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ScienceDirect Materials Today: Proceedings 2 (2015) 2037 – 2045

4th International Conference on Materials Processing and Characterization

Finite Element Validation of Forming Limit Diagram of IN-718 Sheet Metal K.Sajun Prasada, T. Kamala, S.K. Pandaa*,S. Karb,S.V.S. Narayana Murtyc and S.C Sharmac b

a Department of Mechanical Engineering, IIT-Kharagpur,India – 721302 Department of Metallurgical and Materials Engineering, IIT-Kharagpur,India – 721302 c Indian Space Research Organisation , Thiruvananthapuram, India– 695022

Abstract The tensileanisotropy properties of Inconel-718 sheet metal were evaluated and the forming limit diagram (FLD) was established experimentally by deforming the material in different strain paths covering from tension-tension to tension-compression mode. Finite element model of the stretch forming process was developed successfully to predict limiting dome height (LDH) and strain distribution incorporating the Barlat-89 yield criterion and experimental FLD. It was found that the left side of FLD has higher forming limitscompared to right side. The IN-718 has encouraging stretch formability with uniform strain distribution in the cup compared to Ti6Al4V alloy reported in previous literature. © 2015 2014Elsevier The Authors. Ltd. All rights reserved. © Ltd. AllElsevier rights reserved. Selectionand andpeer-review peer-review under responsibility the conference committee members ofInternational the 4th International Selection under responsibility of theofconference committee members of the 4th conferenceconference on Materialson Materials Processing and Characterization. Processing and Characterization. Keywords:Anisotropy properties; Forming limit diagram; Strain distribution; Limiting dome height.

1. Introduction: Aerospace manufacturing industries are very much interested in applications of INCONEL alloys for fabrication of various three dimensional complex sheet metal components due to their high temperature strength and corrosion

* Corresponding author. Tel.: +91 - 3222 – 282910 fax: +91-3222-255303 E-mail address:[email protected]

2214-7853 © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the conference committee members of the 4th International conference on Materials Processing and Characterization. doi:10.1016/j.matpr.2015.07.174

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resistance. Among the various grades of nickel-iron-chromiumbased super alloys, IN-718 is preferred particularly for fabrication of casings, cryogenic tank, fuel cell, gas turbine engines and various aircraft and space vehicles structures [1-3]. This age hardenable material has excellent weldability and formability in order to plastically deform into desired profiles and contours to fulfill the part design requirements [2]. Various sheet metal forming processes like stretch forming, deep drawing, bending, redrawing, ironing, flanging, trimming and piercing are often adopted while fabricating sheet metal components. However, a complex three dimensional desired component is deformed through a combination of above processes, where the sheet metal undergoes different complex strain and stress path. The ability of sheet metal to undergo large plastic deformation into a desired shape without excessive thinning/fracture is referred as formability, and its evaluation is essential for a successful stamping. There are several laboratory scale simulative tests to evaluate sheet metal formability such as limiting dome height (LDH) [3], limiting drawing ratio (LDR) [4], bendability [5], hole expansion ratio (HER) [4] and forming limit diagram (FLD) [6]. The FLD represents the limiting surface strains that a sheet metal can withstand before start of localized necking under a wide range of deformation mode in tensile-tensile and tensile-compressive loading path. This plot representing the combinations of major and minor surface strains that lead to failure of metal is also referred as Keeler-Goodwin diagram [7]. There are several experimental procedures suggested by various researchers to determine the FLD by generating different loading path through which the metal can be plastically deformed [8]. There are also abundant literatures available on generating FLDs of wide range of materials such as low carbon automotive grade steels [9-10], stainless steels[11-12], aluminum [13-14] and titanium [15-16] thin sheet metals, and these database is of immense help to sheet metal manufacturing industries while selecting materials with proper selection of process and tooling design parameters. Also, many theoretical models had been developed to estimate FLDs in order to save cost of tooling, materials and time while carrying out these intensive experimental tests [13, 15]. However these theoretical models are rather complex, and they could not able to predict agreement results with experimental values for all different materials deformed in various different forming operations. Currently, there are very limited formability data on IN-718 thin sheet materials at room temperature. Rather, the researchers in past paid much attentions in evaluating and modeling the super-plastic forming properties [1, 2] of this material. Hence in the present work, the mechanical properties and FLD of IN-718 thin sheet metal are evaluated experimentally at room temperature by conducting the tensile and out-of-plane stretch forming tests. The FE model of the stretch forming process was developed incorporating the experimentally determined anisotropy tensile properties and FLD of IN-718. The limiting dome height and the strain distributions predicted by the model were validated with the experimental data. 2. Material and Experimental Details: 2.1. Materials and specimens preparation Uniaxial tensile and stretch forming specimens were cut from IN-718 sheet of 1.25 mm thickness with high dimensional accuracy and surface finish by wire-cut electro-discharge machining. The dimensions of the tensile specimens were as per the ASTM-E8M standards. Three different rectangular specimens having different widths were designed to determine the right hand side of FLD by stretch forming in tensile-tensile deformation mode. In order to avoid splitting of the sheet metal at draw bead during stretch forming in tensile-compression mode, three circular specimens with recesses of different radii were designed instead of rectangular specimens. All the specimen geometries with dimensions are shown in Fig.1. The tensile specimens were cut along (00), diagonal (450) and transverse (900) to the rolling direction. However, all stretch forming specimens were cut with rolling direction aligned consistently along width of the specimens. The chemical composition of the IN-718 material used in the present study was evaluated by X-ray fluorescence analysis, and the results (shown in Table 1) confirmed to be a nickel-iron-chromium super alloy similar to available literatures [16]. Table 1.Chemical composition of IN-718 (wt. %). Element

