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Predicting forming limit of electrodeposited nickel coating based on practical stress–strain relationship
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
journal homepage: www.elsevier.com/locate/jmatprotec
Predicting forming limit of electrodeposited nickel coating based on practical stress–strain relationship L.Q. Zhou a,b,∗ , J.G. Tang a , Y.P. Li a , Y.C. Zhou b a
Mechanical Engineering School of Xiangtan University, 411105 Hunan, PR China Key Laboratory of Low Dimensional Materials and Application Technology (Xiangtan University), Ministry of Education, Hunan 411105, PR China b
a r t i c l e
i n f o
a b s t r a c t
Article history:
The aim of this study is to determine the practical stress–strain relationships of a nickel
Received 1 September 2007
coating sheet so as to understand its actual forming performance. The polynomials were
Received in revised form
applied to fit the experimental stress–strain data in the coating and substrate. For the nickel
30 October 2007
coating sheet, by using the fitted practical stress–strain relationships, the forming limit
Accepted 14 December 2007
diagram in the right region was precisely plotted and compared with other methods. This investigation revealed that the forming limit diagram drawn by practical stress–strain relationships is great different from others drawn by Hollomon formulae, and the anisotropy
Keywords:
constant of the steel substrate has fairly great effects on the FLD of the coating sheet. When
Electrodeposited nickel coating
the substrate anisotropy constant is bigger than 1 it will favor the sheet formability, but
Stress–strain relationship
the coating’s anisotropy has no obvious influence on the FLD. The thinner nickel coating is
Coating sheet
better for its forming performance as related to the coating thickness. This work will aid the
Forming limit diagram
fabrication of the coating sheet and help the forming of appliances.
Anisotropy constant
1.
Introduction
In recent years many types of coating sheets have been increasingly produced and widely provided for press-forming factories (Zhong and Huang, 2003; Zhang, 2007). The formability of coatings sheet is generally different from that of their component sheet. Hence it is very important for sheet metal engineering to know the extent to which the coatings sheet can be press-formed without any failure. It would be convenient if the press-formability of a coated sheet could be predicted from the mechanical properties of its components and the layers geometry (Wit et al., 1999; Gupta and Kumar, 2006). In most cases, it is the coating that contacts with dies, and the coating should not crack or flake as the metal sheet deforms. Hence the forming performance of coatings is vital
© 2007 Elsevier B.V. All rights reserved.
and their forming characteristics and friction properties are important (Jiang et al., 2004). Early research of Hauw ever studied the stamping process of galvanized sheets, but he used the average mechanical data of the coating and substrate to calculate, his results are coarse (Hauw et al., 1999). Parisot studied the mechanical behavior of a multicrystalline zinc coating on a hot-dip galvanized steel sheet, he obtained the coating thickness of 10 m which seems to be too small for significant strain and stress gradients to develop from the interface to the free surface (Parisot et al., 2000). Kim studied the forming characteristics of coated sheet metals by experiments, he found the coating material’s forming limit is restricted by the coating’s defects (cracking, flaking, scratching, etc.) (Kim et al., 2002). In recent years, various coated steel sheets were extensively studied for their mechanical properties and formability
∗ Corresponding author at: Mechanical Engineering School of Xiangtan University, 411105 Hunan, PR China. Tel.: +86 732 8292209; fax: +86 732 8292210. E-mail address: [email protected] (L.Q. Zhou). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.12.087
432
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
(Safaeirad et al., 2008; Garza and Van Tyne, 2007; Lee et al., 2007). Electrodeposited coatings are used as wear-resistant, corrosion-resistant, decorative and functional surface layers in lots of regions, such as aviation, space flight and electron (Hu and Song, 2000). Electroplated nickel coating is widely used in the fabrication of metallic microdevices or microsystems due to some outstanding properties such as soft, ductile, shapeable and dense (Basrour and Robert, 2000). The electrodeposited nickel coating can also be used as the shell of high quality and high energy-storing batteries. As a good corrosive-resistant coating, the electrodeposited nickel coating must have high interface intensity, good thermalmechanical match between substrate and coating and good residual stress distribution. In battery industry, in the past the steel sheet is first deep drawn into parts and then nickel coating is electrodeposited. Nowadays, the technology has advanced and the coating and substrate can be bonded and formed at the same time. This results in the study of nickel coating forming performance. The nickel coating of thickness 2–10 m is electrodeposited on a substrate of low carbon steel sheet, then the coated sheet was treated with heat to form a transition-layer in the combined interface (Zhou and Zhou, 2004). The reason for choosing the coating thickness to be several microns is because of its preparation cost and working functions. The materials were dynamically impacted by projectiles in a 57-mm light air cannon, and it was found that the nickel electrodeposited coating had good interface quality (Zhou et al., 2004a). So as to study the formability of these materials, their forming limit diagrams were studied according to approximate stress–strain curves (Zhou et al., 2006; Zhou et al., 2007b). In this paper, the materials forming performance was carefully studied by forming limit diagrams which are based on practical stress–strain relationships. The forming limit diagrams for the materials are precisely re-plotted and its forming performance was analyzed.
