Granite strength and toughness from small notched three-point-bend specimens of geometry dissimilarity

Maximum fracture loads (P_max)of small notched granite specimens under three-point-bending (3-p-b)conditions can be easily measured with any notch/size ratio. In this study, we report a simple closed-form solution of a non-Linear Elastic Fracture Mechanics (non-LEFM)model emphasizing the influence of average grain size G on quasi-brittle fracture of granite. This simple analytical solution containing the grain size G can be conveniently used to determine granite tensile strength f_t and fracture toughness K_IC from P_max measurements of small notched 3-p-b specimens of geometry dissimilarity. The span/width (S/W)ratios of small 3-p-b specimens can vary, e.g. 2.5 or 4. The notch/width (a₀/W)can also vary, e.g. the notch a₀ can be as short as the average grain size (G), or close to width W. However, specimens with α-ratio (=a₀/W)around 0.2 are recommended to minimize the boundary influence/effect from both the front and back specimen boundaries as proven by the Boundary Effect Model (BEM). Blue granite with the average grain size around 2 (mm)was selected to test the new method. Total 64 granite samples from four different groups (different 3-p-b sample designs)were tested, with W = 27, 40 and 70 (mm), S/W = 2.5, 4.0 and a₀ = 4, 6 and 8 (mm). The tensile strength f_t and fracture toughness K_IC estimated from every group is fairly close to the values determined from the entire population of 64 tests. Therefore, tests from any specimen group of given geometry and size are sufficient. Estimations for G = 1.5 and 2.5 (mm)were also provided and compared with those for G = 2 (mm)to show the grain size influence. Advantages and disadvantages of BEM and well-known SEL (size effect law)are also discussed using the granite results.