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An experimental study on the effect of thinning band on the sheet formability in negative incremental forming
ARTICLE IN PRESS
International Journal of Machine Tools & Manufacture 48 (2008) 1170–1178 www.elsevier.com/locate/ijmactool
Short Communication
An experimental study on the effect of thinning band on the sheet formability in negative incremental forming G. Hussain, N. Hayat, L. Gao College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, 29-Yudao Street, Nanjing, Jiangsu 210016, PR China Received 5 September 2007; received in revised form 21 January 2008; accepted 4 February 2008 Available online 20 February 2008
Abstract In negative incremental forming, a characteristic thinning band occurs on the parts when wall angles approach the maximum obtainable [D. Young, J. Jeswiet, Wall thickness variations in single point incremental forming, Proceedings of the Institute of Mechanical Engineers, Part B, Journal of Engineering Manufacture 218 (2004) 1453–1459]. The effect of this ultra-thin band on the fracture occurrence of part was studied in the current investigation. It was found that the occurrence of a thinning band on the test specimen of a formability test does not mean an effect on the test result. A reduction in the formability due to the occurrence of the thinning band occurs only if the specimen fractures in the flange area. In order to evaluate the real forming limit of a sheet metal, a condition regarding the occurrence of part fracture is proposed. r 2008 Elsevier Ltd. All rights reserved. Keywords: Negative incremental forming; Thinning band; Formability; Part fracture; Real forming limit
1. Introduction Single-point incremental forming (SPIF) is a flexible sheet metal-forming process that is economically promising for low production-run manufacturing. In this process, a small-sized tool moves along a programmed tool path and shapes the part in an incremental fashion. The process is mainly performed by shear deformations, at least in the regions of the work piece where the horizontal radius of the curvature (r, as defined in Fig. 1(a)) is large [1]. The process has two principal variants: (1) positive incremental forming (PIF), and (2) negative incremental forming (NIF) [2]. It has been reported that, in NIF, a characteristic thinning band (see Fig. 1(b)) occurs along the surface of the part when wall angles (y) approach the maximum achievable [3]. Also, the Sine law (t ¼ t0 cos y, where t is the wall thickness, t0 is the blank thickness and y is the wall angle as defined in Fig. 1(b)) can not predict the part thickness in this unexpected band. As can be seen from Corresponding author. Tel.: +86 136 751 61625.
E-mail addresses: [email protected] (G. Hussain), [email protected] (N. Hayat), [email protected] (L. Gao). 0890-6955/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2008.02.003
Fig. 1(b), the part thickness in the band region is smaller than that of the remainder of the part. Therefore, if steeper walls are attempted, fracture will occur at this location prior to reaching the real forming limit of sheet. The effect of the thinning band on the sheet formability has not been investigated, in explicit terms. Moreover, no method to determine the actual forming limit of a sheet metal has been proposed in literature. The present work is an attempt in these directions. The experiments were performed with four different aluminum sheet metals. In order to quantify the formability, it was defined as the maximum wall angle (ymax) without sheet fracture. The current study was carried out by employing the varying wall angle conical frustum (VWACF) test proposed by the authors in [4].
2. Part geometry and mathematical expressions The part geometry employed for the present investigations is shown in Fig. 2(a). An arc of a circle with 115 mm radius (R) was used as a generatrix to generate the surface. This is obvious from the figure that the wall angle continuously increases along the generatrix from point Pi(xi, yi) to Pf(xf, yf), thus inducing a corresponding change
ARTICLE IN PRESS G. Hussain et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1170–1178
Nomenclature
rf
sy su n K d y
h hd
yield strength ultimate tensile strength strain hardening index strength co-efficient percent elongation in tensile test wall/forming angle of a part having constant slope (see Fig. 1(b)) yi wall/forming angle at the initial point Pi(xi, yi) of a part having varying wall angle (see Fig. 2(a)), or the wall angle imposed on the sheet in the beginning of the forming process yf wall/forming angle at the final point Pf(xf, yf) of a part having varying wall angle (see Fig. 2(b)) ymax maximum wall angle that a sheet could endure without fracturing yi(critical) the minimum value of yi on imposing which a thinning band affects the occurrence of part fracture, or the condition hd ¼ hb is met R radius of curvature of generatrix of part having varying wall angle (see Fig. 2(a)) ri curvature radius of the base of a part (see Fig. 2(a))
in the wall thickness (t) of the specimen (see [4] for details). Due to these variations in thickness, a fracture on a point D(xd, yd) could occur whenever the thinning limit is surpassed. The instantaneous wall angle (yp) and the nominal thickness (tp) on an arbitrary point P(xp, yp) can be computed as derived in [4] and presented below y p 1 yi hp yp ¼ cos ¼ cos R R 1
tp ¼ t0 cos y ¼
t0 ðy hp Þ R i
(1)
(2)
Making use of Eq. (2), the nominal thickness strain (e3(p)) on point P(xp, yp)can be calculated as 3ðpÞ ¼ ln
yi hp R
(3)
To obtain its safe value, the wall angle at a point M(xm, ym) situated 1 mm prior to the fracture point D(xd, yd) (see Fig. 2(a)) was regarded as the maximum wall angle1 ymax without sheet fracture.
