Description of the effect of softening in elastomeric composites observed in tests with increasing strain amplitude
Author details
- Institute of Continuous Media Mechanics UB RAS, Perm, Russian Federation
- Institute of Continuous Media Mechanics UB RAS, Perm, Russian Federation
- Institute of Continuous Media Mechanics UB RAS, Perm, Russian Federation
- Institute of Continuous Media Mechanics UB RAS, Perm, Russian Federation
Abstract
This paper presents the results of complex uniaxial mechanical tests conducted to study polymer nanocomposites with SKU-PPL-2102 prepolymer as a matrix. The unfilled elastomer is a structurally heterogeneous material – it has solid domain structures and therefore can be considered as a nanocomposite exhibiting complex mechanical behavior. Tests were carried out on the samples prepared of polyurethane without filler and with 0.5 phr of few-layer graphene filler under conditions of increasing deformation cycles and long time-delays between changes in the direction of gripper motion. These tests made it possible to monitor the degree of softening in the material subjected to loading and the increase of dissipative losses at different elongation ratios. It was found that, even at low filler content, the mechanical properties of the material changed significantly. In addition, note that the viscoelastic properties of the materials’ samples manifest themselves insignificantly (i.e., the "trained" materials can be considered elastic with a certain degree of accuracy) during repeated deformations. An elastic potential that is based on the notion of the effective behavior of loaded polymer chains was used to describe the elastic properties of the material taking into account the Mullins softening effect. The viscoelastic behavior of the nanocomposite under study was described in the framework of the previously described thermodynamic model. The Mullins softening effect was taken into account in both elastic and dissipative terms of the Cauchy stress tensor. The obtained data demonstrate that the consideration of this effect has a considerable effect on the dissipative component of the stress tensor.
Keywords
Описание эффекта размягчения эластомерных композитов, наблюдаемого в экспериментах с возрастающей амплитудой деформирования
Представлены результаты сложных одноосных механических испытаний с образцами полимерных нанокомпозитов, связующим которых является полиуретан на основе форполимера СКУ-ППЛ-2102. Данный эластомер является структурно-неоднородным материалом: в нем имеются твердые доменные структуры, благодаря которым материал можно рассматривать как нанокомпозит со сложным механическим поведением. Испытания были проведены с образцами полиуретана без наполнителя и полиуретана, наполненного малослойным графеном в количестве 0,5 массовых частей (м.ч. на 100 м.ч. матрицы). Были осуществлены эксперименты с возрастающими циклами деформирования и продолжительными временными остановками перед сменой направления движения захватов. Такие испытания позволяют отслеживать степень размягчения материала в ходе нагружения и рост диссипативных потерь при разных кратностях удлинений. Согласно полученным данным было установлено, что даже при низком содержании наполнителя механические свойства материала существенно изменяются. Также отметим, что при повторных деформированиях образцов материалов вязкоупругие свойства проявляются несущественно (т.е. «тренированные» материалы с определенной степенью точности можно считать упругими). Для описания упругих свойств материала с учетом эффекта размягчения Маллинза использовался потенциал, в основу которого положено представление об эффективном поведении нагруженных полимерных цепей. Для описания вязкоупругого поведения рассмотренного нанокомпозита была использована ранее описанная термодинамическая модель. Эффект размягчения Маллинза учитывался как в упругом, так и в диссипативном слагаемых тензора напряжений Коши. И, согласно полученным данным, учет данного эффекта в модели оказывает большее влияние на диссипативное слагаемое тензора напряжений.
