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Vol. 8. Issue 5.
Pages 4163-4172 (September - October 2019)
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Vol. 8. Issue 5.
Pages 4163-4172 (September - October 2019)
Original Article
DOI: 10.1016/j.jmrt.2019.07.025
Open Access
Evaluation of the formability of 90/10 brass produced by different casting processes and investigation of the effect of Forming Limit Diagram determination procedure
Leandro de Almeidaa,b,1, Cláudio Geraldo Schöna,
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Corresponding author.
a Department of Metallurgical and Materials Engineering, Escola Politécnica da Universidade de São Paulo, Av. Prof. Mello Moraes, 2463 – CEP 05508 – 030, São Paulo, SP, Brazil
b Paranapanema SA, Rua Felipe Camarão, 500 – CEP 09229 – 580, Santo André, SP, Brazil
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Figures (9)
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Tables (4)
Table 1. Composition of the investigated materials (in wt.%).
Table 2. Average grain sizes and corresponding standard deviations (in parenthesis) of the samples in annealed condition.
Table 3. Results of the tensile tests of the finished sheets produced by the CC and SCC processes. Average values of five samples for each case, standard deviation is shown in parenthesis.
Table 4. Parameters of the polynomial fits shown in Figs. 4 and 5. The asymptotic standard error of the parameters is shown in parenthesis and the sum of square of residuals for the fit X2, refers to the number of degrees of freedom, f.
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The present work investigated the formability of 1.1 mm thick sheets of 90/10 brass (UNS C22000) alloy obtained by two different process routes: continuous casting (CC) and semi-continuous casting (SCC). Formability was accessed using forming limit diagrams determined by two different methodologies: one suggested by the Commission of the European Communities (CEC, with grooved tensile samples to access the deep-drawing side of the diagram) and the standard Nakazima procedure. Final microstructures are equivalent, consisting of equiaxed recrystallized grains, with a smaller grain size for the CC sheet. In spite of this, the obtained FLDs suggest that both sheets have equivalent formabilities, with some slight better performance observed for the SCC sheet. This inconsistency was discussed in terms of the recrystallization texture observed for both sheets.

Materials processing
Forming limit diagram
Strain path effects
Full Text

Forming Limit Diagrams (FLDs) are plots of biaxial principal real strains in the plane of a sheet (denominated respectively, major, ε1, and minor, ε2 strains) in situations which are critical for forming, e.g. necking, fracture [1].

The concept of Forming Limit Diagram (FLD) was introduced in parts, by Keeler and Backofen [2], to model the stretching side of the curve, which presents stress states closer to biaxial traction (ε2 > 0), and then by Goodwin [3], who extended the concept to the deep drawing side of the curve (ε2 < 0), which presents stress states closer to pure shear.

The procedure for construction of a FLD involves testing a large number of samples in an attempt to span deformation paths which cover the entire ε1, ε2 space. Originally this was achieved by using a single matrix/punch/press system and samples with different geometries, as well as using different lubrication conditions to probe different strain paths [4]. Traditionally established test (e.g. Marciniak or Nakazima) are used for this purpose. The strains are typically measured using a grid of circles marked over the blank surface in an industry environment.

It turns out that the obtained FLD is influenced by many extrinsic factors, among them the sheet thickness [5], variations of the strain path (whether it is in-plane or out-of-plane) [6,7] and the friction between the punch and the sample surface [8].

This led to the development of FLD determination procedures based on tensile samples, such as the one proposed by the Commission of the European Communities (CEC) [9], or the ones proposed by Wagoner [10]. In these methodologies, data are collected by means of tensile tests (uniaxial) with specimens of different geometries, having specific side grooves (notches) to change the stress state in the necking zone, obtaining different deformation paths. In the tests carried in-plane of the sheet, as in the case of uniaxial tensile tests, there is no influence of the punch, both in its curvature and in friction. The obtained forming limit curve is positioned at lower critical strains compared to those obtained by either Nakazima or Marciniak tests [11].

