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Article(id=1241408882220790599, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.08.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1703520000000, receivedDateStr=2023-12-26, revisedDate=1712073600000, revisedDateStr=2024-04-03, acceptedDate=null, acceptedDateStr=null, onlineDate=1773904541783, onlineDateStr=2026-03-19, pubDate=1755187200000, pubDateStr=2025-08-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773904541783, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773904541783, creator=13701087609, updateTime=1773904541783, updator=13701087609, issue=Issue{id=1241408875602178849, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='8', pageStart='1', pageEnd='174', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773904540204, creator=13701087609, updateTime=1773904658798, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241409373071798309, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241409373071798310, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241408875602178849, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=108, endPage=114, ext={EN=ArticleExt(id=1241408882598277970, articleId=1241408882220790599, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Research on crystal plasticity constitutive model considering the strain softening effect of ultra-fine grain metal materials, columnId=1228282192162390694, journalTitle=Journal of Mechanical Strength, columnName=Experimental Research·Testing Technology, runingTitle=null, highlight=null, articleAbstract=

In order to study the strain softening phenomenon of ultra-fine grain (UFG) metal materials under uniaxial tensile loading, a modified model considering the effect of residual internal stress was proposed based on the classical crystal plasticity constitutive model, and the specific form of residual internal stress and its evolution were programmed into the user subroutine. The uniaxial tensile test data were fitted to verify the validity of the model, and the finite element simulation results of crystal plasticity were compared with and without the residual internal stress. The results show that the simulation results obtained by using the modified crystal plasticity constitutive model are in good agreement with the experimental results, indicating that the modified crystal plasticity constitutive model can effectively capture the strain-softening phenomenon of UFG metal materials, and the simulation results show different properties under the two conditions whether the residual internal stress is taken into account. It is reasonable to explain the strain softening phenomenon of UFG metal materials from the perspective of the formation and action of residual internal stress.

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ZHENG Zhanguang, E-mail：
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为了研究超细晶金属材料（Ultra-Fine Grain, UFG）在单轴拉伸加载条件下出现的应变软化现象，基于经典的晶体塑性本构模型提出了一种考虑残余内应力作用的修正模型，并将残余内应力及其演化的具体形式编成用户子程序。通过生成宏观试样的代表性体积单元，对单轴拉伸试验数据进行拟合以验证模型的有效性，同时将有、无残余内应力作用这2种情况下的模拟结果进行比较。结果表明，利用修正的晶体塑性本构模型计算得到的模拟结果与试验结果吻合较好，说明了所修正的晶体塑性本构模型能够有效地捕捉到UFG金属材料的应变软化现象，而有、无残余内应力作用这2种情况下的晶体塑性模拟结果表现出不同的性质，说明从残余内应力形成及作用的角度上解释UFG金属材料应变软化现象是合理的。

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郑战光，男，1975年生，江西抚州人，博士，教授；主要研究方向为机械强度理论；E-mail：。

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郑战光，男，1975年生，江西抚州人，博士，教授；主要研究方向为机械强度理论；E-mail：。

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郑战光，男，1975年生，江西抚州人，博士，教授；主要研究方向为机械强度理论；E-mail：。

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Chemical composition of AA1050 commercial pure aluminum

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AlFeSiCuMnMgTi其余
Balance
0.9950.20.10.010.0190.0290.010.132
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AA1050商业纯铝化学成分

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AlFeSiCuMnMgTi其余
Balance
0.9950.20.10.010.0190.0290.010.132
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Material parameters of ultra-fine grain aluminum constitutive model

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C11/MPaC12/MPaC44/MPaτs/MPaτ0/MPa
224 475110 56256 9567569
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超细晶铝本构模型的材料参数

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考虑超细晶金属材料应变软化效应的晶体塑性本构模型研究
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郑战光 1 , 樊佳楠 1 , 孙腾 2 , 谢昌吉 1 , 黄增 1, 3
机械强度 | 实验研究·测试技术 2025,47(8): 108-114
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机械强度 | 实验研究·测试技术 2025, 47(8): 108-114
考虑超细晶金属材料应变软化效应的晶体塑性本构模型研究
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郑战光1 , 樊佳楠1, 孙腾2, 谢昌吉1, 黄增1, 3
作者信息
  • 1.广西大学 机械工程学院，南宁　530004
  • 2.北部湾大学 机械与船舶海洋工程学院，钦州　535011
  • 3.广西机电职业技术学院 机械工程学院，南宁　530007

