Abstract
A systematic constitutive modeling and calibration methodology were developed based on rate-independent crystal plasticity to predict the quasi static macroscopic behavior of 3rd generation multiphase advanced high strength steels (3GAHSS) prepared with a quenching and partitioning (Q&P) process. In the constitutive law, martensitic phase transformation induced by the elastic-plastic deformation of the retained austenite is represented by considering the Bain strain, the lattice invariant shear deformation, and the orientation relationship between parent austenite and transformed martensite. The amount that each martensite variant evolves is obtained through an optimization scheme that constrains the plastic deformation of the retained austenite to have minimum-energy during phase transformation. In-situ high energy X-ray diffraction (HEXRD) tensile test data was utilized for the characterization and calibration of the material model. Dislocation density based hardening parameters were separately obtained for each phase by iteratively performing crystal plasticity finite element (CPFE) simulations until the simulated stress-strain curves matched the experimentally measured curves from in-situ HEXRD. The 3D representative volume element (RVE) for the 3GAHSS was generated by utilizing Dream.3D and the MTEX Matlab toolbox software. The distributions of grain size and crystal orientation were analyzed based on the measured EBSD data and accounted for in the generation of the 3D RVE. For verification and validation of the constitutive model, crystal plasticity finite element simulations of a uniaxial tensile test were performed using the developed material model and the generated 3D RVE. Additional hypothetical RVEs were also generated by manipulating phase volume fractions, phase transformation speed, and phase properties to determine if these virtual 3GAHSS steels have improved mechanical properties. Also, forming limit curves (FLC) for the multiphase 3GAHSS were predicted from the CPFE simulation results.
| Original language | English |
|---|---|
| Pages (from-to) | 1-46 |
| Number of pages | 46 |
| Journal | International Journal of Plasticity |
| Volume | 120 |
| DOIs | |
| State | Published - Sep 2019 |
Funding
This material is based upon work supported by the Department of Energy under Cooperative Agreement Number DOE DE-EE000597 , with United States Automotive Materials Partnership LLC (USAMP). This report was prepared as an account of work sponsored by an agency of the United States Government . Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. Appendix A The developed rate-independent CP model with the phase transformation model was implemented into the FE code based on the predictor-corrector scheme ( Simo and Hughes, 1998 ; Park and Chung, 2012 ). The trial Cauchy stress, σ n + 1 k = 0 , for the next ( n + 1 )-th discretized time step is initially calculated based on the given discrete strain increment, Δ ε n ( ≡ ε n + 1 − ε n ), (A1) σ n + 1 k = 0 = σ n + Δ σ n + 1 k = 0 = σ n + C ˜ e ⋅ Δ ε n Here, a purely elastic step is assumed and the state variables from the previous n -th time step are preserved ( Δ ε n = Δ ε n e and ρ n + 1 α , k = 0 = ρ n α ). Hereafter, the superscript, k , denotes the iteration number ( k = 0 : trial step), the subscripts, n and n + 1 , denote the discrete time step number. The ( n + 1)-th step is purely elastic if the following condition is satisfied: (A2) 1 ρ ln { ∑ α = 1 N exp [ ρ m ( | σ n + 1 k = 0 : P α | τ y α ( ρ n + 1 β , k = 0 ) − 1 ) ] } ≤ 0 Otherwise, the ( n + 1)-th step is elasto-plastic, then the dislocation density, ρ n + 1 α , and the corresponding Cauchy stress, σ n + 1 , need to be iteratively obtained to satisfy the consistency condition in Eq. (A3) .
Keywords
- 3D RVE
- 3GAHSS
- Crystal plasticity
- Forming limit curves
- In-situ HEXRD
- Martensitic phase transformation