The cracked chevron notched Brazilian disc(CCNBD) method，which is suggested by the International Society for Rock Mechanics(ISRM) for measuring mode-I fracture toughness of rocks，was numerically investigated by a code based on microscopic damage mechanics. Varying notch width，sample geometries，material parameters and inhomogeneity are considered，and the progressive fracture process of the CCNBD specimen was intuitively presented. Through the simulated stress distributions and acoustic emission activities，the straight- through crack assumption(STCA) was strictly assessed，which is used by traditional methods for calibrating the dimensionless stress intensity factor(SIF). Numerical results show that，crack fronts of CCNBD specimens are always curved regardless of rock heterogeneity，significantly violating the STCA. For the specimen with a more slender chevron ligament，the crack front is curved more severely. Traditional critical SIFs are found to be only 90 to 95 percent of the values that are calibrated by utilizing the simulated critical crack fronts. CCNBD samples always crack from two sides of the notch width of the chevron ligament tip，and thus the specimens with relatively smaller notch width are suggested，so that the realistic fracture route of CCNBD can align well with the ideal test principle. The numerical results call for more attention to the real fracture mechanism of the chevron notched samples. A better calibration of dimensionless SIFs should consider more realistic fracture characteristics for a better measure of fracture toughness.