2. Stress–strain relationships and numerical fitting 2.1.
Sample preparation
Nickel coating was prepared by electrodeposition method. A lower carbon steel of cold rolled sheet with the thickness of 0.25 mm was used as substrate. The substrate of cold rolled steel sheet is supplied by a steel factory with very good surface roughness. Its size tolerance in thickness is −0.02 mm. Prior to electroplating, the substrates were degreased and submerged in 6 M hydrochloric acid for 2 min and rinsed in distilled water. The samples were obtained with nickel sulphate electrolyte. The nickel sulphate electrolyte was composed of 240 g NiSO4 ·6H2 O, 40 g NiCl2 ·6H2 O, 40 g H3 BO3 per liter. Pure nickel was used as the anode. Before electroplating, H2 O2 and active carbon were used to get rid of the impurities. Moreover the electrolyte solution was electrolyzed for 24 h. In the case, the pH of the solution was 4.0 ± 0.1 and the temperature was 50 ± 0.5 ◦ C. The current density was 2 A/dm2 . The cell was automatically agitated. The thickness could be measured by
Fig. 1 – Section of the interface between electrodeposited nickel coating and steel substrate observed by SEM. Point A is coating, points B and C are interfaces, and point D is substrate.
a thickness tester of ZWB. In order to precisely measure the thickness of the coating, the section of the coating/substrate composite was observed by (JEOL)JSM-5600LV SEM and in this case the measured thickness of the coating could be checked by SEM measurement. The chemical composition near interface between electrodeposited nickel coating and steel substrate and the microstructure of the coating is concerned. Fig. 1 shows the section of the interface between electrodeposited nickel coating and steel substrate observed by SEM. In the figure, point A is coating, points B and C are interfaces, and point D is substrate. It illustrates that the thickness of coating was same at any place and its thickness was 5 m. Fig. 2 shows the chemical compositions at points A–D. The chemical composition near interface shown in Fig. 2 demonstrates that the chemical composition gradient exists at the interface between nickel coating and the substrate. The gradient change in chemical composition can enhance the interface strength.
Fig. 2 – Chemical compositions at points A–D.
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2.3. Numerical fitting for the stress–strain relationships The stress–strain data of the nickel coating and steel substrate should be fitted so as to apply them to the analysis and calculation of forming limit. In terms of the polynomial fitting theory in MATLAB, through the calculation of a quantity 2 (Chi2 ) and a probabilistic value Q (Zhong, 2000), it is found that the polynomial of its degree equaling to 5 is most suitable for the fitting. That is 5
(i)
(i)
4
3
(i)
2
(i)
(i)
(i)
(i) = a1 ε(i) + a2 ε(i) + a3 ε(i) + a4 ε(i) + a5 ε(i) + a6 d (i) dε Fig. 3 – The stress–strain data and fitted curve for the substrate.
2.2.
Stress–strain relationship for the composite
By using a mechanical model, the stress–strain properties and main mechanical parameters of the nickel coating and the steel substrate could be obtained by a (JEOL)JSM-5600LV SEM (scanning electron microscopy) in which the tensile force could be applied by a tensile equipment. In this method, the tensile force-strain properties of the substrate without coating were first determined, then the force-strain properties of coating/substrate composite were determined (Zhou et al., 2007a). The cold rolled steel sheet with a thickness of 0.25 mm was used as the substrate. The nickel coatings of thickness 6.2 m, 8.1 m and 9.6 m were bilaterally electrodeposited on the substrate respectively by adjusting different electrodeposition time. Afterwards the coated sheets were wire cut as specimens which can be fixed on JSM-5600LV SEM. The stress–strain relationships of the nickel coating and steel substrate can be worked out as experimental data shown in Figs. 3 and 4 according to the measure data.
(i)
4
3
(i)
(i)
2
(i)
(1)
(i)
= 5a1 ε(i) + 4a2 ε(i) + 3a3 ε(i) + 2a4 ε(i) + a5
(i)
(2)
(i)
where aj for j = 1, 2 . . . 6 represents the coefficient of fitted polynomial for ith layer stress–strain relationships. After calculation, the coefficients of fitted polynomial for ith layer stress–strain relationships are shown in Table 1. The stress–strain relationships may also be fitted as the Hollomon formulae according to traditional modus operandi. That is through a least squares method, the stress–strain data are fitted as = 946.3ε0.3696 (MPa) for the low carbon steel substrate and = 1805.6ε0.3570 (MPa) for the nickel coating (Zhou et al., 2007b). The fitted polynomials and Hollomon formulae are indicated in Figs. 3 and 4 combined with the experimental data.
3. Constitutive equations for the coating sheet By utilizing the Hill yield function the equivalent stress and equivalent strain may be deduced for laminate sheet materials (Peng and She, 1999). This modus operandi may be adopted for the sandwich coating sheet. In coating sheet, the equivalent (i) stress in ith layer ¯ (i) related to the principal stress in 1 axis 1 is
¯
(i)
=
3(1 + R(i) ) 4(2 + R(i) )
(1 −
1/2
2R(i)
(i)
1 + R(i)
(i)2
˛ +˛
)
(i)
(i)
1 = B(i) 1
(3)
here,
B(i)=
3(1 + R(i) ) 4(2 + R(i) )
(1 −
1/2
2R(i)
2
1 + R(i)
˛(i) + ˛(i) )
(4)
where R(i) is the normal anisotropic constant in ith layer, and ˛(i) is the principal stress ratio 2 / 1 in the layer. Eqs. (3) and (4) indicated that in the laminated coating sheet, the equivalent stress in different layers is different. By analogy, the equivalent strain increment in ith layer dε(i) related to the first principal strain increment dε1 (i) is
dε(i) = Fig. 4 – The stress–strain data and fitted curve for the coating.