Ru

Mo

Nb

Zn

Cu

Ni

Co

Fe

Mn

Cr

Ti

Composition (%)

0.013

2.94

5.22

0.133

0.068

52.59

0.106

19.72

0.076

18.07

0.986

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Figure 1.Specimens cut from 1.25mm thickness IN-718 sheet for various experiments (all dimensions are in mm).

2.2. Tensile testing The uniaxial tensile tests were carried in all the three directions in a computer controlled 50 ton Universal Testing Machine (UTM) at a constant quasi-static deformation speed of 2 mm/min. The load-displacement data obtained from UTM were used to plot true stress- true strain curves. Hollomon’s power law (Eq.1) was used to characterize the strain hardening coefficient (n-value) of the materials. The material having higher n-value distributes more uniformly the plastic strainwhich delays the onset of necking, and hence it is an important parameter for formability characterization. ߪതൌߝҧ௡ 

(1)

Where, ߪത -flow stress, K- strength coefficient, ߝҧ- flow strain and n- strain hardening exponent of the material. The Lankford coefficient (R-value), a measure of anisotropy property of sheet material, was evaluated using the Eq.2. The width and parallel length of the specimens were carefully measured both prior and after tensile deformation up to 75-80% of the maximum load. The R-values were evaluated in all the three direction to characterize R0, R45 and R90 values, and the normal (ܴത ) and planar (οܴ) anisotropy of the sheet materials were evaluated using Eq.3 and Eq.4. ఌ

ೢ೑

ఌೢ

ൌ ఌೢൌିሺఌ ೟

ೢ

೗

௟௡ሺ

ሻ

ೢ೚ ೗ ೢ ௟௡ሺ ೚ ೚ ሻ ೗ ೑ ೢ೑

ൌ ାఌ ሻ

ഥ =ோబ ାଶோరఱ ାோవబ ܴ ସ

ோబ ିଶோరఱ ାோవబ

οܴ=

ଶ

(2)

(3) (4)

Where, ‫ݓ‬௙ -final width, ‫ݓ‬௢ - initial width, ݈௢ - initial parallel length and݈௙ - final parallel length. 2.3. Stretch forming test The laboratory scale out-of-plane stretch forming set-up was fabricated consisting of hemispherical punch, upper

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and lower die incorporating drawbead. The important dimensions in the setup are given in Table 2. All the tools were mounted in a computer controlled double acting hydraulic press with 50 ton main ram and secondary ram capacity. To evaluate the limiting strains in the FLD, the stretch forming specimens were initially circular grid marked by electrochemical etching. The grid marked specimens were rigidly clamped between the upper and lower die with sufficient blank holding force to ensure complete restriction of material flow from the flange region. All the specimens were stretch formed by moving the punch in downward direction at a constant speed of 10 mm/min. The test was stopped as soon as necking/failure was observed in the cups through a mirror placed below. The failure was also monitored by the sharp drop in load from the data acquisition system. The major and minor diameter of the deformed ellipses in the tested specimens were measured using a stereo-zoom microscope to evaluate the engineering major and minor strain using the Eq.5 and Eq.6, and then transformed into true major and minor strain respectively. The major and minor strain data in the safe, necked and fractured region was evaluated in all the specimens. To get the repeatability, four specimens in each condition were tested. The limiting dome height of the specimens was measured using height gauge with least count of 0.001 mm. Table 2.Geometrical parameters of stretch forming setup (dimensions are in mm). Parameter Punch diameter Die Outside Diameter Die Inside Diameter Draw Bead Diameter