1 During experiments it was observed that a part could be formed safely if the forming operation was terminated when the tool reached the depth (hd1) mm. Therefore, in case of fracture, the wall angle on the point corresponding to (hd1) can be regarded as the maximum wall angle without sheet fracture (see Fig. 2a).
hb t0 t/tp
*t/*tp
e3(frac) *e3(frac)
De Smax Ft
1171
curvature radius of the bottom of a part (see Fig. 2(a)) design depth of part (see Fig. 2(a)) distance of fracture point, along y-axis, from the part flange (see Fig. 2(a)) distance of the extreme end of the thinning band from the part flange (see Fig. 3(b)) thickness of blank (see Fig. 1(a)) nominal wall thickness of part based on Sine law Eq. (2), or nominal wall thickness at an arbitrary point P(xp, yp) actual wall thickness of part measured with a dial gauge, or actual wall thickness at an arbitrary point P(xp, yp) nominal fracture strain (in thickness direction) based on Eq. (3) actual fracture strain (in thickness direction) based on actual thickness measured at fracture point deviation of actual fracture strain from the nominal one maximum standard deviation forming force imposed by the tool on the sheet prior to its fracturing
3. Process parameters The process of NIF is now well-known to the researcher’s community. Its schematic representation along with the real experimental setup has been shown in a previous paper of the authors [4] and many others. For this reason, the process setup is not presented here. However, some important process parameters used in the experiments are as below: Tool material ¼ high-speed steel; radius of the hemispherical tool end ¼ 4 mm; feed rate ¼ 500 mm/min; step size ¼ 0.32 mm/revolution; lubricant ¼ machine oil; and blank size ¼ 150 150 mm square. 4. Preliminary experiments and the design of test specimens As mentioned previously, the thinning bands occur on the parts only when the wall angles approach the maximum attainable. Therefore, in order to design test specimens to investigate the effect of a thinning band on the formability of a sheet metal, an approximate value of the minimum initial wall/forming angle (yi), as defined in Fig. 2(a), on imposing which on a sheet a thinning band could occur was required. For this purpose, the VWACF tests were performed with four different sheet metals (see thickness and mechanical properties of sheets in Table 1) namely AA 2024 (annealed), AA 3003 (annealed), AA 1060-H24 (extremely strain-hardened) and AA 2024-T4 (tempered). The tests were conducted using the process parameters listed in Section 3, and the part dimensions as given in the
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obtained for four sheets is as follows: AA 2024: 691, AA 3003: 81.51, AA 1060-H24: 791 and AA 2024-T4: 471. Since thinning bands did not occur on the parts of the AA 2024T4 sheet, as stated earlier, it was dropped from the list of the potential materials needed for further experimentation. The formability of the AA 1060-H24 sheet was comparable to that of the AA 3003 sheet; therefore, further investigations were carried out only with two sheet metals, i.e., AA 2024 and AA 3003. For further experimentation, a set of specimens, for each of the AA 2024 and AA 3003 sheets, with a variety of yi was designed (see Table 2). The value of yi was increased in small steps between 521 (or below as for the AA 2024 sheet) and the respective ymax of each sheet, while the curvature radius (rf) of the bottom underwent a variation due to variation in yi as clear from Fig. 2(b) and Table 2. The value of rf in each specimen was kept large so as to avoid any negative effect of bi-axial stretching, which is dangerous for material formability as reported in [1], on the occurrence of sheet fracture. 5. Brief experimental procedure
Fig. 1. (a) Definition of curvature radius r, and (b) schematic representation of a thinning band present on the part formed with constant wall angle y.
footnote.2 A set of parts of each sheet was formed by varying yi, in an equal increment of 41, from 361 to 521. In order to see the occurrence of a thinning band on a part, the wall thickness profile of each specimen was determined. To do so, a number of points (in an equal increment of 1 mm) were marked on the specimen’s surface along the depth and the actual wall thickness (*t) was measured on each marked point. The points were marked with a depth gauge (0.01 mm least count), and *t on a marked point was measured with a dial gauge (0.001 mm least count). The thickness profiles of the parts were examined and the deviation of the actual thickness from the nominal one (t based on Eq. (2)), was seen. It was found that three (AA 2024, AA 3003 and AA 2024-T4) of the four sheets showed thinning bands at about 521, yi; there can be deviation of 31 in this value because yi was increased in the step of 41. However, no thinning band occurred on the parts of the AA 2024-T4 sheet, as it could endure the maximum wall angle ymax of only 471. The value of ymax (without any effect of the thinning band) for each sheet was also evaluated from these tests. An approximate value of ymax 2 The curvature radius (ri), as defined in Fig. 2(a), of the base of part was kept constant (55 mm) in each specimen of each sheet, and the final wall angle (yf) in each specimen of the AA 2024, AA 3003, AA 1086-H24 and AA 2024-T4 sheet was maintained at 751, 851, 851 and 601, respectively.
The forming forces were measured by employing a force dynamometer (Kistler 9443B) under the forming fixture, as explained in [5]. The test specimens were formed to fracture using the process parameters listed earlier. Some representative test specimens formed for the current investigations are shown in Fig. 2(c). The wall thickness profile of a specimen was outlined as described in the preceding section. The actual fracture strain (*e3(frac)) in thickness direction was computed, as reported in [6], using the following equation: and shown below: *e3(frac) ¼ ln(*td/t0), where *td is the actual thickness measured on the fracture point D(xd, yd) and t0 is the blank thickness. The nominal fracture strain (e3(frac)) on point D(xd, yd) was calculated using Eq. (3). In order to determine the strain state at part fracture, the lengths (l2) of the minor axes of the fractured grid circles, which (with 2 mm diameter (l)) were printed in ink on the sheet blanks before forming, were measured with a traveling microscope (0.01 mm least count). From a measured length l2, the minor strain (e2) was calculated as: e2 ¼ ln(l2/l) and the corresponding major strain (e1) was computed using the relation: e1+e2+e3 ¼ 0 (see [6] for details). 6. Results and discussion Fig. 3(a) represents the fracture strain states of various parts made of two different sheets (AA 2024 and AA 3003). This is obvious from the figure that all the parts fractured in the same deformation mode, i.e., plane-strain stretching, as expected. Therefore, it can be said that the results of the formability tests to be discussed in the coming paragraphs are free of any negative effect of the hoop strains, i.e., e2.
