Dynamic Materials Testing, Texture, and Yield-Surface Calculation of an Automotive Sheet Steel CARL M. CADY, SHUH RONG CHEN, GEORGE T. GRAY III, DAVID A. KORZEKWA, and JOHN F. BINGERT The relationships between the stress state and anisotropic mechanical response for a drawing-quality, special-killed (DQSK) mild sheet steel has been analyzed. The strain rate and temperature sensitivity of the flow stress and the insensitivity of the strain hardening to strain rate are shown to be consistent with thermal activation over a Peierls barrier as the rate-controlling mechanism for deformation in DQSK. A calculated yield surface, using the quadratic Hill criterion, is shown to produce an accurate correlation with the experimental results as a function of stress state. Annealing of the DQSK sheet steel at 773 K for 1 hour reduced some of the residual stresses developed during the forming process, but had little effect on the texture. The R values derived from computed yield surfaces suggested very little difference between in-plane (IP) and transverse tensile tests, consistent with the experimental results. A comparison of the stress-strain response with the calculated yield-surface and texture measurements correlates well with the relationships between the IP and through-thickness (TT) deformation. I. INTRODUCTION STEEL sheet, possessing a high in-plane isotropy (low Dr) and high plastic-strain ratio (r), is widely used in the automotive industry to meet the requirement for good drawability when forming panels and possessing complex shapes. In recent years, it has become increasingly important to reduce the thickness and weight of the sheet steel used in automobiles. This reduction has been driven by growing global environmental concerns pressuring automobile manufacturers to produce ever-increasingly more efficient, cleaner products while simultaneously improving vehicle safety.[1–4] One obvious way to increase fuel efficiency is to reduce the overall weight of the steel used in cars and trucks. However, designers must also maintain strength and damage-resistance criteria in the final product. Significant research has gone into the compositional and production development of sheet steels that will improve the formability of thinner gages of steel without sacrificing either the yield or flow strength of the steel sheets.[5,6] The UltraLight Steel Auto Body (ULSAB) program initiated by AISI and IISI was created to design just such a vehicle.[7] The divergence of plastic-strain ratios from unity is a consequence of plastic anisotropy, and this anisotropy is derived from polycrystalline textures evolved during thermomechanical processing. There are several factors affecting texture development in DQSK steel. Deformation textures, especially their sharpness, are most strongly influenced by total reduction, while recrystallization textures are controlled by carbon content and intragranular heterogeneities, such as aluminum nitride precipitation during annealing.[8–11] The primary texture components in rolled steel consist of the g fiber ({111} planes parallel to the rolling CARL M. CADY, SHUH RONG CHEN, DAVID A. KORZEKWA, and JOHN F. BINGERT, Staff Members, and GEORGE T. GRAY III, Team Leader, are with the Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545. Manuscript submitted July 8, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A plane) and a fiber (^110& direction parallel to the rolling direction). Since ^111& represents a strong crystallographic direction in bcc metals, the formation of a sharp g-fiber texture leads to an increase in the through-thickness (TT) strength as compared to the in-plane (IP) strength.[12,13] The anisotropic behavior of steels is usually characterized by means of the coefficient of normal plastic anisotropy, conventionally reported as the r value (Lankford parameter), an average of the r values measured in the plane of the sheet. Several industrially important mechanical properties of rolled steel sheets are determined by the nature and intensity of its texture, and the r value is one of these. It has been shown to be an effective tool to characterize the drawability of steel sheet.[14–22] In this study, emphases were placed on investigating (1) the influence of strain rate, temperature, and heat treatment on the stress-strain response of an as-manufactured drawingquality, special-killed (DQSK) mild steel, (2) the development of yield-surface predictions, and (3) the texture and r value for a DQSK steel. II. EXPERIMENTAL PROCEDURE The material examined in this study was DQSK mild sheet steel, a low-carbon steel commonly used in the manufacture of automobiles, produced by National Steel Corporation (Livonia, MI). The analyzed composition of the DQSK steel studied was (in wt pct): 99.6 Fe, 0.23 Mn, 0.049 Cr, 0.04 Al, 0.023 C, and ,0.006 P, Si, Ni, Mo, and Sn.[23] The as-received cold-rolled sheet stock had a gage of 2.8 mm and exhibited a “pancake” grain structure with a nominally equiaxed shape in the IP direction of 80 and 30 mm in the TT direction. Tensile specimens and compression cylinders were wire electrodischarge-machined from the as-received steel plates, as shown schematically in Figure 1. During the machining process, the galvanized surface coating on the as-received steel plates was removed. Tensile specimens were machined both axially and transverse to the rolling direction. Two U.S. GOVERNMENT WORK NOT PROTECTED BY U.S. COPYRIGHT VOLUME 31A, OCTOBER 2000—2439 Fig. 1—Schematic of the DQSK mild steel plate showing the orientations and geometries of the tensile and compression specimens utilized. geometries of tensile specimens were tested, both having a dog-bone shape, with a gage length of 43 mm and a gage width of 6.7 mm. The difference between the two tensile specimens was in the thickness: for one geometry, the DQSK steel was tested in the as-received