| 三维脆性破裂的拉应力判据 |
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| 引用本文： | 李世愚.三维脆性破裂的拉应力判据[J].地球物理学报,1990,33(5):547-555. |
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| 作者姓名： | 李世愚 |
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| 作者单位： | 国家地震局地球物理研究所, 北京 |
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| 摘 要： | 用线弹性断裂力学对连续介质中三维裂纹(KⅢ≠0)破裂的拉应力断裂准则提出了补充性假说和相应的计算方法（第一主微分面定点法）。对于给定应力强度因子Ki（i=Ⅰ,Ⅱ,Ⅲ）的裂纹问题,从理论上给出了初始破裂面完整形式的解析表示或数值计算结果。推导结果是,三维拉张破裂的初始破裂面是以破裂点为顶点的广角锥面,跨在原始裂纹面的前缘,它的外缘为螺旋线,锥面的每一条母线都与过该线的第一主微分面重合。大量的这样的初始破裂面叠错密接,互不相交。推算的结果与已有的三锥破裂实验结果基本符合。把补充后的拉应力判据和最大拉应力理论相比较,发现在应力分量只保留奇异项的情况下,这两种判据是等价的;但如果对应力分量作零阶项修正,则两种判据只在三维(KⅢ≠0)问题中等价,在二维(KⅢ=0)问题中不完全等价。
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| 关 键 词： | 三维脆性破裂 拉应力判据 初始破裂面 最大主拉应力 第一主微分面 |
| 收稿时间： | 1987-11-23 |
NORMAL STRESS CRITERION OF THREE-DIMENSIONAL BRITTLE FRACTURE |
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| LI SHI-YU.NORMAL STRESS CRITERION OF THREE-DIMENSIONAL BRITTLE FRACTURE[J].Chinese Journal of Geophysics,1990,33(5):547-555. |
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| Authors: | LI SHI-YU |
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| Institution: | Institute of Geophysics, State Seismological Bureau, Beijing |
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| Abstract: | The normal stress criterion of three-dimensional brittle fracture （KⅢ≠0） of continuum medium is further studied by using the theory of linear elastic fracture mechanics.Some complementary assumptions and the corresponding calculation method （method of locating principal differential planes） are proposed.The conditions of initial fracture are inferred.The shapes of the initial fracture surfaces for given stress intensity factors Ki（i=Ⅰ,Ⅱ,Ⅲ） are described both analytically and quantitatively The results show that the shape of a three-dimensional initial brittle fracture surface is a wide angle cone with initial point as its apex.The cone straddles the crack front,and its outline is a quasi-helical.Every generatrix of the cone coincides with the principal differential plane passing through it.A lot of similar fracture surfaces which generated from the original crack front distributed closely but never intercross each other.The calculating results are in good agreement with the previous experimental results.Comparing the complementary normal stress criterion with the maximal normal stress criterion,it is found that the two types of criteria are compatible when only the singular terms are retained in stress components.However,if the zero order terms are also retained in stress components,the two types of criteria are compatible only in the case of three-dimensional problems （KⅢ≠0）,but incompatible in the case of two-dimensional problems （KⅢ=0）. |
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| Keywords: | Three-dimensional brittle fracture Normal stress criterion Initial fracture surface Maximal principal stress Primary principal differential plane |
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