2(2 + R(i) )(1 + R(i) ) 3(1 + 2R(i) )
= C(i) dε1 (i)
(1 +
2R(i) 1 + R(i)
1/2 ˇ + ˇ2 )
dε1 (i) (5)
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Table 1 – The coefficient of fitted polynomial (i)
Polynomial coefficient (i = 1, 2, 3) Coating (i = 1, 2) Substrate (i = 3)
(i)
(i)
(i)
a1
a2
a3
a4
0.516779 0.404543
−42.5288 −30.9795
1275.16 873.246
−16964.4 −11144.0
(i)
a5
103,767 64944.9
(i)
a6
83821.7 33208.3
where
C(i) =
2(2 + R(i) )(1 + R(i) )
1+
3(1 + 2R(i) )
2R(i) 1 + R(i)
1/2 ˇ + ˇ2
(6)
Eqs. (5) and (6) illustrated that during forming process the equivalent strains are different in each layer. Postulating that the adjacent layer in the coating sheet has equal principal strains, then for the ith layer the principal strains increment are
dε1 =
3d¯ε 1 + R(i) 2¯ 2 + R(i)
dε2 =
3d¯ε 1 + R(i) 2¯ 2 + R(i)
dε3 =
3d¯ε 1 (i) [1 + ˛(i) ]1 2¯ 2 + R(i)
1−
R(i) 1 + R(i)
˛(i) −
(i)
˛(i) 1
R(i) 1 + R(i)
(7)
(i)
1
(8)
(9)
According to Eqs. (7) and (8), the strains increment ratio ˇ can be obtained as ˛(i) (1 + R(i) ) − R(i) dε2 = ˇ= dε1 1 + R(i) − ˛(i) R(i)
R(i) + (1 + R(i) )ˇ 1 + R(i) + ˇR(i)
of same thickness, and the third layer is the substrate of low carbon steel. Under the plane stresses of two axes which are shown in Fig. 6, when diffuse necking appears the loads in two principal directions will reach maximum (Xiao and Jiang, 2000). That is
dp1 = d
(11)
where R(i) may be determined by experiment. Since the normal anisotropic constant in different layers is different, the stress ratio in different layers is different.
dp2 = d
The formability of sheet metal is often evaluated from strain analyses using the concept of forming limit diagrams (FLDs) introduced by Keeler and Goodwin. Many attempts have been made to predict the FLDs on the basis of the theory of plasticity, the material parameters and the instability condition. Wang developed an instability criterion for sheet metals under tensile stresses and plotted the forming limit curves in right region on the base of tensile test (Zutang, 1997). The author investigated the electrodeposited nickel coating’s forming limit in the left region by using Hill localized necking theory (Zhou et al., 2006). The forming limit of electrodeposited nickel coating in the right region will be studied here by using the Swift diffuse necking theory. The structure of the electrodeposited nickel coating sheet is just as Fig. 5. The first and second layers are nickel coatings
(i) (i) A1 1 1
=0
(12)
=0
(13)
(i) (i) A2 2 2
i
where pj is the load in principal direction j, shown in Fig. 4; Aj is the cross-section total area of the coating sheet in principal (i) direction j; j is the stressing in principal direction j and in (i)
(i)
ith layer for the coating sheet; 1 and 2 are the area ratio of the ith layer in the total section area in the principal directions (i) (i) (i) (i) 1 and 2, respectively; and 1 = A1 /A1 , 2 = A2 /A2 , moreover (i)
4. Forming limits of the nickel coating sheet
i
(10)
When the strain increment ratio ˇ is given, the stress ratio ˛ is ˛(i) =
Fig. 5 – Schematic of the electrodeposited nickel coating sheet.
(i)
1 = 2 = (i) = const.. The length, width, and thickness of the nickel coating sheet are denoted respectively by l, b, and t which are shown in Fig. 3. Thus the volume of the coating sheet V = lbt. When thickness t is regarded as constant in the tensile process, it can have,
Fig. 6 – Diffuse necking conditions.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
435
dV = d(lbt) = tbdl + tldb = 0. Thus dA1 = −dε1 A1
(14)
In terms of Eq. (12), substituting Eq. (14), may have
(i)
i
(i)
d1 (i) − 1 dε1
=0
(15)
By utilizing Eqs. (3) and (5), the following will be obtained
(i) i
B(i)
C(i)
d (i) dε(i)
− (i)
=0
(16)
Eq. (16) is the diffusing necking condition equation for the coating sheet. By substituting Eqs. (1) and (2) into the equation, we can obtain a nonlinear equation of unknown parameter ε(i) . (i) By utilizing Eq. (5), and noticing that the strain ε1 in different layer is equal to each other (assuming interface did not delam-
Fig. 8 – Effect of substrate anisotropy on the FLD of the coating sheet.
(i)
inate), ε1 = ε1 . Thus Eq. (16) will become a nonlinear equation of an unknown ε1 , the equation may be solved.
5.
Results and discussion
To investigate the press-forming limits of the electrodeposited nickel coating sheet in the right region, the nonlinear Eq. (16) needs to be solved first. Under the given materials parameters and strain path ˇ (0 ≤ ˇ ≤ 1), parameters (i) , B(i) , C(i) are all known. Iteration method can be adopted to solve the nonlinear equation, iterative scope may be set as [0.001, 2] for the unknown ε1 , and convergence precision may be specified as (i) 10−6 , thus may obtain the principal strain ε1 , ε1 , and equiva(i)
lent strain ε1 , etc. According to the proposed model, extensive calculations are carried out on MATLAB and the results are as follows. Figs. 3 and 4 are the stress–strain relationships and fitted curves for the substrate and coating. From these figures we may find that the fitted polynomial curves have quite good precision to the experimental data, but the fitted Hollomon
Fig. 7 – FLD of the nickel coating steel sheet.
Fig. 9 – Effect of coating anisotropy on the FLD of the coating sheet.
curves have less precision. The polynomial fitted curves are named practical stress–strain relationships. Thus the analysis precision for using the practical relationships in this paper should be quite better than the Hollomon formulae. Fig. 7 is the FLD of the nickel coating sheet. Here the thickness of the nickel coating is 5 m, and the thickness of steel substrate is 0.25 mm, and its normal anisotropic constant 1.41. In this figure, curve 1 is the FLD calculated by the proposed model in this paper which used the practical stress–strain relationships. The FLDs of curves 2, 3 and 4 used Hollomon formulae, and the FLD of the coating sheet is curve 4 which locates in the middle of FLDs of the nickel coating and steel substrate (Zhou et al., 2007b). It is obvious that the FLDs difference in these two methods is comparatively big, and it is necessary to use practical stress–strain relationships for drawing FLDs. The way in which the component anisotropy affects the forming limit of the coating sheet is shown in Figs. 8 and 9.
