RUPTURE VELOCITY OF PLANE STRAIN SHEAR CRACKS
RUPTURE VELOCITY OF PLANE STRAIN SHEAR CRACKS
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DOI：
10.1029/jb081i032p05679
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发表时间：
1976-01-01
影响因子：
--
通讯作者：
ANDREWS, DJ
中科院分区：
文献类型：
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作者：
ANDREWS, DJ
采用二阶精度的有限差分方程对平面应变剪切裂纹的扩展进行了数值计算。破裂模型中，应力随着滑移的增加而逐渐下降，结合了两种不同的破裂准则：（1）滑移开始于有限的应力水平;（2）随着裂纹的前进，每单位面积吸收有限的能量。这个模型的解是非奇异的。在某些情况下，可能会有一个过渡，从破裂速度小于瑞利速度，破裂速度大于剪切波速度。在断裂能、上屈服应力和裂纹长度的参数空间中测量了这种转变的轨迹。该模型的解可以表示为具有突然应力降的奇异解与“断裂分布函数”的卷积。卷积消除了奇点，并在时空中扩展了破裂前沿。如果应力突降的解在裂纹尖端有一个平方根反比的奇异性，就像亚瑞利破裂速度一样，那么卷积解的破裂速度与破裂分布函数无关，只取决于断裂能和裂纹长度。另一方面，具有比剪切波速度更快的突然应力降的裂纹具有低阶奇异性。如果有限的断裂能随着应力的下降而被吸收，那么超剪切破裂前缘必然在时空中展开。
Propagation of plane strain shear cracks is calculated numerically by using finite difference equations with second‐order accuracy. The rupture model, in which stress drops gradually as slip increases, combines two different rupture criteria: (1) slip begins at a finite stress level; (2) finite energy is absorbed per unit area as the crack advances. Solutions for this model are nonsingular. In some cases there may be a transition from rupture velocity less than Rayleigh velocity to rupture velocity greater than shear wave velocity. The locus of this transition is surveyed in the parameter space of fracture energy, upper yield stress, and crack length. A solution for this model can be represented as a convolution of a singular solution having abrupt stress drop with a ‘rupture distribution function.’ The convolution eliminates the singularity and spreads out the rupture front in space‐time. If the solution for abrupt stress drop has an inverse square root singularity at the crack tip, as it does for sub‐Rayleigh rupture velocity, then the rupture velocity of the convolved solution is independent of the rupture distribution function and depends only on the fracture energy and crack length. On the other hand, a crack with abrupt stress drop propagating faster than the shear wave velocity has a lower‐order singularity. A supershear rupture front must necessarily be spread out in space‐time if a finite fracture energy is absorbed as stress drops.