Xavier et al. [12] recently investigated the use of one of Wagoner’s sample geometries to obtain the critical strain under plane strain condition (also known as FLD0), comparing with the same value as obtained using Nakazima procedure, for two different steels. The results confirmed unambiguously the depression of FLD0 when using the tensile sample.

Forming limits curves of the UNS C26000 brass were obtained according to the methodology proposed by Marciniak, and compared with the industrial application of the material, i.e., with the manufacture of electrical connectors, which uses material both in the annealed or in the hard (i.e., strain hardened) state. The results showed excellent correlation between the curves and the soundness of the produced parts [13].

The influence of the chemical composition cannot be overlooked in the determination of the formability. Melander [14] compared the FLDs of UNS C11000 copper alloy with a 400 ppm oxygen content with the ones obtained for UNS C10200 alloy, with a maximum oxygen content of 10 ppm. The results show a decrease of about 16% in the FLD0 of the UNS C11000 alloy. The author attributed this difference to enhanced void formation during the hot and cold rolling stages of processing through the fracture of the internal oxide inclusions contained in the high oxygen material.

One of the variables, which influence the critical strains in the FLD is the grain size of the sheet. Studies carried out with brass 85/15, through the elaboration of FLD by Marciniak method, concluded that an increase in grain size leads to smaller critical strains supported by the material [15].

A third factor, not previously investigated, which may influence the FLD in copper alloys, is the alloy processing route. Copper alloys are usually produced either by continuous casting (CC) or by semi-continuous casting (SCC). Both processing routes result in different microstructures and this potentially will affect the FLD. In parallel, the effect of the procedure of FLD determination, either involving punches or tensile samples, needs to be reassessed. The aims of the present work, therefore are, first, to investigate the FLDs of the C22000 alloy (90/10 Brass) obtained by continuous castings and semi-continuous casting, second, doing this by using two different FLD procedures: the CEC procedure (using tensile samples) and the standard Nakazima procedure.

2Material and methods2.1Material

The sheets used to machine the samples were initially produced by different processes, one by the continuous casting process and the other by the semi-continuous casting process. The CC process basically involves the smelting of the liquid metal in a holding type furnace and the casting of liquid metal into an open graphite mold, positioned horizontally at the outlet of the smelting furnace. The produced plate, with dimensions 650 × 13.7 × 45,000 mm, is then stored in the form of a coil. In the SCC process the liquid metal is cast into a die producing a plate, after solidification the plate is reheated and subjected to the hot rolling. The end products of hot rolling is a plate with dimensions 650 × 13.6 × 52,500 mm, which is stored in the form of a coil as well. Table 1 shows the composition of both plates, as determined by X-ray fluorescence.

Table 1.

Composition of the investigated materials (in wt.%).

Element  CC plate  SCC plate 
Cu  Balance  Balance 
Zn  10.26  10.21 
Fe  0.0050  0.0027 
Sn  0.0078  0.0045 
Cr  0.0028  0.0071 
Cd  0.0011  0.0019 

Both coils were milled 0.6 mm on both sides to remove oxides formed in the casting and hot rolling operations.

After production of the plates, both were subjected to cold rolling, performed in a four-high mill, imposing a total reduction of 85% through 5 passes, with reductions by pass ranging between 34 and 22%. Annealing was carried out in a bell static furnace with gas heating at 530 °C/12 h. The final rolling was conducted in a four-high mill with automatic gage control system and two passes with reductions of 23 and 21%, resulting in 40% total reduction. The resulting sheets had a final thickness of 1.1 mm. Final annealing was carried out in a second bell furnace, with electric heating, at 450 °C/11 h. Surface cleaning was performed by dipping the plate/sheet in a solution containing 13% H2SO4 in water after annealing.