    • 郑战光，男，1975年生，江西抚州人，博士，教授；主要研究方向为机械强度理论；E-mail：。

Research on crystal plasticity constitutive model considering the strain softening effect of ultra-fine grain metal materials
Zhanguang ZHENG1 , Jianan FAN1, Teng SUN2, Changji XIE1, Zeng HUANG1, 3
Affiliations
  • 1.School of Mechanical Engineering, Guangxi University, Nanning 530004, China
  • 2.College of Mechanical and Marine Engineering, Beibu Gulf University, Qinzhou 535011, China
  • 3.School of Mechanical Engineering, Guangxi Technological College of Machinery and Electricity, Nanning 530007, China
出版时间: 2025-08-15 doi: 10.16579/j.issn.1001.9669.2025.08.013
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摘要
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为了研究超细晶金属材料（Ultra-Fine Grain, UFG）在单轴拉伸加载条件下出现的应变软化现象，基于经典的晶体塑性本构模型提出了一种考虑残余内应力作用的修正模型，并将残余内应力及其演化的具体形式编成用户子程序。通过生成宏观试样的代表性体积单元，对单轴拉伸试验数据进行拟合以验证模型的有效性，同时将有、无残余内应力作用这2种情况下的模拟结果进行比较。结果表明，利用修正的晶体塑性本构模型计算得到的模拟结果与试验结果吻合较好，说明了所修正的晶体塑性本构模型能够有效地捕捉到UFG金属材料的应变软化现象，而有、无残余内应力作用这2种情况下的晶体塑性模拟结果表现出不同的性质，说明从残余内应力形成及作用的角度上解释UFG金属材料应变软化现象是合理的。

超细晶金属材料  /  晶体塑性本构模型  /  单轴拉伸  /  应变软化效应  /  残余内应力

In order to study the strain softening phenomenon of ultra-fine grain (UFG) metal materials under uniaxial tensile loading, a modified model considering the effect of residual internal stress was proposed based on the classical crystal plasticity constitutive model, and the specific form of residual internal stress and its evolution were programmed into the user subroutine. The uniaxial tensile test data were fitted to verify the validity of the model, and the finite element simulation results of crystal plasticity were compared with and without the residual internal stress. The results show that the simulation results obtained by using the modified crystal plasticity constitutive model are in good agreement with the experimental results, indicating that the modified crystal plasticity constitutive model can effectively capture the strain-softening phenomenon of UFG metal materials, and the simulation results show different properties under the two conditions whether the residual internal stress is taken into account. It is reasonable to explain the strain softening phenomenon of UFG metal materials from the perspective of the formation and action of residual internal stress.

