Crystallographic texture evolution in 1008 steel sheet during multi-axial tensile strain paths

Steel has been in use for nearly 4000 years, and remains one of the main materials (along with concrete, glass and asphalt) used around the world. A large majority of the steels created are carbon steels, with a large proportion of these carbon steels strained after production to create a required shape. Accurate prediction of the final shape and mechanical properties after straining continues to be an important industrial goal. One of the methods applied to this problem is measurement of the crystallographic texture (or preferred orientation) as a function of strain path and strain increment. Accurate prediction of the crystallographic texture and how the texture evolves will allow better estimates of the flow stress and plastic contraction, which in turn provides a more accurate prediction of the final shape and failure during forming. The particular case of deformation of sheet stock material is discussed in this paper. The majority of the literature discusses the high strain increments relevant for rolling sheet material. Unfortunately existing [1‐6] experimental data on the texture evolution along multiaxial strain states at intermediate strain increments (Δ ε) relevant for forming are incomplete, so assessment of model accuracy is difficult in this regime.

This paper focuses on the measurement of the crystallographic texture evolution in 1008 AISI/SAE low carbon steel sheets after strain increments typical in forming structures from the rolled sheet. The texture is measured by neutron diffraction to interrogate a large number of grains. Five different strain states were investigated: uniaxial strain along the rolling direction (URD), strain along the rolling direction with the transverse direction fixed near zero strain (a plane strain condition, or PSRD), balanced biaxial strain (BB) in the rolling and transverse directions, strain along the transverse direction with the rolling direction fixed near zero strain (PSTD), and uniaxial strain along the transverse direction (UTD). In the plane of the sheet (normal direction or ND) the sample is assumed to be in a plane stress condition. In addition, the texture evolution is predicted from the as received texture using the visco-plastic self consistent (VPSC) model and compared with the experimental data. Data on the texture evolution of low carbon steels will also provide a well characterized reference for comparison to more complicated materials, such as high strength steels (HSS) like high strength low alloy (HSLA) steel or advanced high strength steels (AHSS) such as dual phase (DP) or transformation induced plasticity (TRIP) steels.

The data described in this paper has been submitted to the NIST/MatDL DSpace repository as part of the IMMI General Articles Collection [7]. The repository contains files that include a description of the data contained in the repository, a schematic of the the analysis and computational processes, some of the programs used to analyze the data, a collection of the texture data files at various points in the analysis, and input files to the VPSC model.

Using the American Iron and Steel Institute (AISI) and Society for Automotive Engineers (SAE) grade designation, 1008 steel is defined as an iron alloy possessing a mass fraction of carbon ≤0.0010, a mass fraction of manganese between 0.0030 and 0.0050, a mass fraction of phosphorus ≤0.0004, and a mass fraction of sulfur ≤0.0005 [8]. Owing to the low carbon content and absence of austenitic stabilizers, the structure is almost entirely ferritic (body centered cubic crystal structure) with some carbides. This allows for high ductility (approximately 40% elongation), but low strength (tensile strength approximately 350 MPa) [9].

The texture evolution of steels has been widely studied in the past, particularly with respect to the complete processing path from the melt to hot and cold rolling. These topics are of interest to create desirable textures for deep drawing. Some articles on these topics include [2, 3, 10, 11], which discuss steel textures and their origin from deformation and recrystalization of the austenite phase and subsequent transformation from austenite to ferrite. The complex details of the austenitic transformation are beyond the scope of this paper, but it is important to note that deformation and recrystallization in the austenite phase are one of the primary causes of crystallographic texture in the ferritic phase. The review by Inagaki [12] summarizes work on the inter-relationship between texture, grain boundaries and dislocation structures in low carbon steels. Hutchinson [13] discusses texture control in low carbon steels as a function of processing parameters. Bodin et al. [2] shows the strong effects of processing path and temperature on the texture.

The predicted plastic strain ratio (R value) has been used to correlate the effect of a particular texture component to the macroscopic properties. For deep drawing applications, sheet material that has a large volume of grains aligned with the γ-fiber ({111} plane parallel to the ND) are preferred as they have a high average R value (R ̄) and a planar anisotropy (Δ R) value near 0 [10, 13]. Orientations with the {100} plane parallel to the ND direction such as ‘cube’ and ‘shear’ orientations are not desirable, since they have low average R values [10, 13]. This is due to the orientation of slip systems for body centered cubic (BCC) materials. Conversely, for high strength materials where high ductility is not required, orientations along the α-fiber (〈110〉 crystal direction parallel to rolling direction) are preferred for high strength [14] but may produce anisotropy and brittleness, particularly for the {113}〈110〉 orientation [10].