Ключевые слова
Bibliography
- 1.Mullins, L. Effect of stretching on the properties of rubber, 1948, Rubber Chemistry and Technology, 21(1), pp. 281-300. doi: 10.5254/1.3546914 Scholar
- 2.Diani, J., Fayolle, B., Gilormini, P. A review on the Mullins effect, 2009, European Polymer Journal, 45(3), pp. 601-612. doi: 10.1016/j.eurpolymj.2008.11.017 Scholar
- 3.Plagge J., Ricker A., Kröger N.H., Wriggers P., Klüppel M. Efficient modeling of filled rubber assuming stress-induced microscopic restructurization, 2020, International Journal of Engineering Science, 151, p. 103291. doi: 10.1016/j.ijengsci.2020.103291 Scholar
- 4.Simo, J.C. On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects, 1987, Computer Methods in Applied Mechanics and Engineering, 60(2), pp. 153-173. doi: 10.1016/0045-7825(87)90107-1 Scholar
- 5.Miehe, C. Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials, 1995, European journal of mechanics. A. Solids, 14(5), pp. 697-720. Scholar
- 6.Miehe, C., Keck, J. Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation, 2000, Journal of the Mechanics and Physics of Solids, 48(2), pp. 323-365. doi: 10.1016/S0022-5096(99)00017-4 Scholar
- 7.Chagnon, G., Verron, E., Gornet, L., Marckmann, G., Charrier, P. On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers, 2004, Journal of the Mechanics and Physics of Solids, 52(7), pp. 1627-1650. doi: 10.1016/j.jmps.2003.12.006 Scholar
- 8.Ogden, R.W., Roxburgh, D.G. A pseudo-elastic model for the Mullins effect in filled rubber, 1999, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 455(1988), pp. 2861-2877. doi: 10.1098/rspa.1999.0431 Scholar
- 9.Dorfmann, A., Ogden, R.W. A pseudo-elastic model for loading, partial unloading and reloading of particle reinforced rubber, 2003, International Journal of Solids and Structures, 40(11), pp. 2699-2714. doi: 10.1016/S0020-7683(03)00089-1 Scholar
- 10.Wrubleskiand, E.G.M., Marczak, R.J. A study on the inclusion of softening behavior in hyperelastic incompressible constitutive models, 2015, Constitutive Models for Rubbers IX, pp. 81-85. Scholar
- 11.Andriyana, A., Loo, M.S., Chagnon, G., Verron, E., Ch’ng, S.Y., Modeling the Mullins effect in elastomers swollen by palm biodiesel, 2015, International Journal of Engineering Science, 95(1), pp. 1-22. doi: 10.1016/j.ijengsci.2015.06.005 Scholar
- 12.Fazekas, B., Goda, T.J. Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence, 2021, International Journal of Mechanical Sciences, 210(1), pp. 1-17. doi: 10.1016/j.ijmecsci.2021.106735 Scholar
- 13.Zhang, M., Xu, W., Wu, T., Zhang, X., Zhang, H., Li, Z., Zhang, C., Jiang, H., Chen, M. Investigation on Mullins effect of rubber materials by spherical indentation method, 2021, Forces in Mechanics, 4(1), pp. 1-7. doi: 10.1016/j.finmec.2021.100037 Scholar
- 14.Danming, Z.,Y,X., Tenghao, Y., Honghui, Y., Shaoxing, Q., Wei, Y. A physically-based damage model for soft elastomeric materials with anisotropic, 2019, International Journal of Solids and Structures, 176-177(1), pp. 121-134. doi: 10.1016/j.ijsolstr.2019.05.018 Scholar
- 15.Ustinov K.B. O navedennoj anizotropii mehanicheskih svojstv jelastomerov [On the induced anisotropy of mechanical properties of elastomers]. Mechanics of Solids, 2019, No.5, pp.27-36. doi: 10.1134/S0572329919050167 Scholar
- 16.Cantournet, S., Desmorat, R., Besson, J. Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model, 2009, International Journal of Solids and Structures, 46(11-12), pp. 2255-2264. doi: 10.1016/j.ijsolstr.2008.12.025 Scholar
- 17.Hanson, D., Hawley, M., Houlton, R., Chitanvis, K., Rae, P., Orler, E.B., Wrobleski, D. Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect, 2005, Polymer, 46(24), pp. 10989-10995. doi: 10.1016/j.polymer.2005.09.039 Scholar
