English
Русский 15-23 p.
The article is devoted to the problem of processing the experimental creep curves of polymers. The task is to determine their rheological characteristics from tests for any of the simplest types of deformation. The basis for the approximation of the experimental curves is the nonlinear Maxwell-Gurevich equation.
The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value.
To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear.
A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers.
The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value.
To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear.
A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers.
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6. Yazyev B.M., Chepurnenko A.S., Savchenko A.A. Calculation of Three-Layer Panels with Polyurethane Foam Filler Taking into Account the Rheological Properties of the Middle Layer. Materials Science Forum. 2018. 935. P. 144 – 149. DOI: 10.4028/www.scientific.net/MSF.935.144
7. Figueira D. et al. Influence of service temperature on shear creep behaviour of a rigid low-density closed-cell PIR foam. Construction and Building Materials. 2019. 225. P. 1052 – 1063.
8. Garrido M., Correia J.R., Keller T. Effect of service temperature on the shear creep response of rigid polyurethane foam used in composite sandwich floor panels. Construction and Building Materials. 2016. 118. P. 235 – 244.
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10. Mayookh Lal H. et al. Experimental Study on the Flexural Creep Behaviors of Pultruded Unidirectional Carbon. Glass Fiber-Reinforced Hybrid Bars. Materials. 2020. 13 (4). P. 976.
11. Xu Y. et al. Creep behavior of bagasse fiber reinforced polymer composites. Bioresource technology. 2010. 101 (9). P. 3280 – 3286.
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13. Hanzon D.W. et al. Creep-induced anisotropy in covalent adaptable network polymers. Soft Matter. 2017. 13 (39). P. 7061 – 7073.
14. Zakhariev G., Khadzhikov L., Marinov P. A rheological model of polymers and glass-reinforced plastics. Polymer Mechanics. 1971. 7 (5). P. 761 – 775.
15. Trush L., Litvinov S., Zakieva N., Bayramukov S. Optimization of the solution of a plane stress problem of a polymeric cylindrical object in thermoviscoelastic statement. Advances in Intelligent Systems and Computing. 2017. 692. P. 885 – 893. DOI: 10.1007/978-3-319-70987-1_95
16. Cybin N.YU., Andreev V.I., Turusov R.A. Issledovanie polzuchesti polimerov v razlichnyh usloviyah deformirovaniya. Stroitel'naya mekhanika i raschet sooruzhenij. 2018. 3. P. 30 – 35. (rus.)
17. Tsybin N.Y., Turusov R.A., Andreev V.I. Comparison of creep in free polymer rod and creep in polymer layer of the layered composite. Procedia Engineering. 2016. 153. P. 51 – 58. DOI: 10.1016/j.proeng.2016.08.079
18. Chepurnenko V., Yazyev B., Dubovitskaya L. Features of compressed rods calculations with account of initial imperfections and creep effects. E3S Web of Conferences. 2020. 164. URL: https://www.e3s-conferences.org/articles/e3sconf/abs/2020/24/e3sconf_tpacee2020_02003/e3sconf_tpacee2020_02003.html
19. Andreev V.I., Frolova I.I., Sigunova L.Y. Calculation of temperature stresses in polymers in the cycles heating-cooling process. Material Science Forum. 2018. 931. P. 9 – 13.
20. Kuperman A.M., Turusov R.A. Relaxation characteristics of reinforced plastics in tension of ring specimens by split disks. Mechanics of composite materials. 2012. 48. P. 305 – 312.
2. Tezel T., Kovan V., Topal E.S. Effects of the printing parameters on short‐term creep behaviors of three‐dimensional printed polymers. Journal of Applied Polymer Science. 2019. 136 (21). P. 47564.
3. Guangjian Xiang, Deshun Yin, Ruifan Meng, Siyu Lu. Creep model for natural fiber polymer composites (NFPCs) based on variable order fractional derivatives: Simulation and parameter study. Journal of Applied Polymer Science. 2020. 137 (24). P. 48796.
4. Amjadi M., Fatemi A. Creep and fatigue behaviors of High-Density Polyethylene (HDPE): Effects of temperature, mean stress, frequency, and processing technique. International Journal of Fatigue. 2020. 141. P. 105871.
