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of the forming operation unfeasible [1]. Therefore .... (1). Tensile strain hardening exponent (n-value) is calculated ... according to the ASME Y14.36M standard.

Proceedings of ASME 2010 International Design Engineering Technical Conference & Computers and Information in Engineering Conference IDETC/CIE 2010 August 15-18, 2010, Montreal, Quebec, Canada


Mohamadreza Nourani* Materials Research and Engineering Dep. Supplying Automotive Parts Company Tehran, 1389911498 Iran [email protected] Hamid Khorsand Faculty of Mechanical Engineering K. N. Toosi University of Technology Tehran, 19395-1999 Iran [email protected]


Hossein Aliverdilu Faculty of Mechanical Engineering K. N. Toosi University of Technology Tehran, 19395-1999 Iran [email protected] Ali Shokuhfar Faculty of Mechanical Engineering K. N. Toosi University of Technology Tehran, 19395-1999 Iran [email protected]

Hossein Monajati Zadeh Faculty of Material Engineering Islamic Azad University,Najafabad Branch Najafabad, Isfahan, 517 Iran [email protected] Abbas S Milani School of Engineering University of British Columbia- Okanagan Kelowna, BC, V1V 1V7 Canada [email protected]

Address all correspondence to this author (currently a PhD Candidate of Mechanical Engineering at UBC Okanagan)


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ABSTRACT Steel sheet metals are widely used in different industries due to their high strength, good weldability, availability, moderate cost, and the ability to form to complex 3D parts. The study of the formability of sheet metals is often done by means of Forming Limit Diagram (FLD) which presents the major and minor engineering strain thresholds under different deformation states. In this article, the formability parameters of three different steel sheet metals with the same thickness have been determined by uniaxial tension test and their FLDs have been produced by Hecker method: RRSt14O3, Zinc coated IF steel and uncoated IF steel. Also the materials’ formability during the stamping process of a car door inner panel has been investigated as a case study. Among the tested materials to form the part, the uniaxial tension results showed that the formability parameters of uncoated IF steel was higher than the coated IF steel and the parameters of RRSt14O3 sheet metal was the lowest. The FLD of coated IF steel sheet was the highest. Differences among the formability parameters in uniaxial tension, the FLDs, and the stamping behavior of the part with different steel sheet metals have been explained by their surface roughnesses and the friction coefficients that affect the material flow during the FLD test as well as the stamping process.

INTRODUCTION Steel sheets are widely used in the automotive industry. Their successful forming depends on formability of the steel, part and tool design, surface conditions of the sheet, selection and application of a lubricant, and the speed of the press. To achieve the desired shape in a part, the steel sheet must be permanently deformed. Even for a rather simple part, the anisotropy of the steel sheet, variations in the sheet thickness, and local irregularities in the tooling can make exact analysis of the forming operation unfeasible [1]. Therefore, understanding the formability of sheet metals via experimentation is essential for the successful production of stamped parts. In forming a sheet into a specific shape, since the design variables are fixed, the process variables have the greatest influence on the overall formability and are usually assessed during die tryouts. However, in a shop floor, process variables can be optimized to yield maximum production rates at a minimum cost. The maximum exploitation of material ductility is greatly dependent on the material properties. Due to the complex interaction mechanisms of design variables, which in turn affect the formability of sheet metals, there is no single parameter which can comprehensively describe the forming characteristics of a material under various conditions in the actual press work [2]. Forming limits are determined by analyzing strain distributions obtained from 0.2 to 0.05-inch grids imprinted on blanks; failure generally occurs in the region of stretchforming where all strains are positive (tensile) in the plane of the sheet. Experimental results can be useful to find predictable critical strain levels beyond which failure is anticipated. The most effective method of increasing stretching limits is the development of more nearly uniform