2.2Materials characterization

Grain size analysis was performed at all stages of the sheet metal manufacturing process in which the materials were in the annealed state. Samples of 20 × 20 mm with the thickness of the product were extracted, ground in SiC paper down to mesh # 1200, and then electrolytically polished. Electrolytic polishing was carried out on a Struers Lectoprol-5 equipment, using a solution of 40% H3PO4 in water as electrolyte, at 1.7 V for a period of 7 min.

Metallographic samples were etched in Klemm II (saturated aqueous sodium thiosulfate solution – 90 g in 200 ml distilled water and 6 g potassium metabisulphite) reagent for 1–3 min. The samples were then analyzed by optical microscopy.

Grain size measurement was performed using the photos and ImageJ® software, marking the perimeters of 150 grains in the initial plate (produced by CC), since this sample had the largest detected grain size, and 450 grains for the remaining stages of processing. From the perimeters it is possible to obtain the average area of the grains. Average grain size, d, was determined by the equivalent circle diameter method, based on the average grain area, A[16]:

Fig. 1 shows the microstructures obtained for both sheets after the final recrystallization step. This shows that recrystallization was total in both materials.

Fig. 1.

Microstructures of the sheets produced by (a) continuous casting and (b) semi-continuous casting in the final recrystallized state. Klemm II etching (optical microscope).

2.3Texture analysis

Texture was measured by X-ray diffraction in a Rigaku DMAX Rint 2000 goniometer, belonging to the Instituto de Pesquisas Energéticas e Nucleares/Comissão Nacional de Energia Nuclear (IPEN/CNEN-SP), operating with a chromium tube (Cr Kα radiation wavelength, λ = 0.229092 nm). Three pole figures corresponding to planes (111), (200), (220) where acquired in 20 × 20 mm mm samples used for metallography, and were converted into orientation distribution functions (ODFs) using the Texture Analysis Program (PAT), developed by Galego [17]. The original plate/sheet rolling direction was used as reference for pole figure measurement and ODFs.

2.4Testing2.4.1Tensile tests

Five strips of the final sheets were extracted from three orientations: 0°, 45° and 90° relative to the rolling direction (RD). Tensile samples were produced according to ASTM E8/E8M [18] using a standard milling cutter. Tests were conducted in an electromechanical universal testing machine (Tinius Olsen, model H25 KL) equipped with a calibrated 250,000 N load cell, with a constant displacement rate of 15 mm min−1.

Yield strength (0.2% offset), σy, ultimate tensile strength, UTS, fracture elongation (referring to a 50 mm length), εf, and the Lankford coefficients, rα, were determined for all orientations. In addition data from 0° orientation was used to quantify the true stress and true strains and hence, to obtain the parameters of the Hollomon equation for the material:

where σ and ε represent true stress and true strain, respectively, K is a pre-factor and n is the strain hardening exponent.

2.4.2FLD determination (CEC procedure)

The CEC procedure [9] specifies four sample geometries, as depicted in Fig. 2[19]. The samples were cut from the sheets with orientation 0° using wire electrical discharge machining, due to the complexity of the shapes and the desired surface finishing in the cut.

Fig. 2.

Tensile sample geometries used in the CEC procedure.


The specimens were silk screen printed with a grid of circles with inner diameter of 2 mm and outer diameter of 2.5 mm, as specified by the ISO 12004-2:2008 [20] standard. Measuring limit strains with a grid of circles introduce some imprecision, since the size of the circle defines the minimum spacial resolution of the strain gradients. In this regard, using optical techniques like Digital Image Correlation [21] would be preferable. The strain gradients observed in the samples, however, were considerably flat, justifying the adoption of this simplified procedure.

The grooving regions of the specimens were subjected to the measurement of the internal diameters of the circles before the tests were performed. Measurements were made on the Olympus stereo microscope, since this machine could carry out measurements on all the specimens before and after the tests. The samples were then tested on the Tinius Olsen traction machine, model H25 KL, with a fixed displacement speed of 15 mm min−1. The critical strains were evaluated using a simplified procedure. Instead of the interpolation method, prescribed by ISO 12004-2:2008 [20], the circles adjacent to the observed crack were measured. This is possible due to the flat strain gradient observed in the samples. In fact, measuring circles around 5 mm away from the fracture line resulted in strains which are only 1.2% smaller, compared with the ones obtained in the simplified procedure. This shows that the difference between these strains and the ones which would be obtained by extrapolation is even smaller, since the strain gradient is presumably symmetric along the length of the specimen, with a maximum located at the fracture line.

