Mechanical Properties Identification of Sheet Metals by 2D-Digital Image Correlation Method

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ScienceDirect Procedia Engineering 184 (2017) 381 – 389

Advances in Material & Processing Technologies Conference

Mechanical Properties Identification of Sheet Metals by 2D-Digital Image Correlation Method Van-Thuong Nguyen1, Seong-Jin Kwon2, Oh-Heon Kwon3 and Young-Suk Kim1,* 1

School of Mechanical Engineering, Kyungpook National University, Daegu 41566, Republic Korea Daegu-Gyeongbuk Center, Korea Automotive Technology Institute, Daegu 43011, Republic Korea 3 Division of Safety Engineering, Pukuong National University, Busan 48513, Republic Korea

2

Abstract Digital Image Correlation (DIC) method is a powerful technique for measuring material deformation field. By comparison of digital images of the undeformed and deformed configuration, DIC provides full-field displacements to sub-pixel accuracy and full-field strains in recorded images. Recently, the DIC method has been developed and used increasingly in various researches because of its advantages. However, a commercial 2D-DIC system requires a high initial investment. In this study, an in-house 2D-DIC system is developed to measure Young’s modulus, Poisson’s ratio, anisotropic plastic ratio parameters and flow curve under uniaxial tension of AL5052-O and high strength steel (DP980) sheets in rolling direction. The measured 2D-DIC results were compared with those of standard test method using strain-gauge type extensometer. The good agreement between the two measurement methods verifies the accuracy of the established 2D-DIC system. Furthermore, this method has been utilized in order to observe Portevin-Le Chatelier (PLC) band behaviour, Lüders band behaviour and shear band behaviour during tensile deformation of materials. The results of DIC method revealed reasonable results in measuring strain and local strain to capture ductile fracture behaviour of materials. © 2017 The Authors. Published by Elsevier Ltd. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of the Advances in Material & Processing Technologies (http://creativecommons.org/licenses/by-nc-nd/4.0/). Conference.under responsibility of the organizing committee of the Urban Transitions Conference Peer-review Keywords: digital image correlation (DIC); tensile test; speckle; full-field measurement; mechanical property.

* Corresponding author. Tel: +82-53-950-5580 E-mail address: [email protected]

1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the Urban Transitions Conference

doi:10.1016/j.proeng.2017.04.108

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1. Introduction Nowadays, displacement and strain fields can be measured by various methods such as interferometric method, strain-gauge method, digital image correlation (DIC) [1]. Due to the rapid development of digital image processing and these applications in last decade, the digital image correlation techniques for full-field strain measurement have been studied by many researchers. The material properties such as Young’s modulus, Poisson’s ratio, anisotropic plastic ratio parameters, etc. were required for optimization of the designing and manufacturing processes by finite element analyses. The most commonly used method for finding the material properties is tensile test with strain-gauge type extensometer. However, the results from extensometer are not applicable to measure strain at local point and onset of diffuse necking [2]. The DIC method is a state of the art technique that can be used for an accurate strain measurement of material properties. It also has an advantage of full field, non-contact and considerately high accuracy for full-field displacement and strain measurements [3]. Before necking occurs, the “normal” mechanical behaviour of materials in tensile test is the smooth transition from elastic to elastic-plastic region with a steadily rising stress-strain curve. In contrast to this, in some materials the yield point phenomenon shows an abrupt transition from the elastic to elastic-plastic behaviour with a characteristic dropped in the stress-strain curve, as shown in Fig. 6 for DP980 material. This phenomenon was known as a Lüders band behaviour [4]. The effect such as an unstable plastic flow during tensile test of some dilute alloys under certain regimes of strain rate and temperate. The plastic strain becomes localized in the form of bands which move along a specimen gauge as the Portevin-Le Chatelier (PLC) effect occurs [5, 6]. In this paper, a 2D-DIC system using NCORR software [7] was employed to measure the full-field strain distribution, Young's modulus, Poisson's ratio as well as the anisotropic plastic ratio parameters for aluminum AL5052-O and high strength steel DP980 sheets in rolling direction. These DIC results were used to observe PLC effect for DP980 material and Lüders band, shear band phenomenon for AL5052-O material. A better understanding of the impact of these phenomenon in materials can be used to develop better applications of the materials in the automotive industry. Furthermore, post-necking prediction of Kim-Tuan model [8, 9] in comparing with the effective stress-strain data was conducted in this study. 2. 2D-DIC system In general, the 2D DIC method includes the following three consecutive steps, namely (1) spraying speckled patterns on the specimen surface to show a random grey intensity distribution; (2) recording the digital images of the undeformed and deformed specimen surface; (3) applying DIC software to obtain full-field displacement and strain. 2.1 Basic principle and concept