strain distribution. Factors controlling this distribution are the material strain hardening characteristics, die design, etc. During the forming process if the strain in a region of the part is above the Forming Limit Diagram (FLD), the localization with necking and fracture often appears. FLD can be used to improve the forming process and reduce the drawing steps. It is worth noting that the concept of FLD was first introduced by Keeler in 1964 [3]. In1967, Marciniak et al. determined the limiting strains in experiments on biaxial stretch-forming of a grooved sheet metal and compared them with theoretical results of an anisotropic plasticity theory [4]. In 1968, Goodwin plotted FLD for a combined stretch-forming and drawing of sheet metals with different width-to-thickness ratios [5]. Generally there are theoretical and experimental methods to generate FLDs. Examples of the theoretical methods are proposed by Marciniak-Kuczynski, Swift-Hill [6-7], Sing-Rao [8-9], and NADDRG (North American Deep Drawing Research Group) [10]. Experimental methods are more extensively used to determine FLDs. Occasionally, from experimental methods on in-plane (Marciniak [4]) and out-of- plane (Nakazima [11]) forming states, comparable results are concluded. The above mentioned experimental methods by Marciniak and Nakazima have been based on forming different samples with the same lengths and different widths and some of the samples have had two symmetric semi circle notches with different radii on the length. The difference between samples of the two methods is the shape of the punch which is flat in Marciniak’s method and a carrier blank is used to provide uniform straining in the pole region of the sample without a contact/friction with the punch; the punch in Nakazima’s method is hemispherical. The latter is also called LDH method (Limiting Dome Height). In the current study, the FLDs for three steel sheet metals with a thickness of 0.7 mm are determined using Hecker’s method [12]. The method is based on using a hemispherical punch to draw rectangular samples with the common length and varying widths without any circle notches. The chosen materials for the study are: RRSt14O3, Zinc coated IF steel and uncoated IF steel. The materials’ formabilities in a car door inner panel are compared and their differences are discussed.

EXPERIMENTAL PROCEDURE Chemical Composition Steel sheet metals used in this study were plain Carbon Deep Drawing Quality RRSt14O3, Interstitial Free Extra Deep Drawing Quality (EDDQ) with no coating, and Zn coated IF EDDQ steels. The chemical compositions of the samples were determined by quantometery. Mechanical Properties Tensile tests were carried out using specimens machined as per ASTM standard E8M specification. The specimens were tested along three directions, with the tensile axis being parallel (0o), diagonal (45 o), and perpendicular (90 o) to the

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rolling direction of the sheet, on a 1000 kN capacity Instron servo-hydraulic testing machine. The standard tensile properties, namely, 0.2% yield stress (YS), ultimate tensile stress (UTS), and elongation percentage (El%), were determined from the load–elongation data. Three samples were tested in each of the three directions and average values were reported to account for the data scatter. Vickers hardness of each material was also measured by averaging the hardness of three points on each specimen.

By loading the punch, the circular grids started becoming ellipse. The loading was stopped when a neck is formed in the samples, and a transparent Mayler tape was used to directly measure the major and minor engineering strains in the deformed circles (Fig 2).

Formability Parameters Some important parameters which indicates the formability of a sheet metal are the tensile strain hardening exponent, plastic strain ratio, and their interaction (i.e., n, , ), as well as the planar anisotropy (∆r) which is calculated according to Equation 1. ∆r= ½(r0-2r45+r90)


Tensile strain hardening exponent (n-value) is calculated by a regression of the Hollomon equation σ=kεn in each direction; plastic strain ratio (r-value) in each direction is the ratio of the width strain to the thickness strain during deformation. The above indices can also indicate the angel between the rolling direction and the sample direction. The calculations of n-value and r-value were done according to the EN 10130 standard. Average plastic strain ratio or normal anisotropy was calculated according to Equation 2. r=1/4(r0+2r45+r90)


Forming Limit Diagrams (FLDs) A common and fast method to generate an FLD is the Hecker method [12]. Test procedure for plotting FLDs was conducted according to ASTM E2218. Rectangular strips with the width of 120 mm which was parallel to rolling direction were cut to various widths ranging from 12 mm up to 120 mm in increments of 12 mm. All samples were prepared for Circle Grid Analysis (CGA) by electrochemical etching with a stencil pattern of 2.5 mm diameter circles. An Erichsen testing machine with a ball punch diameter of 75 mm was used as shown in Fig 1.