5. Dudnik A.E., Chepurnenko A.S., Litvinov S.V. Determining the rheological parameters of polyvinyl chloride, with change in temperature taken into account. International Polymer Science and Technology. 2017. 44. P. 43 – 48. DOI: 10.1177/0307174X1704400109
6. Yazyev B.M., Chepurnenko A.S., Savchenko A.A. Calculation of Three-Layer Panels with Polyurethane Foam Filler Taking into Account the Rheological Properties of the Middle Layer. Materials Science Forum. 2018. 935. P. 144 – 149. DOI: 10.4028/www.scientific.net/MSF.935.144
7. Figueira D. et al. Influence of service temperature on shear creep behaviour of a rigid low-density closed-cell PIR foam. Construction and Building Materials. 2019. 225. P. 1052 – 1063.
8. Garrido M., Correia J.R., Keller T. Effect of service temperature on the shear creep response of rigid polyurethane foam used in composite sandwich floor panels. Construction and Building Materials. 2016. 118. P. 235 – 244.
9. Sá M., Gomes A., Correia J., Silvestre N. Flexural creep response of pultruded GFRP deck panels: Proposal for obtaining full-section viscoelastic moduli and creep coefficients. Composites Part B: Engineering. 2016. 98. P. 213 – 224.
10. Mayookh Lal H. et al. Experimental Study on the Flexural Creep Behaviors of Pultruded Unidirectional Carbon. Glass Fiber-Reinforced Hybrid Bars. Materials. 2020. 13 (4). P. 976.
11. Xu Y. et al. Creep behavior of bagasse fiber reinforced polymer composites. Bioresource technology. 2010. 101 (9). P. 3280 – 3286.
12. Shojaei A.K., Wedgewood A.R. An anisotropic cyclic plasticity, creep and fatigue predictive tool for unfilled polymers. Mechanics of Materials. 2017. 106. P. 20 – 34.
13. Hanzon D.W. et al. Creep-induced anisotropy in covalent adaptable network polymers. Soft Matter. 2017. 13 (39). P. 7061 – 7073.
14. Zakhariev G., Khadzhikov L., Marinov P. A rheological model of polymers and glass-reinforced plastics. Polymer Mechanics. 1971. 7 (5). P. 761 – 775.
15. Trush L., Litvinov S., Zakieva N., Bayramukov S. Optimization of the solution of a plane stress problem of a polymeric cylindrical object in thermoviscoelastic statement. Advances in Intelligent Systems and Computing. 2017. 692. P. 885 – 893. DOI: 10.1007/978-3-319-70987-1_95
16. Cybin N.YU., Andreev V.I., Turusov R.A. Issledovanie polzuchesti polimerov v razlichnyh usloviyah deformirovaniya. Stroitel'naya mekhanika i raschet sooruzhenij. 2018. 3. P. 30 – 35. (rus.)
17. Tsybin N.Y., Turusov R.A., Andreev V.I. Comparison of creep in free polymer rod and creep in polymer layer of the layered composite. Procedia Engineering. 2016. 153. P. 51 – 58. DOI: 10.1016/j.proeng.2016.08.079
18. Chepurnenko V., Yazyev B., Dubovitskaya L. Features of compressed rods calculations with account of initial imperfections and creep effects. E3S Web of Conferences. 2020. 164. URL: https://www.e3s-conferences.org/articles/e3sconf/abs/2020/24/e3sconf_tpacee2020_02003/e3sconf_tpacee2020_02003.html
19. Andreev V.I., Frolova I.I., Sigunova L.Y. Calculation of temperature stresses in polymers in the cycles heating-cooling process. Material Science Forum. 2018. 931. P. 9 – 13.
20. Kuperman A.M., Turusov R.A. Relaxation characteristics of reinforced plastics in tension of ring specimens by split disks. Mechanics of composite materials. 2012. 48. P. 305 – 312.
Yazyev S.B., Chepurnenko A.S., Litvinov S.V. Determination of rheological parameters of polymeric materials using nonlinear optimization methods. Construction Materials and Products. 2020. 3 (5). P. 15 – 23. https://doi.org/10.34031/2618-7183-2020-3-5-15-23