An extended maximum tangential strain energy density criterion considering T‐stress for combined mode I–III brittle fracture

Abstract

The maximum tangential strain energy density (MTSED) criterion was modified by taking the influences of stress intensity factors and T-stress into consideration for combined mode I-III brittle fracture. Furthermore, the Poisson's ratio and T-stress influencing the fracture characteristics of cracked components were discussed by using the extended MTSED criterion. Moreover, the predicted values of this extended MTSED criterion and some testing results were comparatively analysed. The results indicate that the Poisson's ratio and T-stress have no impact on the out-of-plane initiation angle; however, their effects on fracture resistance ratios are significant especially for pure mode III. A positive T-stress increases the fracture resistance ratio, and it is opposite for a negative T-stress. The predicted values calculated by the extended MTSED criterion agree very well with the testing data obtained with edge-notched disc bend samples especially for pure mode III case.

Analysis of Mixed-Mode I/II/III Fracture Toughness Based on a Three-Point Bending Sandstone Specimen with an Inclined Crack

“…The experimental results of pure mode III fracture toughness were also in good agreement with the theoretical predictions of the MTSED criterion [38]. However, an extended MTSED criterion considering T-stress was proposed, which was considered to better predict the testing results of ENDB specimens, especially for the pure mode III case [46].…”

“…According to Hooke's law, ′ = [ ′ − ( + ′ )]/ , therefore the tangential strain energy density factor C is: where η is the relative critical distance defined as = √ 2 . Ayatollahi and Saboori [45] and Hua [46] used α to represent the relative critical distance, however, α was used to represent horizontal deflection angle in the previous section, so η was used here. All the coefficients ( ) are shown in Tables A3 and A4.…”

“…where is the biaxiality ratio for the pure mode I loading. Part of the derivation process can refer to Hua [46]. When different fracture parameters (i.e., , , and ) are confirmed, the in-plane and out-of-plane fracture angles can be obtained by Equations (13) and (14), and the mixed-mode fracture toughness ratio can also be predicted by Equations (12) and (16).…”

On the use of different diametral compression cracked disc shape specimens for introducing mode III deformation

“…In general, a positive T stress in a cracked specimen increases the mixed mode I/III fracture toughness and conversely negative sign of T stress decreases the mixed mode I/III fracture resistance. 70 However, compared to many other mixed mode fracture test specimens employed in several papers (that the absolute values of Biaxilaty ratio are higher than 1.5 [65][66][67] ), the magnitude of Biaxiality ratio in the analyzed ENDC, DNDC, and UNDC specimens is not very significant demonstrating the lesser importance of nonsingular terms (such as Tstress) relative to the effect of singular terms (SIFs). Therefore, by considering only the SIFs (K I and K III ), the mixed mode I/III fracture behavior of the mentioned samples can be investigated and described with sufficient accuracy from the engineering viewpoint.…”

Higher order stress terms in sharp notch problems under pure‐out‐of‐plane loading

“…Linear elastic fracture mechanics (LEFM) can provide a suitable framework for studying the initiation of fracture in various brittle and quasi‐brittle materials including rocks, concretes, and some polymers, where the size of the damage zone created in front of the notch tip is comparatively small. Since the utilization of a failure mechanism is based on the accurate estimation of stress and displacement fields, it is vital to have a good insight on the variation of stress and displacement fields around the notch tip 1,2 . Hence, several studies have been allocated to derive the stress and displacement fields around notches.…”