Ultra-fine grain metal materials  /  Crystal plasticity constitutive model  /  Uniaxial tension  /  Strain softening effect  /  Residual internal stress
郑战光, 樊佳楠, 孙腾, 谢昌吉, 黄增. 考虑超细晶金属材料应变软化效应的晶体塑性本构模型研究. 机械强度, 2025 , 47 (8) : 108 -114 . DOI: 10.16579/j.issn.1001.9669.2025.08.013
Zhanguang ZHENG, Jianan FAN, Teng SUN, Changji XIE, Zeng HUANG. Research on crystal plasticity constitutive model considering the strain softening effect of ultra-fine grain metal materials[J]. Journal of Mechanical Strength, 2025 , 47 (8) : 108 -114 . DOI: 10.16579/j.issn.1001.9669.2025.08.013
正文
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0　引言
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当晶粒尺寸大于1 μm时，金属材料称为粗晶（Coares Grain, CG）材料；当晶粒尺寸在100 nm~1 μm时，此类材料称为超细晶（Ultra-Fine Grain, UFG）材料；当晶粒尺寸小于100 nm时，此类材料称为纳米晶（Nano Crystalline, NC）材料[1]。通常粗晶金属材料在外力作用下，表现为应变 硬化现象，即所施加的应力随着应变增加而逐渐增加。然而，在纳米晶和超细晶金属材料的单轴拉伸试验中却观察到应变软化现象，即所施加的应力随着应变增加而逐渐减小，如NC铜的单轴拉伸试验[2]310-311、UFG铝的单轴拉伸试验[3]359-363等，这引起了许多学者的关注和研究。应变软化现象出现在材料的塑性变形阶段，而金属材料的塑性变形不仅能够改变其外形和尺寸，还会引起其微观组织和力学性能的改变。对于应变软化现象内在机制的深入理解可以为改善NC/UFG金属材料的力学性能和应用场景提供新的机会。
目前，关于NC/UFG金属材料在单轴拉伸加载下表现出的应变软化现象，许多学者已经进行了相关的试验研究，并且给出了许多不同的解释。YU等[3]360将在UFG商业纯铝的单轴拉伸试验中观察到的应变软化现象归因于试样的早期局部颈缩。但是，CHAMPION等[2]311开展的NC纯铜的单轴拉伸试验中，也观察到了应变软化现象，然而试样却并没有出现颈缩行为，而且由于试验现象与他们所考虑的准则相悖，最后他们也没有给出合理的解释。WANG等[4]对UFG纯铝进行了不同应变率下的单轴拉伸试验，结果发现，无论是高应变率还是低应变率，材料都表现出应变软化现象，并且认为高应变率下UFG纯铝的应变软化现象是位错之间的交互作用导致的，而低应变率下的UFG纯铝的应变软化现象可能和晶界滑动及晶粒旋转有关。
还有一些关于NC/UFG金属材料应变软化现象的解释：位错结构的粗化[5]、位错密度的减少[6]249-251、晶界处位错的湮灭[7]或动态回复[8]等。这些从位错角度解释NC/UFG金属材料应变软化现象的说法也具有一定的参考意义，TANG等[9]101-103在总结前人关于NC/UFG材料应变软化现象相关成果的基础上，从材料塑性变形期间残余内应力形成及其作用的角度出发更加合理地解释了NC/UFG金属中出现的应变软化现象。
描述晶体材料的塑性变形特征通常依赖于晶体塑性模型及其本构关系。本文的主要工作就是基于TANG等[9]101-103所提出的残余内应力及其演化的具体形式引入到经典的晶体塑性本构模型中，得到能够反映UFG金属材料应变软化效应的晶体塑性本构模型，从残余内应力形成及其作用的角度去捕捉UFG金属材料的应变软化现象。
1　考虑应变软化效应的晶体塑性模型
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1.1　经典的晶体塑性模型
与宏观塑性建模通常所采用的唯象本构方程的形式不同，晶体塑性建模因为考虑滑移系层面的微观结构和变形机制而更加准确。晶体塑性本构理论的主旨是建立符合塑性变形机制的塑性流动模型、加工硬化模型以及内变量演化模型。目前，晶体塑性的本构理论基本形成2类体系，即唯象的晶体塑性模型和基于物理机制的晶体塑性模型。在晶体塑性框架中主要有3部分：①运动学，将宏观变形率与每个滑移系上的滑移率联系起来；②流动规律，确定在某应力状态下某一微观结构每个滑移系的滑移率；③描述内部状态变量随变形演变的规律[10]。
