Three-Dimensional Effect of Tensile Strength in the Standard Brazilian Test Considering Contact Length

The tensile strength formula for the standard Brazilian test is based on plane elastic theory, which ignores the three-dimensional geometrical factor, the material factor, and the change in length of the contact rim during the test, thereby suggesting that the tensile strength formula for this test is incomplete. Using a numerical method, we determined that geometrical factors, such as the ratio of thickness to radius, material factors, such as Poisson's ratio, and testing factors such as contact angle, influenced the effectiveness of this test. Moreover, we found that, on the basis of the Griffith criterion and the central crack initiation index Q defined in this paper, when the Poisson's ratio increased or the contact angle decreased, the central crack initiation index Q increased, consequently making it difficult to guarantee the effectiveness of this test. Meanwhile, when the ratio of thickness to radius increased, the central crack initiation index Q initially increased and then trended smoothly. Based on these findings, we suggested that the ratio of thickness to radius should be as small as possible within the range from 0.5 to 0.8. In addition, an effective range of the contact angle under different Poisson's ratios was suggested. With the consideration of all of the abovementioned factors, a modified tensile strength formula was established, and the results had good agreement with other studies.