On the Constitutive Modeling of Strain Rate and Temperature Dependent Materials. Part II − An Enhanced Johnson-Cook Strength Model for Splitting Strain Rate and Temperature Effects on Lower Yield Stress and Plastic Flow

This work deals with the constitutive modeling of strain rate and temperature dependent elastoplastic materials, by considering theoretical, experimental and computational aspects. Present Part II aims at introducing and discussing a new empiric strength model, named here Split Johnson-Cook model. The model is formulated as a generalization of the Johnson-Cook strength model, previously discussed in Part I. The aims are those of improving the original Johnson-Cook hardening function, in order to mitigate shortcomings such as the fact that the equivalent plastic strain, the equivalent plastic strain rate and the temperature effects on the yield stress are totally independent from each other. In particular, the new model tackles the issue that the effects of the equivalent plastic strain rate and of the temperature need to be assumed as equal for each equivalent plastic strain, a factor which may lead to heavy modeling errors for the prediction of either the lower yield stress or the subsequent plastic flow. Two main issues of the original Johnson-Cook model are framed and discussed, together with a commented review of several modifications of the model proposed in the literature. After that, the new Split Johnson-Cook strength model is introduced and thoroughly described. A comprehensive discussion on its calibration strategies follows. Through a reasoned approach, three different calibration approaches are presented and widely described. The new model is then applied to the same three real material cases already considered in Part I for the original Johnson-Cook model, i.e. the determination of the Split Johnson-Cook parameters for a structural steel, a commercially pure metal and a stainless steel, by relying on experimental data taken from the literature, consisting in a set of hardening functions at different equivalent plastic strain rates and temperatures. Results are presented in terms of plots showing the predicted Split Johnson-Cook hardening functions against the experimental trends, considering each calibration strategy, together with tables reporting the fitting problematics which arise in each case, by assessing both lower yield stress and plastic flow introduced errors. The obtained results are also checked against the results provided by the original Johnson-Cook model, by relying on the results achieved in Part I. The replacement of the original Johnson-Cook model with the new model appears to almost exclusively introduce positive consequences. The Split Johnson-Cook model shows the capability to remarkably improve the fitting to experimental data for the three considered material cases, both for the lower yield stress and for the overall plastic flow predictions, comparing to the original Johnson-Cook model predictions. Also, the fact of presenting a form very similar to that of the original Johnson-Cook model allows for further interesting options, such as the possibility to substitute one or more of the Split Johnson-Cook model lower yield stress and plastic flow strain rate and temperature terms with some of the substitutive terms proposed in the literature. Furthermore, having a form very similar to that of the original Johnson-Cook model allows to partially reuse some of the material parameters of the original Johnson-Cook model, that may be already known from previous calibrations. Also, the Split Johnson-Cook model is conceived in such a way as to be capable of maintaining the same computational appeal of the original Johnson-Cook model. The need of experimental data for calibrating the model, the heaviness of calibration and the computational burden remain almost unchanged, comparing to the original Johnson-Cook model. Negative implications, if really any, appear to be very limited.