Fig. 1 Basic principle of subset-based DIC method [1]

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The basic principle of DIC is the tracking of the same image points located in the two digital images of the test specimen surface recorded before and after deformation. 2.1.1 Displacement mapping function. It is reasonable to assume that the shape of the reference square subset is changed in the deformed images. Therefore, as schematically shown in Fig. 1, a square reference subset of (2M+1) x (2M+1) pixels, the coordinates of point Q(x i , y i ) around the subset center P(x 0 , y 0 ) in the reference subset can be mapped to point Q(x i' , yi' ) in the deformed subset according to the so-called displacement mapping function is defined by: x i' = x i + ξ(x i , yi )

(1)

yi' = yi + η(x i , yi )

The shape function that allows translation, rotation and their combinations of the subset is most commonly used: ξ(x i , yi ) = u + u x Δx + u y Δy η(x i , yi ) = v + v x Δx + v y Δy

(2)

In these equation, Δx = x i - x 0 ; Δy = yi - y0 ; u, v are the x - and y - directional displacement components of the reference subset centre, and u x , u y , vx ,v y are the first-order displacement gradients of the reference subset. 2.1.2 Correlation criterion. To evaluate the similarity degree between the reference and deformed subset, a correlation criterion should be defined before correlation analysis. In order to find the deformation of the subset, DIC algorithms find the extremum of a correlation cost function. The normalized cross-correlation (NCC) [1] is one of these functions at integer location, which can be written in form: ª f(x i , y j )g(x i' , y'j ) º « » fg i=-M j=-M ¬ « ¼» M

C NCC =

M

¦ ¦

(3)

Here ˆ and ‰ are respectively the reference and current image grayscale intensity functions at a specified locationሺšǡ ›ሻ. ˆҧ and ‰ത are determined by using functions in form: M

f =

M

¦ ¦

i=-M j=-M M

g=

M

¦ ¦

i=-M j=-M

ª¬f(x i , y j ) º¼

2

(4) ª¬g(x , y ) º¼ ' i

' j

2

2.1.3 Computation of strain Lagrangian strains are obtained by using the four displacement gradients as following:

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E xx =

1 § wu § wu · § wv · +¨ ¸  ¨ ¸ ¨2 ¨ 2 © wx © wx ¹ © wx ¹

E xy =

1 § wu wv wu wu wv wv · + + + ¨ ¸ 2 © wy wx wx wy wx wy ¹

E yy =

§ wv · 1 § wv § wu · ¨2 +¨ ¸  ¨ ¸ 2 ©¨ wy © wy ¹ © wy ¹

2

2

2

2

· ¸¸ ¹ (5)

· ¸ ¸ ¹

Strain contour maps computed by DIC method were used to calculate local true strain as following: ε eng = -1+ 2×ε Lag +1 ε true = ln(1+ε eng )

(6)

Here the subscripts “eng”, “Lag”, “true” mean engineering, Lagrangian, true, respectively. Hence, the average true strain ሺɂୟ୴ୣǤ ሻ is calculated as: ε ave. =

1 N M ¦¦ ε(i, j) M×N 1 1

(7)

