10Ni5CrMoV钢焊缝针状铁素体相变热力学分析

10Ni5CrMoV钢焊缝针状铁素体相变热力学分析 Thermodynamic Analysis on Phase Transformation of Acicular Ferrite in Weld of 10Ni5CrMoV Steel 1 first-author 郝　红（1981—），女，博士，主要从事材料的可靠性评价工作。 郝　红（1981—），女，博士，主要从事材料的可靠性评价工作。 2 corresp 丁　敏（1981—），男，博士，副教授，主要从事材料及焊接技术研究。E-mail： dingmin415@126.com。 丁　敏（1981—），男，博士，副教授，主要从事材料及焊接技术研究。E-mail： dingmin415@126.com。 dingmin415@126.com 太原科技大学 环境与安全学院,山西 太原 030024 太原科技大学 环境与安全学院,山西 太原 030024 College of Environment and Safety, Taiyuan University of Science and Technology, Taiyuan 030024, China College of Environment and Safety, Taiyuan University of Science and Technology, Taiyuan 030024, China 太原理工大学 材料科学与工程学院,山西 太原 030024 太原理工大学 材料科学与工程学院,山西 太原 030024 School of Material Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China School of Material Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China 基于各种相变热力学模型，计算了10Ni5CrMoV钢焊缝针状铁素体相变热力学模型，通过对焊缝金属相变驱动力的计算，以期揭示10Ni5CrMoV钢焊缝奥氏体变成针状铁素体机制。利用传统扩散模型、类珠光体转变模型和贫碳区切变模型探讨热力学的转变机制，结果表明，针状铁素体相变驱动力与原奥氏体中C含量相关，C含量越低，其驱动力越大。随着奥氏体转变针状铁素体的温度降低，贫碳区C原子的活度增大，针状铁素体的长大驱动力变大，从而温度的降低有利于针状铁素体的形成。在中温相变温度区间，700 K时的针状铁素体相变驱动力约为950 K时的6.1倍。基于热力学计算推测10Ni5CrMoV钢焊缝主要以贫碳区切变模式形成针状铁素体。适当延长焊接时中温相变停留时间，是提高针状铁素体含量的较好工艺选择。 Based on various thermodynamic models of phase transformation, the thermal model of acicular ferrite transformation in 10Ni5CrMoV steel weld was calculated. The driving force of weld metal transformation was calculated to reveal the mechanism of austenite transforming into acicular ferrite in 10Ni5CrMoV steel weld. The traditional diffusion model, pearlite transformation model and carbon lean zone shear model were used to explore the thermodynamic transformation mechanism. The results show that the lower the carbon contents in the original austenite, the greater the driving force of the acicular ferrite transformation. When the temperature of the austenite transforming into acicular ferrite reduces, the activity of carbon atoms in the carbon poor zone increases, and the growth driving force of acicular ferrite improves, which is conducive to the formation of acicular ferrite. The driving force of acicular ferrite transformation at 700 K was about 6.1 times of that at 950 K. Based on thermodynamic calculation, it is inferred that acicular ferrite is formed mainly in the form of shearing transition in carbon poor zone. It's a better process choice to increase the content of acicular ferrite by prolonging the residence time of medium temperature transformation during welding process. 针状铁素体 相变热力学 驱动力 切变 acicular ferrite phase transformation thermodynamics driving force shear 前言 1 10Ni5CrMoV钢是一种屈服强度不小于785 MPa的低碳NiCrMoV系舰船压壳体用钢，具有高强度、高韧性以及良好的焊接性能等特点。该钢是我国在NiCrMoV系基础上研制的一种船压壳体耐压钢种 ［ 1 1 ］ 。10Ni5CrMoV钢的焊缝金属显微组织是决定焊缝金属力学性能的重要因素。一般来说，其焊缝金属主要类别有奥氏体 ［ 2 2 ］ 、贝氏体、针状铁素体 ［ 1 1 ， 3 3 - 5 5 3-5 ］ 。当焊缝金属为奥氏体时，焊缝容易形成超标的气孔，影响焊接质量 ［ 2 2 ］ 。贝氏体与针状铁素体都是奥氏体在中温阶段转变形成的产物，且针状铁素体实质上是晶内形核的贝氏体铁素体，贝氏体的形成温度要高于针状铁素体，两者形态上的唯一区别是贝氏体形核于奥氏体晶界部位，而针状铁素体往往形核于奥氏体晶粒内部 ［ 3 3 - 5 5 3-5 ］ 。一般来说，当焊缝金属中含有65%以上且平均尺寸约为1 μm的针状铁素体时，焊缝金属具有良好的综合力学性能 ［ 6 6 ］ 。有研究表明，焊缝中有Ni元素相比无Ni元素的情况，能够得到更多的针状铁素体组织，从而有利于抑制冷裂纹 ［ 7 7 ］ 。因此，研究10Ni5CrMoV钢焊缝金属中针状铁素体形成的相变热力学机理，具有重要的理论和实际应用价值。 试验用10Ni5CrMoV钢的化学成分和力学性能分别如 表1 表1 、 表2 表2 所示，其供货为调质态，显微组织为索氏体，焊接性分析见前期研究 ［ 8 8 ］ ，比较难焊接，但是选择合适的焊接方法与工艺措施可以防止接头韧性下降。优化焊接材料及焊接工艺可以提高接头韧性储备。试验用焊丝牌号为JS80，其力学性能和化学成分分别如 表2 表2 、 表3 表3 所示。一般来说，针状铁素体为大角度晶界，杂乱无章，且具有优良的韧性和抗裂性，基于相变热力学模型，通过对焊缝金属相变驱动力的计算以期揭示奥氏体变成针状铁素体的机制，提高针状铁素体含量从而提高焊缝质量。 Fe Cr Mn Mo Ni Si C V P S 93.41 0.55 0.55 0.425 4.6 0.27 0.11 0.06 0.015 0.01 材料 屈服强度 R eL /MPa 抗拉强度 R m /MPa 冲击功 A kv /J 10Ni5CrMoV钢 785 940 195（-50 ℃） JS80焊丝 720 820 47（-40 ℃） Fe Cr Mn Mo Ni Si C 其他 93.85 0.6 1.7 0.6 2.5 0.4 0.05 Bal. 焊缝区针状铁素体相变驱动力热力学模型的建立 1 Fe-C 合金相中 C 元素和 Fe 元素的活度计算 2 基于文献［ 8 8 ］及实验，本文采用熔化极旋转窄间隙焊焊接方法，U形坡口，热输入25 kJ/cm，多层单道焊，层间温度150~200 ℃，以期焊层之间相成分均匀。相变驱动力与元素的成分、活度是有关联的，计算焊缝针状铁素体的相变驱动力需要明确Fe元素和C元素在奥氏体和针状铁素体中的活度。 计算活度的模型主要有KRC模型、LFG模型、MD模型。KRC模型是Kaufman等人于1962年建立，随后许多研究者基于KRC模型进行了改进。本文基于Shiflet等人 ［ 6 6 ， 9 9 - 12 12 9-12 ］ 提出的改进性模型计算10Ni5CrMoV钢焊缝金属中Fe和C的活度。 