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Bubble assisted vacuum thermoforming: considerations to extend the use of in-situ stereo-DIC measurements to stretching of sagged thermoplastic sheets

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Abstract

In bubble assisted vacuum thermoforming, measuring pressure-induced mechanical strains through the stereo-digital image correlation (stereo-DIC) technique while shaping thermoplastic sheet requires consideration of an appropriate reference state of surface deformations. However, when the stereoscopic measurements can be only performed after the heating step, the correlation problem should be well-posed otherwise the reliability of results is limited. This study focuses on stretching by bubble inflation processes following thermal warpage and sagging of initially flat sheets. For this purpose, an experimental rig is instrumented to heat high impact polystyrene (HIPS) sheets and to perform synchronized pressure and stereoscopic measurements during 1.5 s stretching. A two-step method is introduced to separate mechanical strains which are affected by the uncontrollable change of initial conditions from the global stereo-DIC strains. The first step relies on amplification of damped oscillations at the initiation of the inflation process due to sagging. Out-of-plane displacements confirm the existence of a temperature-dependent characteristic time that marks the transition from the sagged to the strained surface shapes. The second step uses these characteristic times to objectively shift the reference of image-correlation computations. To evaluate the effectiveness of the suggested method, inaccuracy levels of global strains are evaluated at a fixed pressure level under different thermal conditions. It is shown that inaccuracy levels are the highest when stereo-DIC measurements followed warpage and they decrease with amplification of sagging. The developed approach extends the use of in-situ stereo-DIC measurements when changes of initial conditions are uncontrollable and thermal strains cannot be measured.

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References

  1. Ayadi A, Lacrampe M-F, Krawczak P (2018) A comprehensive study of bubble inflation in vacuum- assisted thermoforming based on whole-field strain measurements. In: AIP Conference Proceedings 1960. American Institute of Physics

  2. Leite W, Campos Rubio J, Mata Cabrera F et al (2018) Vacuum thermoforming process: an approach to modeling and optimization using artificial neural networks. Polymers (Basel) 10:143. https://doi.org/10.3390/polym10020143

    Article  Google Scholar 

  3. Yoo YG, Lee HS (2011) Effects of processing conditions on thickness distribution for a laminated film during vacuum-assisted thermoforming. Trans Mater Process 20:250–256. https://doi.org/10.5228/KSTP.2011.20.3.250

    Article  Google Scholar 

  4. Sasimowski E (2017) A pressure-bubble vacuum forming process for polystyrene sheet. Adv Sci Technol Res J 11:180–186. https://doi.org/10.12913/22998624/70801

    Article  Google Scholar 

  5. Jenkins CH (1996) Nonlinear dynamic response of membranes: State of the art - Update. Appl Mech Rev 49:S41. https://doi.org/10.1115/1.3101975

    Article  Google Scholar 

  6. Jenkins CH, Leonard JW (1991) Nonlinear dynamic response of membranes : State of the art. Am Soc Mech Eng 44:319–328. https://doi.org/10.1115/1.3101975

    Article  MathSciNet  Google Scholar 

  7. Machado G, Favier D, Chagnon G (2012) Membrane curvatures and stress-strain full fields of axisymmetric bulge tests from 3D-DIC measurements. Theory and validation on virtual and experimental results. Exp Mech 52:865–880. https://doi.org/10.1007/s11340-011-9571-3

    Article  Google Scholar 

  8. Lăzărescu L, Nicodim I, Ciobanu I et al (2013) Determination of material parameters of sheet metals using the hydraulic bulge test. Acta Metall Slovaca 19:4–12. https://doi.org/10.12776/ams.v19i1.81

    Article  Google Scholar 

  9. Patil A, Dasgupta A (2013) Finite inflation of an initially stretched hyperelastic circular membrane. Eur J Mech A/Solids 41:28–36. https://doi.org/10.1016/j.euromechsol.2013.02.007

    Article  MathSciNet  MATH  Google Scholar 

  10. Kumar N, Dasgupta A (2013) On the contact problem of an inflated spherical hyperelastic membrane. Int J Non Linear Mech 57:130–139. https://doi.org/10.1016/j.ijnonlinmec.2013.06.015