FIG 2. MAYLER TAPE SCALE Case Study: Strain Distribution in High Failure Risk Regions of a Car Door Inner Panel In order to measure the strain distribution in a car door inner panel, which was successfully produced by the coated IF steel and failed to produce by RRSt14O3 and uncoated IF steel of the same thickness (0.7 mm), the following procedure was used. The strain distribution in the part was measured in the regions of high failure risk by creating Circle Grid Analysis (CGA) via electrochemical etching with a stencil pattern of 2.5 mm diameter circles on the related regions before stamping. Then the gridded steel sheet blanks were used to produce the part and the related strains were measured by Mayler’s tape. Friction Coefficient and Surface Roughness As deep surface scratches were seen after the production As deep surface scratches were seen after the production of the part with uncoated IF steel and RRSt14O3, the coefficient of kinetic friction and surface roughness of the sheets were measured. Friction coefficient was measured using a ball on flat sliding wear according to ASTM G133. The direction of the relative motion between sliding surfaces reverses in a periodic fashion such that the sliding occurs back and forth and in a straight line. Surface roughness parameters (Ra and Rz) were measured according to the ASME Y14.36M standard.

RESULTS AND DISCUSSION Chemical Composition The chemical compositions of the chosen steel sheet metals are given in Table 1. The amount of Carbon in RRSt14O3, uncoated IF, and coated IF steels are 0.023, 0.002, and 0.010 Wt%, respectively. Higher carbon content leads to a decrease in the formability parameter, r-value. This is attributed to an increase in the amount of cementite and a decrease in the grain size. High r-values (>1.6) have been observed in case of Extra Deep Drawing Quality (EDDQ) steel sheets containing carbon less than 0.05% [13]. In this study, the uncoated IF steel sheet with 0.002 Wt% of Carbon had the highest r-value (1.907).



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TABLE 1. CHEMICAL COMPOSITION OF THE STEEL SHEET METALS IN WT% Steel/Element RRSt14O3 Uncoated IF Coated IF Steel/Element RRSt14O3 Uncoated IF Coated IF

C 0.023 0.002 0.010 W 0.001

Si 0.005 0.004 0.004 Ti 0.048 0.048

S 0.009 0.007 0.008 As 0.001 0.002 0.003

P 0.014 0.014 0.016 Sn 0.004 0.001

Mn 0.173 0.060 0.153 Co 0.005 0.002 0.003

Mizui and Okamoto [14] studied the effect of Mn content (in the range 0.02–0.14%) on deep drawability of continuous annealed Al-killed sheet steels. They concluded that the rvalue in the rolling direction exhibited a maximum value at a medium Mn content, which increases with an increase in the coiling temperature. They attributed this observation to the changes in the distribution of Mn/S inclusion and the precipitation of Al/N. It is to note that for the materials tested, there is different Mn content which shows different metallurgical road maps in rolling process of their production. Also, there are some Tungsten, Molybdenum, and Zinc in the coated IF steel sheets and there are some Titanium in both coated and uncoated IF steel sheets. Generally there are lower alloying elements in the uncoated IF steel and thus a better formability should be expected from this material. Dasarathy and Hudd [15] indicated that the presence of aluminum up to 0.08% has no adverse effect on the mechanical properties, which was in fact the case for the tested materials.

Ni 0.024 0.006 0.016 Al 0.058 0.047 0.040

Cr 0.007 0.009 0.028 Sb 0.001 0.001

Mo 0.004 Zn 0.001 0.001 0.051

V 0.002 0.002 0.002 Fe Balance Balance Balance

Cu 0.013 0.007 0.016

TABLE 2. MECHANICAL PROPERTIES OF THE STEEL SHEET METALS Specimen Steel sheet axis with YS UTS El Hardness materials Rolling (MPa) (MPa) (%) (Vickers) direction 0 148 279 41 RRSt14O3 45 155 286 43 90 155 276 47 Average 152.67 280.3 43.67 91.5 0 158 296 44 Uncoated 45 171 303 43 IF 90 169 298 43 Average 166 299 43.3 92.1 0 165 300 45 Coated IF 45 185 313 44 90 174 305 45 Average 174.67 306 44.67 93.3