晶体变形运动学通常认为晶体的变形是由晶体的位错沿着特定的结晶学平面的滑移和晶格的畸变造成的。ASARO等[11-13]对晶体塑性本构行为进行了综合论述，将材料的变形分为弹性部分和塑性部分，总的变形梯度张量F可以表示为
式中，Fe为晶格畸变和刚性转动所产生的变形梯度；Fp为晶体沿着滑移方向的均匀剪切所对应的变形梯度，也即塑性速度梯度。
滑移剪切率和宏观变形率通过晶体变形的运动学公式相关联，即
式中，Lp为塑性变形梯度；为第α个滑移系上的滑移速率；sα、mα分别为第α个滑移系上的滑移方向矢量和滑移面法向矢量。
流动规律通常描述变形过程中剪切应变率与分切应力间的依赖关系。经典的率相关流动模型通常用如下的幂函数来描述第α个滑移系上位错滑移导致的剪切应变率，为
式中，为参考剪切应变率；n为率敏感系数；sgn（）为符号函数；τα、gα分别为第α个滑移系上的分解剪切应力和滑移阻力。
金属材料在塑性变形过程中由于各滑移系位错之间的相互作用，强度会随变形量的增加而增大，即材料的加工硬化。合理的硬化模型是描述材料加工硬化行为的前提，经典的晶体塑性模型的加工硬化行为通过滑移阻力的演化形式进行描述，即
式中，N为晶体滑移系个数；为第β个滑移系上的剪切率；hαβ为自硬化和潜硬化引起的应变硬化模量，可表示为
式中，q为硬化比例系数；hαα为自硬化模量。hαα的具体形式为
式中，h0为初始硬化模量；sech（·）为双曲正割函数；τs为饱和流动应力；τ0为初始屈服应力；γ为所有滑移系的总累积剪切应变。
式（7）中，所有滑移系的总累积剪切应变γ的具体形式为
式中，t为时间。
1.2　UFG材料应变软化效应的合理解释
TANG等[9]103在研究UFG金属材料的应变软化现象时提出了合理的解释：在材料塑性变形期间，晶界处产生的位错以及位错被晶界吸收会导致出现残余内应力，正是在晶粒周围残余内应力场的作用下，晶粒进一步发生塑性变形时所需要的外力会有所减小，从而出现应变软化现象。
该研究关于残余内应力的形成及其作用说明，当外部施加的应力大于材料的屈服应力时，材料晶体内部就会产生位错，而且位错会从晶粒的一边晶界穿过晶粒内部移动到另一边晶界被吸收，这会导致几何必须位错的产生或者周边晶粒的旋转。此时，即使外力卸载了，晶粒发生的塑性变形仍然存在，位错自身产生的能量将会转化为弹性能储存在晶粒周围[9]102。以最先发生塑性变形的晶粒为例，在晶体塑性模型中，该晶粒产生的总剪切应变为γ，考虑到发生的塑性变形部分会受到周围晶粒的约束，因此该晶粒周围会存在残余弹性应变场，其平均残余弹性应变γr<γ，那么平均残余弹性应变可表达为γr=(1-a)γ，其中，a为比例系数；0<a≤1；当a=1时，无残余内应力的作用；当a≠1时，有残余内应力的作用。
其他学者认为残余内应力是存在的，且作为外应力的补偿应力，对材料的塑性变形起到正向的促进作用，因此，随着塑性变形的逐渐累积，会不断形成新的残余内应力场，在其作用下，材料进一步发生塑性变形所需要的外应力会逐渐减小，从而在宏观上表现出应变软化现象。结合引文给出的残余弹性应变及残余内应力的具体形式[9]102-103，本文基于经典的晶体塑性模型进行了简单修改，即
式中，τr为塑性变形期间滑移系上产生的残余内应力；G为弹性剪切模量。
1.3　考虑残余内应力的流动规律
室温下，UFG金属材料的变形仍以位错滑移为主[14-15]。本文基于TANG等[9]101-103的研究，主要考虑了材料在塑性变形期间残余内应力的形成及残余内应力场对位错滑移的正向促进作用，在经典的晶体塑性模型（唯象的晶体塑性模型）基础上进行修正，以反映UFG金属材料在单轴拉伸载荷作用下的应变软化效应。
在修正模型之前，首先需要在微观尺度评估晶体的应力状态，通常晶体的应力状态可分为2个部分：①由外部施加的牵引力或在变形体表面所规定的位移而产生的外应力；②在塑性变形时由材料的不均匀性所产生的内应力[16]。总的应力状态为外应力+内应力（外应力方向为正，内应力方向根据内应力对位错的作用可正可负），而残余内应力是材料在发生塑性变形时产生的，也视为内应力。
前文提到残余内应力是作为外应力的一种补偿应力，本文考虑将施加的外界分解剪切应力τ+残余内应力τr作为材料塑性变形时的净驱动力。若残余内应力的方向与施加的外界分解剪切应力的方向相反，那么将会阻碍位错滑移；若残余内应力的方向与施加的外界分解剪切应力的方向相同，那么将会促进位错滑移[17]。当残余内应力促进位错滑移时，滑移系开动所需要的外界分解剪切应力将会减小，随着塑性变形的逐渐积累，残余内应力进一步增加，将导致所需的外界剪切应力不断减小，这就导致了材料的应变软化。
上文从残余内应力对位错滑移的作用上合理地解释了UFG金属材料在单轴拉伸加载下应变软化现象发生的原因，为了使经典的晶体塑性模型能够反映材料的应变软化效应，必须将残余内应力及其演化的具体形式引入到晶体塑性本构模型中，因此对经典的率相关流动方程进行修正，则有
式中，为塑性变形期间第α个滑移系上产生的残余内应力。
由式（10）可知，残余内应力与塑性剪切应变线性相关，因此可以确定残余内应力的演化形式为