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
Fig. 10 – Effect of substrate anisotropy on the effective strain in substrate.
Fig. 12 – Effect of coating thickness on the FLD of the coating sheet.
And Figs. 10 and 11 are the effect of substrate anisotropy on the effective strain of the component. Fig. 8 apparently shows that the bigger the substrate anisotropy constant is, the higher the forming limit of the coating sheet is. This is because the bigger the substrate anisotropy constant is, the greater the effective strain in the component is, which is shown in Figs. 10 and 11, and it can withstand greater deformation. Hence the substrate anisotropy being bigger than 1 will favor the sheet forming, and raising the substrate anisotropy constant will improve the material’s forming limit. This is why the coating sheet should be rolled before leaving factory. How the coating anisotropy affects the forming limit of the coating sheet is not obvious just as Fig. 9. This may be due to the nickel coating which is too thin, but it can be found that it obeys the same rule as the substrate by enlarging the figure. The figures that the coating anisotropy affects the effective strain in the components do not give out since its influence is fairly small. Figs. 10 and 11 also show that the strain path clearly affects the effective strain in the coating and substrate.
The coating thickness affecting the forming limit of the coating sheet is shown in Fig. 12. From the four kinds of thickness it is found that the thicker the coating is, the worse the forming limit of the composite is. This arises because the forming limit of the nickel coating is not as good as the steel substrate which is shown in Fig. 7 in which curve 3 for individual substrate is higher than curve 2 for individual coating. So the thinner nickel coating is better is the forming performance with the steel substrate. The suitable thickness of the nickel coating is recommended to be 3–5 m to consider the thinning during forming processes (Zhou et al., 2004b).
Fig. 11 – Effect of substrate anisotropy on the effective strain in nickel coating.
6.
Conclusions
Thin coatings have become a key technology in a wide range of industries for a wide range of engineering purposes. There are many technologies that use thin layers of dissimilar materials in order to achieve functional requirements. Surface modification by electrodeposited nickel coating is an important technology. It is designed and constructed production lines to electrodeposit uniform nickel coatings on the substrate of low carbon steel sheet. By utilizing Hill yield function and the equivalent stress and equivalent strain of laminated sheet materials, the forming limit of electrodeposited nickel coating in the right region is studied through the Swift diffuse necking theory. This study determined the stress–strain properties of the coating layers and its working performance and the following conclusions may be drawn: (1) The stress–strain properties of the nickel coating and steel substrate may be determined by improved scanning electron microscopy. The degree 5 polynomial is most suitable for fitting the stress–strain data in the coating and substrate as the practical stress–strain relationships. (2) The FLD drawn by practical stress–strain relationship is great different from that drawn by Hollomon formula. (3) The anisotropy constant of the steel substrate has fairly great effects on the FLD of the coating sheet, but the coat-
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
ing’s anisotropy has no obvious influence on it. When the substrate anisotropy constant is bigger than 1 it will favor the sheet formability. (4) The thinner nickel coating is better for its forming performance as related to the coating thickness.
Acknowledgments This work was supported by the Open Project Program of Key Laboratory of Low Dimensional Materials & Application Technology, Ministry of Education, China (No. KF0613) and the Key Foundation of Xiangtan University (No. 06IND04). The supports are gratefully acknowledged.
references
Basrour, S., Robert, L., 2000. X-ray characterization of residual stresses in electroplated nickel used in LIGA technique. Mater. Sci. Eng. A288 (2), 270–274. Garza, L.G., Van Tyne, C.J., 2007. Friction and formability of galvannealed interstitial free sheet steel. J. Mater. Process. Technol. 187–188, 164–168. Gupta, A.K., Kumar, R., 2006. Formability of galvanized interstitial-free sheets. J. Mater. Process. Technol. 172, 225–237. Hauw, B., Dubar, L., Oudin, J., 1999. Improvement of stamping computations by means of the identification of the bulk behaviour of coatings: application to galvanized sheets. J. Mater. Process. Technol. 94, 23–29. Hu, C.-X., Song, Y.-H., 2000. Coating Technology Theory and Application. Chemical Industry Press, Beijing, pp. 207–212. Jiang, H.M., Chen, X.P., Wu, H., Li, C.H., 2004. Forming characteristics and mechanical parameter sensitivity study on pre-phosphated electro-galvanized sheet steel. J. Mater. Process. Technol. 151, 248–254. Zhang, J., 2007. Optimization of contact forces in tailor-welded blanks forming process. Int. J. Adv. Manuf. Technol. 33, 460–468. Kim, H.Y., Hwang, B.C., Bae, W.B., 2002. An experimental study on forming characteristics of pre-coated sheet metals. J. Mater. Process. Technol. 120, 290–295.
