Abstract
In this paper, the fractional Burgers model is proposed to depict the creep and creep-recovery behavior of 332 aluminum alloy. Both the creep stage during loading and creep-recovery stage after the load is suddenly removed are considered. Based on the whole-stage experimental data, parameter identification for the fractional model as well as parameter analysis are conducted. By comparison with the existing research findings and the simplified models, the results show that for the entire range, the proposed fractional Burgers model is much more suitable and efficient for modeling the whole creep and creep-recovery behavior of 332 aluminum alloy.
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Data Availability
All data analyzed in this study can refer to the cited previous work (Dandrea and Lakes 2009).
References
Adeyeri, J.B., Krizek, R.J., Achenbach, J.D.: Multiple integral description of the nonlinear viscoelastic behavior of a clay soil. Trans. Soc. Rheol. 14(3), 375–392 (1970)
Brito-Oliveira, T.C., Moraes, I.C., Pinho, S.C., Campanella, O.H.: Modeling creep/recovery behavior of cold-set gels using different approaches. Food Hydrocoll. 123, 107183 (2022)
Calaf-Chica, J., Díez, P.M.B., Calzada, M.P.: Viscoelasticity and the Small Punch Creep recovery Test: numerical analysis and experimental tests on the applicability for polyvinyl chloride (PVC). Mech. Mater. 161, 104016 (2021)
Celauro, C., Fecarotti, C., Pirrotta, A., Collop, A.: Experimental validation of a fractional model for creep/recovery testing of asphalt mixtures. Constr. Build. Mater. 36, 458–466 (2012)
Chen, P., Fan, X., Yang, Q., Zhang, Z., Jia, Z., Liu, Q.: Creep behavior and microstructural evolution of 8030 aluminum alloys compressed at intermediate temperature. J. Mater. Res. Technol. 12, 1755–1761 (2021)
Colombaro, I., Garra, R., Giusti, A., Mainardi, F.: Scott-blair models with time-varying viscosity. Appl. Math. Lett. 86, 57–63 (2018)
Dandrea, J.C., Lakes, R.: Creep and creep recovery of cast aluminum alloys. Mech. Time-Depend. Mater. 13(4), 303–315 (2009)
Di Paola, M., Pirrotta, A., Valenza, A.: Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results. Mech. Mater. 43(12), 799–806 (2011)
Gao, Y., Yin, D.: A full-stage creep model for rocks based on the variable-order fractional calculus. Appl. Math. Model. 95, 435–446 (2021)
Haj-Ali, R.M., Muliana, A.H.: A multi-scale constitutive formulation for the nonlinear viscoelastic analysis of laminated composite materials and structures. Int. J. Solids Struct. 41(13), 3461–3490 (2004)
Hajikarimi, P., Nejad, F.M., Khodaii, A., Fini, E.H.: Introducing a stress-dependent fractional nonlinear viscoelastic model for modified asphalt binders. Constr. Build. Mater. 183, 102–113 (2018)
Hanyga, A., Seredyńska, M.: Multiple-integral viscoelastic constitutive equations. Int. J. Non-Linear Mech. 42(5), 722–732 (2007)
Hei, X., Chen, W., Pang, G., Xiao, R., Zhang, C.: A new visco–elasto-plastic model via time–space fractional derivative. Mech. Time-Depend. Mater. 22(1), 129–141 (2018)
Luo, X., Ma, F., Birgisson, B., Huang, Z.: Coupled mechanical and kinetic modeling of recovery in asphalt mixtures. Constr. Build. Mater. 254, 118889 (2020)
Mendiguren, J., Cortés, F., Galdos, L.: A generalised fractional derivative model to represent elastoplastic behaviour of metals. Int. J. Mech. Sci. 65(1), 12–17 (2012)
Nutting, P.: A new general law of deformation. J. Franklin Inst. 191(5), 679–685 (1921)
Oeser, M., Pellinen, T., Scarpas, T., Kasbergen, C.: Studies on creep and recovery of rheological bodies based upon conventional and fractional formulations and their application on asphalt mixture. Int. J. Pavement Eng. 9(5), 373–386 (2008)
Onaran, K., Findley, W.N.: Experimental determination of some kernel functions in the multiple integral method for nonlinear creep of polyvinyl chloride. J. Appl. Mech. 38(1), 30–38 (1971). https://doi.org/10.1115/1.3408763. https://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/38/1/30/5451056/30_1.pdf
Ornaghi, H.L. Jr., Almeida, J.H.S. Jr., Monticeli, F.M., Neves, R.M.: Stress relaxation, creep, and recovery of carbon fiber non-crimp fabric composites. Compos. Part C, Open Access 3, 100051 (2020)
Peng, Y., Zhao, J., Sepehrnoori, K., Li, Z.: Fractional model for simulating the viscoelastic behavior of artificial fracture in shale gas. Eng. Fract. Mech. 228, 106892 (2020)
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Elsevier, Amsterdam (1998)
Ribeiro, J.G.T., de Castro, J.T.P., Meggiolaro, M.A.: Modeling concrete and polymer creep using fractional calculus. J. Mater. Res. Technol. 12, 1184–1193 (2021)
Rouzegar, J., Gholami, M.: Creep and recovery of viscoelastic laminated composite plates. Compos. Struct. 181, 256–272 (2017)
Schapery, R.A.: On the characterization of nonlinear viscoelastic materials. Polym. Eng. Sci. 9(4), 295–310 (1969)
Schiessel, H., Metzler, R., Blumen, A., Nonnenmacher, T.: Generalized viscoelastic models: their fractional equations with solutions. J. Phys. A, Math. Gen. 28(23), 6567 (1995)
Stiassnie, M.: On the application of fractional calculus for the formulation of viscoelastic models. Appl. Math. Model. 3(4), 300–302 (1979)
Van Bockstaele, F., De Leyn, I., Eeckhout, M., Dewettinck, K.: Non-linear creep-recovery measurements as a tool for evaluating the viscoelastic properties of wheat flour dough. J. Food Eng. 107(1), 50–59 (2011)
Wu, F., Zhang, H., Zou, Q., Li, C., Chen, J., Gao, R.: Viscoelastic-plastic damage creep model for salt rock based on fractional derivative theory. Mech. Mater. 150, 103600 (2020)
Xu, F., Zeng, N., Cheng, K., Wang, X., Long, S., Ding, Y., Yang, C.: A study of the nanoindentation creep behavior of (La0.5Ce0.5)65Al10Co25 metallic glass based on fractional differential rheological model. J. Non-Cryst. Solids 490, 50–60 (2018)
Xu, H., Jiang, X.: Creep constitutive models for viscoelastic materials based on fractional derivatives. Comput. Math. Appl. 73(6), 1377–1384 (2017)
Zhang, W., Capilnasiu, A., Sommer, G., Holzapfel, G.A., Nordsletten, D.A.: An efficient and accurate method for modeling nonlinear fractional viscoelastic biomaterials. Comput. Methods Appl. Mech. Eng. 362, 112834 (2020)
Funding
This work was supported by the National Natural Science Foundation of China (Grant No. 11801221) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20180586).
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Fan, W., Huang, Y. Modeling creep and creep recovery of 332 aluminum alloy using fractional calculus. Mech Time-Depend Mater 27, 35–44 (2023). https://doi.org/10.1007/s11043-021-09528-7
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DOI: https://doi.org/10.1007/s11043-021-09528-7
Keywords
- Creep-recovery behavior
- Aluminum alloy
- Fractional Burgers model
- Parameter analysis
- Viscoelastic material