C元素在Fe-C合金中形成固溶体时其原子位置不会改变，因此C元素在奥氏体中活度 <math id="M1"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34292999&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34292998&type= 3.47133350 4.06400013 可表示为： <math display="block" id="M2"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup><mi>T</mi></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293001&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293000&type= 51.56200027 9.73666668 式中　 <math id="M3"><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293003&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293002&type= 2.62466669 3.72533321 为C元素在奥氏体中的摩尔分数； <math id="M4"><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293005&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293004&type= 3.04800010 3.72533321 为间隙位置的配位数，可表示为： <math id="M5"><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">14</mn><mo>-</mo><mn mathvariant="normal">12</mn><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mtext> </mtext><mo stretchy="false">(</mo><mfrac><mrow><mo>-</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293007&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293006&type= 32.68133163 7.61999989 ； <math id="M6"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293009&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293008&type= 7.87400007 4.82600021 为C元素在奥氏体中的偏摩尔非配置熵； <math id="M7"><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293011&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293010&type= 7.02733374 4.14866638 为C元素在奥氏体中的偏摩尔焓； T 为热力学转变温度，单位：K； <math id="M8"><msub><mrow><mi>W</mi></mrow><mrow><mi>γ</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293013&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293012&type= 4.06400013 3.72533321 为C元素在奥氏体中的交互作用能； R 为摩尔气体常数。 从而C元素在针状铁素体中的活度 <math id="M9"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293015&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293014&type= 4.65666676 4.06400013 可表示为： <math display="block" id="M10"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mrow><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi mathvariant="normal">α</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup><mi>T</mi></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293017&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293016&type= 55.03333664 9.14400005 式中　 <math id="M11"><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293019&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293018&type= 4.40266657 3.72533321 为C元素在铁素体中的摩尔分数； <math id="M12"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293021&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293020&type= 7.87400007 4.40266657 为C元素在铁素体中的偏摩尔非配置熵； <math id="M13"><mi mathvariant="normal">Δ</mi><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293023&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293022&type= 5.67266655 3.21733332 <math id="M14"><msub><mrow/><mrow><mi>α</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293025&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293024&type= 1.26999998 4.06400013 为C元素在铁素体中的偏摩尔焓； <math id="M15"><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">12</mn><mo>-</mo><mn mathvariant="normal">8</mn><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mtext> </mtext><mo stretchy="false">(</mo><mfrac><mrow><mo>-</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>α</mi></mrow></msub></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293027&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293026&type= 31.49600029 7.28133297 ； <math id="M16"><msub><mrow><mi>W</mi></mrow><mrow><mi>α</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293029&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293028&type= 4.31799984 3.72533321 为C元素在铁素体中的交互作用能。 Fe元素在奥氏体中的活度 <math id="M17"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293031&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293030&type= 4.14866638 4.06400013 可表示为： <math display="block" id="M18"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293033&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293032&type= 36.74533463 8.63599968 同理，Fe元素在针状铁素体中的活度 <math id="M19"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293035&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293034&type= 4.65666676 4.06400013 可表示为： <math display="block" id="M20"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">3</mn></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">3</mn></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">3</mn><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293037&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293036&type= 40.30133438 8.04333401 在奥氏体与针状铁素体界面处，相界面处于平衡状态，从而界面处Fe元素和C元素的偏摩尔自由能相等。