A modified 3D G-criterion for the prediction of crack propagation under mixed mode I-III loadings

•A modified 3D G-criterion is established for the mixed mode I-III crack.•The new criterion differentiates the volumetric and distortional energy release rates and considers the influence of T-stress.•The twist angles (critical SIFs) get increased (decreased) as the Poisson ratio increases.•The negative (positive) T-stress will enhance (decrease) the critical SIFs.•The critical SIFs reduce as the critical volumetric to distortional ERR ratio increases.