Since the samples prescribed by the CEC procedure allow to investigate only the deep drawing region of the FLD (ε2 ≤ 0), the Erichsen test was used investigate the stretching side to complete the FLD. Ten 90 × 90 mm samples were silk screen printed with a grid of 2 mm circles, by the electrochemical method. The specimens were tested on with a 10 kN blank holding force. The 33 mm diameter punch used in the test was lubricated with Vaseline.

2.4.3FLD determination (Nakazima)

The specimens were prepared for the Nakazima test in accordance with standard ISO 12004-2:2008 [20], but scaled down by 60% following the procedure suggested by Schwindt et al. [19]. The geometry of the samples is schematically shown in Fig. 3.

Fig. 3.

Schematic representation of the samples used for the Nakazima test.


The specimens were produced using the widths (W): 20, 40, 50, 55, 60, 70 and 80 mm [19]. Samples were spark erosion machined and the circles were silk screen printed by the electrochemical corrosion process. Tests were carried out on a electromechanical universal testing machine (Kratos K10000) working with a calibrated 100000 N load cell and a displacement speed of 15 mm min−1. The samples were lubricated with Molykote grease®, and the used tooling was scaled down by 60% in accordance with the reduction in the sample geometry. We point out that using a different lubricant may affect the comparison with the results obtained in the Nakazima test. This change, however, was unavoidable and the results obtained in the present work suggest that this effect is small.

3Results3.1Grain size evolution

The grain size distributions for all samples in annealed state have been determined, and resulted in well behaved log-normal distribution functions in all cases. In the present work only average and standard deviation will be shown, but the interested reader is referred to the work of Almeida [22] for more details on the grain size distributions.

Table 2 shows the values obtained for all samples. Condition HR refers to the plate obtained at the end of the continuous casting for the CC plate and to the plate obtained after hot rolling for the SCC plate. Condition A1 refers to the plate obtained after the intermediate annealing and condition A2 refers to the finished sheet. Notice that the final grain size of the CC is smaller than the one observed for the SCC plate under apparently the same deformation schedule. This is justified by the different initial grain sizes obtained in the casting processes. The reader is referred to the work of Almeida [22] for a thorough analysis of the microstructure evolution during plate processing.

Table 2.

Average grain sizes and corresponding standard deviations (in parenthesis) of the samples in annealed condition.

Sheet  HR  A1  A2 
CC  600 (494) μm  15 (6) μm  8 (3) μm 
SCC  17 (6) μm  28 (15) μm  15 (5) μm 

HR, “as rolled”; A1, after intermediate annealing; A2, finished sheet.

The grain size of the “as rolled” CC sample is very large, as expected, since this corresponds to an “as cast” condition. During processing, however, the grain distribution of the CC samples become finer and less disperse in comparison with the SCC samples. This situation is inherited by the finished sheets and the grain size of the SCC sheet is about twice as large as the one of the CC sheet (see Fig. 1).

More detailed information on microsctructure evolution on processing in the two processing routes can be found in Ref. [22].

3.2Tensile tests

Table 3 shows the results of the tensile tests for the finished sheets obtained with both processing methods in the three orientations. The results show small differences in strength, which are easily attributable to the finer grain size of the CC sheet.

Table 3.

Results of the tensile tests of the finished sheets produced by the CC and SCC processes. Average values of five samples for each case, standard deviation is shown in parenthesis.