由此可以推导出 γ /（ γ +AF）界面相界成分 <math id="M21"><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293041&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293040&type= 6.09600019 4.06400013 为： <math display="block" id="M22"><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293043&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293042&type= 26.75466537 8.29733276 <math display="block" id="M23"><mi>φ</mi><mo>=</mo><mfrac><mrow><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293045&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293044&type= 26.33133125 7.87400007 式中　 <math id="M24"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293050&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293047&type= 9.56733322 4.06400013 为超组元S与 <math id="M25"><mi>γ</mi><mo>→</mo><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293055&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293053&type= 8.38199997 3.38666677 相变相联系的自由能变化，表达式为： <math display="block" id="M26"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>=</mo><mn mathvariant="normal">141</mn><mo>∑</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup><mo>-</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>N</mi><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup></mtd></mtr><mtr><mtd><mtext>      </mtext><mfenced open="{" close="}" separators="|"><mrow><mi>T</mi><mo>-</mo><mn mathvariant="normal">100</mn><mo>∑</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293062&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293057&type= 58.41999817 12.44600010 式中　 <math id="M27"><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293067&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293065&type= 2.37066650 3.72533321 为置换型合金元素 X i 的摩尔分数； <math id="M28"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293072&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293069&type= 6.18066692 4.06400013 、 <math id="M29"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>N</mi><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293078&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293075&type= 7.45066643 4.06400013 分别为自由能的磁性和非磁性分量所对应的温度位移，其取值见 表1 表1 ［ 13 13 ］ 。 <math id="M30"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293091&type= 9.56733322 4.06400013 为纯铁中奥氏体转变铁素体的相变自由能，是温度变化的函数。 <math id="M31"><mfenced open="{" close="}" separators="|"><mrow><mi>T</mi><mo>-</mo><mn mathvariant="normal">100</mn><mo>∑</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293089&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293087&type= 27.68600082 5.84200001 表示 <math id="M32"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293093&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293091&type= 9.56733322 4.06400013 为 <math id="M33"><mfenced open="{" close="}" separators="|"><mrow><mi>T</mi><mo>-</mo><mn mathvariant="normal">100</mn><mo>∑</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293099&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293095&type= 27.68600082 5.84200001 的函数。 <math id="M34"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mtext> </mtext></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293103&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293101&type= 10.07533360 4.06400013 取值为： <math display="block" id="M35"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>=</mo><mo>-</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">40.7</mn><mo>-</mo><mn mathvariant="normal">9.98</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup><mo>•</mo><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">1.5</mn></mrow></msup><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>×</mo><mtext>       </mtext><mn mathvariant="normal">4.18</mn><mtext> </mtext><mi mathvariant="normal">J</mi><mo>/</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">500</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo>≤</mo><mi>T</mi><mo>≤</mo><mn