The legitimacy of decoupled dynamic flow stress equations and their representation based on discrete experimental data

In this study, the legitimacy of a decoupled empirical dynamic flow stress equations, typically the type of Johnson-Cook (J-C) (flow stress) equations, is mathematically verified and a criterion of J-C type equation is provided. The mechanical experimental data are assembled as 2D matrix (two variables of strain and strain-rate or temperature) or 3D array (three variables of strain, strain-rate and temperature). With low-rank approximation method, i.e. singular value decomposition (SVD) for 2D matrix and CANDECOMP/PARAFAC (CP) for 3D array, the experimental data matrix/array (N) can be decomposed into a heavily-weighted matrix/array (N₁) and several matrices/arrays with reduced weights (N₂, N₃, …). The criterion of J-C type equation is that N₁ can approximately represent N with acceptable error. Otherwise, the use of J-C type equation is invalid. A method to describe the dynamic flow stress based on discrete experimental dataset is further proposed based on the SVD/CP method. The advantages of coupled and decoupled flow stress equations and the problems associated with the original J-C equation are discussed.