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Fig. 2. (a) Part geometry, (b) methodology to design test specimens, and (c) some representative test specimens formed for the current investigations.
Table 1 Mechanical properties and the thickness of the experimental materials Material type
sy (MPa) su (MPa) n
K (MPa) d (%) to (mm)
AA AA AA AA
80.4 54.3 132.6 296.3
312 172 171 676
2024 3003 1060-H24 2024-T4
166.6 103.7 140.4 427.5
0.2 0.24 0.08 0.17
18.7 41 5.5 19.4
1.42 1.41 1.2 0.98
Note: See nomenclature for symbols.
Some examples of the thinning bands occurred on the parts of the AA 2024 sheet are presented in Fig. 3(b). The variations in the wall thickness of the parts indicate that two parts (parts 4 and 6) fractured due to the effect of the
occurrence of the thinning bands and one part (part 2), inspite of having a thinning band, fractured normally (see deviation of wall thickness profile of each part from the nominal one). This is due to the fact that a thinning band occurs in the flange area of a part (see the wall thickness profiles and schematic shown in Fig. 3(b) and, therefore, affects the fracture occurrence of the part when the fracture limit of its base sheet metal falls in the flange area. In other words, the part fracture is affected by the thinning band when hd becomes equal to hb, where hd is the distance of the fracture point from the part flange, and hb is the distance of the extreme end of the thinning band from the part flange (see Fig. 3(b)). This can be seen from Fig. 3(c), that the minimum value of the initial forming
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Table 2 Design data of the test specimens Material type
Part ]
yi (degree)
yf (degree)
ri (mm)
rf (mm)
h (mm)
No. of tested values
AA-2024
1 2 3 4 5 6
48 51 54 58 61 64
75 75 75 75 75 75
55.5 55.5 55.5 55.5 55.5 55.5
29.8 33 37.3 41.85 45.5 47.7
47.3 43.5 38 31.3 25 20.8
3 4 4 3 4 3
AA-3003
1 2 3 4 5 6
55 60 65 68 70 72
85 85 85 85 85 85
55.5 55.5 55.5 55.5 55.5 55.5
35.1 40.45 45 47.5 48.9 50.25
56 47.5 38.6 33 29.4 25.5
3 4 4 3 4 3
Note: See nomenclature for symbols.
angle, i.e., yI (critical), on imposing which on the sheet the condition hd ¼ hb is met is different for each of the testing materials (541 and 651 for the AA 2024 and AA 3003 sheet, respectively). Actually the AA 3003 sheet has higher formability (81.51) than the AA 2024 sheet (691). Therefore, for the same value of yi, the former can be formed to a larger depth without fracturing than the latter (as an example, compare the hd values of the two sheets at 591). Due to this reason, yi(critical) for the former is larger than that for the latter. The maximum value of hb (or the maximum length of thinning band) is about 26 and 34 mm for the AA 2024 and AA 3003 sheet, respectively. This discrepancy between the hb values of the two sheets can again be attributed to their formability, as explained earlier. Hence, it can be concluded that both yi(critical) and the maximum value of hb depends on the sheet formability. These values will be larger for the materials having high formability and vice versa. In Fig. 4(a), the effect of the occurrence of a thinning band on the fracture occurrence of sheet is shown in a quantified form. The figure shows that the actual fracture strain *e3(frac) of each of the first two parts of the AA 2024 sheet and that of the AA 3003 sheet is a little higher than its respective nominal fracture strain *e3(frac). While, *e3(frac) of each of the remainder parts of each sheet is lower than its respective e3(frac). This reveals that the first two parts of each of the two sheets fractured when the real fracture limit of the respective sheet was surpassed. Whereas, the remaining parts of the sheets fractured due to unexpected sheet over-stretching and, therefore, they fractured before the real forming limit, i.e.,ymax, of their respective blank material could reach. This proves that the thinning bands, which represent the over-stretching of sheet, have negative effect on the occurrence of sheet fracture. However, their occurrence on a part does not influence the sheet fracture until the condition hd ¼ hb is not met, as mentioned before. After exceeding yi(critical), as defined earlier, the severity of the phenomenon of sheet over-stretching on the fracture occurrence of sheet increases as yi increases, which can be
seen from the deviation of the actual fracture strain from the nominal one, i.e., De 3 shown in Fig. 4(a). A decrease in Ft (forming force prior to sheet fracturing as defined in Fig. 4(b)), which occurs due to decrease in the sheet thickness, with an increase in yi also verifies this finding. As a consequence of increase in excessive thinning (negative value of De), the sheet fracture occurs at smaller wall angles prior to reaching its real forming limit and thus the formability, i.e.,ymax, reduces (see the plot of ymax drawn against De presented in Fig. 4(c)). A decrease in the formability of the AA 2024 sheet due to the maximum excessive thinning (15%) is about 3.5%. Similarly, a reduction in the formability of the AA 3003 sheet due to about 22% excessive thinning is approximately 4.5%. For each sheet, ymax and De can be related by a quadratic empirical model as presented in Fig. 4(c). In addition to the initial forming angle yi, clamping force exerted on the sheet blank could be another factor having an effect on the occurrence of the thinning band. In order to investigate this point, the potential effect of increase in the clamping force on the forming force required to deform a sheet (AA 2024 sheet) was examined. For the said purpose, a part with constant wall angle (as a one shown in Fig. 1(b)) of 641 was formed. Its geometrical parameters were as follows: ri ¼ 55 mm, and rf ¼ 47 mm. A manual torque wrench was used to increase the clamping force on the sheet blank, and the forming forces imposed by the forming tool on the sheet were measured by adopting the procedure reported in [5]. The torque was increased from 6 to 22 NM in equal steps of 4 NM. All other process parameters were kept the same as listed in Section 4. The force curves for 6 and 22NM blank holding torque are presented in Fig. 5. It can be seen from the figure that an increase in the clamping torque/force does not have any visible effect on the magnitude of the forming force required to deform the sheet. Therefore, it can be said
3
De ¼ 100 (e3(frac)*e3(frac))/e3(frac).