- 18.Diani, J., Brieu, M., Vacherand, J.M. A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy, 2006, European Journal of Mechanics. A/Solids, 25(3), pp. 483-496. doi: 10.1016/j.euromechsol.2005.09.011 Scholar
- 19.Pebdani, M.H. Study Mullins effect of polyurethane reinforcement with halloysite nanotube by molecular dynamics simulation, 2022, Journal of Elastomers and Plastics, 54(5), pp. 659-675. doi: 10.1177/00952443211060407 Scholar
- 20.Allen, V., Chen, L., Englert, M., Moussaoui, A., Pisula, W. Control of Mullins stress softening in silicone elastomer composites by rational design of fumed silica fillers, 2021, Composites Science and Technology, 214(1), pp. 1-9. doi: 10.1016/j.compscitech.2021.108955 Scholar
- 21.Qian, D., Meng, F. Modelling Mullins effect induced by chain delamination and reattachment, 2021, Polymer, 222(1), pp. 1-8. doi: 10.1016/j.polymer.2021.123608 Scholar
- 22.Wen, F., Li, W., Jianning, H., Cuiwen, L., Wenlong, P., Haotuo, X., Shenglin, L. Mechanical properties and Mullins effect in natural rubber reinforced by grafted carbon black, 2019, Advances in Polymer Technology, 2019(1), pp. 1-12. doi: 10.1155/2019/4523696 Scholar
- 23.Machado, G., Chagnon, G., Favier, D. Theory and identification of a constitutive model of induced anisotropy by the Mullins effect, 2014, Journal of the Mechanics and Physics of Solids, 63 (1), pp. 29-39. doi: 10.1016/j.jmps.2013.10.008 Scholar
- 24.Kislitsyn V.D., Svistkov A.L., Mokhireva K.A., Shadrin V.V. Determination of the inelastic behavior of viscoelastic materials using the new thermodynamic model, 2019, AIP Conference Proceedings, 2627(1), p. 030002. DOI: 10.1063/5.0119254 Scholar
- 25.Verron, E., Gros, A. An equal force theory for network models of soft materials with arbitrary molecular weight distribution, 2017, Journal of the Mechanics and Physics of Solids, 106 (1), pp. 176-190. doi: 10.1016/j.jmps.2017.05.018 Scholar
- 26.Vozniakovskii, A.A., Vozniakovskii, A.P., Kidalov, S.V., Osipov, V.Yu. Structure and Paramagnetic Properties of Graphene Nanoplatelets Prepared from Biopolymers Using Self-Propagating High-Temperature Synthesis, 2020, Journal of Structural Chemistry, 61(5), pp. 869-878. doi: 10.1134/S0022476620050200 Scholar
- 27.Vozniakovskii, A.A., Vozniakovskii, A.P., Kidalov, S.V. New Way of Synthesis of Few-Layer Graphene Nanosheets by the Self Propagating High-Temperature Synthesis Method from Biopolymers, 2022, Nanomaterials, 12(4), pp. 657-671. doi: 10.3390/nano12040657 Scholar
- 28.Vozniakovskii, A.A., Vozniakovskii, A.P., Kidalov, S.V. Phenomenological model of synthesis of fewlayer graphene (FLG) by the selfpropagating high-temperature synthesis (SHS) method from biopolymers, 2022, Fullerenes, Nanotubes and Carbon Nanostructures, 30(1), pp. 59-65. DOI: 10.1080/1536383X.2021.1993831 Scholar
- 1.Mullins L. Effect of stretching on the properties of rubber // Rubber Chemistry and Technology. – 1948. – Vol. 21, no. 1. – P. 281–300. DOI: 10.5254/1.3546914 Scholar
- 2.Diani J., Fayolle B., Gilormini P. A review on the Mullins effect // European Polymer Journal. – 2009. – Vol. 45, no. 3. – P. 601–612. DOI: 10.1016/j.eurpolymj.2008.11.017 Scholar
- 3.Efficient modeling of filled rubber assuming stress-induced microscopic restructurization / J. Plagge, A. Ricker, N.H. Kröger, P. Wriggers, M. Klüppel // International Journal of Engineering Science. – 2020. – Vol. 151. – P. 103291. DOI: 10.1016/j.ijengsci.2020.103291 Scholar
- 4.Simo, J.C. On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects // Computer Methods in Applied Mechanics and Engineering. – 1987. – Vol. 60, no. 2. – P. 153–173. DOI: 10.1016/0045-7825(87)90107-1 Scholar
