAQUS and we performed free blowing simulations. The effect of the temperature and the induced anisotropy are taken into account in these simulations. Both numerical and experimental results of the self heating phenomena are compared and discussed in the last section.

Experimental study of free blowing case

Injected preforms designed for carbonated soft drinks are provided by SIDEL. They are used to study the self heating phenomena. We prepare these preforms by heating it with 8 infrared lamps in order to provide different initial thermal conditions. A free blowing apparatus developed at laboratory MSME (Fig. 1) allows to produce different blowing pressure. The temperature distribution on the external surface of the preform was measured using a FLIR B250 infrared camera. The camera’s wavelength range is 7.5–13 μm and is used to follow the evolution of the preform during the entire blowing process. The PET material is opaque under the wavelength in the range of 8–12 μm. The assumption is made of a constant emissivity value for this temperature level.

Fig. 1

Experimental set-up for free blowing: preform is heated by 8 infrared lamps and a thermal camera is used to measure the evolution of temperature

For the pressure measurement, we use the manometer shown on Fig. 2. The sampling rate of this manometer is 10 values of pressure per second.

Fig. 2

Manometer for measuring the pressure

Figure 3 shows under different heating temperature, the pressure rise rate is same to obtain the setting pressure. The history of pressure can be implemented as the boundary condition in the numerical simulation.

Fig. 3

Evolution of pressure during the blowing stage

Table 1 shows the different initial temperature and the different pressure condition used to obtain similar final elongation. Temperature is measured from thermal camera that gives the outside surface temperature. This temperature can be very different from the inside surface one at the beginning of the process but the bubble thickness becomes very small and we can assume the final temperature is uniform in the thickness direction.

Table 1 Measured elongations of blown preform in longitudinal and circumferential directions

The volume of a bottle is measured from the weight of the water needed to fill the bottle. Higher the initial temperature is lower pressure is needed for the same volume of bottle. The cross means the exploded case.

Furthermore, the longitudinal and circumferential elongations λ_z and λ_θ are measured by comparing the distance between regular spots on the preform and the same ones on the blown bottle. As presented in [7], biaxial elongations are measured from an initial grid drawn on the preform before blowing and measured after blowing. In Table 1, mean values of these elongations are listed in different region of the bottle for the selected tests. The circumferential elongation in the center part is around 4 for 85 °C, 100 °C and 105 °C, and it equals 3.5 for the 90 °C and 95 °C. This value is about 1.5 times larger than the longitudinal elongation (2.5 for all cases). Longitudinal and circumferential elongation difference induces anisotropy in the morphology of the PET material during the process that must be taken into account if one needs to model the blowing process. It also induces anisotropy in the mechanical properties, especially longitudinal and circumferential elastic modulus are different.

Temperature measurements during free blowing of PET preform is illustrated on Fig. 4. We determine the increase of temperature by comparison between the initial temperature in three zones located near the neck, in the middle of the preform height, near the bottom; with the final temperature in these three zones located near the neck, in the middle of the bottle height and near the bottom.

Fig. 4

Pictures of temperature field and strain measurements during free blowing of PET preform.a Snapshot of the temperature field and location of area where initial temperature is measured, b large rectangles on the final bottle give the corresponding final temperature, c preform captured from classical camera, black spots are regularly drawn on the preform, d blown bottle: dark spots enable the evaluation of the stretch ratio for each direction longitudinal and circumferential

Table 2 gives the increase of temperature in these three zone for different initial temperature. One can see that the self heating phenomena can lead to 18 °C of increase of the temperature and does not vary significantly from different zone and different initial temperature. In particular, zone 5–6 has a bigger elongation in the hoop direction and also an initial temperature lower than in other region of the preform. Consequently, the increase is higher in this zone.

Table 2 Increase of the mean temperature during free blowing: for 3 different areas chosen and the mean value

The mean difference does not exceed 20% and this means that initial temperature has not an important effect on the self heating phenomena.

Temperature-dependent viscohyperelastic model

The non linear incompressible visco-hyperelastic (VHE) model has been presented and identified in author’s previous publications [6, 22]. Our isotropic version of the model failed to predict the correct aspect ratio between length and radius of the blown bottle so an anisotropic version has been developed. The anisotropy is introduced in both the viscous and elastic parts of the model in order to represent the strain hardening effect that appears during elongations at this temperature slightly over T_g [24]. The anisotropic version of the VHE model has a Maxwell like form in finite strain.

