Prediction of the Short – Term Stress Relaxation Behavior of Polypropylene Block Copolymer Material Using an ANSYS Three Network Model Calibrated with Low Quasi – Static Tensile Tests

Öz

The aim of this study is the development of an approach capable of modeling the short – term time – dependent mechanical behavior of a pure polypropylene block copolymer (PPB) using finite element method software with high accuracy. This objective was achieved by calibrating the finite element – based ANSYS Three Network Model (ANSYS TNM) using experimental data obtained from a limited number of low – rate quasi – static tensile tests. Multipurpose test specimens manufactured by injection molding from pure PPB material in accordance with the ISO 3167 Type A standard were subjected to uniaxial tensile tests at low quasi – static strain rates (0.0003 s⁻¹, 0.000725 s⁻¹, and 0.00145 s⁻¹) up to the stress plateau region. Stress relaxation tests were subsequently performed with a holding time of 600 s at the yield strain levels determined for each strain rate. The time – strain – stress data obtained from the uniaxial tensile tests were used to identify PPB – specific ANSYS TNM parameters through the MCalibration software. High correlations are observed between the simulation and experimental results for both uniaxial tensile and stress relaxation tests, with this agreement quantitatively confirmed by coefficients of determination of R² ≥ 0.91. In conclusion, the proposed ANSYS TNM – based modeling approach has demonstrated a high level of predictive accuracy for the strain – rate – dependent mechanical behavior of semicrystalline polymers such as PPB, while also providing significant gains in terms of time, cost, and labor efficiency in engineering design applications.

Anahtar Kelimeler

• Polypropylene Block Copolymer
• ANSYS Three Network Model
• Finite Element Method
• Tensile Test
• Stress Relaxation

Teşekkür

The authors gratefully acknowledge the academic software licenses for MCalibration and PolyUMod provided by Numesys Advanced Engineering Services through the facilitation of Ms. Sema Kaya.

Düşük Yarı Statik Hızlı Çekme Testleri ile Kalibre Edilmiş ANSYS Üç Ağ Modeli Kullanılarak Polipropilen Blok Kopolimer Malzemenin Kısa Vadeli Gerilme Gevşeme Davranışının Tahmini

Öz

Bu çalışmanın amacı, saf bir polipropilen blok kopolimerin (PPB) kısa süreli, zamana bağlı mekanik davranışını sonlu elemanlar yöntemi yazılımı kullanarak yüksek doğrulukla modelleyebilen bir yaklaşım geliştirmektir. Bu amaç, sınırlı sayıda düşük hızlı sanki statik çekme testlerinden elde edilen deneysel veriler kullanılarak sonlu elemanlar temelli ANSYS Üç Ağlı Modeli’nin (ANSYS TNM) kalibre edilmesiyle gerçekleştirilmiştir. ISO 3167 Tip A standardına uygun olarak saf PPB malzemeden enjeksiyon kalıplama yöntemiyle üretilen çok amaçlı numuneler, düşük sanki statik genleme hızlarında (0.0003 s⁻¹, 0.000725 s⁻¹ ve 0.00145 s⁻¹) gerilme plato bölgesine kadar tek eksenli çekme testlerine tabi tutulmuştur. Ardından, her bir şekil değiştirme hızı için belirlenen akma genleme seviyelerinde 600 s bekleme süresiyle gerilme gevşemesi testleri gerçekleştirilmiştir. Tek eksenli çekme testlerinden elde edilen zaman – genleme – gerilme verileri, MCalibration yazılımı aracılığıyla PPB’ye özgü ANSYS TNM parametrelerinin belirlenmesinde kullanılmıştır. Tek eksenli çekme ve gerilme gevşemesi testleri için simülasyon ve deneysel sonuçlar arasında yüksek düzeyde korelasyonlar gözlenmiş olup, bu uyum R² ≥ 0.91 olan regresyon uyum katsayıları ile nicel olarak doğrulanmıştır. Sonuç olarak, önerilen ANSYS TNM tabanlı modelleme yaklaşımıyla PPB gibi yarı kristalin polimerlerin gerinim hızı bağımlı mekanik davranışını yüksek doğrulukla öngörebilme başarımı sergilenmiştir ve aynı zamanda mühendislik tasarım uygulamalarında zaman, maliyet ve iş gücü açısından önemli kazanımlar sağlanmıştır.