mathvariant="normal">1</mn><mtext> </mtext><mn mathvariant="normal">184</mn><mtext> </mtext><mi mathvariant="normal">K</mi><mo stretchy="false">)</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293107&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293105&type= 106.93399811 4.82600021 AF/（AF+ γ ）界面相界成分 <math id="M36"><msubsup><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>/</mo><mtext> </mtext><mi>γ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293111&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293109&type= 6.09600019 4.06400013 为： <math display="block" id="M37"><mi>x</mi><msubsup><mrow><mtext> </mtext></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>/</mo><mtext> </mtext><mi>γ</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">3</mn><mi>τ</mi></mrow><mrow><mn mathvariant="normal">1</mn><mo>+</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mi>τ</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293114&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293113&type= 21.25133324 7.95866632 式中 <math display="block" id="M38"><mi>τ</mi><mtext> </mtext><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mtext> </mtext><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo></mrow><mrow><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">(</mo><mi>φ</mi><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mrow></mfrac><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mo stretchy="false">[</mo><mfrac><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub><mtext> </mtext><mo>-</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mo>-</mo><mtext> </mtext><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup><mo>-</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">X</mi><mi mathvariant="normal">S</mi></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mi>T</mi></mrow><mrow><mi>R</mi><mi>T</mi></mrow></mfrac><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293118&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293116&type= 78.90933228 9.73666668 针状铁素体相变过程中，C原子和Fe原子分别在奥氏体、铁素体中的活度随温度变化计算结果如 图1 图1 所示。随着温度降低，C原子在奥氏体和铁素体中的活度增大，且增大幅度随温度下降而降低；Fe原子在奥氏体中的活度减小，在铁素体中的活度增大。 1,2;3,4; C含量对C原子和Fe原子在针状铁素体相变中活度的变化影响如 图2 图2 所示，随着C含量增加，奥氏体和铁素体中C原子的活度增大，Fe原子在铁素体中的活度增大，在奥氏体中的活度减小。 1,2;3,4; 10Ni5CrMoV钢焊缝金属实际是一种多元素合金，使用超组元模型计算活度具有更高的可靠性和准确度。本研究将∑ X i 视为一个超组元S，与Fe-C合金类比，进行Fe-∑ X i 的活度计算，则超组元S在奥氏体中的活度 <math id="M47"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293184&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293183&type= 3.21733332 4.06400013 为： <math display="block" id="M48"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow/><mrow><mi>γ</mi></mrow></msub></mrow></msub></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><msub><mrow/><mrow><mi>γ</mi></mrow></msub></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293186&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293185&type= 35.64466476 9.31333351 超组元S在铁素体中的活度 <math id="M49"><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293188&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293187&type= 4.65666676 4.06400013 为： <math display="block" id="M50"><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mfrac><mrow><mn mathvariant="normal">3</mn></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">3</mn></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">3</mn><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293190&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293189&type= 40.38600159 8.04333401 <math id="M51"><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293192&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293191&type= 1.77800000 2.70933342 <math id="M52"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293194&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293193&type= 4.57200003 2.87866688 <math id="M53"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>T</mi></mrow><mrow><mi>N</mi><mi>M</mi></mrow><mrow><mi>i</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293196&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293195&type= 5.67266655 2.87866688 Si 8 26 Mn -6.1+3.8［C］-1.3［Si］-2.5［Al］ -33.5+3［C］-6［Si］ Ni -3 -31 Co 4.5 5 Mo 3.6+126.6［C］-8.6［Si］-127［Al］ 39+94.5［C］-485［C］ 2 -0.9［Si］+100［Al］ Al -5 47 Cu -10 -23 Cr -22.5+21［C］-3.8［Si］-28.2［Al］+5.6［Mn］+1［Ni］-1.7［Mo］ -16.5+42［C］-6.5［Si］-26.2［Al］+4.8［Mn］+1.8［Ni］-2.6［Mo］ 焊缝针状铁素体相变驱动力模型 2 针状铁素体是中温转变产物 ［ 1 1 ， 3 3 - 4 4 3-4 ］ ，本文计算焊缝针状铁素体相变驱动力来揭示奥氏体变成针状铁素体机制。