Mechanical Properties The room-temperature mechanical properties of the three steel sheet metals, determined by a tensile testing with the specimen axis oriented at 0, 45, and 90 degrees to the rolling direction, are reported in Table 2. In all cases, the UTS and YS values were higher at 45 degree to the rolling direction than in the direction parallel or perpendicular to the rolling direction. The average of three points for the measurement of hardness (in Vickers scale) for each of the sheet metals is also given in Table 2. The coated IF steel sheet showed the highest average YS, UTS, El%, and hardness. Formability Parameters The conventional indicators of formability, viz, n , r, nr and ∆r are summarized in Table 3. The strain hardening exponent n is the highest for the uncoated IF steel and the lowest for RRSt14O3 steel sheets. The product , which is an indicative of overall press performance, is also the highest for the uncoated IF steel and the lowest for the RRSt14O3 steel sheet. However, this factor has no physical significance and it is merely a numerical index used as a rough measure of formability [16]. The planar anisotropy value, which gives an estimate of the type of earing that occurs during the drawing of sheet metals, is rather high for the RRSt14O3 steel sheet, making it most susceptible to the earing problem among the tested materials.


TABLE 3. FORMABILITY PARAMETERS Steel sheet materials RRSt14O3 Uncoated IF Coated IF


























A sheet with a high  value generally possesses a high ∆r value. It is also to note that the ideal situation of a high , and a low ∆r is difficult to achieve under normal processing conditions, as was the case for the uncoated IF steel sheet. It has already been emphasized that the stretchability of sheet metals is strongly influenced by the average value of the strain hardening exponent (n-value) and the drawability of the sheet metal is strongly influenced by the value of average strain ratio (). Table 4 gives the n value for the three steel sheets as determined by two methods (regression and Eq. (3)). The values obtained by equating n to the true uniform strain (Εu), calculated using empirical relation for low carbon mild steels in Equation (3) [17], agreed well with the values obtained from the regression of the Hollomon equation σ=kεn. for the coated IF steel sheets. Εu= 0.28-0.2[C]-0.25[Mn]-0.44[Si]-0.39[Sn]-1.2[N] (3)

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According to the aforementioned results, the uncoated IF steel has the best drawability (r-value) and stretchability (nvalue) properties (i.e., formability) among the tested samples.

TABLE 4. STRAIN HARDENING EXPONENT () FOR THE THREE STEEL SHEETS USING TWO METHODS Steel sheet n from regression n from Equation (3) materials RRSt14O3 0.231 0.228 Uncoated IF 0.242 0.263 Coated IF



The Friction Coefficient and Surface Roughness The kinetic friction coefficient results found by Ball on Flat Sliding Wear test are given in Fig. 3. At the start of the test the value of friction coefficient is equal to zero in the three sheet metals which is due to the existence of surface roughness and should be removed before the moving pin reaches the underneath layer; then the real value of friction coefficient is revealed. In the coated IF steel sheet, the surface roughness is removed after about 4.5m while for uncoated steel sheet it is about 5.5m and for RRSt14O3 about 7m. Hence, the surface roughness of the coated IF steel sheet is the lowest and it is the highest for the RRSt14O3 steel sheet. Also the value of kinetic friction coefficient for the coated IF and uncoated IF steel sheet is approximately equal to 0.1 and 0.3, respectively. This value for RRSt14O3 is between 0.1 and 0.2. The friction coefficient and Surface roughness parameters, Ra (arithmetic average) and Rz (average distance between the highest peak and lowest valley in each sampling length), for steel sheets are summarized in Table 5. It is clear that RRSt14O3 has the highest surface roughness and the coated IF has had the lowest surface roughness among the steel sheets.

TABLE 5. FRICTION COEFFICIENT AND SURFACE ROUGHNESS PARAMETERS Steel sheet µk Ra (µm) Rz (µm) materials 0.1 to 0.2 RRSt14O3 1.23 5.82 Uncoated IF




Coated IF






FLDs, evaluated experimentally for the Al-killed coated EDDQ, uncoated EDDQ, and DDQ steel sheets following Hecker’s method, are shown in Fig. 4.

When plotting the FLDs, the fitting procedure was divided into two sides, the left and the right side. Because the left side is mostly a straight line and the right is not, fitting all the data at once would not be a good representation of the FLD [18]. In Fig 3, when ei =0 (plain strain), FLD0 is the highest for the uncoated IF steel sheet and is the lowest for RRSt14O3. This agrees well with Equation (4).


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Forming Limit Diagrams (FLDs)

. .   . 