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Fig. 3. (a) Representation of the fracture strain states, in the e1e2 space, of the parts of AA 2024 and AA 3003 sheets, (b) wall-thickness profiles of some parts of the AA 2024 sheet, and (c) description of the condition hd ¼ hb.
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Fig. 4. (a) The effect of the initial forming angle on the occurrence of sheet fracture, (b) force curves of some parts of the AA 2024 sheet, and (c) a plot of ymax as a function of the percent deviation of actual fracture strain from the nominal one.
ARTICLE IN PRESS G. Hussain et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1170–1178
Fig. 5. The effect of blank-holding force on the forming force.
that the occurrence of a thinning band does not depend on the clamping force. As found above, when the fracture limit of a sheet falls in the flange area of part, its fracture occurrence is negatively affected by the thinning band and, therefore, the sheet fractures earlier than its real forming limit. The real forming limit of a sheet metal having good forming ability (i.e.,ymaxX521)4 can, therefore, be obtained only if the part fracture occurs away from the thin band’s site. The conventional formability testing method cannot serve the purpose because the failure of the test specimen, employed by the method, occurs at the thin band as reported in [3]. Therefore, the VWACF test, as proposed in [4] and employed in the current study, in which the fracture point D(xd, yd), as defined in Fig. 2(a), can be adjusted as required is suggested to be employed for the said purpose.
7. Conclusions In the present study, the influence of the thinning band on the fracture occurrence of the part was investigated. The experiments were performed with four different aluminum sheet metals. One of the four experimental materials, i.e., AA 2024-T4, did not show any thinning band on deforming with the wall angles approaching its ymax (471). This revealed that, in contrast to the finding reported in [3], the occurrence of thinning bands on the parts when wall angles approach ymax is not obligatory. 4 The minimum value of yi required for the occurrence of a thinning band falls around 521 (with an error of 31) for the current experimental sheet metals. Therefore, a sheet with ymaxo521 may not show a thinning band, as found in the case of the AA 2024-T4 sheet stated in Section 4.
1177
Regarding the effect of a thinning band on the occurrence of the part fracture, it was found that a thinning band occurred on a part does not negatively affects its fracture occurrence until the condition hd ¼ hb is not met, where hd is the distance of the fracture point of the part from the flange and hb is the distance of the extreme end of the thinning band from the flange. In addition, the minimum initial forming angle yi at which the above condition was met and the maximum value of hb (or the maximum possible height of thinning band) showed dependence on the formability of the experimental material. They were large for the material having high formability and small for the material having low formability. The influence of the occurrence of a thinning band, which represents over-stretching of sheet, on the sheet formability, i.e., ymax was also quantified in this study. A parameter De (percent deviation of actual fracture strain form the nominal one) was used to represent sheet overstretching. It was found that a quadratic fit could accurately represent the effect of De on ymax. The fit showed that the formability decreases as the negative value of De (excessive sheet thinning) increases. The decrease in the sheet formability of each of the AA 2024 and AA 3003 sheets (the sheets whose parts bore thinning bands and had different values of ymax) due to 15% and 22% De was found as about 3.5% and 4.5%, respectively. The experiments conducted to investigate the influence of variation in the blank clamping force on the occurrence of a thinning band showed that an increase in the clamping force does not have any effect on the said phenomenon. In order to avoid the negative effect of the thinning band on the occurrence of sheet fracture and to determine the real forming limit of a sheet metal with ymaxX521 (approximately), the use of the VWACF test is recommended. The relevant geometrical parameters (i.e., part depth h and the initial forming angle yi) should be selected in such a way that the condition hd4hb could be maintained. As the value of hb depends on the formability of the test material, no definite limit of hd can be defined. However, it is suggested, on the basis of the hb value corresponding to 81.51 ymax that is considered as a large formability value in negative incremental forming, to achieve the condition hd434 mm so as to reduce the number of trial experiments. This investigation will prove to be helpful for the standardization of the VWACF test specimen, as well as will provide guidance to the test users to design the right test specimen for obtaining the real forming limits of sheet metals. References [1] M.S. Shim, J.J. Park, The formability of an aluminum sheet in incremental forming, Journal of Materials Processing Technology 113 (2001) 654–658. [2] J.J. Park, Y.H. Kim, Fundamental studies on the incremental sheet metal forming technique, Journal of Materials Processing Technology 40 (2003) 447–453.
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[3] D. Young, J. Jeswiet, Wall thickness variations in single point incremental forming, proceedings of institution of mechanical engineers, Part B, Journal of Engineering Manufacture 218 (2004) 1453–1459. [4] G. Hussain, L. Gao, A novel method to test the thinning limits of sheet-metals in negative incremental forming, International Journal of Machine Tools & Manufacture 47 (2007) 419–435.
[5] J. Duflou, Y. Tunckol, A. Szekeres, P. Vanherck, Experimental study on force measurements for single point incremental forming, Journal of Materials Processing Technology 189 (2007) 65–72. [6] K. Yoshida, K. Abe, K. Miyauchi, T. Nakagama, Instability and fracture behaviour in sheet metal forming, Metallurgia Italiana La (8) (1968) 685–699.
