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Criterion of local symmetry visualized in small eccentric single edge notched bend (E-SENB) rock specimens
Engineering Fracture Mechanics ( IF 4.7 ) Pub Date : 2021-03-31 , DOI: 10.1016/j.engfracmech.2021.107709
Qing Lin , Xin Bian , Peng-Zhi Pan , Yue Gao , Yunhu Lu

Fracture criterion of local symmetry has been widely used to predict the fracture kink and simulate the fracture trajectory in rocks under the mixed-mode loading. Under small scale yielding, it must include two aspects: the local mode I stress intensity factor (SIF) kI is maximum and the local mode II SIF kII is zero. When fracture just initiates, the local kII is not zero, but it will be gradually eliminated after the crack propagates. Eventually two aspects are equivalent. Thus, a curved fracture, as a consequence from combination of the local kI and kII, already supports the criterion in reality. Once specimen size is small, the condition changes to large scale yielding such that two aspects change to: the local tensile stress is maximum and the local shear stress is zero. It poses the difficulties for the criterion, e.g., the initiated fracture is observed to keep extension after the first fracture kink, suggesting the kink angle is not sensitive to the local shear stress. To study the criterion, the eccentric single edge notched bend (E-SENB) specimens of Berea sandstone were tested and digital image correlation (DIC) was used to measure the surface displacements. DIC observations provide essential supports for two aspects: (i) the fracture initiation is dominated by opening displacements without any slips, indicating that it is the maximum value of the local tensile stress that reaches tensile strength to initiate the fracture; (ii) the challenge is about evaluation of the local shear stress, but fortunately, an interesting phenomenon provides a valuable assistance: a non-symmetric pattern of opening/orthogonal displacements. This study introduces a parameter η, i.e., the ratio of normal displacements at two fracture sides, to quantitatively evaluate the local shear stress and its influence. Parameter η change demonstrates the local shear influence change. For tested specimens, parameter η is observed to decrease from a finite value of larger than 1 to 1, which suggests the local shear influence is gradually removed to be zero. Thus, criterion of local symmetry is visually validated for small E-SENB specimens. Finally, this study provides a helpful insight about the tip condition of a kinked fracture in rocks under mixed-mode loading when the condition of small scale yielding applies.



中文翻译:

在小偏心单边缺口弯(E-SENB)岩石样本中可视化的局部对称性准则

局部对称的断裂准则已被广泛地用于预测岩石在混合模式载荷下的扭折和模拟断裂轨迹。在小规模屈服下,它必须包括两个方面:局部模式I应力强度因子(SIF)k I最大,局部模式II SIF k II为零。当刚开始断裂时,局部k II不为零,但在裂纹扩展后将逐渐消除。最终,两个方面是等效的。因此,由于局部k I和k II的组合而导致弯曲的骨折,已在现实中支持标准。一旦样品尺寸变小,条件就变成了大规模屈服,从而使两个方面变为:局部拉伸应力最大,局部剪切应力为零。这给标准带来了困难,例如,观察到起始断裂在第一次断裂扭结后仍保持延伸,这表明扭折角对局部切应力不敏感。为了研究该标准,测试了Berea砂岩的偏心单边切口弯曲(E-SENB)标本,并使用数字图像相关(DIC)测量了表面位移。DIC的观察为两个方面提供了必要的支持:(i)骨折的发生主要由没有任何滑移的张开位移主导,表示达到拉伸强度以引起断裂的是局部拉伸应力的最大值;(ii)挑战在于评估局部剪切应力,但幸运的是,一个有趣的现象提供了宝贵的帮助:开口/正交位移的非对称模式。这项研究引入了一个参数η,即两个裂缝侧的法向位移比,以定量评估局部剪应力及其影响。参数η变化表明局部剪力影响变化。对于测试的样本,观察到参数η从大于1的有限值减小到1,这表明局部剪切影响逐渐消除为零。因此,对于小的E-SENB标本,可以在视觉上验证局部对称性的标准。最后,

更新日期:2021-04-18
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