Application of the virtual fields method to the identification of the homogeneous anisotropic hardening parameters for advanced high strength steels

Abstract

In the present paper, an inverse problem solution so called the virtual fields method (VFM) is implemented to identify the parameters of the homogeneous anisotropic hardening (HAH) model, a distortional plasticity-based model that describes the material plastic behavior when subjected to strain path changes. The framework of the identification method that combines the formulation of the yield condition, the constitutive stress-strain relation and the principle of virtual work is presented. For validation purpose, the proposed identification method was first attempted on finite element (FE) generated data for a forward-reverse simple shear test to investigate its capability in retrieving the input constitutive parameters. The influence of noise was also evaluated. Then, the identification method was applied to a selection of advanced high strength steel (AHSS), namely DP600, TRIP780 and TWIP980, sheet specimens, subjected to a small number of forward-reverse simple shear cycles. The material constitutive parameters were identified using the VFM based on which shear stress-strain curves were calculated and compared with their experimental counterparts. Good agreement was found between the calculated and the experimental curves despite the larger discrepancies observed in the reverse loading paths. To adjust these discrepancies, the original HAH model was modified with respect to the permanent softening related state variables. After modification, the model was simplified with only one state variable related to permanent softening. It was found that the discrepancies observed in the reverse loading paths were reduced with the modified HAH model.

Single‐camera special stereo‐digital image correlation applied for accurate virtual fields method identification

“…The proposed SS‐DIC using a 3CCD colour camera combines the advantages of SS‐DIC and single‐camera stereo‐DIC. In comparison of the existing DIC methods, the proposed method offers three advantages: (1) As a stereo‐DIC method, it offers accurate in‐plane full‐field deformation without being affected by unavoidable out‐of‐plane movements of tested object (compared with 2D‐DIC); (2) as a SS‐DIC method, it provides strain fields with the measured points homogeneously distributed on the specimen surface (compared with regular stereo‐DIC), which would dramatically decrease the time consuming of VFM identification when a number of deformation fields to be processed, such as constitutive parameters identification in elastic‐plasticity or viscoelasticity plasticity; (3) compared with the two cameras‐based SS‐DIC method and regular stereo‐DIC, the system of the proposed method is simpler (only one camera was employed) and easier in realisation (without complicated synchronous triggering device). Furthermore, the proposed SS‐DIC is highly desirable in the identification of dynamic mechanical parameters employing two high‐speed cameras .…”

“…In recent years, digital image correlation (DIC), a powerful and versatile optical technique for non‐contact, full‐field deformation measurement, has been widely accepted and used as an alternative deformation measurement technique for VFM identification. Based on the full‐field measurements provided by DIC, VFM has been successfully used for the characterisation of materials with various constitutive relations, such as metals under different temperatures and different strain rates, polymeric foams, composites, biological materials, and wood …”

“…Inaccurate internal virtual work estimation would finally lead to low‐accuracy or erroneous VFM identification. To eliminate the impact of the non‐uniform distributed data points, the finite element method (FEM) was employed for determining the internal virtual work . However, the strain field estimation and filtering using would greatly increase the computational complexity and cost.…”

Identification of nonlinear kinematic hardening constitutive model parameters using the virtual fields method for advanced high strength steels

“…It should be mentioned that the experiments were previously performed for parameter identification of the homogeneous anisotropic hardening (HAH) model (Barlat et al, 2011). A detailed description of the experiments has been provided elsewhere (Fu et al, 2016). In the present work, these experimental measurements were reused for the calibration of the NLKH models.…”

Investigation of assumptions and approximations in the virtual fields method for a viscoplastic material model

“…The Virtual Fields Method (VFM) is a powerful inverse technique for calibrating material models, based on the principle of virtual work. [1] First developed for homogeneous, isotropic, and linearly elastic materials, VFM has matured and been applied to anisotropic materials, [2][3][4][5][6][7][8] heterogeneous materials, [9][10][11][12] elasto-plastic materials, [13][14][15][16][17][18][19][20] and viscoplastic materials, [21][22][23][24] among other applications.…”