驱动力计算模型主要有传统扩散模型、类珠光体转变模型和贫碳区切变模型，用于探讨不同转变机制之间的热力学关系。 传统扩散模型 3 扩散模型相变驱动力 <math id="M54"><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293200&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293199&type= 14.22399998 2.96333337 为： <math display="block" id="M55"><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msup><mo>=</mo><mi>R</mi><mi>T</mi><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></msub></mrow><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow/></msubsup></mrow></msub></mrow></mfrac><mo>+</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfrac><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293203&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293202&type= 64.76999664 12.53066730 所以， <math display="block" id="M56"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msup><mo>=</mo><mi>R</mi><mi>T</mi><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup><mo stretchy="false">)</mo></mrow></mfrac><mo>+</mo></mtd></mtr><mtr><mtd><mtext>                     </mtext><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac><mo stretchy="false">]</mo><mtext>                            </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">13</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293205&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293204&type= 73.82933807 19.89666748 类珠光体转变模型 3 类珠光体转变时，由奥氏体转变为铁素体和渗碳体，转变模型中铁素体的自由能可以近似于纯铁的自由能，从而相变驱动力为： <math display="block" id="M57"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi><mo>+</mo><mi mathvariant="normal">F</mi><msub><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mi mathvariant="normal">C</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><msub><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mi mathvariant="normal">C</mi></mrow></msup><mo>-</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">s</mi></mrow></msubsup><mi>T</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mtext>                       </mtext><mo>-</mo><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mtext>                        </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">]</mo><mtext>                   </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">14</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293207&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293206&type= 77.47000122 21.50533485 式中 <math id="M58"><msup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">F</mi><msub><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mi mathvariant="normal">C</mi></mrow></msup><mo>=</mo><mn mathvariant="normal">22</mn><mtext> </mtext><mn mathvariant="normal">344</mn><mo>+</mo><mn mathvariant="normal">6.64</mn><mi>T</mi><mo>-</mo><mn mathvariant="normal">0.056</mn><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup><mo>+</mo><mn mathvariant="normal">0.28</mn><mo>×</mo><msup><mrow><mn mathvariant="normal">10</mn></mrow><mrow><mo>-</mo><mn mathvariant="normal">4</mn></mrow></msup><msup><mrow><mi>T</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293209&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293208&type= 69.76532745 3.38666677 ［ 9 9 ］ 贫碳区扩散转变热力学模型 3 针状铁素体在奥氏体贫碳区的转变机制为： <math display="block" id="M59"><mi>γ</mi><mo>→</mo><msup><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>+</mo><msup><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293211&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293210&type= 29.97200012 4.82600021 奥氏体贫碳区形成有两个阶段，第一阶段为形成贫碳区（ <math id="M60"><msup><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293213&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293212&type= 1.94733346 3.72533321 ）及富碳区（ <math id="M61"><msup><mrow><msup><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293215&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293214&type= 2.87866688 3.72533321 ）；第二阶段为针状铁素体在奥氏体贫碳区形核及长大，且剩余一部分奥氏体，最后逐渐转变完全。 （18） 因此， <math display="block" id="M62"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mo>=</mo><mi>R</mi><mi>T</mi><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></msub><mo>•</mo><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi>A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></msub></mrow><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mtext>                       </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></msub><mo>•</mo><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>/</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></msub></mrow><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo stretchy="false">]</mo><mtext>                               </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">16</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293217&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293216&type= 73.49066925 26.75466537 因此， <math display="block" id="M63"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><mtext> </mtext><mo>→</mo><mtext> </mtext><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi><mo>+</mo><mtext> </mtext><msub><mrow><mi>γ</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></msubsup><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>R</mi><mi>T</mi><mfenced open="{" close="}" separators="|"><mrow><mtable columnalign="left"><mtr><mtd><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac><mo>+</mo><mtext> </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mtext> </mtext><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo><mtext> </mtext><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup></mrow></mfrac><mo>-</mo></mtd></mtr><mtr><mtd><mn mathvariant="normal">2</mn><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac><mo stretchy="false">]</mo><mtext> </mtext><mo>+</mo><mfrac><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow><mrow><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn></mrow></mfrac></mtd></mtr><mtr><mtd><mo stretchy="false">[</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><msup><mrow><mi mathvariant="normal">e</mi></mrow><mrow><mi>φ</mi></mrow></msup></mrow><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></mfrac><mo>-</mo><mn mathvariant="normal">2</mn><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac><mo stretchy="false">]</mo></mtd></mtr></mtable></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293219&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293218&type= 67.05599976 30.56466866 马氏体切变模型 3 针状铁素体以马氏体转变的相变机制为 <math id="M64"><mi>γ</mi><mo>→</mo><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293221&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293220&type= 8.38199997 3.38666677 ，其相变驱动力 <math id="M65"><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293223&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293222&type= 9.56733322 2.96333337 为： <math display="block" id="M66"><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msup><mo>=</mo><mtext> </mtext><mo stretchy="false">[</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>α</mi></mrow></msubsup><msubsup><mrow><mi>u</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mtext> </mtext><mo>+</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><msubsup><mrow><mi>u</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo stretchy="false">]</mo><mtext> </mtext><mo>-</mo><mtext> </mtext><mo stretchy="false">[</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><msubsup><mrow><mi>u</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo>+</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msubsup><mrow><mi>x</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>α</mi><mtext> </mtext><mi>γ</mi></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><msubsup><mrow><mi>u</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">e</mi></mrow><mrow><mi>γ</mi></mrow></msubsup><mo stretchy="false">]</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293225&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293224&type= 67.73333740 4.82600021 因此， <math