Material viscoelasticity is of particular importance for polymers,biotissues and many others,due to the significant influence not only on the elastic response of structures,but also on their failure mechanism in actua...Material viscoelasticity is of particular importance for polymers,biotissues and many others,due to the significant influence not only on the elastic response of structures,but also on their failure mechanism in actual applications.In this study,the experimental tests by nanoindentations are cate gorized according to the objective parameter combined with the indenter sha pe into four distinct cases,and the Fractional Derivative Zener model(FDZM)is employed to characterize this time-dependent property.The explicit data-fitting formulas are derived to determine the relaxation modulus and creep compliance te sted with the conical and spherical inde nters.Besides,a fitting scheme is provided to facilitate the identification of these viscoelastic parameters.In comparison with the general methods adopting the Prony series or empirical models,two silent merits present:(1)fewer model coefficients necessitate being determined based on the experimental data;(2)the relaxation modulus G(t)and the creep compliance J(t)can be obtained through one indentation test,and their exact interconversion is guaranteed as well.Several sets of experimental data are applied to examine the validity of the developed approach,and three more examples are adopted to demonstrate the exact interconversion between G(t)and J(t).A few concluding remarks are drawn eventually.展开更多
基金National Natural Science Foundation of China(grant nos.51290291,51675447,51305362,11772274)the Young Scientific Innovation Team of Science and Technology of Sichuan(grant no.2017TD0017)the Fundamental Research Funds for the Central Universities(grant no.2682016CX024)。
文摘Material viscoelasticity is of particular importance for polymers,biotissues and many others,due to the significant influence not only on the elastic response of structures,but also on their failure mechanism in actual applications.In this study,the experimental tests by nanoindentations are cate gorized according to the objective parameter combined with the indenter sha pe into four distinct cases,and the Fractional Derivative Zener model(FDZM)is employed to characterize this time-dependent property.The explicit data-fitting formulas are derived to determine the relaxation modulus and creep compliance te sted with the conical and spherical inde nters.Besides,a fitting scheme is provided to facilitate the identification of these viscoelastic parameters.In comparison with the general methods adopting the Prony series or empirical models,two silent merits present:(1)fewer model coefficients necessitate being determined based on the experimental data;(2)the relaxation modulus G(t)and the creep compliance J(t)can be obtained through one indentation test,and their exact interconversion is guaranteed as well.Several sets of experimental data are applied to examine the validity of the developed approach,and three more examples are adopted to demonstrate the exact interconversion between G(t)and J(t).A few concluding remarks are drawn eventually.