- 5.Miehe C. Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials // European journal of mechanics. A. Solids. – 1995. – Vol. 14, no. 5. – P. 697–720. Scholar
- 6.Miehe C., Keck J. Superimposed finite elastic–viscoelastic–plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation // Journal of the Mechanics and Physics of Solids. – 2000. – Vol. 48, no. 2. – P. 323–365. DOI: 10.1016/S0022-5096(99)00017-4 Scholar
- 7.On the relevance of Continuum Damage Mechanics as applied to the Mullins effect in elastomers / G. Chagnon, E. Verron, L. Gornet, G. Marckmann, P. Charrier // Journal of the Mechanics and Physics of Solids. – 2004. – Vol. 52, no. 7. – P. 1627–1650. DOI: 10.1016/j.jmps.2003.12.006 Scholar
- 8.Ogden R.W., Roxburgh D.G. A pseudo-elastic model for the Mullins effect in filled rubber // Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. – 1999. – Vol. 455, no. 1988. – P. 2861–2877. DOI: 10.1098/rspa.1999.0431 Scholar
- 9.Dorfmann A., Ogden R.W. A pseudo-elastic model for loading, partial unloading and reloading of particle reinforced rubber // International Journal of Solids and Structures. – 2003. – Vol. 40, no. 11. – P. 2699–2714. DOI: 10.1016/S0020-7683(03)00089-1 Scholar
- 10.Wrubleskiand E.G.M., Marczak R.J. A study on the inclusion of softening behavior in hyperelastic incompressible constitutive models // Constitutive Models for Rubbers IX. – 2015. – P. 81–85. Scholar
- 11.Modeling the Mullins effect in elastomers swollen by palm biodiesel / A. Andriyana, M.S. Loo, G. Chagnon, E. Verron, S.Y. Ch’ng // International Journal of Engineering Science. – 2015. – Vol. 95, no. 1. – P. 1–22. DOI: 10.1016/j.ijengsci.2015.06.005 Scholar
- 12.Fazekas B., Goda T.J. Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence // International Journal of Mechanical Sciences. – 2021. – Vol. 210, no. 1. – P. 1–17. DOI: 10.1016/j.ijmecsci.2021.106735 Scholar
- 13.Investigation on Mullins effect of rubber materials by spherical indentation method / M. Zhang, W. Xu, T. Wu, X. Zhang, H. Zhang, Z. Li, C. Zhang, H. Jiang, M. Chen // Forces in Mechanics. – 2021. – Vol. 4, no. 1. – P. 1–7. DOI: 10.1016/j.finmec.2021.100037 Scholar
- 14.A physically-based damage model for soft elastomeric materials with anisotropic / Z.Y.X. Danming, Y. Tenghao, Y. Honghui, Q. Shaoxing, Y. Wei // International Journal of Solids and Structures. – 2019. – Vol. 176-177, no. 1. – P. 121–134. DOI: 10.1016/j.ijsolstr.2019.05.018 Scholar
- 15.Устинов К.Б. О наведенной анизотропии механических свойств эластомеров // Известия Российской Академии Наук. Механика твердого тела. – 2019. – No 5. – С. 27–36. DOI: 10.1134/S0572329919050167 Scholar
- 16.Cantournet S., Desmorat R., Besson J. Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model // International Journal of Solids and Structures – 2019. – Vol. 46, no. 11–12. – P. 2255–2264. DOI: 10.1016/j.ijsolstr.2008.12.025 Scholar
- 17.Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect / D. Hanson, M. Hawley, R. Houlton, K. Chitanvis, P. Rae, E.B. Orler, D. Wrobleski // Polymer. – 2005. – Vol. 46, no. 24. – P. 10989–10995. DOI: 10.1016/j.polymer.2005.09.039 Scholar
- 18.Diani J., Brieu M., Vacherand J.M. A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy // European Journal of Mechanics. A/Solids. – 2006. – Vol. 25, no. 3. – P. 483–496. DOI: 10.1016/j.euromechsol.2005.09.011 Scholar
- 19.Pebdani M.H. Study Mullins effect of polyurethane reinforcement with halloysite nanotube by molecular dynamics simulation // Journal of Elastomers and Plastics. – 2022. – Vol. 54, no. 5. – P. 659–675. DOI: 10.1177/00952443211060407 Scholar
- 20.Control of Mullins stress softening in silicone elastomer composites by rational design of fumed silica fillers / V. Allen, L. Chen, M. Englert, A. Moussaoui, W. Pisula // Composites Science and Technology. – 2021. – Vol. 214, no. 1. – P. 1–9. DOI: 10.1016/j.compscitech.2021.108955 Scholar
