15CrMoG耐高温合金钢Johnson-Cook本构模型建立与精度分析.pdf

第 15 卷 第 9 期 精 密 成 形 工 程 2023 年 9 月 JOURNAL OF NETSHAPE FORMING ENGINEERING 159 收稿日期：2023-06-10 Received：2023-06-10 基金项目：河北省自然科学基金（E2021208025，E2020208044）；河北省创新能力提升计划（225A2201D）Fund：Natural Science Foundation of Hebei Province(E2021208025,E2020208044);Innovation Ability Improvement Plan of Hebei Province(225A2201D)引文格式：杨京,王伟,张双杰,等.15CrMoG 耐高温合金钢 Johnson-Cook 本构模型建立与精度分析J.精密成形工程,2023,15(9):159-167.YANG Jing,WANG Wei,ZHANG Shuang-jie,et al.Establishment and Accuracy Analysis of Johnson-Cook Constitutive Model for 15CrMoG High-temperature Resistant Alloy SteelJ.Journal of Netshape Forming Engineering,2023,15(9):159-167.15CrMoG 耐高温合金钢 Johnson-Cook 本构模型建立与精度分析 杨京1，王伟1*，张双杰1,2，马世博1,3，闫华军1,4（1.河北科技大学 材料科学与工程学院 河北省材料近净成形技术重点实验室，石家庄 050018；2.河北省汽车冲压模具产业技术研究院，河北 沧州 062150；3.河北省机电五金部件产业技术研究院，河北 沧州 061500，4.河北省楔横轧技术创新中心，石家庄 050031）摘要：目的目的 掌握不同条件下 15CrMoG 的高温流变规律。方法方法 在变形温度为 1 173.15、1 273.15、1 373.15、1 473.15 K，应变速率为5、10、15、20 s1条件下，对15CrMoG 进行等温压缩实验。根据实验数据构建15CrMoG的 Johnson-Cook 本构模型，并对应变速率强化参数 C 和温度敏感系数 D 进行分别修正和同时修正。将修正后的 3 种模型预测值与实验值进行线性拟合，分别得到各模型的相关系数。引入相对误差 ARE 函数，计算不同条件下各模型的平均误差，通过对比得到精度较高的模型。结果结果 15CrMoG 具有温度和应变速率敏感性，高温流变曲线整体呈现先上升后平稳的趋势。拟合取值的局限性导致未修正的本构模型的精度较差。在较低变形温度下，修正后的模型均具有良好的预测精度，在高变形温度下，修正温度敏感系数的模型具有更好的适应性。3 种修正模型预测值与实验值的线性相关系数均在 0.9 以上，具有良好的相关性。在低变形温度下，3 种模型的相对误差均较小；在高变形温度下，修正温度敏感系数的 Johnson-Cook 模型具有较高的预测精度，最大误差为 4.75%。结论结论 对 Johnson-Cook 进行修正可更准确地描述 15CrMoG 的高温变形行为，其中修正温度敏感系数模型的误差最小，为推荐本构模型。关键词：15CrMoG；等温压缩实验；高温变形行为；Johnson-Cook 本构模型；模型修正 DOI：10.3969/j.issn.1674-6457.2023.09.019 中图分类号：TG115；TG142 文献标识码：A 文章编号：1674-6457(2023)09-0159-09 Establishment and Accuracy Analysis of Johnson-Cook Constitutive Model for 15CrMoG High-temperature Resistant Alloy Steel YANG Jing1,WANG Wei1*,ZHANG Shuang-jie1,2,MA Shi-bo1,3,YAN Hua-jun1,4(1.Hebei Key Laboratory of Material Near-net Forming Technology,School of Materials Science and Engineering,Hebei Uni-versity of Science and Technology,Shijiazhuang 050018,China;2.Hebei Industry Technology Research Institute of Automotive Stamping Die,Hebei Cangzhou 062150,China;3.Hebei Industry Technology Research Institute of Electromechanical Hardware Parts,Hebei Cangzhou 061500,China;4.Hebei Technology Innovation Center of Cross Wedge Rolling,Shijiazhuang 050031,China)160 精 密 成 形 工 程 2023 年 9 月 ABSTRACT:The work aims to grasp the high-temperature rheological law of the material under different conditions.Isother-mal compression experiments were conducted on 15CrMoG at deformation temperatures of 1 173.15,1 273.15,1 373.15,1 473.15 K,and strain rates of 5,10,15,20 s1.A Johnson Cook constitutive model of 15CrMoG was constructed based on ex-perimental data,and the strain rate enhancement parameter C and the temperature sensitivity coefficient D were corrected sepa-rately and simultaneously.The predicted values of the three modified models were linearly fitted with the experimental values to obtain the correlation coefficients for each model.The relative error ARE function was introduced to calculate the average error of each model under different conditions,and obtain a model with high accuracy through comparison.The result showed that 15CrMoG was sensitive to temperature and strain rate,and the high-temperature rheological curve showed a trend of first in-crease and then stable.The uncorrected constitutive model had poor accuracy due to the limitations of fitting values.The modi-fied model had good prediction accuracy at lower deformation temperatures,while the model with a modified temperature sensi-tivity coefficient D had better adaptability at higher deformation temperatures.The linear correlation coefficients between the predicted values of the three modified models and the experimental values were all above 0.9,indicating good correlation.The relative errors of the three models were relatively small at low deformation temperatures.At high deformation temperatures,the Johnson Cook model,which corrected the temperature sensitivity coefficient D,had higher prediction accuracy,with a maxi-mum error of 4.75%.The conclusion indicates that modifying Johnson Cook can more accurately describe the high-temperature deformation behavior of 15CrMoG,with the model error of the temperature sensitivity coefficient D being the smallest,making it the recommended constitutive model.KEY WORDS:15CrMoG steel;isothermal compression experiment;high-temperature deformation behavior;Johnson-Cook constitutive model;model correction 本构模型是描述金属高温变形行为和制定加工工艺的重要依据1，已广泛应用于有限元数值模拟中2。作为描述金属材料高温流动行为的数学表述，本构方程的准确性直接影响着数值模拟的精度3。目前，已有 多 种 描 述 材 料 本 构 关 系 的 数 学 模 型，如Arrhenius4-6、Zerilli-Armstrong7-9、Johnson-Cook10-12等。其中 Johnson-Cook 模型为 Johnson 与 Cook 提出的描述金属在高温、高应变速率下的唯象本构模型13，与其他模型相比，该模型因具备简单的多项乘法形式、更少的求解参数和较为准确的预测能力而受到了学者们的广泛关注14，已被广泛用于描述金属材料的高温变形行为。刘晶等15对 B280VK 进行了拉伸实验并建立了 Johnson-Cook 本构模型，该模型与实验数据具有高度的一致性。Qian 等16利用分离式霍普金森实验研究了 CuCrZr 合金在宽应变率（5002 200 s1）和20600 温度范围内的动态压缩行为，并修正了Johnson-Cook 模型。Niu 等17为了提高 A356 应变软化机理的可预测性，提出了一种改进的 Johnson-Cook模型，并进行了有限元仿真对比，载荷位移曲线的一致性表明模型具有良好的预测精度。Jang 等18研究了接触面表面粗糙度形成的间隙对