Anahtar Kelimeler

• Polipropilen Blok Kopolimer
• ANSYS Three Network Model
• Sonlu Elemanlar
• Çekme Testi
• Gerilme Gevşemesi Testi

Teşekkür

Yazarlar, MCalibration ve PolyUMod yazılımlarına yönelik akademik yazılım lisanslarının sağlanmasında Sayın Sema Kaya aracılığıyla verdikleri destekten dolayı Numesys İleri Mühendislik Hizmetlerine teşekkür etmektedirler.

Kaynakça

1. Uyor, U. O., Popoola, P. A., Popoola, O. M., Aigbodion, V. S. (2023). "A review of recent advances on the properties of polypropylene-carbon nanotubes composites" Journal of Thermoplastic Composite Materials, 36(9), 3737-3770, 2023, doi: 10.1177/08927057221077868.
2. Reis, M., Cakan, B. G., Durmuş, A., Reis, M. "Sıcaklık değişimi ve dinamik yol yüklerinin polipropilen gıda depolama kutularının deformasyonuna etkisi" Nevşehir Bilim ve Teknoloji Dergisi, 99-105, 2020, doi: 10.17100/nevbiltek.726470.
3. Hossain, M. T., Shahid, M. A., Mahmud, N., Habib, A., Rana, M. M., Khan, S. A., Hossain, M. D. "Research and application of polypropylene: a review" Discover Nano, 19(1), 2, 2024, doi: 10.1186/s11671-023-03952-z.
4. Murariu, M., Laoutid, F., Paint, Y., Murariu, O., Raquez, J. M., Dubois, P. "Balancing the strength–impact relationship and other key properties in polypropylene copolymer–natural CaSO4 (Anhydrite)-filled composites" International Journal of Molecular Sciences, 24(16), 12659, 2023, doi: 10.3390/ijms241612659.
5. Shao, W., Liu, L. Z., Wang, Y., Wang, Y., Shi, Y., Song, L. "Investigation of crystallization, morphology, and mechanical properties of polypropylene/polypropylene-polyethylene block copolymer blends" Polymers, 15(24), 4680, 2023, doi: 10.3390/polym15244680.
6. Tang, Y. H., Zhang, N., Bao, W., Jiang, W., Lin, Y., Su, Z. H. "Critical role of ethylene-propylene block copolymer in impact polypropylene copolymer" Chinese Journal of Polymer Science, 42(3), 344-351, 2024, doi: 10.1007/s10118-023-3058-4.
7. Deng, Y. M., Edwards, K. L. "The role of materials identification and selection in engineering design" Materials & design, 28(1), 131-139, 2007, doi: https://doi.org/10.1016/j.matdes.2005.05.003.
8. Arıcıoğlu, M., Mert, B., Soydan, Y. "Mechanical analysis of polymeric materials" Sakarya University Journal of Science, 4(1-2), 51-58, 2000, doi: 10.16984/saufbed.75940.

