On the Constitutive Modeling of Strain Rate and Temperature Dependent Materials. Part I − Calibration Strategies of the Johnson-Cook Strength Model: Discussion and Applications to Experimental Data

This work deals with the constitutive modeling of strain rate and temperature dependent elastoplastic materials, by considering theoretical, experimental and computational aspects. Present Part I aims at assessing the various procedures adoptable for calibrating the material parameters of the so-called Johnson-Cook strength model, expressing the deviatoric behavior of elastoplastic materials, with particular reference to the description of High Strain Rate (HSR) phenomena. The procedures rely on input experimental data corresponding to a set of hardening functions recorded at different equivalent plastic strain rates and temperatures. After a brief review of the main characteristics of the Johnson-Cook strength model, five different calibration strategies are framed and described. Each calibration method is widely analyzed and discussed. The assessment is implemented through a systematic application of each calibration strategy to three different real material cases, i.e. a DH-36 structural steel, a commercially pure niobium and an AL-6XN stainless steel. Experimental data available in the literature are considered, consisting of a set of hardening functions at different equivalent plastic strain rates and temperatures. Results are presented in terms of plots showing the predicted Johnson-Cook hardening functions against the experimental trends, considering each calibration strategy, together with tables describing the fitting problematics which arise in each case, by assessing both lower yield stress and overall plastic flow introduced errors. The consequences determined by each calibration approach are then carefully evaluated and compared. A discussion on the positive and negative aspects of each strategy is presented and appropriate suggestions on how to choose the best calibration approach are outlined, by considering the available experimental data and the objectives of the modeling process. The proposed considerations should provide a useful guideline in the process of determining the best Johnson-Cook parameters in each specific situation in which the model is going to be adopted. A last section introduces additional considerations about the calibration of the Johnson-Cook strength model through experimental data different from those consisting in a set of hardening functions relative to different equivalent plastic strain rates and temperatures. In particular, the opportunity of using experimental data coming from Taylor impact tests is assessed, together with an evaluation of the possibility of using other less popular and somehow innovative ways for obtaining the Johnson-Cook strength model parameters. Subsequent Part II of the present work will complete the analysis, by discussing the introduction of a new strength model, which directly derives from the original Johnson-Cook model. Comparing to such original model, this new formulation appears capable to provide significant improvements in the analytical interpretation of the experimental data.