Process  Orientation [oσ y [MPa]  UTS [MPa]  ε f [%]  rα 
CC  120 (4)  298 (1)  40.1 (0.7)  0.96 (0.06) 
  45  116 (3)  279 (2)  42.3 (2.3)  0.96 (0.04) 
  90  120 (1)  281 (2)  39.4 (1.4)  1.06 (0.06) 
SCC  105 (1)  272 (1)  42.4 (1.4)  0.97 (0.04) 
  45  109 (5)  273 (0.5)  43.1 (0.8)  0.93 (0.02) 
  90  113 (5)  270 (1)  41.1 (1.1)  0.92 (0.08) 

Based on the measured Lankford coefficients, it is possible to calculate the normal anisotropy, rn, and the planar anisotropy, △r, [1,4] resulting respectively in 0.99 and 0.03 for the CC sheet and 0.94 and 0.01 for the SCC sheet.

The parameters of Hollomon's constitutive equation (Eq. 2) where determined for the 0° orientation, resulting in K = 590 ± 7 MPa and n = 0.439 ± 0.011 for the CC sheet and K = 558 ± 18 MPa and n = 0.431 ± 0.029 for the SCC sheet (average values of linear regression parameters for the logarithmic fit of five samples each in the range of true strains between 0.01 and 0.56, individual fits showed r2 > 0.95).

The results suggest that formability of both sheets is equivalent. Normal and planar anisotropies suggest a slightly better behavior for the SCC sheet, but the analysis of the primary data in Table 3 shows that these differences are of the same order as the error in the measure. Also, the results for the Hollomon parameters are consistent with the smaller grain size in the CC sheet, but the differences are very small and, particularly, the strian hardening exponents are indistinguishable.

3.3FLD determination

The forming limit diagrams obtained using the methodology proposed by the CEC are shown in Fig. 4. The points shown in this diagram refer to single circle measurements, and it is clear that some “outliers” are present. On average, however, the curves represent well the critical strains for fracture in a conservative manner. The lines represent constrained third degree polynomial fits, on the form:

Fig. 4.

FLDs determined using the CEC procedure.


This expression is constrained to present a local minimum at ε2 = 0, which corresponds to FLD0. The parameters of these fits are shown in Table 4.

Table 4.

Parameters of the polynomial fits shown in Figs. 4 and 5. The asymptotic standard error of the parameters is shown in parenthesis and the sum of square of residuals for the fit X2, refers to the number of degrees of freedom, f.

Process  a3  a2  FLD0  X2  f 
CC  3.66 (1.99)  5.01 (0.64)  0.206(0.012)  0.742  108 
SCC  1.05 (1.04)  3.20 (0.4)  0.217 (0.009)  0.427  106 
CC  −2.19 (2.16)  2.26 (0.47)  0.245 (0.007)  0.067  52 
SCC  −8.99 (3.66)  2.56 (0.90)  0.268 (0.012)  0.077  35 

The constrained cubic polynomial function was chosen because it presents up to two extrema, being one the minimum located at ε2 = 0. The second extreme, for the present data, is a maximum located in positive values of ε2. Using a quartic polynomial potentially introduces another extreme. Tests made with the data showed that this extreme is another maximum located in negative ε2, which results in FLCs with unexpected form, without any significant reduction in the X2 values. A parabolic function, on the other hand, would be symmetrically centered at the ε2 axis, while the data show marked asymmetry.

The curves show a large dispersion, but it is evident that no large difference exist between the sheets produced by the CC and SCC processing routes. The value of FLD0 is slightly smaller for the CC sheet, and this would indicate that the performance of the SCC is slightly better, but the difference in the parameters is not statistically significant under 95% confidence. The maximum load observed in the tests with the CEC samples was recorded and virtually no difference is observed for the samples produced with the CC and the SCC sheets. This points out to an equivalent stress state at the onset of necking in the plane-strain state. The (eventual) better performance of the SCC sheet cannot be attributed, therefore, to a change in the stress path during testing and must be, therefore, intrinsic to the sheet.