International Journal of Machine Tools & Manufacture 48 (2008) 1170–1178 www.elsevier.com/locate/ijmactool
Short Communication
An experimental study on the effect of thinning band on the sheet formability in negative incremental forming G. Hussain, N. Hayat, L. Gao College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, 29-Yudao Street, Nanjing, Jiangsu 210016, PR China Received 5 September 2007; received in revised form 21 January 2008; accepted 4 February 2008 Available online 20 February 2008
Abstract In negative incremental forming, a characteristic thinning band occurs on the parts when wall angles approach the maximum obtainable [D. Young, J. Jeswiet, Wall thickness variations in single point incremental forming, Proceedings of the Institute of Mechanical Engineers, Part B, Journal of Engineering Manufacture 218 (2004) 1453–1459]. The effect of this ultra-thin band on the fracture occurrence of part was studied in the current investigation. It was found that the occurrence of a thinning band on the test specimen of a formability test does not mean an effect on the test result. A reduction in the formability due to the occurrence of the thinning band occurs only if the specimen fractures in the flange area. In order to evaluate the real forming limit of a sheet metal, a condition regarding the occurrence of part fracture is proposed. r 2008 Elsevier Ltd. All rights reserved. Keywords: Negative incremental forming; Thinning band; Formability; Part fracture; Real forming limit
1. Introduction Single-point incremental forming (SPIF) is a flexible sheet metal-forming process that is economically promising for low production-run manufacturing. In this process, a small-sized tool moves along a programmed tool path and shapes the part in an incremental fashion. The process is mainly performed by shear deformations, at least in the regions of the work piece where the horizontal radius of the curvature (r, as defined in Fig. 1(a)) is large [1]. The process has two principal variants: (1) positive incremental forming (PIF), and (2) negative incremental forming (NIF) [2]. It has been reported that, in NIF, a characteristic thinning band (see Fig. 1(b)) occurs along the surface of the part when wall angles (y) approach the maximum achievable [3]. Also, the Sine law (t ¼ t0 cos y, where t is the wall thickness, t0 is the blank thickness and y is the wall angle as defined in Fig. 1(b)) can not predict the part thickness in this unexpected band. As can be seen from Corresponding author. Tel.: +86 136 751 61625.
E-mail addresses: [email protected] (G. Hussain), [email protected] (N. Hayat), [email protected] (L. Gao). 0890-6955/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2008.02.003
Fig. 1(b), the part thickness in the band region is smaller than that of the remainder of the part. Therefore, if steeper walls are attempted, fracture will occur at this location prior to reaching the real forming limit of sheet. The effect of the thinning band on the sheet formability has not been investigated, in explicit terms. Moreover, no method to determine the actual forming limit of a sheet metal has been proposed in literature. The present work is an attempt in these directions. The experiments were performed with four different aluminum sheet metals. In order to quantify the formability, it was defined as the maximum wall angle (ymax) without sheet fracture. The current study was carried out by employing the varying wall angle conical frustum (VWACF) test proposed by the authors in [4].
2. Part geometry and mathematical expressions The part geometry employed for the present investigations is shown in Fig. 2(a). An arc of a circle with 115 mm radius (R) was used as a generatrix to generate the surface. This is obvious from the figure that the wall angle continuously increases along the generatrix from point Pi(xi, yi) to Pf(xf, yf), thus inducing a corresponding change
ARTICLE IN PRESS G. Hussain et al. / International Journal of Machine Tools & Manufacture 48 (2008) 1170–1178
Nomenclature
rf
sy su n K d y
h hd
yield strength ultimate tensile strength strain hardening index strength co-efficient percent elongation in tensile test wall/forming angle of a part having constant slope (see Fig. 1(b)) yi wall/forming angle at the initial point Pi(xi, yi) of a part having varying wall angle (see Fig. 2(a)), or the wall angle imposed on the sheet in the beginning of the forming process yf wall/forming angle at the final point Pf(xf, yf) of a part having varying wall angle (see Fig. 2(b)) ymax maximum wall angle that a sheet could endure without fracturing yi(critical) the minimum value of yi on imposing which a thinning band affects the occurrence of part fracture, or the condition hd ¼ hb is met R radius of curvature of generatrix of part having varying wall angle (see Fig. 2(a)) ri curvature radius of the base of a part (see Fig. 2(a))
in the wall thickness (t) of the specimen (see [4] for details). Due to these variations in thickness, a fracture on a point D(xd, yd) could occur whenever the thinning limit is surpassed. The instantaneous wall angle (yp) and the nominal thickness (tp) on an arbitrary point P(xp, yp) can be computed as derived in [4] and presented below y p 1 yi hp yp ¼ cos ¼ cos R R 1
tp ¼ t0 cos y ¼
t0 ðy hp Þ R i
(1)
(2)
Making use of Eq. (2), the nominal thickness strain (e3(p)) on point P(xp, yp)can be calculated as 3ðpÞ ¼ ln
yi hp R
(3)
To obtain its safe value, the wall angle at a point M(xm, ym) situated 1 mm prior to the fracture point D(xd, yd) (see Fig. 2(a)) was regarded as the maximum wall angle1 ymax without sheet fracture.