For the elastic part, the strain hardening effect needs to be represented by an exponential function of elongation so we choose a Hart-Smith like model for this part. We use invariants of the elastic left Cauchy Green tensor $\underline {\underline {B_e}}$ associated to the isotropic and anisotropic material behavior have to be defined to build the model. I₁, I₂ and I₃ are the classical invariants, and I₄, I₅ and I₆ are associated to the anisotropic behavior.

$$ {\displaystyle \begin{array}{c}{I}_1= tr\left(\underline {\underline {B_e}}\right),\kern0.5em {I}_2=\frac{1}{2}\left[ tr{\left(\underline {\underline {B_e}}\right)}^2- tr\left(\underline {\underline {B_e^2}}\right)\right],\kern0.5em {I}_3=\det \left(\underline {\underline {B_e}}\right),\\ {}{I}_4=\underline {n_1}\cdotp \underline {\underline {B_e}}\cdotp \underline {n_1},\kern0.5em {I}_5=\underline {n_2}\cdotp \underline {\underline {B_e}}\cdotp \underline {n_2},\kern0.5em {I}_6=\underline {n_3}\cdotp \underline {\underline {B_e}}\cdotp \underline {n_3}\end{array}} $$

(1)

$\underline {n_1}$, $\underline {n_2}$ and $\underline {n_3}$are the privileged directions for orthotropic properties. Three second order structural tensors $\underline {\underline {A_i}}$ can be calculated with the dyadic product of the preferred directions with themselves:

$$ \underline {\underline {A_1}}=\underline {n_1}\otimes \underline {n_1},\kern0.5em \underline {\underline {A_2}}=\underline {n_2}\otimes \underline {n_2},\kern0.5em \underline {\underline {A_3}}=\underline {n_3}\otimes \underline {n_3} $$

(2)

In our case, specimen and bottle are shells and we assume that 1 and 2 are the in-plane direction; 3 is the normal direction. Consequently, invariant related to direction 3 are not used as well as structural tensor A₃. The Hart Smith model chosen to characterize the free energy function writes:

$$ \underline {\underline{\sigma}}=-p\underline {\underline{I}}+2{G}_1{e}^{\Lambda_1{\left({I}_1-3\right)}^2}\underline {\underline {B_e}}+2{I}_4{G}_2{e}^{\Lambda_2{\left({I}_4-1\right)}^2}\underline {\underline {A_1}}+2{I}_5{G}_2{e}^{\Lambda_2{\left({I}_5-1\right)}^2}\underline {\underline {A_2}} $$

(3)

Where σ is the Cauchy stress calculated from the strain energy andG₁, G₂, Λ₁ and Λ₂ are parameters of the elastic part of the visco-hyperelastic model. p is the pressure associated to the incompressibility condition of the elastic part.

For the viscous part of the model, we introduce the deviatoric stress tensor $\underline {\underline {\hat{\sigma}}}$:

$$ \underline {\underline {\hat{\sigma}}}=2\underline {\underline {\underline {\underline{\eta}}}}\underline {\underline {D_v}}\kern1em \mathrm{that}\ \mathrm{also}\ \mathrm{writes}:\kern1em \left(\begin{array}{c}{\hat{\sigma}}_{11}\\ {}{\hat{\sigma}}_{22}\\ {}\sqrt{2}{\sigma}_{12}\end{array}\right)=2\left[\begin{array}{ccc}{\eta}_{11}& {\eta}_{12}& 0\\ {}{\eta}_{12}& {\eta}_{22}& 0\\ {}0& 0& {\eta}_{44}\end{array}\right]\left(\begin{array}{c}{D}_{v11}\\ {}{D}_{v22}\\ {}\sqrt{2}{D}_{v12}\end{array}\right) $$

(4)

where D_v is the viscous strain rate. We choose specific h_i functions for each orthotropic direction. In our case, for the bottle description, i=1is the hoop direction and i=2 the longitudinal one:

$$ \left\{\begin{array}{l}{\eta}_{11}={\eta}_0(T){h}_1f\left(\overline{{\dot{\varepsilon}}_v}\right)\\ {}{\eta}_{12}={\beta \eta}_0(T)\max \left({h}_1,{h}_2\right)f\left(\overline{{\dot{\varepsilon}}_v}\right)\\ {}{\eta}_{22}={\eta}_0(T){h}_2f\left(\overline{{\dot{\varepsilon}}_v}\right)\\ {}{\eta}_{44}={\eta}_0(T)h\left(\overline{\varepsilon_v}\right)f\left(\overline{{\dot{\varepsilon}}_v}\right)\end{array}\right. $$