    Article  Google Scholar 

  11. Cosola E, Genovese K, Lamberti L, Pappalettere C (2008) A general framework for identification of hyper-elastic membranes with moiré techniques and multi-point simulated annealing. Int J Solids Struct 45:6074–6099. https://doi.org/10.1016/j.ijsolstr.2008.07.019

    Article  Google Scholar 

  12. Verron E, Khayat RE, Derdouri A, Peseux B (1999) Dynamic inflation of hyperelastic spherical membranes. J Rheol (N Y N Y) 43:1083–1097. https://doi.org/10.1122/1.551017

    Article  Google Scholar 

  13. Verron E, Marckmann G, Peseux B, et al (2016) Dynamic inflation of non-linear elastic and viscoelastic rubberlike membranes To cite this version

  14. Hild F, Roux S (2006) Digital image correlation: from displacement measurement to identification of elastic properties - a review. Strain 42:69–80. https://doi.org/10.1111/j.1475-1305.2006.00258.x

    Article  Google Scholar 

  15. Palanca M, Tozzi G, Cristofolini L (2016) The use of digital image correlation in the biomechanical area: A review. Int Biomech 3:1–21. https://doi.org/10.1080/23335432.2015.1117395

    Article  Google Scholar 

  16. Shao X, Dai X, Chen Z et al (2016) Calibration of stereo-digital image correlation for deformation measurement of large engineering components. Meas Sci Technol 27:125010. https://doi.org/10.1088/0957-0233/27/12/125010

    Article  Google Scholar 

  17. Zappa E, Matinmanesh A, Mazzoleni P (2014) Evaluation and improvement of digital image correlation uncertainty in dynamic conditions. Opt Lasers Eng 59:82–92. https://doi.org/10.1016/j.optlaseng.2014.03.007

    Article  Google Scholar 

  18. Duchene P, Chaki S, Ayadi A, Krawczak P (2018) A review of non-destructive techniques used for mechanical damage assessment in polymer composites. J Mater Sci 53:7915–7938. https://doi.org/10.1007/s10853-018-2045-6

    Article  Google Scholar 

  19. Van Mieghem B, Desplentere F, Van Bael A, Ivens J (2015) Improvements in thermoforming simulation by use of 3D digital image correlation. Express Polym Lett 9:119–128. https://doi.org/10.3144/expresspolymlett.2015.13

    Article  Google Scholar 

  20. Van Mieghem B, Lava P, Debruyne D et al (2013) Digital image correlation for on-line wall thickness measurements in thick gauge thermoforming. Key Eng Mater 554–557:1583–1591. https://doi.org/10.4028/www.scientific.net/KEM.554-557.1583

    Article  Google Scholar 

  21. Van Mieghem B, Ivens J, Van Bael A (2016) Consistency of strain fields and thickness distributions in thermoforming experiments through stereo DIC. Exp Tech 40:1409–1420. https://doi.org/10.1007/s40799-016-0143-4

    Article  Google Scholar 

  22. Li Y, Nemes JA, Derdouri AA (2001) Membrane inflation of polymeric materials: Experiments and finite element simulations. Polym Eng Sci 41:1399–1412. https://doi.org/10.1002/pen.10840

    Article  Google Scholar 

  23. Hosseini H, Berdyshev BV, Mehrabani-Zeinabad A (2006) A solution for warpage in polymeric products by plug-assisted thermoforming. Eur Polym J 42:1836–1843. https://doi.org/10.1016/j.eurpolymj.2006.03.020

    Article  Google Scholar 

  24. Kurtaran H, Erzurumlu T (2006) Efficient warpage optimization of thin shell plastic parts using response surface methodology and genetic algorithm. Int J Adv Manuf Technol 27:468–472. https://doi.org/10.1007/s00170-004-2321-2

    Article  Google Scholar 

  25. Throne JL (2006) The effect of sheet sag on radiant energy transmission in thermoforming. Thermoforming Q 25:19–24

    Google Scholar 

  26. Giacomin AJ, Mix AW, Mahmood O (2010) Sag in thermoforming. Polym Eng Sci 50:2060–2068. https://doi.org/10.1002/pen.21734

    Article  Google Scholar 

  27. Baek HM, Giacomin AJ, Wurz MJ (2014) Sag in commercial thermoforming. AIChE J 60:1529–1535. https://doi.org/10.1002/aic.14275