display="block" id="M67"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msup><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>∇</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>+</mo><mi>R</mi><mi>T</mi><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfrac><mo>+</mo></mtd></mtr><mtr><mtd><mtext>                 </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfrac><mo stretchy="false">]</mo><mtext>                                            </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">19</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293227&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293226&type= 74.16799927 18.71133423 基于式（18）和式（19）， <math display="block" id="M68"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msup><mo>=</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>∇</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">[</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">s</mi></mrow></msubsup><mo>-</mo></mtd></mtr><mtr><mtd><mtext>               </mtext><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">s</mi></mrow></msubsup><mo stretchy="false">)</mo><mtext> </mtext><mi>T</mi><mtext> </mtext><mo stretchy="false">]</mo><mo>+</mo><mfrac><mrow><mi>R</mi><mi>T</mi></mrow><mrow><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mrow></mfrac><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mtext>               </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mn mathvariant="normal">3</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">3</mn><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>+</mo></mtd></mtr><mtr><mtd><mtext>               </mtext><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">3</mn><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mo>-</mo><mn mathvariant="normal">3</mn><mtext> </mtext><mo stretchy="false">(</mo><msub><mrow><mi>Z</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mtext>               </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mn mathvariant="normal">3</mn><mo stretchy="false">]</mo><mtext>                                                   </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">20</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293228&type= 73.82933807 31.91933441 贫碳区切变模型 3 奥氏体在贫碳区切变形成针状铁素体时，其相变驱动力为针状铁素体切变为马氏体驱动力与贫碳区形成驱动力之和。从而： <math display="block" id="M69"><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">Δ</mi><msup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>+</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><msup><mrow><mtext> </mtext></mrow><mrow><mi mathvariant="normal">'</mi></mrow></msup><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293231&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293230&type= 34.62866592 4.99533367 则 <math display="block" id="M70"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>+</mo><mi>R</mi><mi>T</mi><mo stretchy="false">[</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></msub><mo>•</mo><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></mrow><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">C</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo>+</mo></mtd></mtr><mtr><mtd><mtext>                  </mtext><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">l</mi><mi mathvariant="normal">n</mi><mfrac><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></msub><mo>•</mo><msub><mrow><mfenced open="" close="|" separators="|"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></mrow><mrow><msub><mrow><mfenced open="" close="|" separators="|"><mrow><mo stretchy="false">(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mo stretchy="false">]</mo><mtext>                            </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">21</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293233&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293232&type= 73.99867249 26.75466537 所以， <math display="block" id="M71"><mtable columnalign="left"><mtr><mtd><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi>d</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi mathvariant="normal">A</mi><mi