(5)

With:

$$ \left\{\begin{array}{l}{h}_1=\left(1-\exp \left(-K{\varepsilon}_{v1}\right)\right)\cdot \exp \left({\alpha}_1{\left(\frac{\varepsilon_{v1}}{\varepsilon_{vref}(T)}\right)}^2+{\alpha}_2\left(\frac{\varepsilon_{v1}}{\varepsilon_{vref}(T)}\right)+{\alpha}_3\right)\\ {}{h}_2=\left(1-\exp \left(-K{\varepsilon}_{v2}\right)\right)\cdot \exp \left({\alpha}_1{\left(\frac{\varepsilon_{v2}}{\varepsilon_{vref}(T)}\right)}^2+{\alpha}_2\left(\frac{\varepsilon_{v1}}{\varepsilon_{vref}(T)}\right)+{\alpha}_3\right)\end{array}\right. $$

(6)

The expressions of these equations are purely phenomenological one. For Eq. 6 the form is chosen to reproduce the two change of curvature observed on experimental tests. On test, an asymptotic value seems to be reached for elongations but we choose to represent it with an exponential form to avoid numerical problem.

And, coupling with temperature appears through the expressions:

$$ f\left(\overline{{\dot{\varepsilon}}_v}\right)=\frac{1}{{\left(1+{\left(\lambda \overline{{\dot{\varepsilon}}_v}/{\dot{\varepsilon}}_{ref}\right)}^a\right)}^{\frac{1-m}{a}}} $$

(7)

$$ \ln \left({\alpha}_T\right)=\frac{-{C}_1\left(T-{T}_{ref}\right)}{C_2+T-{T}_{ref}},\kern0.5em {\eta}_0(T)={\alpha}_T{\eta}_0\left({T}_{ref}\right) $$

(8)

$$ {\varepsilon}_{vref}(T)=\frac{\varepsilon_{vref}\left({T}_{ref}\right)}{\exp \left(-{C}_3\left(T-{T}_{ref}\right)+{C}_4\right)} $$

(9)

where λ, m, a are parameters of the Carreau type function $f\left(\overline{{\dot{\varepsilon}}_v}\right)$ and ${\dot{\varepsilon}}_{ref}$ is a reference strain rate that can be taken equal to 1 s⁻¹ for sake of simplicity. β is a parameter that indicates the difference between the beginning of the hardening effect in equal biaxial tension test and constant width tension test. From biaxial elongation tests [6] one can identify K, α₁, α₂ and α₃, the parameters of the h function. Variables η₀(T) and ε_vref(T) show a significant dependence on temperature. We choose the Williams-Landel-Ferry (WLF) model for the evolution of η₀(T). C₁ and C₂ are the WLF parameters, T_ref=90 °C.C₃ and C₄ are parameters in the expression of ε_vref(T).

Therefore, putting together the elastic and viscous expressions of the deviatoric part of the stress tensor, one can obtain:

$$ 2\underline {\underline{\eta}}\underline {\underline {D_v}}=2{G}_1{e}^{\Lambda_1{\left({I}_1-3\right)}^2}\underline {\underline {\hat{B_e}}}+2{I}_4{G}_2{e}^{\Lambda_2{\left({I}_4-1\right)}^2}\underline {\underline {\hat{A_1}}}+2{I}_5{G}_2{e}^{\Lambda_2{\left({I}_5-1\right)}^2}\underline {\underline {\hat{A_2}}} $$

(10)

That leads to:

$$ \left(\begin{array}{c}{D}_{v11}\\ {}{D}_{v22}\\ {}{D}_{v12}\end{array}\right)=\left[\begin{array}{ccc}\frac{\eta_{22}}{\eta_{11}{\eta}_{22}-{\eta}_{12}^2}& \frac{-{\eta}_{12}}{\eta_{11}{\eta}_{22}-{\eta}_{12}^2}& 0\\ {}\frac{-{\eta}_{12}}{\eta_{11}{\eta}_{22}-{\eta}_{12}^2}& \frac{\eta_{22}}{\eta_{11}{\eta}_{22}-{\eta}_{12}^2}& 0\\ {}0& 0& \frac{1}{\eta_{44}}\end{array}\right]\left(\begin{array}{c}{\overset{\sim }{d}}_{11}\\ {}{\overset{\sim }{d}}_{22}\\ {}{\overset{\sim }{d}}_{12}\end{array}\right) $$

