Criterion of local symmetry visualized in small eccentric single edge notched bend (E-SENB) rock specimens

Abstract 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. Although its prediction is a tension dominated fracture, under small scale yielding the criterion must include two aspects: the local mode I stress intensity factor (SIF) kI is maximum and the local mode II SIF kII is zero. Two aspects are not identical when fracture just initiates, but they will be equivalent after the crack propagation. It is because the local kII is not zero in the beginning and its elimination is gradual. Thus, criterion validation is usually based on comparison of fracture trajectories between numerical simulation from maximum value of the local kI and experimental observation from optical techniques, because kink angles in the trajectory already provide information about the local kII removal. 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 local symmetry 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 opening 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. Thus, criterion of local symmetry is visually validated for small E-SENB specimens. In addition, this study provides a helpful insight about the tip condition under small scale yielding.