Due to the limited testing methods and high costs, researches on the evolution law of residual stress in the post-weld heat treatment (PWHT) process of pressure equipment are mainly by numerical simulation, in which the selection of a reasonable and reliable creep constitutive model is crucial to ensure the accuracy of numerical predictions. It is worth noting that the temperature changes and residual stress variation during the heat treatment process result in the following creep characteristics: the creep occurs under different temperatures during the heat treatment processes of heating, holding, and cooling; the creep occurs under different residual stress level where the residual stress varies during the heat treatment stages. Thus, to accurately simulate the stress release behavior during the PWHT process, the proper creep constitutive model must involve the influences of the temperature and the stress state. Meanwhile, current heat treatment simulation usually adopts simplified qualitative approaches, and the creep constitutive models often ignore the physical mechanisms and characteristics of actual creep processes, such as the Norton, the Norton-Bailey, and the Omega models. As a result, the accuracy of heat treatment simulation is limited. In this paper, a new creep constitutive relation under varying temperature and stress is proposed. The hyperbolic-sinusoidal function is used to represent the complete three stages of creep, which compensate the inaccuracy prediction at the first and the third creep stages. Moreover, the Arrhenius function is introduced to characterize the creep response under varying temperature conditions, which enables the prediction of residual stress evolution throughout the entire heating-holding-cooling process of heat treatment. Then, a typical pressure vessel cylindrical circumferential weld is simulated. The stress release during the heat treatment is calculated, and the efficacy of the proposed model is validated through surface residual stress testing. It is found that the creep behavior is a crucial factor in numerical simulation of heat treatment, and the creep constitutive relation can significantly affect the accuracy of heat treatment simulation. The simulation utilizing the hyperbolic-sinusoidal temperature-dependent creep model is much more accurate compared to the classical simulation. The simulation results are much more consistent to the experimental results. Specifically, the traditional model often underestimates the stress state, the residual stress drops abruptly during the heating stage. The residual stress evolution mechanism is simulated using the new model: The majority of residual stress are released during the heating process which primarily relies on the creep strain transformation (contributes up to 85%). The stress state does not change during the holding stage and slight higher at the cooling stage.

中文翻译：

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承压设备焊后热处理过程应力消除模拟：考虑温度和应力变化的蠕变本构方程

由于试验手段有限、成本较高，对承压设备焊后热处理（PWHT）过程中残余应力演化规律的研究主要采用数值模拟的方法，其中选择合理可靠的蠕变本构模型对于保证数值预测的准确性至关重要。值得注意的是，热处理过程中的温度变化和残余应力的变化导致了以下蠕变特征：在加热、保温、冷却等热处理过程中，不同温度下发生蠕变；蠕变发生在不同的残余应力水平下，其中残余应力在热处理阶段发生变化。因此，为了准确模拟焊后热处理过程中的应力释放行为，合适的蠕变本构模型必须考虑温度和应力状态的影响。同时，目前的热处理模拟通常采用简化的定性方法，蠕变本构模型往往忽略实际蠕变过程的物理机制和特征，如Norton、Norton-Bailey和Omega模型。因此，热处理模拟的精度受到限制。本文提出了一种新的温度和应力变化下的蠕变本构关系。采用双曲正弦函数来表示完整的蠕变三个阶段，弥补了蠕变第一阶段和第三蠕变阶段的预测误差。此外，引入阿伦尼乌斯函数来表征不同温度条件下的蠕变响应，从而能够预测整个热处理加热-保温-冷却过程中的残余应力演变。然后，对典型的压力容器圆柱形环焊缝进行了模拟。计算了热处理过程中的应力释放，并通过表面残余应力测试验证了所提出模型的有效性。研究发现，蠕变行为是热处理数值模拟的关键因素，蠕变本构关系能够显着影响热处理模拟的准确性。与经典模拟相比，利用双曲正弦温度相关蠕变模型进行的模拟要准确得多。模拟结果与实验结果更加一致。具体来说，传统模型往往低估应力状态，残余应力在加热阶段急剧下降。使用新模型模拟残余应力演化机制：残余应力大部分在加热过程中释放，主要依靠蠕变应变转变（贡献高达85%）。保压阶段应力状态不变，冷却阶段应力状态稍高。