mathvariant="normal">F</mi></mrow></msubsup><mo>=</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mi>G</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mi>γ</mi><mo>→</mo><mi>α</mi></mrow></msubsup><mo>+</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">[</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow></msub><mo>-</mo><mi mathvariant="normal">Δ</mi><msub><mrow><mover><mrow><mi>H</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">s</mi></mrow></msubsup><mo>-</mo></mtd></mtr><mtr><mtd><mtext>                 </mtext><mi mathvariant="normal">Δ</mi><msubsup><mrow><mover><mrow><mi>S</mi></mrow><mo>¯</mo></mover></mrow><mrow><mi>γ</mi></mrow><mrow><mi mathvariant="normal">x</mi><mi mathvariant="normal">s</mi></mrow></msubsup><mo 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mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mtext>                                                    </mtext><mo stretchy="false">(</mo><mtext> </mtext><mn mathvariant="normal">22</mn><mtext> </mtext><mo stretchy="false">)</mo></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293235&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=34293234&type= 74.93000031 47.41333389 焊缝针状铁素体相变驱动力计算结果与分析 2 图3 图3 为基于各种热力学模型的焊缝针状铁素体相变驱动力计算结果。各种模型计算都表明随着温度的降低其相变驱动力不断增大。 1;2; 由 图3a 图3a 可知，在中温相变温度区间，针状铁素体相变驱动力随着温度的降低而增大，700 K时的相变驱动力约为950 K时的6.1倍，最高为1 761.4 J/mol。而 图3b 图3b 中类珠光体转变计算的相变驱动力最高为1 432.3 J/mol，小于先共析转变的相变驱动力，因此针状铁素体以类珠光体模式转变的几率比较小。 图3c 图3c 贫碳区扩散转变的相变驱动力大于 图3b 图3b 计算的相变驱动力，但与 图3a 图3a 同温度且含量相同时计算值相差不大，而 图3d 图3d 贫碳区的切变驱动力大于 图3a 图3a 计算的结果。从而表明贫碳区有利于针状铁素体的转变，且C含量越低，转变驱动力越大。 图3e 图3e 表明针状铁素体以贫碳区切变形式转变的驱动力要大于以贫碳区扩散形式转变的驱动力。在贫碳区，针状铁素体快速长大，与在晶界处形成的侧板条铁素体和贝氏体相交互。 实际焊接时，焊缝熔池金属成分起伏较大，随着转变温度的降低，贫碳区C原子活度减小，针状铁素体的长大驱动力增大。焊接冷却速度影响C元素的分布，C元素富集于晶界，冷却速度越慢C扩散地越充分，越有利于针状铁素体在晶内形成，而晶界处形成侧板条铁素体和贝氏体，可以调控针状铁素体的含量，基于热力学计算来看针状铁素体主要以贫碳区切变形式形成。与文献［ 14 14 ］的相变驱动力计算结果相比较，本文计算的相变驱动力要小于文献中的结果，主要原因是C和Ni含量的不同，本文计算的Ni含量为2.5远大于文献中的1.88，从而可推测Ni含量的变化也可以极大调控针状铁素体的含量，文献［ 1 1 ］和文献［ 7 7 ］中的实验结果也可得到类似推论。从实用性和经济性出发，适当延长焊接时中温相变停留时间，是提高针状铁素体含量的较好选择，但元素贫化容易影响接头可靠性，具体元素的含量与针状铁素体的含量定量关系有待于进一步实验研究。 结论 1 针对10Ni5CrMoV钢材料进行焊接试验，通过热力学计算分析焊缝金属中C原子和Fe原子在奥氏体和铁素体中的活度，以及针状铁素体相变模型，得到以下结论： （1）建立并计算对比了10Ni5CrMoV钢焊缝针状铁素体相变热力学模型。 （2）原奥氏体中C含量越低，其针状铁素体相变驱动力越大。 （3）温度下降可以增大贫碳区C原子的活度，从而增大了针状铁素体的相变驱动力，更有利于针状铁素体的形成。基于热力学计算的结果，10Ni5Cr MoV钢焊缝主要以贫碳区切变形式形成针状铁素体。在中温相变温度区间，700 K时的针状铁素体相变驱动力约为950 K时的6.1倍。适当延长焊接时中温相变停留时间，是提高针状铁素体含量的较好工艺选择。 参考文献 余刚 ， 丁敏 ， 崔海超 ， 等 . 10Ni5CrMoV钢旋转电弧窄间隙GMAW研究 ［J］. 焊接技术 ， 2010 ， 39 （ 11 ）： 12 - 15 . 10Ni5CrMoV钢旋转电弧窄间隙GMAW研究 YU Gang ， DING Min ， CUI Haichao ， et al . 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Mechanical Engineering Materials ， 2017 ， 41 （ 08 ）： 75 - 79 . Microstructure and mechanical properties of MAG we-lded joint of 10Ni5CrMoV steel 宋威 ， 魏博 ， 肖红军 ， 等 . 15Ni3CrMoV与10Ni5CrMoV异种钢对接接头的显微组织及力学性能 ［J］. 机械工程材料 ， 2017 ， 41 （ 03 ）： 7 - 12 . 15Ni3CrMoV与10Ni5CrMoV异种钢对接接头的显微组织及力学性能 SONG Wei ， WEI Bo ， XIAO Hong-jun ， et al . Microstructure and mechanical properties of butt joint of 15Ni3Cr MoV and 10Ni5CrMoV dissimilar steel ［J］. Mechanical Engineering Materials ， 2017 ， 41 （ 03 ）： 7 - 12 . Microstructure and mechanical properties of butt joint of 15Ni3Cr MoV and 10Ni5CrMoV dissimilar steel 周月波 . 10Ni5CrMoV钢MIG焊接接头的组织与力学性能研究 ［D］. 黑龙江 ： 哈尔滨工程大学 ， 2002 . 10Ni5CrMoV钢MIG焊接接头的组织与力学性能研究 ZHOU Yuebo . Study on Microstructure and mechanical properties of MIG welded joint of 10Ni5CrMoV steel ［D］. Heilongjiang ： Harbin Engineering University ， 2002 . 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Thermodynamic study on acicular ferrite phase transformation in micro alloyed steel welded seam ［J］. Hot Working Technology ， 2010 ， 39 （ 03 ）： 5 - 9 . Thermodynamic study on acicular ferrite phase transformation in micro alloyed steel welded seam 10.7512/j.issn.1001-2303.2022.08.11 TG401 A 1001-2303（2022）08-0081-08 郝红，丁敏.10Ni5CrMoV钢焊缝针状铁素体相变热力学分析［J］.电焊机，2022，52（8）：81-88. 郝红，丁敏.10Ni5CrMoV钢焊缝针状铁素体相变热力学分析［J］.电焊机，2022，52（8）：81-88. HAO Hong, DING Min.Thermodynamic Analysis on Phase Transformation of Acicular Ferrite in Weld of 10Ni5CrMoV Steel[J].Electric Welding Machine, 2022, 52(8): 81-88. HAO Hong, DING Min.Thermodynamic Analysis on Phase Transformation of Acicular Ferrite in Weld of 10Ni5CrMoV Steel[J].Electric Welding Machine, 2022, 52(8): 81-88. 山西省自然科学基金（2013021021-1） 2022-01-08 2022-05-07 2022-08-25 2022-09-15 电焊机 8 52