Fig. 5 shows the FLD obtained using the Nakazima methodology, which result in similar trends, with smaller dispersion. Comparing with the CEC methodology, it is possible to observe that the strain paths are more restrained. The results of the fits (parameters in Table 4) suggest a somewhat better performance of the SCC sheet in the deep drawing region of the curve. This can be better appreciated in Fig. 6, which shows all superposed data. The value of FLD0 for the CC sheet is smaller than the one for the SCC sheet (again, the difference is not statistically significant under 95% confidence), and this would indicate that the formability of the SCC is slightly better than that of the CC sheet. The results, however, would also be interpreted as both sheets having equivalent formabilities, as it was the case of the FLDs obtained using the CEC procedure.

Fig. 5.

FLDs determined using the Nakazima procedure.

Fig. 6.

FLDs determined by both procedures, superposed for comparison.


Comparing both procedures (Fig. 6), it is possible to observe that the Nakazima method results in consistently larger FLD0 values, which is in line with the effect of out-of-plane deformation and of friction on the FLDs, as reported in the literature (e.g. Xavier et al. [23], and references therein).


The obtained FLDs, therefore, suggest an equivalent formability of the sheets produced using the two processing routes, with a slight advantage for the SCC sheet. This is not expected, since the CC sheet has a smaller grain size and, hence, should present a better formability. Some additional factor, therefore, is enhancing the formability of the SCC sheet. Texture is one of the possible candidates.

The sheets used for the FLD determination are found in the finished state (recrystallized) and it is this texture which controls formability, at least in the initial stages [23]. The recrystallization texture, however, is generated from the cold rolled texture, and the analysis must start with it.

Fig. 7 shows the orientation distribution functions (ODFs) of the cold rolled sheets produced using the CC process route (Fig. 7a) and the SCC process route (Fig. 7b). In both cases it is possible to identify two major contributions: a strong contribution (above 9 times random) around φ1 = 45°, φ = 35°, φ2 = 0°, (also visible close to φ1 = 50°, φ = 90° and φ2 = 45°), which corresponds to the (011)[211] orientation, also known as “Brass” orientation, and another close to φ1 = 90°, φ = 27°, φ2 = 45°, which corresponds to orientation close to(112)[111¯], known as “Copper” or “Dillamore” orientation [24]. This last contributions shows the major difference between the two sheets. The SCC sheet possesses a strong (above 9 times random) “Copper” contribution, while the CC sheet possesses a weaker contribution (around 6 times random). The formation of these textures is a consequence of the previous processing, and, likely, of the casting texture, but a full characterization of texture evolution on processing of these materials is out of scope of the present manuscript.

Fig. 7.

ODFs of the cold rolled sheets (a) CC processing route and (b) SCC processing route.


Fig. 8 shows the ODFs of the annealed sheets. The main contribution in these cases is found in φ1 = 0°, φ = ˜30–40°, φ2 = 0° (with a symmetric contribution located at φ = ˜ 50–60°), which corresponds to orientations between (102)[010] and (203)[010] also known as “Cube RD” [25]. Recrystallization textures in FCC metals have been traced back from the components of the rolling texture. Xiao et al. [25] showed that the “Brass” component of the deformed brass texture generates a component close to φ1 = 80°, φ = 31°, φ2 = 35° the authors named “Brass-R”, while Lee and Han [26] identified the origin of the cube and rotated cube components in the “Copper” component of the rolling texture. In the case of the present sheets, the main difference is in the extension of the cube RD texture along φ1, forming a fiber.

Fig. 8.

ODFs of the finished sheets (a) CC processing route and (b) SCC processing route.


The intensities along the φ = 35°, φ2 = 0° are shown in Fig. 9. It is possible to identify some preferred orientations along this fiber. The CC sheet presents more uniform intensities, while the SCC sheet shows discrete contributions along the φ1 axis (and some orientations are absent).

Fig. 9.

Recrystallization (cube RD) fiber in the finished sheets.