Where M and N are total number of DIC grid points along the tensile axis and perpendicular to it, respectively. ε(i, j) is the local true strain at grid point (i, j) and ε ave. is the average true strain that was calculated over the entire gauge section. 2.2 Experiment preparation Fig. 2 shows the schematic illustration of an in-house 2D-DIC system. The specimen surface needs to show a random grey intensity distribution. The specimen surface must remain in the same plane parallel to the sensor plane of the camera during loading [1]. The tensile tests were performed on a tensile testing machine with 5-tonnage load capacity at a constant tensile speed of 5mm/min. Full-field strain measurement during uniaxial tensile test at room temperate was performed by using an in-house 2D-DIC system with NCORR software. A CMOS camera with full resolution of 1936x1216 pixels

Fig. 2 Schematic of experimental setup for tensile test.

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was used to record images of entire surface of the gauge section of 50x12.5mm2 area during tensile test. For this test, the camera was set to keep normal to the plane of the specimen and to take images with the speed of 5 frames/second. 3. Results and discussion In this study, the strains determined by the strain-gauge (type extensometer) method and the DIC method for both sheet materials are almost similar. Figs. 3(a) and 3(b) show the stress-strain curves measured by the strain-gauge type extensometer method (solid line) and the DIC method (dotted line). The stress-strain curves for both methods overlap together up to the maximum stress point, but show just a little difference after the necking. The different results after the necking occurrence came from the fact that the strain at necking area as marked by C is larger than the outside area of the neck showing almost uniformly straining. As indicated in Figs. 4(a) and 4(b), the maximum true strain (ε y ) max at C area is 0.436 for AL5052-O sheet and 0.272 for DP980 sheet. However, the average true strain for AL5052-O sheet and DP980 sheet, which is defined by (7), is approximately 0.108 and 0.123, respectively. Also each figure includes animated color contour maps of longitudinal Lagrangian strain component in region of interest at yield point, maximum stress (tensile strength) point and fracture occurrence point, each indicated in Y, M, and F, respectively. The anisotropic coefficients of materials in the form of sheets are defined by ratio of plastic strain rate transversal p (ε p22 ) and plastic strain rates normal (ε33 ): r=

ε p22 p ε 33

(8)

p These coefficients are given from slope of the straight line of the representation of ε p22 according to ε 33 measured during a tensile test. Furthermore, Young’s modulus (E), tensile yield strength (σ YS ) , and Poisson’s ratio (υ) were also calculated from the DIC results. These values are shown in Table 1. The benefit of the DIC is that it provides a more complete true stress-strain curve in all range of straining of the material under loading condition before and after necking until the fracture in the tensile test. However, the traditional extensometer method only provides the stress-strain curve before necking [2]. Bridgman’s research [10] focused on a solution for the problem beyond necking in tensile specimen. However, Bridgman correction method is not convenient to use in practice because it requires a series of test with different loadings to determine the radius of curvature R and the minimum diameter D which are both difficult to measure with sufficient accuracy. By measuring the local strain at the necking area C and sequentially applying the following relationship, we can derive the whole stress-strain curve up to failure occurrence from (6) and using:

σtrue = σeng 1+εeng

(9)

The measured true stress-strain curves after the necking (i.e. post-necking) known as strain hardening curve or flow curve are denoted by the dotted curve after the maximum point M in Figs. 3(a) and (b). The measurement and prediction of the stress-strain curve of material in all range of straining under loading are essential in studying finite element analysis for the plastic forming problem as incremental sheet forming [11], equal-channel forming [12] and forging problem [13]. Figs. 4(a) and (b) show the longitudinal strain distributions along the line AB at three levels of the average strain corresponding to the just three previous steps before fracture occurrence. According to the DIC results, the strain at the necking area C near the fracture occurrence point increases largely and localizes into narrow region on both Table 1. Mechanical properties for AL5052-O and DP980 sheets. Material

AL5052-O

r0 0.763

σ YS

E [GPa]

υ

72.1

0.28

[MPa] 167.8

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DP980

0.761

(a)

759.9

225.8

0.39

(b)

Fig. 3(a) True stress-strain curves for AL5052-O; (b) True stress-strain curves for DP980. (a)

(b)

Fig. 4(a) True strain distribution for AL5052-O; (b) True strain distribution for DP980.

materials. However, the localization tendency and localized width for AL5052-O sheet are more remarkable compared with DP980 sheet. It is clear that local strain at the C area of AL5052-O sheet,  ε y = 0.436, is larger than that of max

DP980 sheet,  ε y = 0.272, although the average strains for both materials are almost similar, in which  ε y = max ave.