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Lee, J.M., Ko, D.C., Lee, K.S., Kim, B.M., 2007. Identification of the bulk behavior of coatings by nano-indentation test and FE-analysis and its application to forming analysis of the coated steel sheet. J. Mater. Process. Technol. 187–188, 309–313. Parisot, R., Forest, S., Gourgues, A.F., Pineau, A., Mareuse, D., 2000. Modeling the mechanical behavior of a multicrystalline zinc coating on a hot-dip galvanized steel sheet. Comp. Mater. Sci. 19, 189–204. Peng, Z.H., She, X.F., 1999. Theoretical analysis and experiment on pressing forming limit strain of stainless-steel clad aluminum. Chin. J. Nonferr. Met. 9 (2), 305–312. Safaeirad, M., Toroghinejad, M.R., Ashrafizadeh, F., 2008. Effect of microstructure and texture on formability and mechanical properties of hot-dip galvanized steel sheets. J. Mater. Process. Technol. 196 (1–3), 205–212. Zutang, W., 1997. Forming limits for sheet metals under tensile stresses. J. Mater. Process. Technol. 71, 418–421. Wit, K.D., Boeck, D.A., Cooman, B.C.D., 1999. Study of the influence of phase composition and iron content on the formability characteristics of zinc–iron electroplated sheet steel. J. Mater. Eng. Perform. 8 (5), 531–537. Xiao, J.-R., Jiang, K.-H., 2000. Press-forming Processing Technology. China Machine Press, Beijing, pp. 150–164. Zhong, Z.-Y., 2000. Familiarity of MATLAB. University of Aeronautics and Astronautics Press, Beijing, pp. 144–146. Zhong, Q.-F., Huang, J.-Z., 2003. Organic Coating Steel Sheet. Chemical Industry Press, Beijing, pp. 1–10. Zhou, L.-Q., Zhou, Y.-C., 2004. Preparation and shock properties of electrodeposited nickel coating (in Chinese). J. Mater. Prot. 37 (2), 26–27. Zhou, L.Q., Zhou, Y.C., Pan, Y., 2004a. Impact performance of electrodeposited nickel coating on steel substrate. J. Mater. Sci. 39, 753–755. Zhou, L.Q., Zhou, Y.C., Pan, Y., 2004b. Coating thickness variation during multistep drawing processes. J. Mater. Sci. 39, 757–760. Zhou, L.Q., Li, Y.P., Zhou, Y.C., 2006. Forming limit of electrodeposited nickel coating in the left region. J. Mater. Eng. Perform. 15 (3), 287–294. Zhou, L.-Q., Tang, J.-G., Li, Y.-P., Zhou, Y.-C., 2007a. Working performance of electrodeposited nickel coating. In: International Conference on Mechanical Engineering and Mechanics, November 5–7, China, Wuxi. Zhou, L.-Q., Li, Y.-P., Zhou, Y.-C., 2007b. Study on forming limits of nickel coating on right region. Trans. Nonferr. Metals. Soc. 17 (5), 913–918.
journal homepage: www.elsevier.com/locate/jmatprotec
Predicting forming limit of electrodeposited nickel coating based on practical stress–strain relationship L.Q. Zhou a,b,∗ , J.G. Tang a , Y.P. Li a , Y.C. Zhou b a
Mechanical Engineering School of Xiangtan University, 411105 Hunan, PR China Key Laboratory of Low Dimensional Materials and Application Technology (Xiangtan University), Ministry of Education, Hunan 411105, PR China b
a r t i c l e
i n f o
a b s t r a c t
Article history:
The aim of this study is to determine the practical stress–strain relationships of a nickel
Received 1 September 2007
coating sheet so as to understand its actual forming performance. The polynomials were
Received in revised form
applied to fit the experimental stress–strain data in the coating and substrate. For the nickel
30 October 2007
coating sheet, by using the fitted practical stress–strain relationships, the forming limit
Accepted 14 December 2007
diagram in the right region was precisely plotted and compared with other methods. This investigation revealed that the forming limit diagram drawn by practical stress–strain relationships is great different from others drawn by Hollomon formulae, and the anisotropy
Keywords:
constant of the steel substrate has fairly great effects on the FLD of the coating sheet. When
Electrodeposited nickel coating
the substrate anisotropy constant is bigger than 1 it will favor the sheet formability, but
Stress–strain relationship
the coating’s anisotropy has no obvious influence on the FLD. The thinner nickel coating is
Coating sheet
better for its forming performance as related to the coating thickness. This work will aid the
Forming limit diagram
fabrication of the coating sheet and help the forming of appliances.
Anisotropy constant
1.
Introduction
In recent years many types of coating sheets have been increasingly produced and widely provided for press-forming factories (Zhong and Huang, 2003; Zhang, 2007). The formability of coatings sheet is generally different from that of their component sheet. Hence it is very important for sheet metal engineering to know the extent to which the coatings sheet can be press-formed without any failure. It would be convenient if the press-formability of a coated sheet could be predicted from the mechanical properties of its components and the layers geometry (Wit et al., 1999; Gupta and Kumar, 2006). In most cases, it is the coating that contacts with dies, and the coating should not crack or flake as the metal sheet deforms. Hence the forming performance of coatings is vital
© 2007 Elsevier B.V. All rights reserved.
