时变泊松比HTPB固体推进剂体积和剪切松弛模量反演

Inversion Method of Bulk and Shear Relaxation Moduli for HTPB Solid Propellant with Time-Dependent Poisson’s Ratio

关键词:  粘弹性泊松比  松弛模量  Prony级数  Volterra积分方程  HTPB固体推进剂

Key words:  Viscoelastic Poisson’s ratio  Relaxation modulus  Prony series  Volterra integration equation  HTPB propellant

摘要:

为表征HTPB复合固体推进剂泊松比的时间相关性，以经典积分型粘弹性本构模型为基础，开展了从单轴受力响应到体积和剪切松弛模量反演问题研究。运用径向基配置法和带近似奇异核的高斯求积公式求解反演问题的第二类Volterra积分方程。将获得的体积和剪切松弛模量导入Abaqus有限元软件并开展材料力学行为仿真。将有限元结果与单轴松弛、蠕变和等速率加载实验数据进行对比，验证反演方法的正确性。分析了粘弹性泊松比Prony级数参数对相对松弛模量的影响规律。结果表明，当泊松比与时间相关时，相对体积和剪切松弛模量曲线出现分离，其分离程度受长期与瞬时泊松比之差的影响，而分离快慢受泊松比迟滞时间影响。采用正确的体积和剪切松弛模量，经典粘弹性本构模型不仅能合理预测HTPB固体推进剂松弛和蠕变等粘弹性行为，还能正确反映泊松比的时间相关性。

Abstract:

In order to represent time-dependent Poisson’s ratio of HTPB composite solid propellant， the inversion problem about determination of bulk and shear relaxation moduli from the uniaxial stress versus strain responses was studied based on the classical integral viscoelastic constitutive model. The collocation method with radial basis functions， as well as Gauss quadrature formulas for approximately singular kernels， was applied for solving the second-kind Volterra integral equations of the inversion problem. The obtained bulk and shear relaxation moduli were imported into Abaqus finite element software to simulate the mechanical behavior of HTPB propellant. The proposed inversion method was validated by comparing the finite element results with the results from uniaxial relaxation， creep， and constant-rate loading tests. Finally， parameter analyses were conducted to find out how the Prony series of viscoelastic Poisson’s ratio affects the relative relaxation moduli. The results show that， the curves of the relative bulk and shear relaxation moduli are separated when Poisson’s ratio is time dependent. The separation degree is affected by the difference between the long-term and instantaneous Poisson’s ratios， while the separation slope by the retarded time. With the correct volume and shear relaxation moduli， the classical viscoelastic constitutive model can reasonably predict not only the relaxation and creep behaviors of HTPB propellant， but also the time dependency of Poisson’s ratio.