基于分数阶三参数模型的HTPB推进剂粘弹性力学响应分析

Viscoelastic mechanical response analysis of HTPB propellant based on fractional-order three-parameter model

为拓展分数阶粘弹性模型在端羟基聚丁二烯(HTPB)推进剂中的应用,研究分数阶粘弹性模型预示推进剂频域下的动态模量变化。推导了三维下的分数阶三参数模型,并结合Grünwald-Letnikov定义编写UMAT子程序。为标定本构参数,推导了带有预加载的蠕变、松弛响应的解析解,并采用遗传算法分别标定了0.4 MPa和0.6 MPa应力下蠕变实验以及10%和30%应变下松弛实验的本构参数。计算得到的有限元数值与解析解、解析解与实验值的时程相对误差均小于5%。采用分数阶三参数模型动态模量对-5、25、60℃下的动态力学实验(DMA)结果进行拟合得到本构参数,动态模量与实验结果误差小于2%,同时随着温度升高,本构参数均减小,体现出HTPB推进剂升温软化现象。结果表明,分数阶三参数模型能精确地描述不同温度下多种频率的HTPB推进剂模量变化,结合二次开发本构,可为后续HTPB推进剂复杂边界下的力学响应的研究提供材料本构模型。

In order to extend the application of fractional-order model in HTPB propellant and study on predicting of dynamic modulus changes of propellants in the frequency domain using fractional-order viscoelastic models.Three-dimensional fractional-order three-parameter constitutive equations were derived,which were transformed into UMAT subroutine combining with the Grünwald-Letnikov definition.In order to calibrate the constitutive parameters,the analytical solutions of creep and relaxation with preloading were derived,and the constitutive parameters corresponding to the creep experiments at 0.4 MPa and 0.6 MPa stresses as well as the relaxation experiments at 10%and 30%strains were calibrated by genetic algorithm.The time-history relative errors between the calculated finite element values and the analytical solutions,the analytical solutions and the experimental values are less than 5%.The complex modulus formulation of the one-dimensional fractional-order three-parameter constitutive equation was used to fit the DMA experimental results at-5℃,25℃and 60℃to obtain the constitutive parameters,and the error between the complex modulus and the experimental results is less than 2%,while the calibrated constitutive parameters all reduce as the temperature increases,reflecting the softening phenomenon of propellant at elevated temperatures.The results show that the fractional-order three-parameter model can accurately describe the variation of propellant modulus of multiple frequencies at different temperatures,which can provide a material constitutive model for the subsequent study of mechanical response of HTPB propellants under complex boundaries.