1 During experiments it was observed that a part could be formed safely if the forming operation was terminated when the tool reached the depth (hd1) mm. Therefore, in case of fracture, the wall angle on the point corresponding to (hd1) can be regarded as the maximum wall angle without sheet fracture (see Fig. 2a).
hb t0 t/tp
*t/*tp
e3(frac) *e3(frac)
De Smax Ft
1171
curvature radius of the bottom of a part (see Fig. 2(a)) design depth of part (see Fig. 2(a)) distance of fracture point, along y-axis, from the part flange (see Fig. 2(a)) distance of the extreme end of the thinning band from the part flange (see Fig. 3(b)) thickness of blank (see Fig. 1(a)) nominal wall thickness of part based on Sine law Eq. (2), or nominal wall thickness at an arbitrary point P(xp, yp) actual wall thickness of part measured with a dial gauge, or actual wall thickness at an arbitrary point P(xp, yp) nominal fracture strain (in thickness direction) based on Eq. (3) actual fracture strain (in thickness direction) based on actual thickness measured at fracture point deviation of actual fracture strain from the nominal one maximum standard deviation forming force imposed by the tool on the sheet prior to its fracturing
3. Process parameters The process of NIF is now well-known to the researcher’s community. Its schematic representation along with the real experimental setup has been shown in a previous paper of the authors [4] and many others. For this reason, the process setup is not presented here. However, some important process parameters used in the experiments are as below: Tool material ¼ high-speed steel; radius of the hemispherical tool end ¼ 4 mm; feed rate ¼ 500 mm/min; step size ¼ 0.32 mm/revolution; lubricant ¼ machine oil; and blank size ¼ 150 150 mm square. 4. Preliminary experiments and the design of test specimens As mentioned previously, the thinning bands occur on the parts only when the wall angles approach the maximum attainable. Therefore, in order to design test specimens to investigate the effect of a thinning band on the formability of a sheet metal, an approximate value of the minimum initial wall/forming angle (yi), as defined in Fig. 2(a), on imposing which on a sheet a thinning band could occur was required. For this purpose, the VWACF tests were performed with four different sheet metals (see thickness and mechanical properties of sheets in Table 1) namely AA 2024 (annealed), AA 3003 (annealed), AA 1060-H24 (extremely strain-hardened) and AA 2024-T4 (tempered). The tests were conducted using the process parameters listed in Section 3, and the part dimensions as given in the
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obtained for four sheets is as follows: AA 2024: 691, AA 3003: 81.51, AA 1060-H24: 791 and AA 2024-T4: 471. Since thinning bands did not occur on the parts of the AA 2024T4 sheet, as stated earlier, it was dropped from the list of the potential materials needed for further experimentation. The formability of the AA 1060-H24 sheet was comparable to that of the AA 3003 sheet; therefore, further investigations were carried out only with two sheet metals, i.e., AA 2024 and AA 3003. For further experimentation, a set of specimens, for each of the AA 2024 and AA 3003 sheets, with a variety of yi was designed (see Table 2). The value of yi was increased in small steps between 521 (or below as for the AA 2024 sheet) and the respective ymax of each sheet, while the curvature radius (rf) of the bottom underwent a variation due to variation in yi as clear from Fig. 2(b) and Table 2. The value of rf in each specimen was kept large so as to avoid any negative effect of bi-axial stretching, which is dangerous for material formability as reported in [1], on the occurrence of sheet fracture. 5. Brief experimental procedure
Fig. 1. (a) Definition of curvature radius r, and (b) schematic representation of a thinning band present on the part formed with constant wall angle y.
footnote.2 A set of parts of each sheet was formed by varying yi, in an equal increment of 41, from 361 to 521. In order to see the occurrence of a thinning band on a part, the wall thickness profile of each specimen was determined. To do so, a number of points (in an equal increment of 1 mm) were marked on the specimen’s surface along the depth and the actual wall thickness (*t) was measured on each marked point. The points were marked with a depth gauge (0.01 mm least count), and *t on a marked point was measured with a dial gauge (0.001 mm least count). The thickness profiles of the parts were examined and the deviation of the actual thickness from the nominal one (t based on Eq. (2)), was seen. It was found that three (AA 2024, AA 3003 and AA 2024-T4) of the four sheets showed thinning bands at about 521, yi; there can be deviation of 31 in this value because yi was increased in the step of 41. However, no thinning band occurred on the parts of the AA 2024-T4 sheet, as it could endure the maximum wall angle ymax of only 471. The value of ymax (without any effect of the thinning band) for each sheet was also evaluated from these tests. An approximate value of ymax 2 The curvature radius (ri), as defined in Fig. 2(a), of the base of part was kept constant (55 mm) in each specimen of each sheet, and the final wall angle (yf) in each specimen of the AA 2024, AA 3003, AA 1086-H24 and AA 2024-T4 sheet was maintained at 751, 851, 851 and 601, respectively.
The forming forces were measured by employing a force dynamometer (Kistler 9443B) under the forming fixture, as explained in [5]. The test specimens were formed to fracture using the process parameters listed earlier. Some representative test specimens formed for the current investigations are shown in Fig. 2(c). The wall thickness profile of a specimen was outlined as described in the preceding section. The actual fracture strain (*e3(frac)) in thickness direction was computed, as reported in [6], using the following equation: and shown below: *e3(frac) ¼ ln(*td/t0), where *td is the actual thickness measured on the fracture point D(xd, yd) and t0 is the blank thickness. The nominal fracture strain (e3(frac)) on point D(xd, yd) was calculated using Eq. (3). In order to determine the strain state at part fracture, the lengths (l2) of the minor axes of the fractured grid circles, which (with 2 mm diameter (l)) were printed in ink on the sheet blanks before forming, were measured with a traveling microscope (0.01 mm least count). From a measured length l2, the minor strain (e2) was calculated as: e2 ¼ ln(l2/l) and the corresponding major strain (e1) was computed using the relation: e1+e2+e3 ¼ 0 (see [6] for details). 6. Results and discussion Fig. 3(a) represents the fracture strain states of various parts made of two different sheets (AA 2024 and AA 3003). This is obvious from the figure that all the parts fractured in the same deformation mode, i.e., plane-strain stretching, as expected. Therefore, it can be said that the results of the formability tests to be discussed in the coming paragraphs are free of any negative effect of the hoop strains, i.e., e2.
