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微裂纹群对主裂纹尖端损伤行为的影响

李煦 苏睿 张欢 翁倩茹 江晓禹

李煦,苏睿,张欢,翁倩茹,江晓禹. 微裂纹群对主裂纹尖端损伤行为的影响 [J]. 应用数学和力学,2022,43(12):1347-1358 doi: 10.21656/1000-0887.420333
引用本文: 李煦,苏睿,张欢,翁倩茹,江晓禹. 微裂纹群对主裂纹尖端损伤行为的影响 [J]. 应用数学和力学,2022,43(12):1347-1358 doi: 10.21656/1000-0887.420333
LI Xu, SU Rui, ZHANG Huan, WENG Qianru, JIANG Xiaoyu. Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1347-1358. doi: 10.21656/1000-0887.420333
Citation: LI Xu, SU Rui, ZHANG Huan, WENG Qianru, JIANG Xiaoyu. Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1347-1358. doi: 10.21656/1000-0887.420333

微裂纹群对主裂纹尖端损伤行为的影响

doi: 10.21656/1000-0887.420333
基金项目: 国家自然科学基金(51705041);四川省应用基础研究重点项目(18YYJC)
详细信息
    作者简介:

    李煦(1992—),女,讲师,博士 (E-mail:xuli127@sina.cn

    江晓禹(1965—),男,教授,博士生导师(通讯作者. E-mail:xiaoyujiang8@sina.com

  • 中图分类号: O346

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip

  • 摘要:

    在单轴拉伸荷载作用下,运用Muskhelishvili复变函数法和逐步递推法对无限大平面内含一个主裂纹和多个任意分布的微裂纹问题进行求解,得到了裂纹尖端的应力场和应力强度因子K。在此基础上,结合损伤力学,重新定义了单轴拉伸条件下主裂纹和微裂纹尖端的损伤参量D,分析了不同的损伤区形式对主裂纹尖端损伤的影响。结果表明,正向链式和反向链式分布的微裂纹均对主裂纹尖端损伤有增强作用,并且主裂纹尖端的损伤参量随微裂纹的倾斜角度和裂纹间距的减小而增大。当微裂纹的倾斜角度较小时,主裂纹和微裂纹尖端损伤均有增强作用,并且主裂纹尖端损伤的增强作用随着微裂纹的长度增加而增大。在连续损伤区内,均匀分布的微裂纹对主裂纹尖端损伤的增强作用随着微裂纹的数量增加而逐渐增大。

  • 图  1  主裂纹尖端附近存在多条微裂纹

    Figure  1.  Several micro cracks were observed near the macro-crack tip

    图  2  无限大平面内含一个主裂纹和多个任意分布的微裂纹

    Figure  2.  An infinite plane containing a macro crack and multiple micro cracks

    图  3  子问题1:只有主裂纹、远场有均匀拉伸载荷σ

    Figure  3.  Sub-problem 1: the macro crack under uniform tensile load σ

    图  4  子问题2:任意多条微裂纹

    Figure  4.  Sub-problem 2: the micro cracks

    图  5  子问题3:只有主裂纹

    Figure  5.  Sub-problem 3: the macro crack

    图  6  共线微裂纹对主裂纹尖端应力强度因子的影响:(a) 无限大平面内的共线裂纹;(b) 裂纹尖端B点的应力强度因子随裂纹间距的变化

    Figure  6.  Influence of the collinear micro crack on the stress intensity factor of the macro crack tip: (a) a collinear micro crack and a macro crack in an infinite plane; (b) ${{{K_B}} / ({{\sigma ^\infty }\sqrt {{\text{π}}{\text{a}}} }})$ vs. $ {d / {{a_1}}} $ for $ {a / {{a_1}}} = 1 $ under tensile load

    图  7  共线裂纹的有限元模型:(a) 整体网格;(b) 裂纹附近网格;(c) 裂纹尖端附近网格

    Figure  7.  The finite element method (FEM) for the collinear crack: (a) the whole FEM mesh; (b) the FEM mesh around the crack; (c) the FEM mesh near the crack tip

    图  8  主裂纹上的正应力在裂纹面上的变化曲线:(a) 子问题1;(b) 子问题3

    注 为了解释图中的颜色,读者可以参考本文的电子网页版本,后同。

    Figure  8.  The normal stress on the crack surface of the macro crack: (a) sub-problem 1; (b) sub-problem 3