(11)

Where:

$$ \left(\begin{array}{c}{\overset{\sim }{d}}_{11}\\ {}{\overset{\sim }{d}}_{22}\\ {}{\overset{\sim }{d}}_{12}\end{array}\right)=\left(\begin{array}{c}{G}_1{e}^{\varLambda_1{\left({I}_1-3\right)}^2}\hat{B_{e11}}+{G}_2{I}_4{e}^{\varLambda_2{\left({I}_4-1\right)}^2}\hat{B_{e11}}\\ {}{G}_1{e}^{\varLambda_1{\left({I}_1-3\right)}^2}\hat{B_{e22}}+{G}_2{I}_5{e}^{\varLambda_2{\left({I}_5-1\right)}^2}\hat{B_{e22}}\\ {}{G}_1{e}^{\varLambda_1{\left({I}_1-3\right)}^2}\hat{B_{e12}}\end{array}\right) $$

(12)

In the following, Eq. 11 is implemented in a finite element code, first to identify the parameters from the tension tests and then, to simulate the ISBM process. Table 3 lists the identified characteristics of the PET near Tg at high strain rate.

Table 3 The characteristics of the PET

Identification of the model is managed using experimental data from constant width test and equi-biaxial test. Using the identified parameters one can plot Fig. 5 and compare the numerical and experimental equal biaxial results: strain rate 8 s⁻¹ for temperature 90, 95, 100, 105 and 110 °C. For each temperature, the mean difference between numerical results and experimental data does not exceed 20%.

Fig. 5

Comparison between experimental results (a) and model simulations (b)

Thermal-mechanical simulation of the free blowing process

The model is implemented into the software ABAQUS / Explicit via a user interface VUMAT [24]. In order to compare the experimental result, we focus on the simulation of the free blowing case. The internal pressure evolution obtained by the manometer from experimental study is implemented as a boundary condition in the simulation. The preform geometry is meshed by 36 shell elements in ABAQUS. The bottle shape and the pressure distribution are axi-symmetric so we use axi-symmetric elements to reduce the number of degrees of freedom of the problem and CPU time. A classical Newton Raphson iterative procedure is used to solve this strongly nonlinear problem.

In order to evaluate the evolution of temperature, we performed a thermal-mechanical simulation. The initial temperature is entered as the initial condition. Because the blowing process is fast (blowing the preform takes less than 5 s) we assume that no heat exchange between the preform and ambient air occurs and that diffusion inside the preform is slow, so that the major contribution to the self heating phenomenon is due to viscous dissipation. The entropy of rubber networks convection or latent heat due to crystallization are neglected so the energy dissipation is evaluated by $\underline {\underline{\sigma}}:\underline {\underline {D_v}}$. Therefore, the thermal part can write as follow:

$$ \rho {C}_p\frac{dT}{dt}=\underline {\underline{\sigma}}:\underline {\underline {D_v}} $$

(13)

With ρ=1330kg⋅m^-3 and C_p=1200J⋅kg^-1⋅K^-1 for PET material in this range of temperature. Thanks to this thermal-mechanical simulation, one can compare the increase of temperature from numerical simulation with the one obtained during the test for each initial temperature.

As an example, Fig. 6 shows the temperature distribution and the shape evolution from the initial preform to the final bottle. The evolution of temperature during blowing from the finite element simulation is compared to the experimental measurements. In this numerical simulation, the initial temperature is 90 °C and the self heating is about 17 °C in the middle part of the bottle. One can appreciate the similarity of the shape evolution and the temperature distribution.

Fig. 6

Comparison between simulation and experimentation for the initial temperature equal to 90 °C. The increase of temperature from thermal camera (upper pictures) and the one from finite element simulation of free blowing (lower snapshots)

The influence of the mesh refinement from 35, 70 and 140 elements has been investigated on the case of 90 °C initial temperature. We note an influence on the final volume that shows an asymptotic evolution reported in Fig. 7.

$$ V(N)={V}_{\infty }+\left({V}_{ref}-{V}_{\infty}\right)\exp \left(-\lambda \left(N-{N}_{ref}\right)\right) $$

(14)

Where: N_ref=35 elements, V_ref=990 ml and V_∞=855 ml. The evolution fits perfectly with λ=0.04. The change of volume is due to the decreasing influence of the mesh on both elongations. The mean increase of temperature is not affected and it remains equal to 16–17 °C. On the other side, the CPU time increases a lot from 5 to 65 h on classical PC. Consequently, we made our discussion on “coarse” mesh.