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Fig. 2. (a) Part geometry, (b) methodology to design test specimens, and (c) some representative test specimens formed for the current investigations.
Table 1 Mechanical properties and the thickness of the experimental materials Material type
sy (MPa) su (MPa) n
K (MPa) d (%) to (mm)
AA AA AA AA
80.4 54.3 132.6 296.3
312 172 171 676
2024 3003 1060-H24 2024-T4
166.6 103.7 140.4 427.5
0.2 0.24 0.08 0.17
18.7 41 5.5 19.4
1.42 1.41 1.2 0.98
Note: See nomenclature for symbols.
Some examples of the thinning bands occurred on the parts of the AA 2024 sheet are presented in Fig. 3(b). The variations in the wall thickness of the parts indicate that two parts (parts 4 and 6) fractured due to the effect of the
occurrence of the thinning bands and one part (part 2), inspite of having a thinning band, fractured normally (see deviation of wall thickness profile of each part from the nominal one). This is due to the fact that a thinning band occurs in the flange area of a part (see the wall thickness profiles and schematic shown in Fig. 3(b) and, therefore, affects the fracture occurrence of the part when the fracture limit of its base sheet metal falls in the flange area. In other words, the part fracture is affected by the thinning band when hd becomes equal to hb, where hd is the distance of the fracture point from the part flange, and hb is the distance of the extreme end of the thinning band from the part flange (see Fig. 3(b)). This can be seen from Fig. 3(c), that the minimum value of the initial forming
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Table 2 Design data of the test specimens Material type
Part ]
yi (degree)
yf (degree)
ri (mm)
rf (mm)
h (mm)
No. of tested values
AA-2024
1 2 3 4 5 6
48 51 54 58 61 64
75 75 75 75 75 75
55.5 55.5 55.5 55.5 55.5 55.5
29.8 33 37.3 41.85 45.5 47.7
47.3 43.5 38 31.3 25 20.8
3 4 4 3 4 3
AA-3003
1 2 3 4 5 6
55 60 65 68 70 72
85 85 85 85 85 85
55.5 55.5 55.5 55.5 55.5 55.5
35.1 40.45 45 47.5 48.9 50.25
56 47.5 38.6 33 29.4 25.5
3 4 4 3 4 3
Note: See nomenclature for symbols.
angle, i.e., yI (critical), on imposing which on the sheet the condition hd ¼ hb is met is different for each of the testing materials (541 and 651 for the AA 2024 and AA 3003 sheet, respectively). Actually the AA 3003 sheet has higher formability (81.51) than the AA 2024 sheet (691). Therefore, for the same value of yi, the former can be formed to a larger depth without fracturing than the latter (as an example, compare the hd values of the two sheets at 591). Due to this reason, yi(critical) for the former is larger than that for the latter. The maximum value of hb (or the maximum length of thinning band) is about 26 and 34 mm for the AA 2024 and AA 3003 sheet, respectively. This discrepancy between the hb values of the two sheets can again be attributed to their formability, as explained earlier. Hence, it can be concluded that both yi(critical) and the maximum value of hb depends on the sheet formability. These values will be larger for the materials having high formability and vice versa. In Fig. 4(a), the effect of the occurrence of a thinning band on the fracture occurrence of sheet is shown in a quantified form. The figure shows that the actual fracture strain *e3(frac) of each of the first two parts of the AA 2024 sheet and that of the AA 3003 sheet is a little higher than its respective nominal fracture strain *e3(frac). While, *e3(frac) of each of the remainder parts of each sheet is lower than its respective e3(frac). This reveals that the first two parts of each of the two sheets fractured when the real fracture limit of the respective sheet was surpassed. Whereas, the remaining parts of the sheets fractured due to unexpected sheet over-stretching and, therefore, they fractured before the real forming limit, i.e.,ymax, of their respective blank material could reach. This proves that the thinning bands, which represent the over-stretching of sheet, have negative effect on the occurrence of sheet fracture. However, their occurrence on a part does not influence the sheet fracture until the condition hd ¼ hb is not met, as mentioned before. After exceeding yi(critical), as defined earlier, the severity of the phenomenon of sheet over-stretching on the fracture occurrence of sheet increases as yi increases, which can be
seen from the deviation of the actual fracture strain from the nominal one, i.e., De 3 shown in Fig. 4(a). A decrease in Ft (forming force prior to sheet fracturing as defined in Fig. 4(b)), which occurs due to decrease in the sheet thickness, with an increase in yi also verifies this finding. As a consequence of increase in excessive thinning (negative value of De), the sheet fracture occurs at smaller wall angles prior to reaching its real forming limit and thus the formability, i.e.,ymax, reduces (see the plot of ymax drawn against De presented in Fig. 4(c)). A decrease in the formability of the AA 2024 sheet due to the maximum excessive thinning (15%) is about 3.5%. Similarly, a reduction in the formability of the AA 3003 sheet due to about 22% excessive thinning is approximately 4.5%. For each sheet, ymax and De can be related by a quadratic empirical model as presented in Fig. 4(c). In addition to the initial forming angle yi, clamping force exerted on the sheet blank could be another factor having an effect on the occurrence of the thinning band. In order to investigate this point, the potential effect of increase in the clamping force on the forming force required to deform a sheet (AA 2024 sheet) was examined. For the said purpose, a part with constant wall angle (as a one shown in Fig. 1(b)) of 641 was formed. Its geometrical parameters were as follows: ri ¼ 55 mm, and rf ¼ 47 mm. A manual torque wrench was used to increase the clamping force on the sheet blank, and the forming forces imposed by the forming tool on the sheet were measured by adopting the procedure reported in [5]. The torque was increased from 6 to 22 NM in equal steps of 4 NM. All other process parameters were kept the same as listed in Section 4. The force curves for 6 and 22NM blank holding torque are presented in Fig. 5. It can be seen from the figure that an increase in the clamping torque/force does not have any visible effect on the magnitude of the forming force required to deform the sheet. Therefore, it can be said
3
De ¼ 100 (e3(frac)*e3(frac))/e3(frac).
