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平面幂律塑性I型裂纹尖端应力场全解

王志强 蔡力勋 黄茂波

王志强, 蔡力勋, 黄茂波. 平面幂律塑性I型裂纹尖端应力场全解. 力学学报, 待出版 doi: 10.6052/0459-1879-22-360
引用本文: 王志强, 蔡力勋, 黄茂波. 平面幂律塑性I型裂纹尖端应力场全解. 力学学报, 待出版 doi: 10.6052/0459-1879-22-360
Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-i crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-360
Citation: Wang Zhiqiang, Cai Lixun, Huang Maobo. Full solution for characterizing stress fields near the tip of mode-i crack under plane and power-law plastic conditions. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-360

平面幂律塑性I型裂纹尖端应力场全解

doi: 10.6052/0459-1879-22-360
基金项目: 国家自然科学基金资助项目(11872320, 12072294)
详细信息
    作者简介:

    蔡力勋, 教授, 主要研究方向: 材料测试理论与技术研究. E-mail: lix_cai@263.net

  • 中图分类号: O346.1

FULL SOLUTION FOR CHARACTERIZING STRESS FIELDS NEAR THE TIP OF MODE-I CRACK UNDER PLANE AND POWER-LAW PLASTIC CONDITIONS

  • 摘要: 在航空航天、船舶、石油管道和核电等领域, 服役结构或部件在长期极端条件下运行, 不可避免地会产生裂纹, 因此, 为研究含裂纹结构的准静态断裂行为, 必须了解裂纹尖端附近区域的应力应变场特点. 对于幂律材料裂纹构元, 研究平面应变和平面应力条件下I型裂纹尖端应力场的解析分布. 基于能量密度等效和量纲分析, 推导了能量密度中值点代表性体积单元 (representative volume element, RVE)的等效应力解析方程, 并定义其为应力因子, 进而针对有限平面应变和平面应力紧凑拉伸(compact tension, CT)试样和单边裂纹弯曲(single edge bend, SEB)试样, 以应力因子作为应力特征量, 并构造用于表征裂尖等效应力等值线的蝶翅轮廓式和扇贝轮廓式三角特殊函数, 提出描述幂律塑性条件下平面I型裂纹尖端应力场的半解析模型. 该半解析模型形式简单, 对CT和SEB试样的裂尖应力场的预测结果与有限元分析的结果比较表明, 两者之间均密切吻合, 模型公式可直接用于预测I型裂纹尖端应力分布, 方便于断裂安全评价和理论发展.

     

  • 图  1  能量密度等效示意图

    Figure  1.  Schematic diagram of energy density equivalence

    图  2  试样示意图

    Figure  2.  Schematic diagram of specimens

    图  3  FEA模型图

    Figure  3.  FEA model of specimens

    图  4  平面应变条件下裂尖附近网格密度对FEA结果的影响

    Figure  4.  Effects of element meshing size around the crack tip on the FEA results under plane strain conditions

    图  5  平面应力条件下裂尖附近网格密度对FEA结果的影响

    Figure  5.  Effects of element meshing size around the crack tip on the FEA results under plane stress conditions

    图  6  参数标定

    Figure  6.  Calibration parameter

    图  7  角度θβ影响

    Figure  7.  Effect of θ on β

    图  8  载荷P和应力硬化系数Kλsub的影响

    Figure  8.  Effects of loading P and strain hardening coefficient K on the λsub

    图  9  角度θNλsub的影响

    Figure  9.  Effects of θ and N on λsub

    图  10  psubk(k = 0,1)与N的关系

    Figure  10.  Relationships between psubk(k = 0,1) and N

    图  11  CT试样平面应变条件下裂尖无量纲应力径向分布对比

    Figure  11.  Comparison with FEA and predicted results by Eq.(25) for normalized stress radial distributions near the crack tip of CT specimens under plane strain conditions

    图  12  CT试样平面应力条件下裂尖无量纲应力径向分布对比

    Figure  12.  Comparison with FEA and predicted results by Eq.(25) for normalized stress radial distributions near the crack tip of CT specimens under plane stress conditions

    图  13  SEB试样平面应变条件下裂尖无量纲应力径向分布对比

    Figure  13.  Comparison with FEA and predicted results by Eq.(25) for normalized stress radial distributions near the crack tip of SEB specimens under plane strain conditions

    图  14  SEB试样平面应力条件下裂尖无量纲应力径向分布对比

    Figure  14.  Comparison with FEA and predicted results by Eq.(25) for normalized stress radial distributions near the crack tip of SEB specimens under plane stress conditions

    图  15  CT试样平面应变条件下裂尖无量纲应力环向分布对比

    Figure  15.  Comparison with FEA and predicted results by Eq.(25) for normalized stress angular distributions near the crack tip of CT specimens under plane strain conditions

    图  16  CT试样平面应力条件下裂尖无量纲应力环向分布对比

    Figure  16.  Comparison with FEA and predicted results by Eq.(25) for normalized stress angular distributions near the crack tip of CT specimens under plane stress conditions

