The article describes the problem of material fracture in metal forming processes. It describes and compares the values of damage functions obtained in classical tensile and torsion tests of two materials, i.e. CW008A copper and S355 steel under cold forming conditions. The presented research methodology includes experimental tests and numerical simulation carried out using Simufact.Forming v.15 software. The damage values were analysed according to various criteria, including the growth and coalescence of micro cracks (Rice&Tracey, Oyane, Argon), the initiation and development of ductile cracking in forming processes (Freudenthal, Cockroft-Latham, Brozzo, Oh) and using extended phenomenological models based on the history of stress triaxiality (Ayada) or the mean and equivalent stress (Zhan). The conducted tests showed that the values of the damage function depend on: the calibration test, the material grade and the geometry of the specimen.