and their forming characteristics and friction properties are important (Jiang et al., 2004). Early research of Hauw ever studied the stamping process of galvanized sheets, but he used the average mechanical data of the coating and substrate to calculate, his results are coarse (Hauw et al., 1999). Parisot studied the mechanical behavior of a multicrystalline zinc coating on a hot-dip galvanized steel sheet, he obtained the coating thickness of 10 m which seems to be too small for significant strain and stress gradients to develop from the interface to the free surface (Parisot et al., 2000). Kim studied the forming characteristics of coated sheet metals by experiments, he found the coating material’s forming limit is restricted by the coating’s defects (cracking, flaking, scratching, etc.) (Kim et al., 2002). In recent years, various coated steel sheets were extensively studied for their mechanical properties and formability
∗ Corresponding author at: Mechanical Engineering School of Xiangtan University, 411105 Hunan, PR China. Tel.: +86 732 8292209; fax: +86 732 8292210. E-mail address: [email protected] (L.Q. Zhou). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.12.087
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(Safaeirad et al., 2008; Garza and Van Tyne, 2007; Lee et al., 2007). Electrodeposited coatings are used as wear-resistant, corrosion-resistant, decorative and functional surface layers in lots of regions, such as aviation, space flight and electron (Hu and Song, 2000). Electroplated nickel coating is widely used in the fabrication of metallic microdevices or microsystems due to some outstanding properties such as soft, ductile, shapeable and dense (Basrour and Robert, 2000). The electrodeposited nickel coating can also be used as the shell of high quality and high energy-storing batteries. As a good corrosive-resistant coating, the electrodeposited nickel coating must have high interface intensity, good thermalmechanical match between substrate and coating and good residual stress distribution. In battery industry, in the past the steel sheet is first deep drawn into parts and then nickel coating is electrodeposited. Nowadays, the technology has advanced and the coating and substrate can be bonded and formed at the same time. This results in the study of nickel coating forming performance. The nickel coating of thickness 2–10 m is electrodeposited on a substrate of low carbon steel sheet, then the coated sheet was treated with heat to form a transition-layer in the combined interface (Zhou and Zhou, 2004). The reason for choosing the coating thickness to be several microns is because of its preparation cost and working functions. The materials were dynamically impacted by projectiles in a 57-mm light air cannon, and it was found that the nickel electrodeposited coating had good interface quality (Zhou et al., 2004a). So as to study the formability of these materials, their forming limit diagrams were studied according to approximate stress–strain curves (Zhou et al., 2006; Zhou et al., 2007b). In this paper, the materials forming performance was carefully studied by forming limit diagrams which are based on practical stress–strain relationships. The forming limit diagrams for the materials are precisely re-plotted and its forming performance was analyzed.
2. Stress–strain relationships and numerical fitting 2.1.
Sample preparation
Nickel coating was prepared by electrodeposition method. A lower carbon steel of cold rolled sheet with the thickness of 0.25 mm was used as substrate. The substrate of cold rolled steel sheet is supplied by a steel factory with very good surface roughness. Its size tolerance in thickness is −0.02 mm. Prior to electroplating, the substrates were degreased and submerged in 6 M hydrochloric acid for 2 min and rinsed in distilled water. The samples were obtained with nickel sulphate electrolyte. The nickel sulphate electrolyte was composed of 240 g NiSO4 ·6H2 O, 40 g NiCl2 ·6H2 O, 40 g H3 BO3 per liter. Pure nickel was used as the anode. Before electroplating, H2 O2 and active carbon were used to get rid of the impurities. Moreover the electrolyte solution was electrolyzed for 24 h. In the case, the pH of the solution was 4.0 ± 0.1 and the temperature was 50 ± 0.5 ◦ C. The current density was 2 A/dm2 . The cell was automatically agitated. The thickness could be measured by
Fig. 1 – Section of the interface between electrodeposited nickel coating and steel substrate observed by SEM. Point A is coating, points B and C are interfaces, and point D is substrate.
a thickness tester of ZWB. In order to precisely measure the thickness of the coating, the section of the coating/substrate composite was observed by (JEOL)JSM-5600LV SEM and in this case the measured thickness of the coating could be checked by SEM measurement. The chemical composition near interface between electrodeposited nickel coating and steel substrate and the microstructure of the coating is concerned. Fig. 1 shows the section of the interface between electrodeposited nickel coating and steel substrate observed by SEM. In the figure, point A is coating, points B and C are interfaces, and point D is substrate. It illustrates that the thickness of coating was same at any place and its thickness was 5 m. Fig. 2 shows the chemical compositions at points A–D. The chemical composition near interface shown in Fig. 2 demonstrates that the chemical composition gradient exists at the interface between nickel coating and the substrate. The gradient change in chemical composition can enhance the interface strength.
Fig. 2 – Chemical compositions at points A–D.
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2.3. Numerical fitting for the stress–strain relationships The stress–strain data of the nickel coating and steel substrate should be fitted so as to apply them to the analysis and calculation of forming limit. In terms of the polynomial fitting theory in MATLAB, through the calculation of a quantity 2 (Chi2 ) and a probabilistic value Q (Zhong, 2000), it is found that the polynomial of its degree equaling to 5 is most suitable for the fitting. That is 5
(i)
(i)
4
3
(i)
2
(i)
(i)
(i)
(i) = a1 ε(i) + a2 ε(i) + a3 ε(i) + a4 ε(i) + a5 ε(i) + a6 d (i) dε Fig. 3 – The stress–strain data and fitted curve for the substrate.
2.2.
Stress–strain relationship for the composite
By using a mechanical model, the stress–strain properties and main mechanical parameters of the nickel coating and the steel substrate could be obtained by a (JEOL)JSM-5600LV SEM (scanning electron microscopy) in which the tensile force could be applied by a tensile equipment. In this method, the tensile force-strain properties of the substrate without coating were first determined, then the force-strain properties of coating/substrate composite were determined (Zhou et al., 2007a). The cold rolled steel sheet with a thickness of 0.25 mm was used as the substrate. The nickel coatings of thickness 6.2 m, 8.1 m and 9.6 m were bilaterally electrodeposited on the substrate respectively by adjusting different electrodeposition time. Afterwards the coated sheets were wire cut as specimens which can be fixed on JSM-5600LV SEM. The stress–strain relationships of the nickel coating and steel substrate can be worked out as experimental data shown in Figs. 3 and 4 according to the measure data.
(i)
4
3
(i)
(i)
2
(i)
(1)
(i)
= 5a1 ε(i) + 4a2 ε(i) + 3a3 ε(i) + 2a4 ε(i) + a5
(i)
(2)
(i)
where aj for j = 1, 2 . . . 6 represents the coefficient of fitted polynomial for ith layer stress–strain relationships. After calculation, the coefficients of fitted polynomial for ith layer stress–strain relationships are shown in Table 1. The stress–strain relationships may also be fitted as the Hollomon formulae according to traditional modus operandi. That is through a least squares method, the stress–strain data are fitted as = 946.3ε0.3696 (MPa) for the low carbon steel substrate and = 1805.6ε0.3570 (MPa) for the nickel coating (Zhou et al., 2007b). The fitted polynomials and Hollomon formulae are indicated in Figs. 3 and 4 combined with the experimental data.