    图  17  SEB试样平面应变条件下裂尖无量纲应力环向分布对比

    Figure  17.  Comparison with FEA and predicted results by Eq.(25) for normalized stress angular distributions near the crack tip of SEB specimens under plane strain conditions

    图  18  SEB试样平面应力条件下裂尖无量纲应力环向分布对比

    Figure  18.  Comparison with FEA and predicted results by Eq.(25) for normalized stress angular distributions near the crack tip of SEB specimens under plane stress conditions

    图  19  CT试样平面应变条件下等效应力σeq等效应力等值线对比

    Figure  19.  Comparison with FEA results predicted by Eq.(26) for contour lines of the equivalent stress σeq near the crack tip of CT specimen under plane strain conditions

    图  20  SEB试样平面应变条件下等效应力σeq等效应力等值线对比

    Figure  20.  Comparison with FEA results predicted by Eq.(26) for contour lines of the equivalent stress σeq near the crack tip of SEB specimen under plane strain conditions

    图  21  CT试样平面应力条件下等效应力σeq等效应力等值线对比

    Figure  21.  Comparison with FEA results predicted by Eq.(26) for contour lines of the equivalent stress σeq near the crack tip of CT specimen under plane stress conditions

    图  22  SEB试样平面应力条件下等效应力σeq等效应力等值线对比

    Figure  22.  Comparison with FEA results predicted by Eq.(26) for contour lines of the equivalent stress σeq near the crack tip of SEB specimen under plane stress conditions

    表  1  方程(15)模型参数

    Table  1.   Parameters of equation (15)

    SpecimenConditionmk5a/W
    CTplane strain2.28001.4308[0.45,0.75]
    plane stress2.28002.0971
    SEBplane strain1.95602.3400[0.40,0.75]
    plane stress1.95603.3024
    下载: 导出CSV

    表  2  方程(19)参数

    Table  2.   Parameters of Eq.(19)

    SpecimenConditionStresssubmsub0msub1a/W
    CTplane strainσsubeq0.00000.0000[0.45,0.75]
    110.08731.1981
    220.08731.1981
    120.01720.4345
    plane stresseq0.00001.2658
    110.00001.2658
    220.00001.2658
    120.00001.2658
    SEBplane strainσsubeq0.07220.5419[0.40,0.75]
    11−0.2441.2000
    22−0.07540.7258
    120.00000.0000
    plane stresseq0.00000.0000
    110.00000.0000
    220.00000.0000
    12−0.0150−0.2903
    下载: 导出CSV

    表  3  方程(23)模型参数

    Table  3.   Parameters of Eq.(23)

    SpecimenConditionStresssubdsub0dsub1dsub2dsub3a/W
    CTplane strainσsubeq1.5013−0.69401.67960.0000[0.45,0.75]
    111.18510.36352.98543.7610
    221.20000.00000.00000.0000
    124.8305−4.0000−0.34901.8316
    plane stresseq1.14480.25241.5459−1.8604
    111.06550.6019−0.8832−1.9732
    22−6.0795−7.0000−0.40004.7810
    121.4504−0.04557−3.0191−4.0356
    SEBplane strainσsubeq0.92500.20673.20361.3810[0.40,0.75]
    111.53390.5333−2.2470−4.0212
    228.1002−7.00000.2605−4.7292
    120.80520.13822.72271.4797
    plane stresseq1.08630.2285−1.8062−1.0613
    110.96740.49682.61074.5223
    22−3.03863.91670.42851.5112
    121.17930.03064.9568−0.1173
    下载: 导出CSV

    表  4  模型参数

    Table  4.   Parameters of model

    SpecimenCondi
    tion
    Stresssubqsub0qsub1qsub2qsub3qsub4csub0csub1bsub0bsub1a/W
    CTplane strainσsubeq1.002.18420.2756−0.42660.2017[0.45,0.75]
    11π/20.33330.33330.9999π/22.33971.55640.1430−0.4930
    22π/20.66670.66672.0001π/20.57546.7272−0.1684−0.0309
    120.001.00002.00000.0000π/20.21534.97420.0698−0.1902
    plane stresseq0.85000.67071.3870−0.3550−0.2910
    11π/20.55500.55501.6550π/2−0.1669−9.5370−0.530.0000
    22π/20.81500.81502.4450π/20.18608.9576−0.32000.0000
    120.001.00002.00000.0000π/20.22615.3946−0.18030.0000
    SEBplane strainσsubeq1.001.98650.2955−0.38120.1566[0.45,0.75]
    11π/20.35610.35611.0683π/21.83850.53540.0117−0.2631
    22π/20.76830.76832.3049π/20.27593.9625−0.23460.1882
    120.001.00002.00000.0000π/20.11823.26120.1091−0.1175
    plane stresseq0.850.24610.6570−0.0420−0.0630
    11π/20.60000.60001.8000π/2−0.04845−8.49690.4000−0.6200
    22π/20.80330.80332.4099π/20.0030146.68881.5301−1.5831
    120.001.00002.00000.0000π/20.13772.6570−0.05510.0465
    下载: 导出CSV
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  • 收稿日期:  2022-08-06
  • 录用日期:  2022-11-14
  • 网络出版日期:  2022-11-17

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