确立了新的晶体塑性本构关系之后，利用编程语言Fortran将其写入到计算机程序代码中，以进行后续的模拟与验证。本研究中对HUANG等[6]249-251开发的Abaqus Umat软件子程序[18]进行了修改，以纳入新的晶体塑性本构关系。
2　晶体塑性有限元模拟及模型验证
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为了验证修正的晶体塑性本构关系能否有效地捕捉UFG材料的应变软化效应，本文以UFG铝为例，对材料进行单轴拉伸加载下的晶体塑性模拟。本文所使用的试验材料为AA1050商业纯铝，相关化学成分如表1所示。在600 ℃均质化处理12 h后风冷至室温，然后通过等径角挤压工艺制备UFG铝试样，材料的制备流程详见SUN等[19]的工作。其单轴拉伸试验在英斯特朗5582型万能试验机上进行。试验初始应变率为7.1×10-4 s-1，具体试验方案参考YU等[3]360的工作。
2.1　晶体塑性有限元模型
晶体塑性模拟开展之前，需要先进行代表性体积单元（Representative Volume Element, RVE）建模。本文采用能反映单相多晶材料微观织构和晶体取向的Voronoi建模方法建立UFG铝的RVE模型。为了符合材料的宏观力学响应，采用100个随机取向的晶粒[20]，划分为10 648个八结点减缩积分单元（C3D8R）进行模拟。借助开源软件Neper实现了多晶集合体的建模以及网格单元的划分。然后通过Matlab软件实现材料参数的赋予，最后在Abaqus软件中进行载荷及边界条件的设定。载荷及边界条件如图1所示。沿y方向单轴加载，图1中不能直接观察到3个面约束其各自所在平面法向的平动，顶部平面施加位移约束。模拟过程中，通过调整位移约束值，使模拟的结果经后处理之后得到的应变值与试样的试验数据基本保持一致。
2.2　拉伸应力、应变模拟结果
在建立RVE模型并设置边界条件之后，需要对UFG铝的晶体塑性模型参数进行标定。对于简单的立方结构材料，需要3个独立的参数C11、C12、C44来描述弹性行为。弹性参数的具体取值可以参考文献[21]中的公式，由材料的弹性模量和泊松比计算标定，材料的弹性模量可以由单轴拉伸试验数据的线性段拟合得到，泊松比选取0.33。在修正的本构关系中用到的塑性参数有τs、τ0、h0、n、、q、a。由于塑性参数与材料微观性质有关，无法通过试验数据直接获得[22]，因此文中参数的标定是通过RVE模型的单轴拉伸模拟结果与拉伸试验结果比对而实现的。其中，和q参考文献[23]，其余参数τs、τ0、h0、n及a的具体取值是通过控制变量法逐个研究各参数对应力-应变曲线的影响之后，再利用试错法对目标参数进行优化，最终完成材料参数的标定。由于试错法过程工作量比较大，文中不再详细说明过程。最终确定的UFG铝的材料参数如表2所示。
图2所示为UFG铝在单轴拉伸加载情况下的晶体塑性有限元方法（Crystal Plasticity Finite Element Method, CPFEM）模拟结果和试验结果，其中黑色曲线代表沿y方向加载下CPFEM模拟的结果，黑色散点代表试验数据。由图2可知，材料在单轴拉伸加载下CPFEM模拟的结果与试验数据吻合较好，因此所建立的RVE模型及相应的晶体塑性本构关系能够有效地捕捉到UFG铝单轴拉伸加载下的应变软化现象。
2.3　残余内应力的作用机制
可以知道，经典的晶体塑性本构模型在模拟材料的单轴拉伸力学响应时往往得到材料的应变硬化行为，不能体现应变软化效应。图3所示为考虑残余内应力作用（a≠1）和不考虑残余内应力作用（a=1）2种情况下（其余条件均保持一致）CPFEM模拟的对比结果，其中黑色曲线为考虑残余内应力作用的CPFEM模拟结果，黑色散点为不考虑残余内应力作用的CPFEM模拟结果，残余内应力的演化发生在塑性变形期间。由图3可知，材料的弹性变形阶段不受影响，塑性变形阶段区别明显，不考虑残余内应力作用时表现为明显的应变硬化行为，考虑残余内应力作用时表现为明显的应变软化行为，比较符合预期的结果。
在材料发生塑性变形期间，各晶粒内的位错会沿着不同的滑移系进行滑移，并累积一定程度的剪切应变。由于形成的残余内应力与剪切应变呈线性相关，所以残余内应力会随着剪切应变的累积而逐渐增大，且作为外应力的补偿应力，会导致材料进一步发生塑性变形时滑移系开动所需的分解剪切应力有逐渐减小的趋势，而分解剪切应力和外应力通过施密特因子联系起来，往往在应变范围不是很大的情况下，施密特因子的变化是比较小的，可以忽略，那么外应力的变化也将呈现出逐渐减小的趋势，从而材料在宏观上表现出应变软化现象。