3. Constitutive equations for the coating sheet By utilizing the Hill yield function the equivalent stress and equivalent strain may be deduced for laminate sheet materials (Peng and She, 1999). This modus operandi may be adopted for the sandwich coating sheet. In coating sheet, the equivalent (i) stress in ith layer ¯ (i) related to the principal stress in 1 axis 1 is
¯
(i)
=
3(1 + R(i) ) 4(2 + R(i) )
(1 −
1/2
2R(i)
(i)
1 + R(i)
(i)2
˛ +˛
)
(i)
(i)
1 = B(i) 1
(3)
here,
B(i)=
3(1 + R(i) ) 4(2 + R(i) )
(1 −
1/2
2R(i)
2
1 + R(i)
˛(i) + ˛(i) )
(4)
where R(i) is the normal anisotropic constant in ith layer, and ˛(i) is the principal stress ratio 2 / 1 in the layer. Eqs. (3) and (4) indicated that in the laminated coating sheet, the equivalent stress in different layers is different. By analogy, the equivalent strain increment in ith layer dε(i) related to the first principal strain increment dε1 (i) is
dε(i) = Fig. 4 – The stress–strain data and fitted curve for the coating.
2(2 + R(i) )(1 + R(i) ) 3(1 + 2R(i) )
= C(i) dε1 (i)
(1 +
2R(i) 1 + R(i)
1/2 ˇ + ˇ2 )
dε1 (i) (5)
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Table 1 – The coefficient of fitted polynomial (i)
Polynomial coefficient (i = 1, 2, 3) Coating (i = 1, 2) Substrate (i = 3)
(i)
(i)
(i)
a1
a2
a3
a4
0.516779 0.404543
−42.5288 −30.9795
1275.16 873.246
−16964.4 −11144.0
(i)
a5
103,767 64944.9
(i)
a6
83821.7 33208.3
where
C(i) =
2(2 + R(i) )(1 + R(i) )
1+
3(1 + 2R(i) )
2R(i) 1 + R(i)
1/2 ˇ + ˇ2
(6)
Eqs. (5) and (6) illustrated that during forming process the equivalent strains are different in each layer. Postulating that the adjacent layer in the coating sheet has equal principal strains, then for the ith layer the principal strains increment are
dε1 =
3d¯ε 1 + R(i) 2¯ 2 + R(i)
dε2 =
3d¯ε 1 + R(i) 2¯ 2 + R(i)
dε3 =
3d¯ε 1 (i) [1 + ˛(i) ]1 2¯ 2 + R(i)
1−
R(i) 1 + R(i)
˛(i) −
(i)
˛(i) 1
R(i) 1 + R(i)
(7)
(i)
1
(8)
(9)
According to Eqs. (7) and (8), the strains increment ratio ˇ can be obtained as ˛(i) (1 + R(i) ) − R(i) dε2 = ˇ= dε1 1 + R(i) − ˛(i) R(i)
R(i) + (1 + R(i) )ˇ 1 + R(i) + ˇR(i)
of same thickness, and the third layer is the substrate of low carbon steel. Under the plane stresses of two axes which are shown in Fig. 6, when diffuse necking appears the loads in two principal directions will reach maximum (Xiao and Jiang, 2000). That is
dp1 = d
(11)
where R(i) may be determined by experiment. Since the normal anisotropic constant in different layers is different, the stress ratio in different layers is different.
dp2 = d
The formability of sheet metal is often evaluated from strain analyses using the concept of forming limit diagrams (FLDs) introduced by Keeler and Goodwin. Many attempts have been made to predict the FLDs on the basis of the theory of plasticity, the material parameters and the instability condition. Wang developed an instability criterion for sheet metals under tensile stresses and plotted the forming limit curves in right region on the base of tensile test (Zutang, 1997). The author investigated the electrodeposited nickel coating’s forming limit in the left region by using Hill localized necking theory (Zhou et al., 2006). The forming limit of electrodeposited nickel coating in the right region will be studied here by using the Swift diffuse necking theory. The structure of the electrodeposited nickel coating sheet is just as Fig. 5. The first and second layers are nickel coatings
(i) (i) A1 1 1
=0
(12)
=0
(13)
(i) (i) A2 2 2
i
where pj is the load in principal direction j, shown in Fig. 4; Aj is the cross-section total area of the coating sheet in principal (i) direction j; j is the stressing in principal direction j and in (i)
(i)
ith layer for the coating sheet; 1 and 2 are the area ratio of the ith layer in the total section area in the principal directions (i) (i) (i) (i) 1 and 2, respectively; and 1 = A1 /A1 , 2 = A2 /A2 , moreover (i)
4. Forming limits of the nickel coating sheet
i
(10)
When the strain increment ratio ˇ is given, the stress ratio ˛ is ˛(i) =
Fig. 5 – Schematic of the electrodeposited nickel coating sheet.
(i)
1 = 2 = (i) = const.. The length, width, and thickness of the nickel coating sheet are denoted respectively by l, b, and t which are shown in Fig. 3. Thus the volume of the coating sheet V = lbt. When thickness t is regarded as constant in the tensile process, it can have,
Fig. 6 – Diffuse necking conditions.