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Fig. 3. (a) Representation of the fracture strain states, in the e1e2 space, of the parts of AA 2024 and AA 3003 sheets, (b) wall-thickness profiles of some parts of the AA 2024 sheet, and (c) description of the condition hd ¼ hb.
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Fig. 4. (a) The effect of the initial forming angle on the occurrence of sheet fracture, (b) force curves of some parts of the AA 2024 sheet, and (c) a plot of ymax as a function of the percent deviation of actual fracture strain from the nominal one.
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Fig. 5. The effect of blank-holding force on the forming force.
that the occurrence of a thinning band does not depend on the clamping force. As found above, when the fracture limit of a sheet falls in the flange area of part, its fracture occurrence is negatively affected by the thinning band and, therefore, the sheet fractures earlier than its real forming limit. The real forming limit of a sheet metal having good forming ability (i.e.,ymaxX521)4 can, therefore, be obtained only if the part fracture occurs away from the thin band’s site. The conventional formability testing method cannot serve the purpose because the failure of the test specimen, employed by the method, occurs at the thin band as reported in [3]. Therefore, the VWACF test, as proposed in [4] and employed in the current study, in which the fracture point D(xd, yd), as defined in Fig. 2(a), can be adjusted as required is suggested to be employed for the said purpose.
7. Conclusions In the present study, the influence of the thinning band on the fracture occurrence of the part was investigated. The experiments were performed with four different aluminum sheet metals. One of the four experimental materials, i.e., AA 2024-T4, did not show any thinning band on deforming with the wall angles approaching its ymax (471). This revealed that, in contrast to the finding reported in [3], the occurrence of thinning bands on the parts when wall angles approach ymax is not obligatory. 4 The minimum value of yi required for the occurrence of a thinning band falls around 521 (with an error of 31) for the current experimental sheet metals. Therefore, a sheet with ymaxo521 may not show a thinning band, as found in the case of the AA 2024-T4 sheet stated in Section 4.
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Regarding the effect of a thinning band on the occurrence of the part fracture, it was found that a thinning band occurred on a part does not negatively affects its fracture occurrence until the condition hd ¼ hb is not met, where hd is the distance of the fracture point of the part from the flange and hb is the distance of the extreme end of the thinning band from the flange. In addition, the minimum initial forming angle yi at which the above condition was met and the maximum value of hb (or the maximum possible height of thinning band) showed dependence on the formability of the experimental material. They were large for the material having high formability and small for the material having low formability. The influence of the occurrence of a thinning band, which represents over-stretching of sheet, on the sheet formability, i.e., ymax was also quantified in this study. A parameter De (percent deviation of actual fracture strain form the nominal one) was used to represent sheet overstretching. It was found that a quadratic fit could accurately represent the effect of De on ymax. The fit showed that the formability decreases as the negative value of De (excessive sheet thinning) increases. The decrease in the sheet formability of each of the AA 2024 and AA 3003 sheets (the sheets whose parts bore thinning bands and had different values of ymax) due to 15% and 22% De was found as about 3.5% and 4.5%, respectively. The experiments conducted to investigate the influence of variation in the blank clamping force on the occurrence of a thinning band showed that an increase in the clamping force does not have any effect on the said phenomenon. In order to avoid the negative effect of the thinning band on the occurrence of sheet fracture and to determine the real forming limit of a sheet metal with ymaxX521 (approximately), the use of the VWACF test is recommended. The relevant geometrical parameters (i.e., part depth h and the initial forming angle yi) should be selected in such a way that the condition hd4hb could be maintained. As the value of hb depends on the formability of the test material, no definite limit of hd can be defined. However, it is suggested, on the basis of the hb value corresponding to 81.51 ymax that is considered as a large formability value in negative incremental forming, to achieve the condition hd434 mm so as to reduce the number of trial experiments. This investigation will prove to be helpful for the standardization of the VWACF test specimen, as well as will provide guidance to the test users to design the right test specimen for obtaining the real forming limits of sheet metals. References [1] M.S. Shim, J.J. Park, The formability of an aluminum sheet in incremental forming, Journal of Materials Processing Technology 113 (2001) 654–658. [2] J.J. Park, Y.H. Kim, Fundamental studies on the incremental sheet metal forming technique, Journal of Materials Processing Technology 40 (2003) 447–453.
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[3] D. Young, J. Jeswiet, Wall thickness variations in single point incremental forming, proceedings of institution of mechanical engineers, Part B, Journal of Engineering Manufacture 218 (2004) 1453–1459. [4] G. Hussain, L. Gao, A novel method to test the thinning limits of sheet-metals in negative incremental forming, International Journal of Machine Tools & Manufacture 47 (2007) 419–435.
[5] J. Duflou, Y. Tunckol, A. Szekeres, P. Vanherck, Experimental study on force measurements for single point incremental forming, Journal of Materials Processing Technology 189 (2007) 65–72. [6] K. Yoshida, K. Abe, K. Miyauchi, T. Nakagama, Instability and fracture behaviour in sheet metal forming, Metallurgia Italiana La (8) (1968) 685–699.