图4所示为12个滑移系各自的累积剪切应变。为了能够简单反映出整体的变化趋势，以累积剪切应变最大的滑移系为例（图4中所示的(11-1)[101]滑移系），当真实应变达到0.1时，提取考虑残余内应力（a≠1）和未考虑残余内应力（a=1）2种情况下RVE模型的累积剪切应变云图［图5（a）、图5（b）］、残余内应力云图［图5（d）］、分解剪切应力云图［图5（e）、图5（f）］以及累积剪切应变和分解剪切应力与真应变之间的关系曲线［图5（c）、图5（g）］来研究残余内应力的作用机制。其中，图5（c）和图5（g）中，黑色曲线分别表示考虑残余内应力（a≠1）时的累积剪切应变及分解剪切应力，黑色散点分别表示未考虑残余内应力（a=1）时的累积剪切应变及分解剪切应力。结合图5（a）~图5（c）可知，当考虑残余内应力时，累积剪切应变的数值比不考虑残余内应力时明显增加。这是因为在材料的塑性变形期间，滑移系上产生了残余内应力，在残余内应力对位错滑移的正向促进作用下，材料的塑性变形更加容易发生，从而导致累积剪切应变增加了。图5（d）给出了残余内应力的云图，与图5（a）一起分析可知，考虑残余内应力时，累积剪切应变数值较大的区域，它的残余内应力值也是较大的，因为式（10）表明两者是呈线性关系的。由图5（e）~图5（g）可知，材料在塑性变形期间，考虑残余内应力时的分解剪切应力确实要比未考虑残余内应力作用时的数值要小。这也说明了当残余内应力促进位错滑移时，导致材料进一步发生塑性变形时所需要的分解剪切应力有所减小，外应力和分解剪切应力通过施密特因子联系起来，在应变值不大的情况下，施密特因子的变化影响较小，因此外应力也将减小，进而在宏观上表现出应变软化现象。
从上述的对比结果中可以看出，本文基于经典的晶体塑性模型所发展的考虑残余内应力作用的修正模型能够有效地反映UFG铝在单轴拉伸加载下的应变软化现象，而且从残余内应力形成及其作用的角度去解释UFG金属中的应变软化现象也是合理的。
3　结论
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在晶体塑性理论框架下，对经典的晶体塑性模型进行修正，考虑了材料塑性变形期间形成的残余内应力及其对晶粒位错滑移的促进作用，将τ+τr作为滑移系开动时的净驱动力，并根据残余内应力的具体演化形式，对HUANG等[6]249-251开发的Abaqus Umat软件子程序进行修改，纳入了新的晶体塑性本构关系。在此基础上，对UFG铝的单轴拉伸加载情况进行了数值模拟，得到如下主要结论：
1）CPFEM模拟结果与试验数据基本相符，说明所建立的RVE模型及修正的晶体塑性本构关系能够有效地捕捉到UFG金属材料在单轴拉伸加载情况下的应变软化现象。
2）考虑残余内应力作用（a≠1）和不考虑残余内应力作用（a=1）2种情况下，CPFEM模拟的对比结果表明，从残余内应力作用的角度去解释UFG金属材料在单轴拉伸加载情况下的应变软化现象是合理的。
基金
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  • 国家自然科学基金项目(52265018; 51675110)
  • 广西自然科学基金项目(2021GXNSFAA220119)
  • 柳州市科技计划项目重大专项(2022ABA0101)
文献
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2025年第47卷第8期
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doi: 10.16579/j.issn.1001.9669.2025.08.013
  • 接收时间：2023-12-26
  • 首发时间：2026-03-19
  • 出版时间：2025-08-15
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  • 收稿日期：2023-12-26
  • 修回日期：2024-04-03
基金
National Natural Science Foundation of China(52265018; 51675110)
国家自然科学基金项目(52265018; 51675110)
Guangxi Natural Science Foundation(2021GXNSFAA220119)
广西自然科学基金项目(2021GXNSFAA220119)
Liuzhou City Science and Technology Planning Project(2022ABA0101)
柳州市科技计划项目重大专项(2022ABA0101)
作者信息
    1.广西大学 机械工程学院，南宁　530004
    2.北部湾大学 机械与船舶海洋工程学院，钦州　535011
    3.广西机电职业技术学院 机械工程学院，南宁　530007
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2种不同金属材料的力学参数
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Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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