基于不可逆热力学的宏细观粘弹性损伤本构模型

A Marco-Micro Viscoelastic Damage Constitutive ModelBased on Irreversible Thermodynamic

关键词:  宏损伤效应张量  细观损伤效应函数  有效柔度  微裂纹密度  损伤演化

Key words:  Macro-damage effect tensor  Micro-damage effect functions  Effective creep compliance  Microcrack density  Damage evolution

摘要:

为建立复合固体推进剂的损伤本构模型，基于不可逆热力学和叠加原理，通过引入宏观损伤效应张量，推导出一个通过有效应力表征损伤的蠕变型损伤本构方程。假设材料为初始各向同性，进一步引入细观标量损伤效应函数表征材料对称性的改变，进而得到由细观损伤效应函数表征宏观损伤效应张量的一般表达式。通过选取合适的细观损伤效应函数，文中建立的本构方程可以用于表征材料的正交各向异性损伤、横观各向同性损伤和各向同性损伤。最后，基于Schapery粘弹性微裂纹扩展模型，选取相对微裂纹密度为损伤内变量，建立了一个由损伤热力学对偶力表征的幂律型损伤演化方程。数值结果表明，建立的模型能够较好地反映材料损伤的率相关性和温度依赖性，具有良好的预测精度。

Abstract:

In order to obtain a damage constitutive model for solid composite propellants， based on irreversible thermodynamic and superposition principle， a creep damage constitutive equation was derived which including damage effects by effective stress， via introducing the concept of macro-damage effect tensor. Providing material is isotropic originally， a general form of macro-damage effect tensor was presented， which consisted of several micro-damage effect functions and those used for presenting symmetric change of material due to damage. Thus， the constitutive equation presented in the paper can be used to model orthogonal anisotropic damage， transversely isotropic damage and isotropic damage by choosing micro-damage effect functions properly. Finally， a power law of damage evolution which presented by the thermodynamic force conjugate to damage internal variable was derived in which damage internal variable was defined as the relative micro-crack density on the basis of Schapery’s crack propagation model in viscoelastic materials. Numerical results indicate that the model has a fine prediction accuracy， and it can reflect the dependence of material damage on strain rate and temperature correctly.