= 0.123 for DP980. 0.108 for AL5052-O and  ε y ave.

A series of strain maps obtained from DIC measurements on the tested sample at room temperature are shown in Figs. 5(a), (b) and Fig. (6). DIC results can observe clearly PLC band, shear band for AL5052-O and Lüders band phenomenon for DP980. Fig. 5(a) shows strain map from true strain of 0.05 to true strain of 0.07. It clearly shows the characteristics of type-B PLC band, where deformation bands are nucleated at random locations. This PLC band phenomenon fixed angle ranging from 58o to 60o with respect to the tensile axis. Spencer et al. [14] have pointed out that the shear localization process occurs prior to fracture occurrence. All these findings suggest that shear localization enhances local damage processes and therefore this one has a crucial role in

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Van-Thuong Nguyen et al. / Procedia Engineering 184 (2017) 381 – 389 (a)

(b)

Fig. 5(a) Growth of the PLC band for AL5052-O; (b) Growth of the shear band for AL5052-O.

Fig. 6 Growth of the Lüders band for DP980.

determining the ultimate conditions for failure of materials. Moreover, this specimen did not fail by shear localization within one band, as observed in Fig. 5(b). The Lüders band effect, referred to the yield point phenomenon, which is affected by the applied strain rate, the test temperature and the grain size, etc. [4]. Fig. 6 shows Lüders band for DP980 material that was aligned about to 57o with respect to the tensile axis. The Lüders band starts at one of specimen and propagates toward the other end. The results of and Lüders band from DIC method predict the existence of critical nuclei of the strain-fluctuation region, which cause loss of plastic-deformation stability. To describe the flow curve of the tested sheets into an analytical form for FEM simulation of the sheet metal forming, Kim-Tuan hardening model that has been developed by one of the authors was applied. Formulation of KimTuan model is expressed in following equation: σ = σ 0 + T  ε + ε 0 1 - exp - cε m

(10)

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Van-Thuong Nguyen et al. / Procedia Engineering 184 (2017) 381 – 389 Table 2. The parameters of Kim-Tuan model for flow curves of tested materials. Material

ε0

σ0

T

[MPa]

[MPa]

m

c

AL5052-O

0.002

166

120.49

0.28

71

DP980

0.002

760

691.35

0.26

72

Fig. 7 Post-necking prediction of Kim-Tuan model in comparing with the effective stress-strain data obtained from DIC method.

Here T, m, and c are parameters of hardening model;  ε 0 , σ 0 is the limit of elastic behaviour of material. Detail on identifying the value of these parameters is referred to Ref [8, 9]. Parameters of Kim-Tuan model used to generate the predicted flow curves of two tested materials are reported in Table 2. In order to highlight the benefit of DIC method on determining the stress-strain data at a local area on specimen, Fig. 7 shows the comparisons of the local stress-strain curves (solid curves) in Fig. 3 and the predicted flow curves (dotted curves) based on Kim–Tuan hardening model. In this figure H M and H F denoted the strains at the maximum stress point and the fracture occurrence point as indicated in Figs. 3(a) and (b). It is clear that Kim-Tuan hardening model described well the experimental stress-strain curves over the whole range of straining of the material under loading in both tested materials of aluminum and high strength steel sheets even though the measured data after onset of necking are a little higher than the predicted curves. This difference may be induced from the strain rate effect, the rate of deformation in the local area of necking is higher than the average strain rate estimated on other area on the specimen and shows higher stress. We left future works to reveal the effect of the strain rate and temperature on the measured stress-strain data beyond the occurrence of diffuse necking, especially, on the critical area on the specimen. DIC method is a good choice to reach this goal. 4. Conclusion The developed an in-house 2D DIC system provided a precise measurement for strain distribution on the tensile specimen in comparing with traditional measurement method of using extensometer. Furthermore, the advantage of DIC measurement method for evaluating the strain evolution in the critical area was supported in this study for two different materials. The DIC measurement shows that two different phenomena, namely PLC banding and shear banding occur in the AL5052-O material. PLC band aligned 59o ± 1 degree with respect to the tensile axis. For DP980, Lüders banding was observed with the bands aligned about to 57o with respect to the tensile axis.

