Estimation of Planar Anisotropy of the <I>r</I>-Value in Ferritic Stainless Steel Sheets

Abstract

Planar anisotropies of r-values are calculated from crystallite orientation distribution functions (ODFs) by using the Taylor theory. These values are compared with experimentally obtained values for two kinds of ferritic stainless steel sheets with different planar anisotropies of the rvalues and different texture gradients in the thickness direction. Moreover, the most suitable model for predicting the r-value of ferritic stainless steel sheets is examined. For a material with a remarkable texture gradient in the thickness, the ODF in a particular plane perpendicular to the normal direction was unsuitable for predicting the planar anisotropy of the r-value. On the other hand, r-value calculated using the average ODF through sheet thickness measured in a section perpendicular to the transverse direction shows good agreement with the experimentally obtained. The relaxed-constraints model, in which the shear strain components e 13 and e 23 , are relaxed with a CRSS ratio of 1.1 in the f211gh111i and f110gh111i slip systems is the most suitable model for predicting the planar anisotropy of the r-value in ferritic stainless steel sheets.

Texture and Planar Anisotropy in Lean Duplex Stainless Steel Sheet

“…[23][24][25][26][27][28] In a previous paper, 16) the authors illustrated that the texture of the α phase in Type 329J4L was dominant for the anisotropy of r-value. Furthermore, like a case of single-phase ferritic steels, 20,29) the r-values in Type 329J4L calculated from the texture of the α phase using the relaxed-constraints (RC) model with the RC1323 and a critical resolved shear stress (CRSS) ratio of 1.1 were in good agreement with the experimental values. 16) Here, the RC1323 model, i.e., the pancake version in which e13 and e23 (where 1, 2, and 3 are defined as the tensile, width, and thickness directions, respectively) were left free, and the CRSS ratio was the same as that for the {211} and {110} glide planes (τ c{211} /τ c{110} ).…”

“…From this result, it is concluded that the small anisotropy in r-value of the lean DSS Type 32101 sheet was caused by a weaker texture of the α phase compared with the standard DSS Type 329J4L sheet. In addition, because the r-value of the {100} < 011 > and {211} < 011 > ideal orientations belonging to the α bcc -fiber showed reverse V-type that had the maximum value at the 45° direction and low values at the 0° and 90° directions, 16,20,29) it is estimated that Type 32101 with weaker α bcc -fiber had higher r-values at the 0° and 90° directions and a lower r-value at the 45° Fig. 10.…”

“…Because these materials may have inhomogenious texture along the sheet thickness, we should use the overall texture through sheet thickness for an approximate evaluation. 16,20,29) But in this study, for the purpose of a qualitative comparison of anisotropy of r-value about these DSS sheets, the predictions of anisotropies of r-values by using the RC1323 model with a CRSS ratio of 1.1 were performed from the ODFs of the α phase in the center layer. Figure 10 shows the planar anisotropies of the measured and calculated r-values of the sheets cold rolled to 78% reduction and annealed at 1 050°C.…”

Effect of Texture on r-value of Ferritic Stainless Steel Sheets

“…23,24) Here, the RC1323 model, i.e., the pancake version in which e13 and e23 (where 1, 2, and 3 are defined as the tensile, width, and thickness directions, respectively) were left free, was used as the RC model, because it was an optimal model for BCC steels in previous studies. 21,22,24,27) In the case of the FC model, only the {110} slip plane was considered, and in the case of the RC1323 model, in addition to the {110} slip plane, the values of the critical resolved shear stress (CRSS) ratio for the {211} and {110} glide planes (τc{211}/τc{110}) were assumed to be 0.9, 1.0, and 1.1 in these calculations. Figure 10 shows the measured and calculated planar anisotropies of the r-value for some recrystallized samples of Type 436L and Type 409L with different cold rolling textures of Types A and C, which have high r-values.…”

“…[19][20][21][22][23][24][25][26][27] To determine a suitable model for ferritic stainless steel sheets with extremely high r-values, and to consider the possibility of limitation of slip system by chromium, 12) the anisotropies of the r-values were predicted on the basis of ODF data by using the Taylor full-constraints (FC) model 19) and the relaxed-constraints (RC) model, 20) in which some shear strain components were relaxed relative to those in the fully constrained state. Software developed by one of the authors was used in this calculation.…”