Identification of Johnson–Cook's Viscoplastic Model Parameters Using the Virtual Fields Method: Application to Titanium Alloy Ti6Al4V

Abstract

The identification of viscoplastic material parameters is addressed using a new powerful method: the virtual fields method (VFM). Contrary to classical procedures that are statically determined, the VFM is applied to heterogeneous mechanical fields. Without any hypotheses of homogeneity required, the exploitation of tests with the VFM is not limited to small levels of strains anymore and it can be taken advantage of the large amount of information available thanks to full‐field measurements. In the case of viscoplastic models, the characterisation of strain‐rate sensitivity with the VFM is attempted in this paper using only one test under high‐speed loading conditions, whereas several tests performed at different constant strain‐rates are required for the classical procedures. This article focuses on the development of the VFM for the characterisation of Johnson–Cook's (JC) viscoplastic model. To his aim a return‐mapping algorithm was developed according to the JC's model with an implicit Euler scheme implemented to integrate the constitutive relations. The whole viscoplastic behaviour of a Titanium alloy (Ti6Al4V) is successfully characterised by the VFM using only two tensile tests on notched flat specimens, with full‐field strain measurements by digital image correlation.

Implementation and Evaluation of the Virtual Fields Method: Determining Constitutive Model Parameters From Full-Field Deformation Data.

“…An analytical constitutive model is chosen for the material, and the virtual fields are carefully constructed depending on the type of model, allowing for determination of the constitutive parameters through numerically solving a system of equations that enforces the principle of virtual work, as previously has been addressed in literature [3][4][5][6][7]. Currently, there is limited work in VFM applied to metals for elasto-plasticity [8], heterogeneous elasto-plasticity [9], elasto-visco-plasticity [10], and 3D plasticity in the necking regime [11][12][13]. Depending on the application, VFM can be written in terms of small-strain theory or finite-deformation theory, which are both described in the following sections.…”

“…The second type is called the Constitutive Equation Gap Method (CEGM), where an FEM simulation and an overdetermined set of displacement measurements and force measurements are compared using an equilibrium equation that contains a material model, hence an iterative minimization of the equilibrium gap for material parameter identification. The third type is based on the Principle of Virtual Work, called the Virtual Fields Methods (VFM) [1][2][3][4][5][6][7][8][9][10][11][12][13], where full-field measurements like displacements or strains, and global resultant force measurements are used in the Principle of Virtual Work along with advantageously chosen, kinematically admissible, virtual fields, to directly solve for the material parameters without need for iterative FEM simulations.…”

Beyond Hopkinson's bar

“…More rarely, such test specimens with more complex shapes leading to heterogeneous stress/strain states have been considered [22][23][24], either with a view to validating FE models [23] or to identify constitutive models using FE model updating techniques [25] or the virtual fields method (VFM) [26,27]. Finally, most of the previous examples deal with quasi-static situations, meaning by this that transient inertial effects have vanished when the data are processed.…”

A Modified Eyring Equation for Modeling Yield and Flow Stresses of Metals at Strain Rates Ranging from 10−5to 5 × 104 s−1

“…This equation has been widely used [11][12][13] and included in several commercial finiteelement software types; this is mainly due to the reduced number of constants that it used and the separation of the hardening, temperature, and strain rate effects. It was then applied to model the strain rate sensitivity mainly for metallic alloys as for titanium [14,15], copper [16], aluminum [17,18], and steel [19][20][21][22] alloys.…”