Metodo innovativo per la modellazione di curve di trazione di materiali metallici ad alte temperature = A new modelling method for high temperature tensile curves of metallic materials

In the present work a new modelling procedure with physical meaning is reported to describe the plastic behaviour at high : Temperatures of metallic materials, like stainless steel and : copper. Tensile tests were performed on AISI 316L and OFHC copper specimens at homologous temperatures higher than ; 0.5 with strain rates ranging from 10~5 e 102 s '. True stress ; vs. true strain flow curves were fitted with Voce equation (Eq. 1) that predicts a linear relationship between strain hardening rate da/de and stress a. When plastic deformation j is controlled by dislocation-dislocation interaction, Taylor i equation of stress holds (Eq. 3), that is o = s- A with d ; the threshold stress (the stress to be applied to overcome the I dislocation obstacles without thermal activation) and s the ! thermal activation parameter of flow stress. Analyzing the ; strain hardening data of the materials according to Kocks and Mecking (KM) mechanistic equation of strain hardening, a parameter s', proportional to s, was found and the trend of : The s' with temperature ad strain rate resulted to be consistent ! with what reported in literature [22], Since the parameters ; of Voce equation were related to s', Voce curves could be i determined for any deformation condition investigated of l temperature ad strain rate. ! However, it was observed that Voce equations matched the experimental curves only at intermediate stresses, namely in the Stage III of strain hardening, while failed at low stresses. Therefore, an improved model, combining Voce formalism and a modified KM equation of strain hardening was implemented to approximate flow curves also at low plastic stresses. In the original KM model of evolution of the total dislocation density p with straining and dynamic recovery (Eq.4), the mean free path of mobile dislocation A is assumed to be . with P constant according to the principle of similitude, which states that the dislocation structure scales inversely to the applied stress a. The modified KM model is based on the hypothesis that p is not a constant, but is a new internal variable, p evolves (Fig. 3) with strain from an initial value Pln, related to the dislocation structure prior to the tensile deformation, to an equilibrium value Pv related to the dislocation cells structure typical Stage III of strain hardening, implying the aforesaid KM hypothesis. Therefore a set of two differential equations (Eq. 8), in which three state variable (p, s' and p) are taken in account, is proposed to describe this evolution. The presented model allows to describe adequately tensile curves of AISI 316L steel and OFHC copper (Fig. 5, Fig. 7) even at low stresses, extending the evaluation and study range of the plastic behaviour for the considered materials.