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435
dV = d(lbt) = tbdl + tldb = 0. Thus dA1 = −dε1 A1
(14)
In terms of Eq. (12), substituting Eq. (14), may have
(i)
i
(i)
d1 (i) − 1 dε1
=0
(15)
By utilizing Eqs. (3) and (5), the following will be obtained
(i) i
B(i)
C(i)
d (i) dε(i)
− (i)
=0
(16)
Eq. (16) is the diffusing necking condition equation for the coating sheet. By substituting Eqs. (1) and (2) into the equation, we can obtain a nonlinear equation of unknown parameter ε(i) . (i) By utilizing Eq. (5), and noticing that the strain ε1 in different layer is equal to each other (assuming interface did not delam-
Fig. 8 – Effect of substrate anisotropy on the FLD of the coating sheet.
(i)
inate), ε1 = ε1 . Thus Eq. (16) will become a nonlinear equation of an unknown ε1 , the equation may be solved.
5.
Results and discussion
To investigate the press-forming limits of the electrodeposited nickel coating sheet in the right region, the nonlinear Eq. (16) needs to be solved first. Under the given materials parameters and strain path ˇ (0 ≤ ˇ ≤ 1), parameters (i) , B(i) , C(i) are all known. Iteration method can be adopted to solve the nonlinear equation, iterative scope may be set as [0.001, 2] for the unknown ε1 , and convergence precision may be specified as (i) 10−6 , thus may obtain the principal strain ε1 , ε1 , and equiva(i)
lent strain ε1 , etc. According to the proposed model, extensive calculations are carried out on MATLAB and the results are as follows. Figs. 3 and 4 are the stress–strain relationships and fitted curves for the substrate and coating. From these figures we may find that the fitted polynomial curves have quite good precision to the experimental data, but the fitted Hollomon
Fig. 7 – FLD of the nickel coating steel sheet.
Fig. 9 – Effect of coating anisotropy on the FLD of the coating sheet.
curves have less precision. The polynomial fitted curves are named practical stress–strain relationships. Thus the analysis precision for using the practical relationships in this paper should be quite better than the Hollomon formulae. Fig. 7 is the FLD of the nickel coating sheet. Here the thickness of the nickel coating is 5 m, and the thickness of steel substrate is 0.25 mm, and its normal anisotropic constant 1.41. In this figure, curve 1 is the FLD calculated by the proposed model in this paper which used the practical stress–strain relationships. The FLDs of curves 2, 3 and 4 used Hollomon formulae, and the FLD of the coating sheet is curve 4 which locates in the middle of FLDs of the nickel coating and steel substrate (Zhou et al., 2007b). It is obvious that the FLDs difference in these two methods is comparatively big, and it is necessary to use practical stress–strain relationships for drawing FLDs. The way in which the component anisotropy affects the forming limit of the coating sheet is shown in Figs. 8 and 9.
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Fig. 10 – Effect of substrate anisotropy on the effective strain in substrate.
Fig. 12 – Effect of coating thickness on the FLD of the coating sheet.
And Figs. 10 and 11 are the effect of substrate anisotropy on the effective strain of the component. Fig. 8 apparently shows that the bigger the substrate anisotropy constant is, the higher the forming limit of the coating sheet is. This is because the bigger the substrate anisotropy constant is, the greater the effective strain in the component is, which is shown in Figs. 10 and 11, and it can withstand greater deformation. Hence the substrate anisotropy being bigger than 1 will favor the sheet forming, and raising the substrate anisotropy constant will improve the material’s forming limit. This is why the coating sheet should be rolled before leaving factory. How the coating anisotropy affects the forming limit of the coating sheet is not obvious just as Fig. 9. This may be due to the nickel coating which is too thin, but it can be found that it obeys the same rule as the substrate by enlarging the figure. The figures that the coating anisotropy affects the effective strain in the components do not give out since its influence is fairly small. Figs. 10 and 11 also show that the strain path clearly affects the effective strain in the coating and substrate.
The coating thickness affecting the forming limit of the coating sheet is shown in Fig. 12. From the four kinds of thickness it is found that the thicker the coating is, the worse the forming limit of the composite is. This arises because the forming limit of the nickel coating is not as good as the steel substrate which is shown in Fig. 7 in which curve 3 for individual substrate is higher than curve 2 for individual coating. So the thinner nickel coating is better is the forming performance with the steel substrate. The suitable thickness of the nickel coating is recommended to be 3–5 m to consider the thinning during forming processes (Zhou et al., 2004b).
Fig. 11 – Effect of substrate anisotropy on the effective strain in nickel coating.
6.
Conclusions
Thin coatings have become a key technology in a wide range of industries for a wide range of engineering purposes. There are many technologies that use thin layers of dissimilar materials in order to achieve functional requirements. Surface modification by electrodeposited nickel coating is an important technology. It is designed and constructed production lines to electrodeposit uniform nickel coatings on the substrate of low carbon steel sheet. By utilizing Hill yield function and the equivalent stress and equivalent strain of laminated sheet materials, the forming limit of electrodeposited nickel coating in the right region is studied through the Swift diffuse necking theory. This study determined the stress–strain properties of the coating layers and its working performance and the following conclusions may be drawn: (1) The stress–strain properties of the nickel coating and steel substrate may be determined by improved scanning electron microscopy. The degree 5 polynomial is most suitable for fitting the stress–strain data in the coating and substrate as the practical stress–strain relationships. (2) The FLD drawn by practical stress–strain relationship is great different from that drawn by Hollomon formula. (3) The anisotropy constant of the steel substrate has fairly great effects on the FLD of the coating sheet, but the coat-
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 6 ( 2 0 0 8 ) 431–437
ing’s anisotropy has no obvious influence on it. When the substrate anisotropy constant is bigger than 1 it will favor the sheet formability. (4) The thinner nickel coating is better for its forming performance as related to the coating thickness.
Acknowledgments This work was supported by the Open Project Program of Key Laboratory of Low Dimensional Materials & Application Technology, Ministry of Education, China (No. KF0613) and the Key Foundation of Xiangtan University (No. 06IND04). The supports are gratefully acknowledged.
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