9. Zhou, Y., Mallick, P. K. "Effects of temperature and strain rate on the tensile behavior of unfilled and talc‐filled polypropylene. Part I: Experiments" Polymer Engineering & Science, 42(12), 2449-2460, 2002, doi: https://doi.org/10.1002/pen.11131.
10. Aydemir, B., Şahin, Ş., Şahin, T. "Polipropilen kopolimerinde (PPB) kalsiyum karbonat tane boyutunun kısa süreli çekme sürünme özellikleri üzerine etkisi" Nevşehir Bilim ve Teknoloji Dergisi, 7(2), 206-213, 2018, doi: 10.17100/nevbiltek.368459.
11. Segura-Méndez, K. L., Puente-Córdova, J. G., Rentería-Baltiérrez, F. Y., Luna-Martínez, J. F., Mohamed-Noriega, N. "Modeling of stress relaxation behavior in HDPE and PP using fractional derivatives" Polymers, 17(4), 453, 2025, doi: 10.3390/polym17040453.
12. Siviour, C. R., Jordan, J. L. "High strain rate mechanics of polymers: a review" Journal of Dynamic Behavior of Materials, 2(1), 15-32, 2016, doi: 10.1007/s40870-016-0052-8.
13. Farahani, M. F., Bagheri, R. "A new look at tensile yielding in isotactic polypropylene: role of strain rate and thermal softening" Polymer Bulletin, 79(12), 11157-11176, 2022, doi: 10.1007/s00289-021-03997-z.
14. B. Aydemir, "Plastiklerin ISO 527 standardına göre çekme özelliklerinin belirlenmesi" in "Mühendislik alanındaki gelişmeler", A. Bideci, Ed., Turkey: Duvar Kitapevi, 2022, ch. Chapter 7, pp. 111–128. [Online]. Available: https://www.duvaryayinlari.com/Webkontrol/IcerikYonetimi/Dosyalar/muhendislik-alanindaki-gelismeler_icerik_g3808_nFMAwjoG.pdf
15. Şahin, Y., Sahin, S., İnal, M. "Modelling of the tensile properties of calcium carbonate filled polypropylene composite materials with Taguchi and artificial neural networks" IFAC-PapersOnLine, 51(30), 282-286, 2018, doi: https://doi.org/10.1016/j.ifacol.2018.11.302.
16. Deng, M., Zhou, J. "Effects of temperature and strain level on stress relaxation behaviors of polypropylene sutures" Journal of Materials Science: Materials in Medicine, 17(4), 365-369, 2006, doi: 10.1007/s10856-006-8239-5.
17. Drozdov, A. D., Dusunceli, N. "Inverse relaxation in polypropylene" Iranian Polymer Journal, 21(10), 701-711, 2012, doi: 10.1007/s13726-012-0077-3.
18. Dusunceli, N. "The unusual creep and relaxation behaviour of polypropylene" Journal of Polymer Engineering, 32(3), 167, 2012, doi: doi:10.1515/polyeng-2011-0159.
19. Drozdov, A. D., Dusunceli, N. "Cyclic deformations of polypropylene with a strain‐controlled program" Polymer Engineering & Science, 52(11), 2316-2326, 2012, doi: https://doi.org/10.1002/pen.23188.
20. K. A. Brown, R. Brooks, and N. A. Warrior, “Characterizing the strain rate sensitivity of the tensile mechanical properties of a thermoplastic composite,” JOM, vol. 61, no. 1, pp. 43–46, 2009, doi: 10.1007/s11837-009-0007-9.
21. Wang, Q., Wang, J., Wang, A., Zhou, C., Hu, J., Pan, F. "Effect of strain rate and temperature on the tensile properties of long glass fiber-reinforced polypropylene composites" Polymers, 15(15), 3260, 2023, doi: 10.3390/polym15153260.
22. Amjadi, M., Fatemi, A. "Tensile behavior of high-density polyethylene including the effects of processing technique, thickness, temperature, and strain rate" Polymers, 12(9), 1857, 2020, doi: 10.3390/polym12091857.
23. Chowdhury M., “Thin polymer films out of thermodynamic equilibrium,” Albert Ludwigs University - Mathematics and Physics Department, Ph.D Dissertation, Freiburg, 2012. [Online]. Available: https://www.researchgate.net/publication/279825049_Thin_polymer_films_out_of_thermodynamic_equilibrium
24. Luo, W., Wang, C., Hu, X., Yang, T. "Long-term creep assessment of viscoelastic polymer by time-temperature-stress superposition" Acta Mechanica Solida Sinica, 25(6), 571-578, 2012, doi: 10.1016/S0894-9166(12)60052-4.
25. Tscharnuter, D., Jerabek, M., Major, Z., Pinter, G. "Uniaxial nonlinear viscoelastic viscoplastic modeling of polypropylene" Mechanics of Time-Dependent Materials, 16(3), 275-286, 2012, doi: 10.1007/s11043-011-9158-5.