Van-Thuong Nguyen et al. / Procedia Engineering 184 (2017) 381 – 389

Furthermore, the Kim-Tuan hardening model was compared with local stress-strain obtained in 2D-DIC measurement. Hence, the stress-strain relationship up to large strain level in the post-necking region can be identified by using DIC method. Specially, the detailed effect of strain rate for local stress-strain curve will be reported in the future work. Acknowledgements This work was supported by National Research Foundation of Korea (NRF) grant funded by the Korea Government (MEST) (NRF-2014R1A2A2A01005903) and a grant No. R0003356 for Tuning Professional Support Center in Daegu Metropolitan City from Ministry of Trade, Industry and Energy (MOTIE). References [1] B. Pan, K. Qian, H. Xie, and A. Asundi, Two-dimensional Digital Image Correlation for in-plane displacement and strain measurement: A review, Measure. Sci. Tech., 20-6(2009), 1-17. [2] Y. H. Wang, J.H. Jiang, C. Wanintrudal, C.Du, D.Zhou, L.M. Smith and L.X. Yang, Whole field sheet-metal tensile test using Digital Image Correlation, Exper. Tech., 34 (210), 54-59. [3] O.H.Kwon, S.T. Kim, J.W. Kang, A study of the strain measurement for Al6061-T6 tensile specimen using the Digital Image Correlation, J. Korean Soc. Safety, 28-4 (2013), 26-32. [4] Y.L Cai, S.L Yang, S.H Fu, Q.C Zhang, The influence of specimen thickness on the —ሷ †‡”• effect of a 5456 AL-Based alloy: Experimental observations, Metals 6 (2016), 120. [5] Ahmet Yilmaz, The Portevin-Le Chatelier effect: a review of experimental findings, Sci. Technol. Adv. Mater., 12 (2011). [6] W. Tong, N. Zhang, On serrated plastic flow in an AA5052-H32 sheet, J. Eng. Mater. Technol., 129 (2006), 332-341. [7] J. Blaber, B. Adair, A. Antoniou, Ncorr: Open-Source 2D Digital Image Correlation Matlab Software, Exper. Mech., 55 (2015), 1105-1122. [8] Q. T. Pham, Y. S. Kim, Evaluation of press formability of pure titanium sheets, Engineering Material, 716(2016), 87-98. [9] Q. T. Pham, Y. S. Kim, Identification of the plastic deformation characteristics of AL5052-O sheet based on the non-associated flow rule, Metals and Materials International, be in print 23(March, 2017), (accepted). [10] P. W. Bridgman, Studies in large plastic flow and fracture, McGraw Hill, N.Y., 1952, 32-36. [11] Do, V. C., Nguyen, D. T., Cho, J. H., Kim, Y. S., Incremental forming of 3D structured aluminum sheet, Int. J. Precis. Eng. Manuf., 17 (2016), 217-233. [12] M. Furukawa, Z. Horita, M. Nemoto, Review processing of metals by equal-channel angular pressing, J. Mater. Sci., 36(2001), 2835-2843. [13] T. Altan, and V. Nagpal, Recent developments in closed die forging, Int. Metallurgical Review, 322(Dec. 1976). [14] K. Spencer, S.F. Corbin, D.J. Lloyd, The influence of iron content on the plane strain fracture behaviour of AA 5754 Al–Mg sheet alloys, Mater Sci Eng., A325 (2002), 394-404.

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