Youngung Jeong

Multiaxial constitutive behavior of an interstitial-free steel: Measurements through X-ray and digital image correlation

Constitutive behaviors of an interstitial-free steel sample were measured using an augmented Marciniak experiment. In these tests, multiaxial strain field data of the flat specimens were measured by the digital image correlation technique. In addition, the flow stress was measured using an X-ray diffractometer. The flat specimens in three different geometries were tested in order to achieve 1) balanced biaxial strain, and plane strain tests with zero strain in either 2) rolling direction or 3) transverse direction. The multiaxial stress and strain data were processed to obtain plastic work contours with reference to a uniaxial tension test along the rolling direction. The experimental results show that the mechanical behavior of the subjected specimen deviates significantly from isotropic behavior predicted by the von Mises yield criterion. The initial yield loci measured by a Marciniak tester is in good agreement with what is predicted by Hills yield criterion. However, as deformation increases beyond the vonMises strain of 0.05, the shape of the work contour significantly deviates from that of Hills yield locus. A prediction made by a viscoplastic self-consistent model is in better agreement with the experimental observation than the Hill yield locus with the isotropic work-hardening rule. However, none of the studied models matched the initial or evolving anisotropic behaviors of the interstitial-free steel measured by the augmented Marciniak experiment.

Application of crystal plasticity to an austenitic stainless steel

The visco-plastic self-consistent (VPSC) model is applied to a 304 austenitic stainless-steel sheet sample to investigate its suitability as a constitutive model for sheet metal forming simulations. The factors to which the model prediction is sensitive are explored. In particular, the influence of the textures obtained at three different depths on the in-plane variation of the r-value (Lankford coefficient) and the yield stress is investigated. Then, the grain number sensitivity in the representative volume element is analyzed. Moreover, the influence of the linearization scheme for the crystal constitutive power law on the simulation result is discussed. For simulation, discrete crystallographic orientation distributions are calculated from the pole figures obtained at different depths. Several mechanical experiments are conducted, namely, uniaxial tension, in-plane biaxial and the bulge tests. The mechanical response of the material is simulated using the VPSC model and compared with the model predictions.

Uncertainty in flow stress measurements using X‐ray diffraction for sheet metals subjected to large plastic deformations

X-ray diffraction techniques have been developed to measure flow stresses of polycrystalline sheet metal specimens subjected to large plastic deformation. The uncertainty in the measured stress based on this technique has not been quantified previously owing to the lack of an appropriate method. In this article, the propagation of four selected elements of experimental error is studied on the basis of the elasto-viscoplastic self-consistent modeling framework: (1) the counting statistics error; (2) the range of tilting angles in use; (3) the use of a finite number of tilting angles; and (4) the incomplete measurement of diffraction elastic constants. Uncertainties propagated to the diffraction stress are estimated by conducting virtual experiments based on the Monte Carlo method demonstrated for a rolled interstitial-free steel sheet. A systematic report on the quantitative uncertainty is provided. It is also demonstrated that the results of the Monte Carlo virtual experiments can be used to find an optimal number of tilting angles and diffraction elastic constant measurements to use without loss of quality.

Forming Limit Diagram Predictions Using a Self-Consistent Crystal Plasticity Model: A Parametric Study

A numerical model to predict forming limit diagrams (FLD) for polycrystalline metal sheets is presented. In it, the Marciniak-Kuczynski (MK) approach is incorporated into the framework of the viscoplastic self-consistent (VPSC) crystal plasticity model. The current model, dubbed the VPSC-FLD, can run simulations along individual loading paths in parallel, which can make use of a CPU-cluster to enhance the computational speed. The main objective of the current work is to provide a detailed sensitivity report based on the VPSC-FLD. First of all, the influence of the initial inhomogeneity, f , as defined in the MK approach, is illustrated. Secondly, FLDs resulting from various sizes of the statistical population for the crystallographic texture are examined. Lastly, the computation time spent for various sizes of the statistical population is given.

Microstructural and Crystallographic Aspects of Yield Surface Evolution

The microstructural and crystallographic aspects, reflected at the macroscopic scale on yield surface and its subsequent evolution, are reappraised by application of crystal plasticity simulations. Strain hardening rule in the slip system is coupled to cope with latent hardening and Bauschinger effect. Uniaxial tension simulation on an isotropic polycrystalline aggregate leads to anisotropic strain hardening. Typical elements of phenomenological plastic anisotropy and hardening rules such as expansion, kinematic shift and distortion of the yield surface, are shown to be featured in crystal plasticity by tuning the slip system hardening rules appropriately.

Crystal plasticity-based modeling for predicting anisotropic behaviour and formability of metallic materials

Metallic materials often exhibit anisotropic behaviour under complex load paths because of changes in microstructure, e.g., dislocations and crystallographic texture. In this study, we present the development of constitutive model based on dislocations, point defects and texture in order to predict anisotropic response under complex load paths. In detail, dislocation/solute atom interactions were considered to account for strain aging and static recovery. A hardening matrix based on the interaction of dislocations was built to represent the cross-hardening of different slip systems. Clear differentiation between forward and backward slip directions of dislocations was made to describe back stresses during path changes. In addition, we included dynamic recovery in order to better account for large plastic deformation. The model is validated against experimental data for AA5754-O with path changes, e.g., Figure 1 [1] Another effort is to include microstructure in forming predictions with a minimal increase in computational time. This effort enables comprehensive investigations of the influence of texture-induced anisotropy on formability [2]. Application of these improvements to predict forming limits of various BCC textures, such as γ, ρ, α, η and fibers and a random (R) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the forming limit diagrams (Figure 2). For example, the y fiber texture, that is often sought through thermo-mechanical processing due to high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among textures under consideration.

Crystal Plasticity Predictions of Forward-Reverse Simple Shear Flow Stress

The flow stress behavior of a bake-hardenable steel during a few simple shear cycles is investigated using a crystal plasticity model. The simple shear test provides a stable way to reverse the loading direction. Stress reversals were accompanied with a lower yield stress, i.e., the Bauschinger effect, followed by a transient hardening stage with a plateau region and, permanent softening. The origins of these three distinct stages are discussed using a crystal plasticity model. To this end, the representative discrete grain set is tuned to capture such behavior by coupling slip system hardening appropriately. The simulated results are compared with experimental forward-reverse simple shear stress-strain curves. It is shown that the characteristic flow stress stages are linked to texture evolution and to the Bauschinger effect acting on the different slip systems.