Fig. 7

Influence of mesh refinement on shape evolution (a) the final shape is different near the neck and inside volume reduces when number of element increase (b) an asymptotic influence of the mesh refinement can be modelled by and exponential function

Table 4 presents the increase of temperature for all tested initial temperature: the increase ΔT does not vary significantly for the chosen cases. For a given initial temperature, one can see that the increase of temperature can reach about 19 °C. One can appreciate the good agreement between the experimental increase measured by the thermal camera with the numerical simulation result.

Table 4 Increase of temperature (ΔT) under different initial temperature condition

Table 5 shows the longitudinal and circumferential elongations λ_z and λ_θ in top, center and bottom regions. These are the elongations obtained by numerical simulation; they can be compared to the elongations obtained from experimental measurements.

Table 5 Comparison between the experimental and numerical results

One can see that the final volume from simulation is a little higher than the experimental one, but the difference is less than 15%: the simulated elongation are higher than the experimental one.

These differences are partially due to the experimental conditions: the initial temperature field, for example, is not uniform on the preform. Natural convection that appears during the tests is not taken into account in the simulation but generates a difference of about 3 °C between the bottom of the preform and the mid region. The difference is also due to the elastic strain recovery: the internal volume is measured when no more pressure is inside while the numerical simulation is managed with pressure until the end.

The pressure decreasing generates an elastic recovery of strain that reduces the inside volume. For example, we consider that this elastic return appears at room temperature for an induced Young modulus of PET around 2000 MPa in longitudinal direction and 3000 MPa in the hoop direction. For 5 bar internal pressure, 50 mm radius ant 0.3 mm thickness, the mean stress can reach 37 MPa in the longitudinal direction and 75 MPa in the hoop direction. Consequently, the longitudinal strain recovery is about 0.17% in longitudinal direction and 0.25% in the hoop one. That leads to a decrease of 7% of the internal ratio and explains half of the difference since no elastic return s taken into account in the simulation.

Numerical simulation helps us to explore different conditions of max pressure and initial temperature in order to confirm the tendency observed experimentally. To that issue, new simulations are managed and results have been summarized in Table 6 and Fig. 8. One can see that, on a wide range, the increase of temperature varies with the pressure. For 85 °C of initial temperature and 2.5 bar pressure, the preform is not stretched and there is no self heating phenomena. For 105 °C of initial temperature and 7 bar pressure, the volume of the blown bottle can reach 2790 ml and the increase of temperature is 64 °C. This case leads to the bottle explosion in the experimental case.

Table 6 Different “max pressure / initial temperature” cases managed by simulation

Fig. 8

Final shape and self heating for different pressure and initial temperature

Figure 9 summarizes all results in two graphs that represent the evolution of the mean increase of temperature during the process versus max pressure and the internal volume after blowing versus max pressure. Each curve is corresponding to a different initial temperature. One can see that both series of curves are monotonous even if one can notice a slight plateau around 5-6 bar. This means that there is, in fact an effect of pressure and temperature but the experimental condition chosen were not wide enough to highlight it. One can also notice the correlation between the ΔT evolution and the volume increase and so, when volume is almost equal (as in the experimental series) one can see that the self heating ΔT is also almost constant.

Fig. 9

Effect of pressure on self heating (a) and final volume (b)

Conclusions

An experimental study on PET preform has been managed: free blowing of preforms at various initial temperature and blowing pressure. In order to compare the self-heating phenomenon, bottles with identical internal volume (with the same final strain applied) were selected and the mean increase of temperature (the self heating) during blowing was measured. We did not detect any influence and that means that only the final strain is involved in the self heating phenomena, independently of the strain rate.

On the other hand, a visco-hyperelastic orthotropic model coupled with the temperature and identified from experimental data of biaxial tension tests, has been computed in a user- interface VUMAT and implemented into the ABAQUS software ABAQUS. We performed free blowing simulations, taking into account the anisotropy and the effect of the temperature. The comparison between self heating measured and self heating obtained from numerical simulation are quasi identical and this validates the toughness of our modelling of the PET behavior near T_g at high strain rates.

As a complement, a complete series of numerical simulation has been achieved using the VHE model and final internal volume and self heating follow the same monotonic evolution versus pressure. That confirms that the self heating phenomena is mainly due to the elongation ratio and not from strain rate. As well, it has been shown that more initial temperature more the volume and the self heating but this has to be nuanced for the range 5-7 bar where self heating does not vary much with pressure.