Dimension (mm) 50.0 180.0 54.0 72.0

ா௟௟௜௣௦௘௠௔௝௢௥௔௫௜௦ௗ௜௦௧௔௡௖௘ି௚௥௜ௗௗ௜௔௠௘௧௘௥

݁ଵൌ ݁ଶ =

ா௟௟௜௣௦௘௠௔௝௢௥௔௫௜௦ௗ௜௦௧௔௡௖௘

(5)



ா௟௟௜௣௦௘௠௜௡௢௥௔௫௜௦ௗ௜௦௧௔௡௖௘ି௚௥௜ௗௗ௜௔௠௘௧௘௥

(6)

ா௟௟௜௣௦௘௠௜௡௢௥௔௫௜௦ௗ௜௦௧௔௡௖௘

2.4. Finite element modeling The numerical simulation of stretch forming process of IN-718 was done using a commercially available explicit dynamic code LS-Dyna (version 971 solver). The finite element (FE) models of die, blank, blank holder and punch were constructed, andall the tools (except the blank) were assigned as rigid bodies. A quarter model was developed as shown in Fig. 2(a) to reduce the computational time. The die was fixed, and the punch was moved down in Zdirection with a trapezoidal velocity profile. The analytical drawbead was created on the die, and the blank holding force was applied in downward direction so as to restrict the material flow from the flange region inducing tensile stretching of blank. The blank was treated as a deformable body incorporating both normal and planar anisotropy properties. The Barlat’s yield function (Barlat-89) was chosen as material model, and this was expressed in terms of plane stress state as shown in Eq. [7]. The experimentally evaluated material properties such as yield strength, strength coefficient, strain hardening exponent and Lankford coefficients were input into the material model. The major and minor strain obtained from the FE simulation was imposed inside the experimental FLD to predict failure (Fig.2 (b)). The time step when the surface strains touched the FLD, the simulation was stopped and the LDH was measured as shown in Fig.2(c). The predicted LDH and strain distribution results were compared with the experimental values. ܽȁ݇ଵ ൅ ݇ଶ ȁெ ൅ ܾȁ݇ଵ െ ݇ଶ ȁெ ൅ ܿ ȁʹ݇ଶ ȁெ =ʹߪ௘ ெ ݇ଵ ൌ

ఙೣ ା௛ఙ೤ ଶ

;݇ଶ

ൌ ൤ቀ

ఙೣ ି௛ఙ೤ ଶ ଶ

ቁ ൅ ‫݌‬ଶ ߬௫௬ ଶ ൨

(7) ଵൗ ଶ

(8)

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whereߪ௘ is the effective stress and the coefficients, ݇ଵ and ݇ଶ are invariants of the stress tensor while M is an integer exponent. Also, ܽǡ ܾǡ ܿǡ ݄and ‫ ݌‬are anisotropy coefficients,and these can be expressed in terms of Lankford anisotropy parameters [17].

Figure 2. Finite element model of (a) stretch forming setup (b) major and minor strain and (c) LDH prediction.

3.Results and Discussions 3.1. Tensile Properties The plastic stress-strain responses of IN-718 sheet metal tested in three different directions with respect to rolling direction are compared in Fig.3. The various tensile properties such as 0.2% yield strength (YS), ultimate tensile strength (UTS), % elongation, strain hardening coefficient (n), strength coefficient (K) and normal anisotropy (ܴത) and planar anisotropy (οܴ) were evaluated and shown in Table 3. It can be clearly observed that the rolled sheet did not possess strong directional anisotropy properties as that of low-carbon steel sheets like IF or EDD steels [19, 20]. However, this material had a very high n-value which was responsible for its higher elongation. This material has very high strength and ductility suitable for stretch forming applications.

Figure 3.Plastic stress-strain curves of IN-718 at different orientations at room temperature.

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K. Sajun Prasad et al. / Materials Today: Proceedings 2 (2015) 2037 – 2045 Table 3.Average tensile properties of IN-718 material. Material

YS(N/ mm2)

UTS(N/ mm2)

K(N/ mm2)

n

% Elongation

ܴത

οܴ

IN-718

523

1084

1960

0.404

39.375

0.930

-0.030

3.2. Forming Limit Diagram The deformed specimens obtained from stretch forming experiments of different widths are shown in Fig.4. The surface major and minor strains measured from different width specimens were transformed to true strains and plotted to draw FLD of the IN-718 sheet metal as shown in Fig.4.The fractured, necked and safe ellipses were shown in different colour to distinguish.

