Adam A. Creuziger

Crystallographic Texture Evolution in 1008 Steel Sheet During Multi-axial Tensile Strain Paths

AbstractThis paper considers the crystallographic texture evolution in a 1008 low carbon steel. The texture evolution along uniaxial, plane strain and balanced biaxial strain states were measured. For uniaxial testing, grains tend to rotate such that the {111}〈11̄0〉 slip directions are aligned with the loading axis. For plane strain and balanced biaxial strain states, the majority of grains are distributed with the {111} plane parallel to the sample normal direction. Accompanying visco-plastic self consistent (VPSC) predictions of the texture evolution were made along same strain paths and strain increments. Comparing between the measured texture evolution and computational texture evolution indicate that the VPSC model qualitatively predicts the measured texture evolution, but the rate at which the texture evolution occurs is over predicted.

A model for calculating diffraction elastic constants

A model, dubbed the inverse Kroner model, is proposed to calculate the diffraction elastic constants from the elastic constants of a single crystal. It is related to the classic Kroner model, and both are identified as bounds on the diffraction elastic constants. Through the grain shape as controlling parameter, the classic Kroner model is bound by the hkl-independent mechanical limit given by the bulk elastic constants of the matrix, while the inverse Kroner model approaches the Reuss limit.

In situ structural characterization of ageing kinetics in aluminum alloy 2024 across angstrom-to-micrometer length scales

The precipitate structure and precipitation kinetics in an Al-Cu-Mg alloy (AA2024) aged at 190 °C, 208 °C, and 226 °C have been studied using ex situ Transmission Electron Microscopy (TEM) and in situ synchrotron-based, combined ultra-small angle X-ray scattering, small angle X-ray scattering (SAXS), and wide angle X-ray scattering (WAXS) across a length scale from sub-Angstrom to several micrometers. TEM brings information concerning the nature, morphology, and size of the precipitates while SAXS and WAXS provide qualitative and quantitative information concerning the time-dependent size and volume fraction evolution of the precipitates at different stages of the precipitation sequence. Within the experimental time resolution, precipitation at these ageing temperatures involves dissolution of nanometer-sized small clusters and formation of the planar S phase precipitates. Using a three-parameter scattering model constructed on the basis of TEM results, we established the temperature-dependent kinetics for the cluster-dissolution and S-phase formation processes simultaneously. These two processes are shown to have different kinetic rates, with the cluster-dissolution rate approximately double the S-phase formation rate. We identified a dissolution activation energy at (149.5 ± 14.6) kJ mol-1, which translates to (1.55 ± 0.15) eV/atom, as well as an activation energy for the formation of S precipitates at (129.2 ± 5.4) kJ mol-1, i.e. (1.33 ± 0.06) eV/atom. Importantly, the SAXS/WAXS results show the absence of an intermediate Guinier-Preston Bagaryatsky 2 (GPB2)/S″ phase in the samples under the experimental ageing conditions. These results are further validated by precipitation simulations that are based on Langer-Schwartz theory and a Kampmann-Wagner numerical method.

Advanced Biaxial Cruciform Testing at the NIST Center for Automotive Lightweighting

Modeling of sheet metal forming operations requires mechanical properties data at very large tensile strains and various biaxial strain paths. Typically these data are developed along strain ratio paths that are linear and monotonic, but actual forming strain paths are nonlinear and not necessarily monotonically increasing. A unique planar-biaxial testing facility at the National Institute of Standards and Technology (NIST) has been designed to address non-linear strain paths and other long standing measurement needs. The system uses a combination of four independently controlled hydraulic actuators, with either displacement, force, or strain feedback control, to deform the material, while measurements of the material response is accomplished through a unique combination of digital image correlation and X-ray diffraction. Results of commissioning tests are presented for displacement and force control along different axes. The system was able to deform the sample in the elastic and plastic regimes. The results show the difference between the displacement and strain paths followed, as well as some unexpected behavior (e.g. buckling). Other expanded system capabilities for future use are briefly described.

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.

