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

Abstract

The crack-propagation form may appear as an arbitrary mixed-mode fracture in an engineering structure due to an irregular internal crack. It is of great significance to research the mixed-mode fracture of materials with cracks. The coupling effect of multiple variables (crack height ratio, horizontal deflection angle and vertical deflection angle) on fracture parameters such as the stress intensity factors and the T-stress are the key points in this paper. A three-point bending specimen with an inclined crack was proposed and used to conduct mixed-mode fracture research. The fracture parameters were obtained by finite element analysis, and the computed results showed that the pure mode I fracture and mixed-mode fractures (mode I/II, mode I/III and mode I/II/III) can be realized by changing the deflection angles of the crack. The pure mode I and the mixed-mode fracture toughness of sandstone were obtained by a series of mixed-mode fracture experiments. The experimental results were analyzed with the generalized maximum tangential strain energy density factor criterion considering T-stress. The results showed that the non-singular term T-stress in the fracture parameters cannot be ignored in any mixed-mode fracture research, and the generalized maximum tangential strain energy density factor criterion considering T-stress can better predict the mixed-mode fracture toughness than other criteria.

Experimental and numerical evaluation of semi‐circular bending specimen for mixed mode I/III and pure mode III fracture tests

“…The results of numerical analyses (i.e., K n ) and experiments (i.e., K f ) are given in Table 1. The value of K n can be calculated from the following relation 62 : As is evident from Table 1, there is a good consistency between the numerical and experimental results, and the error between the experimental and numerical results is about 1%, indicating that the experiments have been performed with acceptable precision.…”

“…The maximum load P cr obtained from the experiments are given in Table 1. The value of P cr together with the dimensionless parameters of Y I and Y III and geometrical dimensions of the rock samples are put into the following relation to calculate the fracture toughness K f 49,62 : The averaged values of K f are shown in Figure 12, in which the fracture toughness reduces as the crack angle or portion of mode III at the crack front increases. Hence, the mode III has a negative influence on the fracture resistance of rock materials, such that the rock shows the smallest value of fracture toughness when it is subjected to the pure mode III loading.…”

A novel fracture criterion for elastic‐brittle cracked body under compression and shear conditions

“…Although the fracture problem has been richly researched so far, there is still some confusion of basic concepts, one of which is to confuse the crack loading forms with the crack failure types. [1][2][3][4][5][6] For example, the crack under mode II loading as shown in Figure 2B is called mode II crack and the associated fracture toughness is labeled as shear fracture toughness (K IIc ).…”

“…The corresponding loads for the three basic modes of crack are tensile loading (mode I loading), in‐plane shear loading (mode II loading), and out‐of‐plane shear loading (mode III loading). Although the fracture problem has been richly researched so far, there is still some confusion of basic concepts, one of which is to confuse the crack loading forms with the crack failure types 1–6 . For example, the crack under mode II loading as shown in Figure 2B is called mode II crack and the associated fracture toughness is labeled as shear fracture toughness ( K IIc ).…”