    Article  Google Scholar 

  28. Murienne BJ, Nguyen TD (2016) A comparison of 2D and 3D digital image correlation for a membrane under inflation. Opt Lasers Eng 77:92–99. https://doi.org/10.1016/j.optlaseng.2015.07.013

    Article  Google Scholar 

  29. Sutton MA, Yan JH, Tiwari V et al (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Opt Lasers Eng 46:746–757. https://doi.org/10.1016/j.optlaseng.2008.05.005

    Article  Google Scholar 

  30. Ke X-D, Schreier HW, Sutton MA, Wang YQ (2011) Error assessment in stereo-based deformation measurements. Exp Mech 51:423–441. https://doi.org/10.1007/s11340-010-9450-3

    Article  Google Scholar 

  31. Niu Y, Pham VL, Wang J, Park S (2018) An accurate experimental determination of effective strain for heterogeneous electronic packages with digital image correlation method. IEEE Trans Components, Packag Manuf Technol 8:678–688. https://doi.org/10.1109/TCPMT.2018.2794505

    Article  Google Scholar 

  32. Rokoš O, Hoefnagels JPM, Peerlings RHJ, Geers MGD (2018) On micromechanical parameter identification with integrated DIC and the role of accuracy in kinematic boundary conditions. Int J Solids Struct 146:241–259. https://doi.org/10.1016/j.ijsolstr.2018.04.004

    Article  Google Scholar 

  33. Buffel B, Amerijckx M, Hamblok M et al (2015) Experimental and computational analysis of the heating step during thermoforming of thermoplastics. Key Eng Mater:651–653. https://doi.org/10.4028/www.scientific.net/KEM.651-653.1003

  34. Schmidt FM, Le Maoult Y, Monteix S (2003) Modelling of infrared heating of thermoplastic sheet used in thermoforming process. J Mater Process Technol 143–144:225–231. https://doi.org/10.1016/S0924-0136(03)00291-7

  35. Wang Z, Kieu H, Nguyen H, Le M (2014) Digital image correlation in experimental mechanics and image registration in computer vision: Similarities, differences and complements. Opt Lasers Eng 65:18–27. https://doi.org/10.1016/j.optlaseng.2014.04.002

    Article  Google Scholar 

  36. Selvadurai APS, Selvadurai PA (2010) Surface permeability tests: experiments and modelling for estimating effective permeability. Proc R Soc A Math Phys Eng Sci 466:2819–2846. https://doi.org/10.1098/rspa.2009.0475

    Article  Google Scholar 

  37. Pottier T, Vacher P, Toussaint F et al (2012) Out-of-plane testing procedure for inverse identification purpose: application in sheet metal plasticity. Exp Mech 52:951–963. https://doi.org/10.1007/s11340-011-9555-3

    Article  Google Scholar 

  38. LaVision stereo-DIC manuals (2016) Advanced digital image correlation systems for optical full field measurement of material strain, displacement and shape. https://www.lavision.de

  39. Liu W, Long R (2015) Constructing continuous strain and stress fields from spatially discrete displacement data in soft materials. J Appl Mech 83:011006. https://doi.org/10.1115/1.4031763

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the European Union (European Regional Development Fund FEDER), the French state and the Hauts-de-France Region council for co-funding the ELSAT 2020 by CISIT project (POPCOM action).

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Authors and Affiliations

  1. Institut Mines-Télécom, Polymers and Composites Technology & Mechanical Engineering Department, IMT Lille Douai, 941 rue Charles Bourseul, 59508, Douai, France

    A. Ayadi, M.-F. Lacrampe & P. Krawczak

  2. Université de Lille, 59000, Lille, France

    A. Ayadi, M.-F. Lacrampe & P. Krawczak

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  1. A. Ayadi
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  2. M.-F. Lacrampe
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  3. P. Krawczak
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Correspondence to M.-F. Lacrampe.

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Ayadi, A., Lacrampe, MF. & Krawczak, P. Bubble assisted vacuum thermoforming: considerations to extend the use of in-situ stereo-DIC measurements to stretching of sagged thermoplastic sheets. Int J Mater Form 13, 59–76 (2020). https://doi.org/10.1007/s12289-018-01467-y

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