中文摘要：

采用分数阶黏弹单元替代经典模型中的黏壶，结合非晶合金在外加载荷作用下的微观结构演化，建立了以分数阶微积分表示的非晶合金黏弹性本构模型。并根据Hertz弹性理论及分数阶黏弹性本构模型，推导了块体非晶合金在纳米压痕球形压头下的位移与载荷及时间关系式。基于推导的解析式，对铁基块体非晶合金在表观弹性区的纳米压痕位移与载荷及时间曲线进行了非线性拟合分析。相较于整数阶模型，分数阶模型不仅具有较高的拟合精度，其拟合参数能敏锐地反应加载速率对块体非晶合金黏弹性行为的影响，且参数的变化规律与载荷作用下非晶合金微观结构演化呈现出较强的相关性。

英文摘要：

Combined with the microstructure evolution in amorphous alloys under the external load, a fractional order vis-coelastic constitutive model is first derived by replacing a Newtonian dashpot in the classical Zener model with the fractional derivative Abel dashpot. Based on the Hertzian theory and the fractional order viscoelastic constitutive model, a relationship between displacement and load （or time） for an instrumental nanoindentation test with a spherical indenter is then proposed. Finally, a series of nanoindentation test data for an Fe-base bulk amorphous alloy are employed to verify the derived model, and its viscoelastic behavior in the apparent elastic region is analyzed in detail. Results show that the fractional order rheological model has higher fitting accuracy than that of the integer order model, and the fitting parameters of the proposed model are more suitable to reflect the effect of the loading rate on the viscoelastic behavior in the alloy studied. Variation of the above-mentioned fitting parameters exhibits a strong correlation with the microstructure evolution during the loading of this Fe-base amorphous alloy.