Although the uncoated IF steel has the best formability parameters in the uniaxial tension tests, overall it does not have the highest FLC over the regions of FLDs. It is because the chosen LDH test is complicated by the effects of friction, bending strain, and normal pressure on the sheet samples, and thus it could yield higher forming limits than those of the Marciniak test method. As mentioned before, the uncoated IF steel has a higher friction coefficient than the coated IF steel, which causes a decrease of drawability and stretchability properties in the FLD of the uncoated IF steel when compated to the coated one. This is in a good agreement with the previous findings in the study [19] with regards to the effect of friction on FLDs. Since the in-plane Marciniak test does not include friction, bending strain, and normal pressure on the sheet samples, test results by the out-of-plane LDH test method are higher than results of Marciniak’s test method This result supports existing arguments in the literature claiming that while the LDH test results may provide better correlation with actual panel stamping trials, the Marciniak test results can provide more accurate depiction of material behavior (useful for comparisons to finite element simulations) [20]. Strain Distribution in a Car Door Inner Panel Next, to evaluate the formability of the three steel sheets, they were used to produce an actual car door inner panel. Only the coated IF steel resulted in successful parts during the production. The uncoated IF and RRSt14O3 steel sheets caused five different high failure risk regions which is illustrated in Fig 5.

FIG 6. STRAINS DISTRIBUTION IN FIVE REGIONS WITH HIGH FAILURE RISK OF TEARING According to Fig 6, strains in the region 3 are in the failure region of FLDs of RRSt14O3 and uncoated IF steel sheets, so a safe part cannot be produced by these steel sheets. The failure exists in other regions than region 3 when the part is produced by RRSt14O3 and uncoated IF steel sheets, while there is no interfere between the strain distribution and FLDs. The reason is that a higher friction coefficient in these two materials with stamping die exists (as compared to the coated IF steel) and it moves their FLCs more downward in the real forming conditions. This idea is verified by considering deep scratches in 5 regions when uncoated IF or St1403 steel sheets are used (stick friction) compared to a smooth final surface when the coated IF steel sheets were used (slide friction). The idea also agrees with the measured friction coefficients and surface roughnesses of the aforementioned steel sheets in Table 5, as well as with the severe upward displacement of strain distribution in the region 3 when using uncoated IF and RRSt14O3 steel sheets in Fig 7.

FIG 5. THE FIVE REGIONS WITH HIGH FAILURE RISK OF TEARING The strain distribution points in the five regions with high failure risk of tearing, measured for RRS14O3, uncoated IF, and coated IF steel sheets are given in Fig 6 (for example, plotted points as strains in region 1 are strains created after production of the part with the three steel sheets in region 1), and the strain distribution points in the region 3 separately for each RRS14O3, uncoated IF, and coated IF steel sheets are illustrated in Fig. 7.



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CONCLUSSION In this article, the formability of three steel sheet metals, RRSt14O3, uncoated IF steel, and coated IF steel, was studied and compared using their formability parameters (, , , and ∆r) and Forming Limit Diagrams (FLDs). Also via a case study the reason for the failure in the production of a car door inner panel using RRSt14O3 and uncoated IF steel sheets with respect to their higher kinematic friction coefficients and surface roughness (as compared to the coated IF steel sheet sample) was explained. The uncoated IF steel sheet demonstrated the highest formability parameters under the uniaxial tension. The formability of a steel sheet is highly related to its material formability parameters like average nand r-values. In addition, the friction coefficient and surface roughness of the steel sheets can directly affect the material FLD. The effect of the steel sheet metals and stamping dieface frictional conditions on the material flow were also studied by measuring strain distribution of high failure risk regions in the door panel. It indicated that the highest increase of major strains is seen when using the RRSt14O3 steel sheet, which has the highest friction coefficient among the tested samples. It would be possible to manufacture the studied part by the RRSt14O3 or uncoated IF steel sheets without high failure risk regions, if the surface friction coefficient between the stamping die and steel sheet metals are decreased or the material flow in stamping die is facilitated in the high failure risk regions by some modification on the stamping die-face interface. As a future work, the suggested modification may be verified using a stamping process simulation and a stamping die tryout in the floor shop.

ACKNOWLEDGMENT The authors would like to thank all the staff at Supplying Automotive Parts Company (SAPCO) and IRAN-KHODRO Company (IKCO) for their support and assistance.

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