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Ti40 burn resistant titanium alloy shows excellent burn-resistance performance and good mechanical properties at room temperature. However, it is easy to crack because of low ductility at high temperature, especially during the ingot cogging procedure. An important concern in forming is whether or not the desired deformation can be accomplished without failure of this alloy. This paper described the utilization of ductile fracture criteria in conjunction with the finite element method for predicting failures in hot forming processes of Ti40 alloy. Cylindrical specimens under compression tests at different deformed temperatures and strain rates were experimentally investigated. It is found that the alloy exhibited longitudinal cracking and shear cracking at some conditions of deformation. Subsequently, the finite element numerical simulation of the tests obtained local stress-strain history, which was used to evaluate six previously published ductile fracture criteria for predicting the accuracies of the fracture initiation locations of Ti40 alloy in hot forming. It is proved that only Oyane et al. ductile fracture criteria can accurately predict the initial location of fracture and the damage of Ti40 alloy for all the tests performed in this work.