Experimental determination of the viscoelastic parameters of K-BKZ model and the influence of temperature field on the thickness distribution of ABS thermoforming

  • Jemyung Cha
  • Moonjeong Kim
  • Dongguen Park
  • Jeung Sang GoEmail author
Open Access


This study investigated an influence of the temperature field on thickness distribution of thermoformed products using complex and high-aspect-ratio mold. The optimum temperature field was obtained to achieve a more uniform thickness distribution in the thermoformed products by using finite element simulation. The material properties of acrylonitrile-butadiene-styrene (ABS) polymer sheet were obtained by two rheological measurement tests. The linear viscoelastic properties, such as the storage modulus and loss modulus, were measured by a small amplitude oscillatory shear (SAOS) test for wide ranges of frequency and temperature. The discrete relaxation time and discrete relaxation modulus were obtained by nonlinear regression. The fitting parameters C1 and C2 for the WLF model were obtained by curve fitting. The nonlinear viscoelastic property, such as stress relaxation modulus, was measured by a step strain test. The damping function and fitting parameter α of Wagner-Demarmels (WD) model were determined by curve fitting. Then, the Kaye–Bernstein-Kearsley-Zapas (K-BKZ) constitutive equation was utilized to the thermoforming simulation in order to investigate the material behavior of the polymer sheet. The numerical results showed that a more uniform thickness distribution could be achieved with the optimum temperature field of the sheet. The thinnest part of the products was improved by more than 30%.


Thermoforming Thickness distribution Viscoelastic properties Rheological measurement K-BKZ constitutive equation FE simulation Optimum temperature field 


Funding information

The authors thank the LG Electronics for financial support and useful information on this work. This work was supported by the Ministry of Science, ICT, and Future Planning of the Republic of Korea (No. 2017R1A2B20006264). This work was supported by a 2-Year Research Grant of Pusan National University.


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© The Author(s) 2019

OpenAccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Jemyung Cha
    • 1
  • Moonjeong Kim
    • 1
  • Dongguen Park
    • 2
  • Jeung Sang Go
    • 1
    Email author
  1. 1.School of Mechanical EngineeringPusan National UniversityBusanRepublic of Korea
  2. 2.Department of Advanced Materials and Parts of Transportation SystemsPusan National UniversityBusanRepublic of Korea

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