FCC metals deform by the (111)[11¯0] slip system. Plane (203) is intersected by four planes of the {111} family. Two of these planes present an intersection angle close to 37°, while the two other intersect the (203) plane at about 80°. Obviously, only the first two planes are well oriented referring to the maximum shear stress in the plane of the sheet. Each of these slip planes contains at least one <110> direction well oriented for dislocation slip for the preferred orientations contained in the recrystallization fiber. Therefore it is concluded that the recrystallization fiber present in the finished sheets is ideal for enhanced formability, in the same manner as a γ fiber is beneficial for the formability of a steel sheet [23,27].

The difference between the two processing routes would be the discrete nature of the recrystallization fiber, which allows to concentrate the grains in orientations with high Schmid factors, enhancing formability. Naturally, grains in a polycrystal interact and the present analysis is too simplistic, however, it is sufficient to justify the equivalent formabilities of both sheets. This discrete nature of the fiber in the SCC sheet would be beneficial because these low index grain orientations present all well oriented slip directions. The continuous nature of the fiber in the CC sheet would present also grains which are not so well oriented. It is possible, therefore, that this discrete nature of the fiber contributes to a better strain distribution across the microstructure during plastic straining.


The present work investigated the formability of two 1.1 mm thick sheets of 90/10 brass (alloy UNS C22000) producing two processing routes, continuous casting, CC, and semi-continuous casting, SCC, by determining their forming-limit diagrams (FLD) using two different procedures.

The two processing routes start with quite different microstructures, but this converges to a recrystallized structure consisting of equiaxed homogeneous grains in the final product. Average grain size of the CC sheet is 8 μm, while that of the SCC sheet is 15 μm. Mechanical properties are consistent with these variations, with slightly higher yield and ultimate tensile strengths observed for the continuous casting sheet. The comparison of the FLDs obtained for the two sheets, however, suggests that their formability is equivalent, irrespective of the determination procedure used for FLD determination.

Concerning the FLD determination it was observed that the CEC procedure, using tensile samples in the deep-drawing region, allows to probe a wider critical strain space compared with the Nakazima procedure, adopted by the ISO 12004:2008 standard [20]. The values of critical strain obtained for the CEC procedure are also more conservative, in line with the expected effects that out-of-plane deformation and punch/sample friction would have upon the FLD in the samples used in the Nakazima test. FLD0 values obtained for both sheets were 0.205 ± 0.012 for the CC sheet and 0.217 ± 0.009 for the SCC sheet, as determined by the CEC procedure, and 0.246 ± 0.007 for the CC sheet and 0.268 ± 0.012 for the SCC sheet. This suggests a slightly better formability performance for the SCC sheet, even with larger grain sizes.

Texture was analyzed in the finished sheets (recrystallized) and it was observed that both sheets present a strong (around 6 times random) cube RD fiber, (203)[010], which extends toward (203)[3¯02] in Euler space. The difference is that this fiber is more homogeneous in the CC sheet, while in the SCC sheet, it presents discrete low index orientations. The difference in the recrystallization textures is traced back to the texture in the cold rolled sheets that present both the “brass” orientation and the “copper” orientation, but with lower intensity for the later in the CC sample. It is believed that the discrete nature of the cube RD fiber in the SCC sheet leads to better plastic behavior in the plane of the sheet by maximizing the grains with large Schmid factors and, therefore, providing a more homogeneous strains distribution in the microstructure. This counteracts the effect of the larger grain size, resulting in equivalent formability for both sheets.

Conflicts of interest

The present work was developed as part of Mr. Almeida’s Master in Science thesis at the Escola Politécnica da Universidade de São Paulo, when he was employed as Engineer at Paranapanema SA. This relationship, however, does not constitute a conflict of interests, since no judgement of value is made on the materials here investigated.


The authors thank Dr. Nelson B. Lima (Instituto de Pesquisas Energéticas e Nucleares, CNEN-SP, São Paulo, Brazil) for assistance with the texture analysis and to Mr. Rubens Beserra Carvalho (Escola Politécnica da Universidade de São Paulo, São Paulo, Brazil) for assistance with the Nakazima tests.

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