There is also a significant amount of investigation into the textures caused by cold rolling in the ferrite phase. This data is particularly relevant to this paper as cold rolling, apart from a hydrostatic term, produces a stress state similar to plane strain along the rolling direction (PSRD). As shown in a series of review papers, cold rolling ferrite strengthens the α and γ fibers, particularly the α fiber at higher reduction ratios [3, 10, 11]. Figure thirteen in Kestens and Jonas [11] shows relative amounts of texture intensity as a function of thickness reduction. Inagaki [12] discusses some of the microstructural reasons for this, and theorizes that grain pairs with {111}[uvw] type grain boundaries that allow the grain to rotate easily, keeping orientations along the γ fiber stable.

Kestens and Jonas [11] proposes that {211} 〈011〉 along the α fiber is the stable final orientation in plane strain compression, while {111} 〈110〉 and {554} 〈225〉 orientations are caused by ferritic recrystallization after plane strain compression. Inagaki [12] proposes that the {223} 〈011〉 orientation is the final stable orientation in plane strain compression. There is additional literature on cross-rolling of low carbon steel sheets [5], a strain state similar to plane strain along the transverse direction (PSTD). Results from Wronski et al. [5] show that the shear orientation and γ fiber are stable orientations after near 80% thickness reduction.

There has been limited investigation into the texture evolution along other strain paths relevant for sheet metal forming. Yerra et al. [6] is one of the most complete, following five different strain paths from equal biaxial to uniaxial tension, all with the largest strain values in the rolling direction. The orientation distribution functions (ODFs) are measured at a single level of strain for each strain path. In Yerra et al. [6], the experimental textures were not found to change greatly between the different strain modes nor the volume fractions of specific orientations. However a calculation using the Lamel model by the same authors show a significant difference between the strain paths. Other notable works include Luzin et al. [15], which measured texture after balanced biaxial straining. The γ fiber in a balanced biaxial strain mode is intensified, in agreement with Mirshams et al. [16] and theoretical calculations that predict the θ (〈100〉 parallel to ND direction) and γ fibers to be the stable orientations in uniaxial compression along the ND. Other strain modes, such as torsion [17] and simple shear [18] are outside the scope of this paper.

As steel is such a relevant industrial material, there have been attempts to predict the texture evolution. Savoie and Jonas [19] used a rate sensitive analysis to model the texture along a flange during deep drawing. These simulations include a rotation rate map that shows the stable end orientations for different constraints imposed on the models. They found that all initial orientations tend to rotate toward the {223} 〈110〉 orientation. Toth et al. [20] used a rate dependent slip theory that contains models for pancake, lath and Taylor models to calculate texture evolution in low carbon steels during rolling. Starting with the ‘RGoss’ orientation, {111} 〈110〉, and shear orientations; they found the {111} 〈112〉 orientation also forms, but becomes unstable at higher strains. Many more stable orientations were found using this method, but most were observed along the α fiber and γ fiber as well as {554} 〈225〉. Raabe [21] used a Taylor type model to predict the rolling texture in low carbon deep drawing steel as a function of reduction ratio. The Taylor model showed increases in the intensity of the α fiber and γ fiber in good agreement with experiment [21].

Qualitatively there is good agreement between the experimental and computational texture evolution models. Most changes from the texture evolution have the correct ‘sense’ to them, experimental increases are matched to computational increases and vice versa. Both the computational and experimental textures show significant changes even at relatively low (10%) values of strain. There are some subtle differences between the Experimental and VPSC as received textures. As discussed in the results and methods sections, the VPSC as received texture is less smooth, likely due to the three order of magnitude reduction in the number of grains explored in the VPSC model (24 938 orientations) than in the experimental data (estimated at ≈2×10⁷). For orientations with ϕ₂=45° and Φ<20° there are less than 10 grains for each of the orientations in the 5° bin and at Φ=0 most of the orientations only have 1 grain associated with each bin. This may also be the cause of oddities around the shear orientation in Figure 8, where large peaks are observed 5° from the orientation that are not observed experimentally in Figure 8.

There are a few places where there is qualitative disagreement between the trends in the VPSC predictions and experimental data. In the experimental URD and PSRD strain states there are broad increases in the α fiber, particularly at Φ<55°, shown in Figure 6. The VPSC data in Figure 6 shows some increase in the intensity at Φ<55°, but a larger increase in intensity at Φ>55°. Similarly the increase in cube orientation over the shear orientation observed experimentally in Figure 8 under BB straining was not observed in the VPSC predictions in Figure 8. At higher strain levels the VPSC model seemed to rotate grains away from the γ fiber to orientations ±5° to ±10° away from Φ=55° (γ fiber), as shown by the decreases in intensity along the γ fiber in the difference map in Figure 5. This may also affect the PSTD results data, where the intensity pattern observed experimentally in Figure 7 does not match the VPSC predictions shown in Figure 7.