Uncertainties of Digital Image Correlation Near Strain Localizations

Estimates of the strain errors resulting from digital image correlation (DIC) measurements are desired for many uses. One application is the measurement of the strain localization near failure in forming limit testing of sheet metals. This work measures and statistically characterizes the displacement measurement uncertainties for a typical DIC system. These uncertainties are found to have nearly Normal probability distributions and were used as inputs into a Monte Carlo analysis to determine the resulting strain uncertainty. A limited parameter study was made using the Monte Carlo analysis. The results demonstrate that the strain measurement uncertainty is quantifiable, and reducing the virtual gauge length (over which the strain is determined) tends to increase the strain measurement uncertainty. Based on the results, curves relating the strain uncertainty to the DIC analysis parameters can be developed. These curves suggest a balance must be chosen between the optimum processing parameters to minimize the strain error or the parameters to minimize the virtual gauge length. For some engineering applications (e.g. forming limit testing), a smaller virtual gauge length might be preferred even if it results in a higher strain uncertainty, as long as that uncertainty is quantifiable.

Finite Element Modeling of Deformation Behavior of Steel Specimens under Various Loading Scenarios

Lightweighting materials (e.g., advanced high strength steels, aluminum alloys etc.) are increasingly being used by automotive companies as sheet metal components. However, accurate material models are needed for wider adoption. These constitutive material data are often developed by applying biaxial strain paths with cross-shaped (cruciform) specimens. Optimizing the design of specimens is a major goal in which finite element (FE) analysis can play a major role. However, verification of FE models is necessary. Calibrating models against uniaxial tensile tests is a logical first step. In the present study, reliable stress-strain data up to failure are developed by using digital image correlation (DIC) technique for strain measurement and X-ray techniques and/or force data for stress measurement. Such data are used to model the deformation behavior in uniaxial and biaxial tensile specimens. Model predictions of strains and displacements are compared with experimental data. The role of imperfections on necking behavior in FE modeling results of uniaxial tests is discussed. Computed results of deformation, strain profile, and von Mises plastic strain agree with measured values along critical paths in the cruciform specimens. Such a calibrated FE model can be used to obtain an optimum cruciform specimen design.

Constitutive Modeling based on Evolutionary Multi-junctions of Dislocations

A latent hardening model based on binary junction-induced hardening can effectively describe the anisotropy measured in multiaxial tests. However, this approach still has some descriptive and predictive limitations. Recent findings show that binary junctions generated by interactions of pairs of dislocations can only induce short-term hardening effect due to the unzipping process of binary junctions. By contrast, multi-junctions, which are formed via multiple interactions of dislocations, can exert a strong and enduring influence on the hardening of polycrystals. In this study, we extend the modeling of dislocation junctions from the binary to multi-junctions, and implement this evolution into a self-consistent visco-plastic model. An application of this model for predicting the yield surface and texture evolution of AA5754 during uniaxial and plane strain loadings is given as a demonstration of the capabilities of the evolutionary binary-multi junction approach.

The Strain Path Dependence of Plastic Deformation Response of AA5754: Experiment and Modeling

This work presents modeling of experiments on a balanced biaxial (BB) pre-strained AA5754 alloy, subsequently reloaded uniaxially along the rolling direction and transverse direction. The material exhibits a complex plastic deformation response during the change in strain path due to 1) crystallographic texture, 2) aging (interactions between dislocations and Mg atoms) and 3) recovery (annihilation and re-arrangement of dislocations). With a BB prestrain of about 5 %, the aging process is dominant, and the yield strength for uniaxially deformed samples is observed to be higher than the flow stress during BB straining. The strain hardening rate after changing path is, however, lower than that for pre-straining. Higher degrees of pre-straining make the dynamic recovery more active. The dynamic recovery at higher strain levels compensates for the aging effect, and results in: 1) a reduction of the yield strength, and 2) an increase in the hardening rate of re-strained specimens along other directions. The yi...

Interpretation of Diffraction Data from In Situ Stress Measurements during Biaxial Sheet Metal Forming

Biaxial yield behavior is determined in-situ through X-ray lattice strain measurements. The distributions of d-spacings in different sample directions is affected both by the changes in diffraction elastic constants (DEC) from evolving texture and by the intergranular (IG) strains. Model predictions were found to be lacking, thus, a hybrid approach was developed based on measurements of DEC and IG strains at selected biaxial deformations. In order to convert measured lattice strains to stress for any given biaxial plastic strain a theoretical approximation was fitted to the experimental data, thus allowing the estimation of the evolution of DEC and IG strains with plastic deformation.