工程力学

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GM屈服准则求解I型裂尖塑性区

李灿明, 兰亮云, 宋红宇, 赵德文   

  1. 东北大学轧制技术及连轧自动化国家重点实验室,辽宁,沈阳 110819
  • 收稿日期:2011-04-15 修回日期:2012-02-20 出版日期:2012-06-25 发布日期:2012-06-25
  • 通讯作者: 李灿明(1979―),男,湖南人,博士生,主要从事现代成形理论与轧钢工艺研究(E-mail: cral@mail.neu.edu.cn). E-mail:cral@mail.neu.edu.cn
  • 作者简介:兰亮云(1983―),男,湖南人,博士生,从事焊接理论与成形工艺研究(E-mail: zhangshunhushiti@126.com);
    宋红宇(1986―),男,河北人,硕士生,从事成形理论与工艺研究(E-mail: zhangshunhusci@yahoo.cn);
    赵德文(1946―),男,辽宁人,教授,硕士,博导,主要从事现代成形理论与成形工艺研究(E-mail: zhaodw@ ral.neu.edu.cn).
  • 基金资助:
    国家自然科学基金项目(51074052)

ANALYSIS OF PLASTIC ZONE OF MODE Ⅰ CRACK TIP BY GM YIELD CRITERION

LI Can-ming, LAN Liang-yun, SONG Hong-yu, ZHAO De-wen   

  1. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, Liaoning 110819, China
  • Received:2011-04-15 Revised:2012-02-20 Online:2012-06-25 Published:2012-06-25

摘要: 用几何中线(GM)屈服准则求解了I型裂尖塑性区的形状与尺寸,对比了基于Mises和Tresca准则的求解结果。表明在平面应变条件下,GM准则求解的塑性区面积在Tresca和Mises结果之间,Tresca塑性区面积最大,Mises面积最小,GM塑性区与Mises塑性区非常接近,三者的塑性区均成哑铃状。在平面应力下,GM和Mises塑性区二者仍最接近并为豆芽状,Tresca的塑性区最大。无论平面应力还是平面应变,GM准则计算结果与Mises结果均有最佳接近度。

关键词: GM屈服准则, I型裂尖, 几何中线, 塑性区, 最佳逼近

Abstract: Based on GM (geometrical midline) yield criterion, the analytical solutions for the shape and size of a mode I crack tip plastic zone are derived. Comparing the solutions with those based on Mises and Tresca criteria shows that under a plain strain condition the area of a plastic zone on GM is between both on Tresca and Mises criteria, and very close to Mises one. Among the areas, Tresca’s is the largest and Mises is the smallest and all three zones are dumbbell shaped. However, for plane stress, the plastic zones based on GM and on Mises criteria are also proximal but with a bean-spout shape, while the area on Tresca is still the largest. Whenever plane stress or plane strain conditions the result calculated by GM criterion is always an optimal approximation to that calculated by Mises criterion.

Key words: GM yield criterion, mode I crack tip, geometric midline, plastic zone, optimal approximation

中图分类号: 

  • TG404
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