thickness, nominally 2.5 mm, while the other tests were conducted on the steel after approximately 0.6 mm of material had been removed from each side of the plate. This material was removed in order to assess the effect of the final temper roll on the constitutive response of the surface region compared to the sheet interior. Cylindrical compression samples were machined from the IP axial and IP transverse orientations to the rolling direction as well as in the TT direction. The IP compression cylinders were 3.8 mm in height and 2.3 mm in diameter. The TT specimens had dimensions of 2.5 mm in height and 3.8 mm in diameter. Balanced biaxial bulge tests were also conducted on the as-received 12 3 12 in. DQSK steel plates. The biaxial tests provide important information about the formability and yield and work-hardening characteristics of the plate, as well as confirmation of the TT compression results. These tests also provide information on the biaxial tensile strength of the steel plate, for comparison between the calculated yield surface and the experimental data. Additional compression samples were heat treated to determine the effect of the final temper roll on the yieldand flow-strength behavior of the as-received sheet. Asreceived samples were encapsulated in quartz tubes under vacuum and annealed at 773 K for 1 hour, followed by a slow bench cool. These samples were then loaded at the same range of strain rates and temperatures as the as-received steel plate to determine the change in material properties due to annealing. Additional hardness tests were conducted on both annealed and as-received samples to determine if the heat-treatment process created uniform properties in the TT loading orientation and to quantify the depth to which the temper roll affected the as-received sheet properties. Quasi-static compression tests, with strain rates between 0.001 and 0.1/s, were conducted using a screw-driven load frame (Instron model 1125) at temperatures of 77 and 298 K in displacement control. MoSi2 lubrication was utilized to reduce friction and minimize barreling.[24] Duplicate lowrate compression tests and elevated-temperature compression tests at 373, 473, 573, and 673 K were conducted on a servohydraulic load frame (MTS model 880) in displacement control. The tensile samples were loaded to failure on the screw-driven Instron frame at 298 K and a strain rate of 0.001/s, to allow comparison of the differences between the 2440—VOLUME 31A, OCTOBER 2000 two tensile geometries as well as of the compression behavior. Optical microscopy was used to precisely measure the TT and gage cross-sectional area of the tensile specimens before and after testing. These measurements provide some of the data necessary for determination of the yield-surface shape and an estimate of the r value. Balanced biaxial tensile tests were conducted on a hydraulic bulge tester at quasistatic strain rates (,0.001/s).[25] These three different loading-path tests were utilized to explore the effect of texture on the overall constitutive response of the steel and the effect of the stress state. Intermediate strain-rate tests, between 5 and 500/s at 298 K, were performed using a specially built high-rate MTS frame (model 810). Identical lubrication techniques were used for these tests to minimize the friction stresses between the loading platens and the test samples. Additionally, high-strain-rate dynamic tests, between 1000 and 5000/ s and at temperatures of 77, 298, 473, 673, 773, and 873 K, were conducted using a split-Hopkinson pressure bar (SHPB).[26,27] Due to the inherent oscillations in the dynamic stress-strain curves caused by elastic-wave dispersions and the lack of stress equilibrium in the Hopkinson-bar specimens at low strains, the determination of an accurate yield strength at high strain rates is more difficult. Yield values for the Hopkinson-bar curves were, therefore, chosen by selecting the flow-stress value at the intersection of the elastic-loading line, with a smooth curve back-extrapolated through the entire high-rate flow-stress data for each sample curve. Metallographic sections of the as-received, quasi-statically deformed, heat-treated 1 quasi-statically deformed, and dynamically deformed materials were prepared using standard metallographic techniques for grinding and polishing. The DQSK grain structure was revealed by etching in a solution of 5 pct nitric acid and 95 pct methanol, commonly called Nital; micrographs were obtained using polarized light. Microhardness measurements were also conducted on the polished steel specimens in the TT direction to document to what extent the temper rolling, as the final step in processing, leads to nonuniform material properties through the sheet thickness. Crystallographic textures of the DQSK steel were measured using polished and etched samples for the as-received and annealed sheet conditions. The samples consisted of stacked transverse cross sections, so as to average any gradient that may exist through the sheet thickness. The (111), (110), and (100) pole figures were collected using the Schulz reflection method[28] on a four-circle goniometer using Fe Ka radiation. The orientation distribution function (ODF) was calculated from these pole figures using the Williams, Imhof, Matthies, and Vinel (WIMV) technique, as incorporated in the popLA texture-analysis program.[29] The displayed pole figures were recalculated from the OD. It is possible to use the texture information in conjunction with the mechanical test results to probe the interrelationships between the anisotropy of the DQSK sheet constitutive response and the crystallographic texture. III. RESULTS A. Stress-Strain Response The constitutive data of the DQSK sheet steel is presented as true stress–true strain (s-«) plots in Figures 2 through 9. METALLURGICAL AND MATERIALS TRANSACTIONS A