HTPB黏弹性微裂纹偏折扩展损伤本构模型

为建立端羟基聚丁二烯（HTPB）推进剂的损伤本构模型，采用宏细观相结合的方法，将其细观损伤机理视为初始微裂纹偏折扩展的过程。首先，基于微裂纹稀疏估计理论，推导了Abdel-Tawab宏观本构方程中损伤映射张量的一般形式，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，基于能量释放率和最大周向应力准则，分析了三维币形裂纹偏折扩展的情形，进一步采用两步等效法，将偏折扩展后的裂纹等效为币形裂纹。最后，基于Schapery裂纹模型，推导了微裂纹稳定扩展的速率方程。数值结果表明，建立的模型能够有效地反映材料损伤的应变率、温度依赖性和各向异性特征。

A viscoelastic damage constitutive model for HTPB with kinked growth of microcracks

A constitutive model for the Hydroxyl Terminated PolyButadiene (HTPB) propellant with damage is developed by using a macro-micro coupled method. The micro-damage mechanism was considered as the kinking growth of microcracks. First, based on the dilute estimation theory of microcracks, the general form of the damage mapping tensor in the Abdel-Tawab's macro-constitutive equation was derived, which maps the multiaxial loading on an anisotropic material in the true stress space into more complicated multiaxial loading on an isotropic material in the effective stress space. Second, the kinking growth of a 3D penny crack was analyzed based on the energy release rate criterion and maximum circumferential stress criterion, and a penny microcrack was used to approximate the kinked one by a two-step equivalent method. Finally, a rate equation for stable growth of a microcrack was derived based on the Schapery's crack tip model. Numerical results indicate that the model can effectively reflect the anisotropic damage feature of the material, and the dependence of damage on strain rate and temperature.