26. Gebrehiwot, S. Z., Espinosa-Leal, L. "Characterising the linear viscoelastic behaviour of an injection moulding grade polypropylene polymer" Mechanics of Time-Dependent Materials, 26(4), 791-814, 2022, doi: 10.1007/s11043-021-09513-0.
27. Rosca, N., Najm, S. M., Avrigean, E., Oleksik, M., Trzepieciński, T., Oleksik, V. "Study on the choice of a suitable material model for the numerical simulation of the incremental forming process of polymeric materials" Applied Sciences, 15(13), 7094, 2025. doi: 10.3390/app15137094.
28. J. S. Bergström, J. E. Bischoff, "An advanced thermomechanical constitutive model for UHMWPE" International Journal of Structural Changes in Solids – Mechanics and Applications, vol. 2, no. 1, pp. 31–39, 2010.
29. Dal, H., Kaliske, M. "Bergström–Boyce model for nonlinear finite rubber viscoelasticity: theoretical aspects and algorithmic treatment for the FE method" Computational Mechanics, 44(6), 809-823, 2009, doi: 10.1007/s00466-009-0407-2.
30. Bergström, J. S., Boyce, M. C. "Large strain time-dependent behavior of filled elastomers" Mechanics of Materials, 32(11), 627-644, 2000, doi: https://doi.org/10.1016/S0167-6636(00)00028-4.
31. Alhourani, A., Barsoum, I., Deveci, S., Sheikh-Ahmad, J., Abdelgawad, A. "Constitutive models for the thermo-mechanical and dynamic behavior of high-density polyethylene" Polymer Testing, 108935, 2025, doi: https://doi.org/10.1016/j.polymertesting.2025.108935.
32. Mainardi, F., Spada, G. "Creep, relaxation and viscosity properties for basic fractional models in rheology" The European Physical Journal Special Topics, 193(1), 133-160, 2011, doi: 10.1140/epjst/e2011-01387-1.
33. Bergström, J. S., Kurtz, S. M., Rimnac, C. M., Edidin, A. A. "Constitutive modeling of ultra-high molecular weight polyethylene under large-deformation and cyclic loading conditions" Biomaterials, 23(11), 2329-2343, 2002, doi: 10.1016/S0142-9612(01)00367-2.
34. Almomani, A., Deveci, S., Mourad, A. H. I., Barsoum, I. "Constitutive model calibration for the thermal viscoelastic-viscoplastic behavior of high density polyethylene under monotonic and cyclic loading" Polymer Testing, 118, 107911, 2023, doi: https://doi.org/10.1016/j.polymertesting.2022.107911.
35. Mian, S. H., Umer, U., Moiduddin, K., Alkhalefah, H. "Predicting mechanical properties of polymer materials using rate-dependent material models: Finite element analysis of bespoke upper limb orthoses" Polymers, 16(9), 1220, 2024, doi: 10.3390/polym16091220.
36. O. Volgin, I. Shishkovsky, "Material modelling of FDM printed PLA part" Engineering Solid Mechanics, 153–160, 2021, doi: 10.5267/j.esm.2020.12.004.
37. Knight, J., Salim, H., Elemam, H., Elbelbisi, A. "Calibration of thermal viscoelastic material models for the dynamic responses of PVB and SG interlayer materials" Polymers, 16(13), 1870, 2024, doi: 10.3390/polym16131870.
38. Kulkarni, S. S., Mocko, G. M. "A finite element simulation model of convective heat-assisted single-point incremental forming of thermoplastics" The International Journal of Advanced Manufacturing Technology, 111(11), 3305-3317, 2020, doi: 10.1007/s00170-020-06311-9.
39. Kumar, M., Ravi, K., Singh, S. S. "Predicting the double-yield phenomenon in low-density polyethylene film using three-network viscoplastic model" Mechanics of Materials, 184, 104736, 2023, doi: https://doi.org/10.1016/j.mechmat.2023.104736.
40. Bergström J., "8 - Viscoplasticity Models" in Mechanics of Solid Polymers, J. Bergström, Ed., William Andrew Publishing, 2015, pp. 371–436. doi: https://doi.org/10.1016/B978-0-323-31150-2.00008-X.
41. ANSYS Inc., “ANSYS Mechanical APDL Material Reference: TNM Theory,” ANSYS Help Release 2025 R1. Accessed: Mar. 18, 2026. [Online]. Available: https://ansyshelp.ansys.com/public/account/secured?returnurl=/Views/Secured/corp/v251/en/ans_mat/aQw8sq22dldm.html
42. Dusunceli, N., Colak, O. U. "High density polyethylene (HDPE): Experiments and modeling" Mechanics of Time-Dependent Materials, 10(4), 331-345, 2006, doi: 10.1007/s11043-007-9026-5.