Figure 4. Different width specimens after stretch forming and the corresponding experimental FLD.

The FLD, representing the limiting strains that IN-718 sheet metal can withstand, was distinguishing the safe region from failed ellipses. It can be observed that the FLD of the material has lower limiting strain at plane strain deformation i.e. at the intersection point of FLD with major strain axis (also referred as FLD0). The FLD0 of this material (0.35) is sufficiently higher compared to Ti6Al4V (0.12)reported in previous literature [13, 14, and 18]. The minor strain in the left hand side of the FLDwas negative due to lateral drawing of the material during stretch forming operation, and this helped the limiting major strain to increase before failure. However, the limiting major strain marginally increased in the right hand side of the FLD, and this might be due to the presence of the hard second phase particles or inclusions which will be characterized by fractography analysis in future. The present IN718 material FLD will be useful to the sheet metal manufacturing industries to: (a) predict failure in the IN718 component as a damage model and (b) avoid failure by redesigning the tools and selecting suitable process parameters. 3.3. Validation of FLD In order to validate the experimental FLD, the FE model was implemented to predict failure and strain distribution. The LDH and strain distribution predicted results were compared with the experimental results in three different deformed samples. 3.3.1.Limiting Dome Height The limiting dome height of the three deformed samples and the predicted FE results were compared in Table 4. It can be observed that the predicted results were comparable, and the LDH of specimens increases with the decrease in the width. To get insight, the FE predicted deformed cups with the failure strains imposed inside FLD is compared in Fig.5 (a, b, c).It can be seen that the strain path was lying completely in the left side of the FLD while

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stretch forming the narrow specimen having width of 30 mm. Hence, the failure in the cup was delayed due to the higher limiting strain in the left side of the FLD. However, the strain path in the 100 mm width specimen was completely in tension-tension region, where the limiting strain was lower in the FLD leading to lower LDH.

Figure 5: Experimental and FEM stretched specimenwith FLD(a) 30ൈ100 mm (b) 60 ൈ100 mm and (c) 100ൈ100 mm.

Table 4.Limiting dome height of different width specimens in out of plane stretch forming. Specimen (mm)

Experimental LDH(mm)

Simulated LDH (mm)

30ൈ100 60ൈ100 100ൈ100

21 20.46 20.4

21.670 22.798 20.562

3.3.2. Strain Distribution The major and minor strain distribution profile was plotted for the above three specimens along the longitudinal direction. It can be observed from Fig. 6(a, b, c) that both experimental and simulated curves are having similar profile. The 100 mm width specimen has minor strain well developed indicating tensile-tensile deformation mode. The peak major and minor strain was observed at 20mm from the pole which coincides with the failure/necking location. It was also found that the strain distribution was more uniform compared to low-carbon steels such as IF and EDD steels (19, 20). However, the specimen with 60 mm width had negligible minor strain indicating close to plane strain deformation mode. This parallel width specimen had a wrinkling tendency at the edge, and similar observation was found during the experiments. The peak strain shifted closer towards the pole compared to the biaxial stretch formed specimen. The compressive (negative) minor strain was observed due to increased lateral drawing in the 30 mm width specimen. Hence, the strain distribution pattern completely depends on the strain path during deformation inherited from the specimen design, and this influences the formability measure (LDH).

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Figure 6: Strain distribution curves for (a) draw side(30 mm width) (b) plain strain (60 mm width) and (c) stretch side (100 mm width).

4. Conclusions The following are the major conclusions: 1. The relatively higher value of strain hardening exponent is responsible for higher limiting dome height and elongation due to more uniform strain distribution. The material has relatively lower normal and planar anisotropy, and hence it may be expected to have poor drawability. However, IN-718 has encouraging stretch forming behavior. 2. Different strain paths were achieved during stretch forming experiments by varying the geometry of the samples in the fabricated tooling set up. The forming limit diagram was evaluated successfully experimentally. The FLD of IN-718 material was found to be higher compared to Ti6Al4V available in literatures. 3. The experimentally evaluated FLD was incorporated successfully in FE model incorporating anisotropy properties of the sheet material to predict limiting dome height and strain distribution in three different width samples.