- 21.Qian D., Meng F. Modelling Mullins effect induced by chain delamination and reattachment // Polymer. – 2021. – Vol. 222, no. 1. – P. 1–8. DOI: 10.1016/j.polymer.2021.123608 Scholar
- 22.Mechanical properties and Mullins effect in natural rubber reinforced by grafted carbon black / F. Wen, W. Li, H. Jianning, L. Cuiwen, P. Wenlong, X. Haotuo, L. Shenglin // Advances in Polymer Technology. – 2019. – Vol. 2019, no. 1. – P. 1–12. DOI: 10.1155/2019/4523696 Scholar
- 23.Machado G., Chagnon G., Favier D. Theory and identification of a constitutive model of induced anisotropy by the Mullins effect // Journal of the Mechanics and Physics of Solids. – 2014. – Vol. 63, no. 1. – P. 29–39. DOI: 10.1016/j.jmps.2013.10.008 Scholar
- 24.Determination of the inelastic behavior of viscoelastic materials using the new thermodynamic model / V.D. Kislitsyn, A.L. Svistkov, K.A. Mokhireva, V.V. Shadrin // AIP Conference Proceedings. – 2023. – Vol. 2627, – P. 030002. DOI: 10.1063/5.0119254 Scholar
- 25.Verron E., Gros A. An equal force theory for network models of soft materials with arbitrary molecular weight distribution // Journal of the Mechanics and Physics of Solids. – 2017. – Vol. 106, no. 1. – P. 176–190. DOI: 10.1016/j.jmps.2017.05.018 Scholar
- 26.Vozniakovskii A.A., Vozniakovskii A.P., Kidalov S.V., Osipov V.Yu. Structure and Paramagnetic Properties of Graphene Nanoplatelets Prepared from Biopolymers Using Self-Propagating High-Temperature Synthesis // Journal of Structural Chemistry. – 2020. – Vol. 61, no. 1. – P. 869–878. DOI: 10.1134/S0022476620050200 Scholar
- 27.Vozniakovskii A.A., Vozniakovskii A.P., Kidalov S.V. New Way of Synthesis of Few-Layer Graphene Nanosheets by the Self Propagating High-Temperature Synthesis Method from Biopolymers // Nanomaterials. – 2022. – Vol. 12, no. 4. – P. 657–671. DOI: 10.3390/nano12040657 Scholar
- 28.Vozniakovskii A.A., Vozniakovskii A.P., Kidalov S.V. Phenomenological model of synthesis of fewlayer graphene (FLG) by the selfpropagating high-temperature synthesis (SHS) method from biopolymers // Fullerenes, Nanotubes and Carbon Nanostructures. – 2022. – Vol. 30, no. 1. – P. 59–65. DOI: 10.1080/1536383X.2021.1993831 Scholar
Other articles in this issue
View the whole issue (No. 2, 2023)- DYNAMIC STABILITY OF A STRAIGHT PIPE CONVEYING PULSATILE FLOW UNDER THERMAL LOADSpp. 5–10
- Method for studying the porosity of fluid phase samples by X-ray computed tomography under uniaxial compressionpp. 11–21
- Stress-strain state during draft of wide bands with shearpp. 22–28
- On the reducibility of solutions for the generalized yield criterion to solutions for Tresca’s yield criterion under axial symmetrypp. 29–37
- MODELING OF STEADY-STATE LIQUID FILTRATION IN A PIECEWISE INHOMOGENEOUS ELASTIC-POROUS MEDIUM IN THE CLASS OF ALMOST-PERIODIC FUNCTIONS (PLANE PROBLEM)pp. 38–46
- Identification of stress intensity factors, T-stresses and higher-order coefficients of regular terms in the Williams series expansion through molecular dynamics simulationspp. 47–77
- Dynamics and stability of Kapitsa's two-link pendulumpp. 78–87
- INFLUENCE OF SURFACE CHARGE ON THE FORMATION OF THE CARBONIZED LAYER RELIEF ON THE POLYMER SURFACE DURING ION-PLASMA TREATMENTpp. 88–97
- Peculiarities of SH Wave Propagation in a Two-Layer Structure of Inhomogeneous Piezoelectric and Dielectric Layerspp. 98–109
- Calculation of the tool shape for tube middle part distribution by rigid matrixpp. 110–117
- Dispersional dependences and peculiarities of energy transfer by flexible waves in a beam lying on a generalized elastic basepp. 118–125
- Mechanical behavior of polyurethane composites with nanosized fillerspp. 133–141