Abstract: In order to investigate the analytical calculation method of T-stress for the central cracked Brazilian disk (CCBD) subjected to the compression, a weight function method is used to derive the explicit expressions of the T-stress for CCBD under concentrated loading and the distributed force loading. Compared with the boundary coordination method, the advantage of the explicit expression is that the T-stress for arbitrary relative crack length and any loading angle can be obtained explicitly and easily. Further analysing results show that the deviation of the T-stress under the distributed force and the concentrated force increases with increasing load distributed angle. At a fixed relative crack length, the T-stress increases with the increasing of loading angle under concentrated force. In most cases, T- stress is negative when the central cracked Brazilian disk is under pure mode I and pure mode II fracture tests. The value of T-stress for CCBD affects the fracture toughness testing, and it is difficult for CCBD to eliminate the influence by reducing the T-stress to zero.

Key words: central cracked Brazilian disk (CCBD)；weight function method；T-stress, analytical solutions