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Acknowledgement The financial support received from Indian Space Research Organization (ISRO), Government of India, through Kalpana Chawla Space Technology Cell, IIT Kharagpur (Sanction number-IIT/KCSTC/CHAIR./NEW.APPR./1314/64) is gratefully acknowledged. All the authors are thankful to Prof. DipanwitaRoychowdhury for her encouragement while executing this project. References [1] Xue, Han, Wu Lijun, Xia Hui, Liu Runguang, Wang Shaogang, and Chen Zhonglin. "Superplastic properties of Inconel 718." Journal of materials processing technology 137, no. 1 (2003): 17-20. [2] Qu, F. S., Z. Lu, F. Xing, and K. F. Zhang. "Study on laser beam welding/superplastic forming technology of multi-sheet cylinder sandwich structure for Inconel718 super alloy with ultra-fine grains." Materials & Design 39 (2012): 151-161. [3] Ayres, Robert A., William G. Brazier, and Vincent F. Sajewski. "Evaluating the GMR-limiting dome height test as a new measure of press formability near plane strain." Journal of Applied Metalworking 1, no. 1 (1978): 41-49. [4] Takuda, H., T. Enami, K. Kubota, and N. Hatta. "The formability of a thin sheet of Mg–8.5 Li–1Zn alloy." Journal of Materials Processing Technology 101, no. 1 (2000): 281-286. [5] Leu, Daw-Kwei. "A simplified approach for evaluating bendability and springback in plastic bending of anisotropic sheet metals." Journal of Materials Processing Technology 66, no. 1 (1997): 9-17. [6] Kim, S. B., H. Huh, H. H. Bok, and M. B. Moon. "Forming limit diagram of auto-body steel sheets for high-speed sheet metal forming." Journal of Materials Processing Technology 211, no. 5 (2011): 851-862. [7] Keeler, Stuart P. Determination of forming limits in automotive stampings. No. 650535. SAE Technical Paper, 1965. [8] Bleck, Wolfgang, Zhi Deng, Kostas Papamantellos, and Christopher Oliver Gusek. "A comparative study of the forming-limit diagram models for sheet steels." Journal of Materials Processing Technology 83, no. 1 (1998): 223-230. [9] Bong, Hyuk Jong, Frédéric Barlat, Myoung-Gyu Lee, and Deok Chan Ahn. "The forming limit diagram of ferritic stainless steel sheets: Experiments and modeling." International Journal of Mechanical Sciences 64, no. 1 (2012): 1 -10. [10] Shu, Jun, Hongyun Bi, Xin Li, and Zhou Xu. "Effect of Ti addition on forming limit diagrams of Nb-bearing ferritic stainless steel." Journal of Materials Processing Technology 212, no. 1 (2012): 59-65. [11] He, Min, Fuguo Li, and Zhigang Wang. "Forming limit stress diagram prediction of aluminum alloy 5052 based on GTN model parameters determined by in situ tensile test." Chinese Journal of Aeronautics 24, no. 3 (2011): 378-386. [12] Selvakumar, N., M. Jinnah Sheik Mohamed, R. Narayanasamy, and K. Venkateswarlu. "Forming limit diagram and void coalescence analysis of AA5052 coated with molybdenum-based ceramic nanocomposites." Materials & Design 52 (2013): 393-403. [13] Badr, Ossama Mamdouh, Bernard Rolfe, Peter Hodgson, and Matthias Weiss. "Forming of high strength titanium sheet at room temperature." Materials & Design (2014). [14] Djavanroodi, F., and A. Derogar. "Experimental and numerical evaluation of forming limit diagram for Ti6Al4V titanium and Al6061-T6 aluminum alloys sheets." Materials & Design 31, no. 10 (2010): 4866-4875. [15] Panich, Sansot, Frederic Barlat, Vitoon Uthaisangsuk, Surasak Suranuntchai, and Suwat Jirathearanat. "Experimental and theoretical formability analysis using strain and stress based forming limit diagram for advanced high strength steels." Materials & Design 51 (2013): 756-766. [16] Roamer, P., C. J. Van Tyne, D. K. Matlock, A. M. Meier, H. H. Ruble, and F. S. Suarez. "Room Temperature Formability of Alloys 625LCF, 718 and 718SPF." Superalloys 718, 625, 706 and Various Derivatives: 15-18. [17] Banabic D Ed. Formability of metallic materials: plastic anisotropy, formability testing, forming limits. Springer; 2000. [18] Kotkunde, N.,Deole, Aditya D.AndGupta, Amit Kumar. Prediction of Forming Limit Diagram for Ti-6Al-4V Alloy Using Artificial Neural Network. Procedia Materials Science 2014; 6: 341-346. [19] Ravi Kumar, D. "Formability analysis of extra-deep drawing steel." Journal of Materials Processing Technology 130 (2002): 31-41. [20] Gupta, Amit Kumar, and D. Ravi Kumar. "Formability of galvanized interstitial-free steel sheets." Journal of Materials Processing Technology 172, no. 2 (2006): 225-237.