Quantitatively, the VPSC model tends to over predict the rate of texture evolution leading to much higher intensities and sharper orientation distributions. Overall, the intensity values for experimental data at 30% strain better match the VPSC data at 10% strain. The BB 30% strain state is a particularly good example of the difference in rate of texture evolution, with the intensity predicted by the VPSC over-predicted by a factor of 5. Another example is the PSRD strain state, where the α₄ and {554} orientations are predicted to have increases larger than are observed experimentally.

Comparing this data with prior computational and analytical work, the uniaxial samples show the 〈110〉 slip directions of the {111} plane as stable orientations, and instability of slip directions 〈211〉 in the {111} plane. The PSRD strain state is indeed similar to the predictions for cold rolling the ferrite phase. The experimental data indicates that while the α₄ ({ 223 } 〈 1 1 ̄ 0 〉) orientation is the most stable, there seems to be a broad distribution of orientations that are increasing at the strain levels investigated. The stability of the α fiber changes with more transverse direction strain, such that in the BB and PSTD strain states this fiber is not as stable. This result could be used in production, for applications where α fiber is not desirable, as more lubrication on the rollers or cross rolling could be used to remove some of the α fiber and increase the number of grains with orientations aligned with the γ fiber; albeit with some increase in the cube and shear components as well. The increase in γ fiber agrees well with observations by [15] and [16] but in our work more cube orientated grains are observed than by Luzin et al. [15]. The experimental and VPSC data are more consistent with the Lamel predictions than experimental data from Yerra et al. [6].

A similar study 5754 aluminum compared Los Alamos polycrystal plasticity (LApp), VPSC and visco-plastic fast Fourier transform (VPFFT) models for multiaxial strain states [37]. Hu et al. [37] showed similar trends to those observed here, with the rate of texture evolution over predicted in the VPSC model, particularly for the BB strain state. The VPFFT model calculated a rate of texture evolution closer to those observed experimentally. In the VPFFT model, the inter-grain and intra-grain interactions are included in the model, likely improving the accuracy. However, the VPFFT model described by Hu et al. [37] is discretized as voxel elements. Approximately 500 voxels were required for each grain, as opposed to the single ellipsoid per grain in the VPSC model, resulting in the VPFFT model containing one fifth as many grains as the VPSC model for a similar computational time. The reduction in number of grains resulted in a lower fidelity to the as received texture. The texture in the 5754 aluminum studied was much closer to a uniform distribution than the steel texture measured here, so a larger number of grains would be required to accurately model the steel microstructure. Following work by Dawson et al. [38], the addition of the elastic component to the viscoplastic models (EVPSC or EVPFFT approaches) is not expected to improve the model as the strains in this study are relatively large strains along monotonically increasing strain paths. Additionally, the construction of an accurate microstructure with respect to the spatial correlation of adjacent grains required as an input to a VPFFT or crystal plasticity based finite element analysis (CP-FEA) models is a topic of current research.

However, there is some concern that even accurate microstructure may be insufficient to model the deformation of polycrystalline materials. Pokharel et al. [39] compare a modeled microstructure in VPFFT that is taken from experimental data from near field high-energy X-ray diffraction microscopy (nf-HEDM) [40]. Even with a microstructure model that closely matches the experimental data, the agreement between experiment and model are not as close as desired. Similar to the results shown in this paper, there is reasonable qualitative agreement, but there are significant qualitative and quantitative variations. Pokharel et al. [39] conclude that the “empirically derived constitutive relations used in continuum scale simulations” (i. e. the Voce model in VPFFT and VPSC) as the likely cause of the disagreement and recommend further work on the development of a constitutive relation based on dislocation interactions. Pokharel et al. [39] also touches on CP-FEA, but states that the empirically derived continuum level constitutive relationships used in FEA may suffer similar problems as observed in the VPFFT model.

To summarize, the crystallographic texture evolution in a 1008 low carbon steel along five different strain states have been experimentally measured and computationally predicted using VPSC. Comparisons between measured texture evolution and computational texture evolution indicates that the VPSC model is generally qualitatively accurate in predicting the orientations to which grains rotate. Quantitatively, the VPSC model over predicts the rate at which grains will rotate, particularly in multi-axial strain states such as balanced biaxial.

^a Certain commercial equipment, instruments, or materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose.