复合固体推进剂黏弹性微裂纹损伤本构模型

摘要

In order to establish the constitutive model of solid composite propellants with damage,at a mesoscopic scale,the damage of the material was considered in a micro-cracking form,and the crack density was chosen as in-ternal damage variable.On the basis of Abdel-Tawab's constitutive equation,the damage mapping tensor which was derived in a general form by using the homogeneous theory of microcracks.Usually,the damage mapping tensor is minor symmetric,and its physical significance is that mapping a multiaxial loading on an anisotropic material in true stress space into a more complicated multiaxial loading on an isotropic material in effective stress space.Secondly,a damage evolution equation was obtained based on the dynamic model of crack growth in viscoelastic material and the concept of crack growth resistance curves.There are only four micro-parameters which have clear physical meanings and similar variation tendencies with macro-stress curves in damage evolution equation.Numerical results indicate that the model can correctly reflect the anisotropic damage feature of material,the dependence of damage on strain rate and temperature,and the capacity to predict creep damage behavior reasonably.%为建立复合固体推进剂的损伤本构模型,在介观尺度上视其为微裂纹损伤,选取微裂纹密度为损伤内变量.在 Abdel-Tawab本构方程的基础上,基于微裂纹均匀化理论,推导了损伤映射张量的一般形式.该张量通常具有非完全对称性,其物理意义是将真实应力空间中各向异性材料的多轴加载映射为等效应力空间中各向同性材料的更为复杂的多轴加载.其次,基于黏弹性动态裂纹扩展模型和裂纹扩展阻力曲线的概念,建立了损伤内变量的演化方程.该演化方程仅含4个物理意义明确的细观参数,并且参数的取值规律与宏观应力曲线的变化规律相一致.数值结果表明,建立的模型能够有效反映材料损伤的应变率、温度依赖性及各向异性特征,并且具有一定的蠕变损伤预测能力.