Three-Dimensional Fracture Instability of a Displacement-Weakening Planar Interface under Locally Peaked Nonuniform Loading
Three-Dimensional Fracture Instability of a Displacement-Weakening Planar Interface under Locally Peaked Nonuniform Loading
复制标题
局部峰值非均匀载荷下位移弱化平面界面的三维断裂不稳定性
DOI：
10.1016/j.jmps.2018.03.012
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发表时间：
2018
影响因子：
5.3
通讯作者：
K.
中科院分区：
文献类型：
--
作者：
Uenishi;K.
我们考虑了三维平面界面在加载应力作用下的断裂稳定性，该加载应力在空间上局部达到峰值，其水平在时间上准静态增加。与早期对二维情况的研究(Uenishi和Rice，2003；Rice和Uenishi，2010)类似，随着加载应力的增加，裂纹或位移不连续区域(拉伸张开间隙或剪切断裂的滑移)在根据位移-弱化本构关系假定应力减小的界面上发展。当达到不稳定点时，界面裂纹的扩展不存在进一步的准静态解，动态断裂随之而来。为了研究这一失稳点，我们采用了量纲分析和能量方法，给出了裂纹尺寸和最大位移不连续性与加载应力分布的水平和二次形状的关系的Rayleigh-Ritz近似。我们证明，如果应用线性位移弱化定律，并且裂纹可以假设为椭圆形，则失稳时的临界裂纹尺寸与载荷应力分布的曲率无关，并且对于所有的二维和三维情况都是相同的阶数。
We consider stability of fracture on a three-dimensional planar interface subjected to a loading stress that is locally peaked spatially, the level of which increases quasi-statically in time. Similar to the earlier study on the two-dimensional case (Uenishi and Rice, 2003; Rice and Uenishi, 2010), as the loading stress increases, a crack, or a region of displacement discontinuity (opening gap in tension or slip for shear fracture), develops on the interface where the stress is presumed to decrease according to a displacement-weakening constitutive relation. Upon reaching the instability point at which no further quasi-static solution for the extension of the crack on the interface exists, dynamic fracture follows. For the investigation of this instability point, we employ a dimensional analysis as well as an energy approach that gives a Rayleigh–Ritz approximation for the dependence of crack size and maximum displacement discontinuity on the level and quadratic shape of the loading stress distribution. We show that, if the linear displacement-weakening law is applied and the crack may be assumed of an elliptical form, the critical crack size at instability is independent of the curvature of the loading stress distribution and it is of the same order for all two- and three-dimensional cases.