Analytical investigation on the unstable fracture toughness of fine-grained quartz-diorite rock considering the size effect

An Experimental Study of the Relation between Mode I Fracture Toughness, KIc, and Critical Energy Release Rate, GIc

“…Since energy release rate is uniquely related to stress intensity, G also provides a single-parameter description of crack-tip conditions, and Gc (such as 𝐺 in mode I fracture) is an alternative measure of toughness, which is also called critical energy release rate. In linear elastic conditions, 𝐺 and 𝐾 are correlated with each other by Equations (3) and ( 4) [2]: 𝐺 = 𝐾 /𝐸 for plane stress (3) or 𝐺 = (1 − 𝑣 )𝐾 /𝐸 for plane strain (4) However, many materials such as rock, concrete and ceramics are not linear elastic [9][10][11] and a large number of experimental data have shown that 𝐺 and 𝐾 do not conform to the relation in Equation (2) [9,10,[12][13][14]. For example, it was found that as the length of a crack increases, 𝐺 and 𝐾 /E show a different relation from Equation ( 2), e.g., when a/w is 0-0.1 (a is the length of the crack and w is the width of the specimen), 𝐺 and 𝐾 /E show a power function relation, and when a/w is 0.1-0.85, they are linearly related [15].…”

“…However, many materials such as rock, concrete and ceramics are not linear elastic [ 9 , 10 , 11 ] and a large number of experimental data have shown that and do not conform to the relation in Equation (2) [ 9 , 10 , 12 , 13 , 14 ]. For example, it was found that as the length of a crack increases, and show a different relation from Equation (2), e.g., when a/w is 0–0.1 (a is the length of the crack and w is the width of the specimen), and show a power function relation, and when a/w is 0.1–0.85, they are linearly related [ 15 ].…”

Mode I Microscopic Cracking Process of Granite Considering the Criticality of Failure

“…(2020) found that the unstable fracture toughness was approximately 1.5 times of mode I fracture toughness via testing notched semicircular bending (NSCB) specimens of granite. The unstable fracture toughness and initial fracture toughness converged to a constant as the specimen depth was sufficiently large (Wu et al., 2022; X. Zhang et al., 2007). In addition, the double‐K parameters varied with material heterogeneity.…”

“…When we have obtained the parameters (i.e., P ini , P max , a 0 , and a c ) from cracking tests, $${K}_{Ic}^{\mathit{ini}}$$ and $${K}_{Ic}^{un}$$ can be calculated using the LEFM formula. For the three‐point bending (TPB) specimen, the mode I fracture toughness is (Wu et al., 2022): $$${K}_{I}(P,a)=\frac{3PS\sqrt{a}}{2{{H}_{1}}^{2}B}F(\alpha )$$$ where P is the applied load; a is the effective crack length; H 1 , B , and S are the sample geometries shown in Figure 3; α = a / H 1 ; and F ( α ) is the dimensionless stress intensity factor, which depends on the span‐to‐depth ratio S / H 1 . For S / H 1 = 4: $$${F}_{4}(\alpha )=\frac{1.99-\alpha (1-\alpha )\left(2.15-3.93\alpha +2.7{\alpha }^{2}\right)}{{\pi }^{1/2}(1+2\alpha ){(1-\alpha )}^{3/2}}$$$ …”

Research of Dynamic Tensile Properties of Five Rocks under Three Loading Modes Based on SHPB Device

“…Rock masses in deep underground projects are usually subjected to dynamic loads caused by excavation, blasting, and drilling [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 ]. Since local tensile failure often occurs under dynamic loads, many scholars have been attracted to conduct research on the dynamic tensile properties and fracture mechanism of rock materials [ 11 , 12 , 13 , 14 ]. The test methods for rock tensile strength include direct stretching and indirect stretching, i.e., the Brazilian disc [ 15 , 16 ].…”