Phase-field finite element (PFFE) modeling of the quenching-partitioning-tempering (Q-P-T) process is proposed, and the two-dimensional PFFE-QPT model considering carbide precipitation and the interface migration between martensite and austenite is used to investigate microstructural evolution and the elastic/plastic strain distribution at quenching, partitioning and tempering stages in a high-carbon steel, respectively. The simulation results of the high carbon Q-P-T steel indicate that the precipitation strengthening of carbides occurs not only because they can block the movement of dislocations, but also because they can produce high internal stress. Meanwhile, the volume fractions of different phases (including primary martensite, retained austenite, secondary martensite, and carbide) and the carbon content in retained austenite predicted by the PFFE-QPT model are slightly better than those predicted by the novel one-dimensional QPT-LE (local equilibrium) model and much closer to experimental values. The PFFE-QPT model is also used to successfully predict the volume fractions of different phases in low-carbon and medium-carbon Q-P-T steels. More importantly, the microstructural morphologies closely related to mechanical properties can be demonstrated by the PFFE-QPT model and are comparable with the experimental observation. Therefore, the PFFE-QPT model will be a more powerful tool for guiding the process and microstructure design of Q-P-T steels compared with the QPT-LE model.

中文翻译：

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高碳钢淬火-配分-回火过程中碳化物析出引起的多界面迁移机制

提出了淬火-分配-回火（QPT）过程的相场有限元（PFFE）模型，并使用考虑碳化物析出和马氏体与奥氏体之间的界面迁移的二维PFFE-QPT模型来研究微观结构演化和分别是高碳钢在淬火、分配和回火阶段的弹/塑性应变分布。高碳QPT钢的模拟结果表明，碳化物的析出强化不仅是因为它们能阻碍位错的运动，而且还因为它们能产生较高的内应力。同时，PFFE-QPT模型预测的不同相（包括初生马氏体、残余奥氏体、二次马氏体和碳化物）的体积分数和残余奥氏体中的碳含量略好于新型一维QPT-模型预测的结果。 LE（局部平衡）模型更接近实验值。 PFFE-QPT 模型还用于成功预测低碳和中碳 QPT 钢中不同相的体积分数。更重要的是，与力学性能密切相关的微观结构形貌可以通过PFFE-QPT模型得到证明，并且与实验观察结果具有可比性。因此，与QPT-LE模型相比，PFFE-QPT模型将成为指导QPT钢工艺和微观组织设计的更强大的工具。