    图  9  无限大平面内含一条主裂纹和链式分布的微裂纹,在无限远处有均匀拉伸应力

    Figure  9.  An infinite plane with a macro crack and chain-distribution micro cracks under tensile load

    图  10  微裂纹是正向链式分布时,损伤参量Dβ1的变化,d1/a=0.2:(a) DMA;(b) DMI

    Figure  10.  Damage parameter D vs. inclination parameter β1 for chain-distribution micro cracks, d1/a=0.2: (a) DMA; (b) DMI

    图  11  无限大平面内含一条主裂纹和反向链式分布的微裂纹,在无限远处有均匀拉伸应力

    Figure  11.  An infinite plane with a macro crack and reversed chain-distribution micro cracks under tensile load

    图  12  微裂纹是反向链式分布时,损伤参量Dβ1的变化,d1/a=0.2:(a) DMA;(b) DMI

    Figure  12.  Damage parameter D vs. inclination parameter β1 for reversed chain-distribution micro cracks, d1/a=0.2: (a) DMA; (b) DMI

    图  13  静止裂纹尖端的损伤分区结构

    Figure  13.  The damage zoning structure of the static crack tip

    图  14  微裂纹在连续损伤区内均匀分布时,损伤参量DMAak/a的变化:(a) 4条微裂纹;(b) 8条微裂纹

    Figure  14.  Damage parameter DMA vs. micro crack length ak/a for evenly distributed micro cracks: (a) 4 micro cracks; (b) 8 micro cracks

    图  15  损伤参量随微裂纹长度的变化:(a) βk=15°;(b) βk=45°;(c) βk=60°

    Figure  15.  Damage parameter DMA vs. micro crack length for evenly distributed micro cracks: (a) βk=15°; (b) βk=45°; (c) βk=60°

    表  1  主裂纹尖端到微裂纹中心的距离 dk/a (k=1, 2, ···, 7)

    Table  1.   The distance dk/a (k=1, 2, ···, 7) between the macro crack and each micro crack

    d1/ad2,3/a=d1/a + 0.3d4,5,6,7/a=d1/a + 0.6
    0.20.50.8
    0.30.60.9
    0.40.71
    0.50.81.1
    下载: 导出CSV

    表  2  微裂纹的倾斜角度βk (k=1, 2, ···, 7)

    Table  2.   The inclination angle βk (k=1, 2, ···, 7) of each micro crack

    $ {\beta _1}/{(^ \circ }) $$ ({\beta _2} = {{{\beta _1}} /2}) /{(^ \circ }) $$ ({\beta _3} = {{ - {\beta _1}} / 2}) /{(^ \circ }) $$ ({\beta _4} = {{{\beta _1}} / 4}) /{(^ \circ }) $$ ({\beta _5} = {{ - {\beta _1}} / 4}) /{(^ \circ }) $$ ({\beta _6} = {{{\beta _1}} / 4}) /{(^ \circ }) $$ ({\beta _7} = {{ - {\beta _1}} / 4}) /{(^ \circ }) $
    105−52.5−2.52.5−2.5
    2010−105−55−5
    3015−157.5−7.57.5−7.5
    4020−2010−1010−10
    5025−2512.5−12.512.5−12.5
    下载: 导出CSV

    表  3  主裂纹尖端到微裂纹中心的距离 dk/a (k=1, 2, ···, 7)

    Table  3.   The distance dk/a (k=1, 2, ···, 7) between the macro crack and each micro crack

    d1,2,3,4/a=d1/ad5,6/a=d1/a + 0.3d7/a=d1/a + 0.6
    0.20.50.8
    0.30.60.9
    0.40.71
    0.50.81.1
    下载: 导出CSV

    表  4  微裂纹的倾斜角度 βk (k=1, 2, ···, 7)

    Table  4.   The inclination angle βk (k=1, 2, ···, 7) of each micro crack

    β1/$(^ \circ ) $(β2=−β1)/$(^ \circ ) $(β3=β1)/$(^ \circ ) $(β4=−β1)/$(^ \circ ) $(β5=2β1)/$(^ \circ ) $(β6=−2β1)/(°)(β7=4β1)/$(^ \circ ) $
    2.5−2.52.5−2.55−510
    5−55−510−1020
    7.5−7.57.5−7.515−1530
    10−1010−1020−2040
    12.5−12.512.5−12.525−2550
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-11-02
  • 录用日期:  2022-04-16
  • 修回日期:  2022-04-16
  • 网络出版日期:  2022-10-27
  • 刊出日期:  2022-12-01

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