Abstract In this paper, a unified multi-mechanism continuum viscoplastic damage model is proposed to simulate the thermomechanical behavior of high-Cr steels at elevated temperatures. To represent the effects of material degradation under external loads, a total damage tensor is incorporated, which is composed of the low-cycle fatigue damage, the creep damage and the ductile damage. Within the small strain framework, the model is established through a thermodynamically consistent approach. First, some kinematic assumptions are proposed and the concept of effective stress is adopted. Then, based on a state potential with proper constitutive form, the constitutive equations can be derived from the second law of thermodynamics. By further considering the postulate of maximum dissipation, a Lagrangian functional is constructed through a regularization scheme. The stationary points of the Lagrangian functional yield the evolution equations of the dissipative variables. For the isotropic damage case, the damage tensor can be represented by a scalar damage variable and the constitutive evolution equations in the model can be simplified. To be prepared for practical applications, numerical integration algorithms are proposed to solve the constitutive evolution equations, and the material parameters in the model are identified based on the experimental data. To demonstrate the efficiency of the current model, it is applied to simulate the thermomechanical response of high-Cr steels under different loading conditions. The simulation results can fit the experimental data at a quantitative level and the damage mechanisms under the different loading conditions can be revealed. Besides that, the model is further modified to take into account the microcracks closure effect of the ductile damage. The current model would be helpful for the safety design and lifetime evaluation of high-Cr steel components in practical applications.

中文翻译：

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应用于高铬钢的统一多机制连续粘塑性损伤模型的热力学公式

摘要 本文提出了一种统一的多机制连续粘塑性损伤模型来模拟高铬钢在高温下的热机械行为。为了表示外部载荷下材料退化的影响，引入了一个总损伤张量，它由低周疲劳损伤、蠕变损伤和延性损伤组成。在小应变框架内，该模型是通过热力学一致的方法建立的。首先，提出了一些运动学假设，并采用了有效应力的概念。然后，基于具有适当本构形式的状态势，可以从热力学第二定律导出本构方程。通过进一步考虑最大耗散假设，拉格朗日泛函是通过正则化方案构建的。拉格朗日函数的驻点产生耗散变量的演化方程。对于各向同性损伤情况，损伤张量可以用标量损伤变量表示，模型中的本构演化方程可以简化。为了为实际应用做好准备，提出了数值积分算法来求解本构演化方程，并根据实验数据确定模型中的材料参数。为了证明当前模型的效率，它被用于模拟不同加载条件下高铬钢的热机械响应。模拟结果可以在定量水平上拟合实验数据，并且可以揭示不同加载条件下的损坏机制。除此之外，进一步修改模型以考虑延性损伤的微裂纹闭合效应。目前的模型将有助于高铬钢部件在实际应用中的安全设计和寿命评估。