This paper presents a study on the creep-ageing behaviour of a peak-aged aluminium alloy 7B04 under different tensile loads at 115oC and subsequently modelling it for creep-age forming (CAF) applications. Mechanical properties and microstructural evolutions of creep-aged specimens were investigated. The material was modelled using a set of unified constitutive equations, which not only captures the material's creep deformation but also takes into account yield strength contributions from solid solution hardening, age hardening and dislocation hardening during creep-ageing. A possible application of the present work is demonstrated by implementing the determined material model into a commercial finite element analysis solver via a user-defined subroutine for springback prediction of creep-age formed plates. A good agreement is observed between the simulated springback values and experimental results. This material model now enables further investigations of 7B04 under various CAF scenarios to be conducted inexpensively via computational modelling

Huang, X

Lam, ACL

Lin, J

Shi, Z

Yang, Y-L

Zeng, Y

MATEC Web of Conferences

Aaron C.L. Lam

Zhusheng Shi

Xia Huang

Yo-Lun Yang

Yuansong Zeng

Jianguo Lin

Crossref

Material modelling for creep-age forming of aluminium alloy 7B04

Spiral - Imperial College Digital Repository

MATEC Web of Conferences 21, 12006 (2015)DOI: 10.1051/matecconf/20152112006C© Owned by the authors, published by EDP Sciences, 2015Material modelling for creep-age forming of aluminiumalloy 7B04Aaron C.L. Lam1, Zhusheng Shi1,a , Xia Huang2, Yo-Lun Yang1, Yuansong Zeng2, and Jianguo Lin11 Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK2 AVIC Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100024, PR ChinaAbstract. This paper presents a study on the creep-ageing behaviour of a peak-agedaluminium alloy 7B04 under different tensile loads at 115oC and subsequently modellingit for creep-age forming (CAF) applications. Mechanical properties and microstructuralevolutions of creep-aged specimens were investigated. The material was modelled usinga set of unified constitutive equations, which not only captures the material’s creepdeformation but also takes into account yield strength contributions from solid solutionhardening, age hardening and dislocation hardening during creep-ageing. A possibleapplication of the present work is demonstrated by implementing the determined materialmodel into a commercial finite element analysis solver via a user-defined subroutine forspringback prediction of creep-age formed plates. A good agreement is observed betweenthe simulated springback values and experimental results. This material model now enablesfurther investigations of 7B04 under various CAF scenarios to be conducted inexpensivelyvia computational modelling.1. IntroductionCreep-age forming (CAF) is a metal forming technique that utilises the collective behaviour ofviscoplastic deformation (creep) and microstructural change (ageing) of aluminium alloys underexternal loading at elevated temperature [1]. Manufacturing using this technique, in addition to betterformed part quality and industrial environment, can reduce the number of manufacturing operationsto form a part and thus the associated costs as well [2, 3]. As current deformation of a metallicalloy also depends on its microstructure, which changes dynamically during CAF, accurate predictionof formed part quality cannot be achieved solely using conventional viscoplastic creep equations.Attention has been drawn towards developing mechanism-based creep-ageing constitutive equations thatconsider evolutions of microstructure and mechanical properties, and efforts have been made towardsthe concurrent modelling of both the shaping and material processing functions of CAF as a result [3, 4].In this work, the creep-ageing behaviour of a peak-aged aluminium alloy 7B04 is experimentallyinvestigated and then modelled using a set of unified constitutive equations. The equation set wasemployed in finite element analysis to simulate an actual forming process of the alloy. Finally, aa Corresponding author: Zhusheng.Shi@Imperial.ac.ukThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.matec-conferences.org or http://dx.doi.org/10.1051/matecconf/20152112006MATEC Web of ConferencesTable 1. Chemical composition (wt%) of 7B04.Zn Mg Cu Mn Fe Cr Si Ni Ti Al5.97 2.48 1.51 0.33 0.16 0.16 0.07 < 0.05 < 0.05 Bal.9036 1221M1588.2Figure 1. Geometry and key dimensions of the test piece (units in mm).47511520Temp. (oC)0 1 24 Time (h)Solution heat treatmentArtificial ageingAs-received materialStretchingInterrupted creep-ageing testsRoom temperature tensile tests22Figure 2. Heat treatment history of the material.comparison is made between the simulated and experimentally measured springback values and thespringback predictive ability using the material model is briefly discussed.2. Experimental details2.1 MaterialThe material used was aluminium alloy 7B04 whose chemical composition is presented in Table 1.Creep-ageing tensile test pieces of geometry and dimensions shown in Fig. 1 and plates of dimensions600 mm × 350 mm × 8.2 mm had been machined from the same bulk material in the longitudinal rollingorientation and provided in T651 temper by AVIC BAMTRI (Beijing, PR China).2.2 Material testingFigure 2 illustrates a schematic of the material’s heat treatment cycle from solutionising to thesubsequent material testing operations.The creep-ageing test procedure used by Ho et al. [4] was adopted and the tests were carried out at115oC under four tensile stress levels: 200, 240, 260 and 280 MPa. Room temperature tensile tests werecarried out on selected creep-aged specimens. In addition, samples of the as-received material and thosethat had received a further 22 h stress-free ageing were analysed using transmission electron microscopy(TEM) to enable subsequent calibration of the alloy’s precipitate growth.12006-p.2ICNFT 2015Top dieBottom dieFlexible surfacePlateElastomeric sheetFlexible surfaceForming pinsThermo-couplesFigure 3. Experimental setup for the creep-age forming tests.2.3 Creep-age forming testsA novel flexible CAF tool was used for the CAF tests. The tooling setup, as shown in Fig. 3, comprisedof twenty-five sparsely spaced forming pins on each side of the top and bottom dies. Flexible formingsurfaces were on both sides of the plate with an additional elastomeric sheet layer between the plateand lower flexible surface. Further details of the CAF tool design and test setup can be found in [5].The main steps of the forming test include: (I) Setup the forming tool surface by adjusting the heightsof forming pins; (II) Load the top die to deform the plate to the required shape; (III) Lock the top andbottom dies using nuts and bolts; (IV) Run the creep-ageing thermal cycle; (V) Release the load byloosening the nuts whilst springback occurs.CAF tests were carried out on two plates at a single curvature bending radius of 1200 mm. Afterunloading, profiles of the unloaded plates were measured and springback of the plates (S) werecalculated using S = 1 − (f /l)), where f and l are the final and loaded centre deflections of eachplate respectively. Repeated deflection measurements were obtained from each side of the formed platesand the final average value was taken.3. Material modelling3.1 Unified creep-ageing constitutive equations7B04 is an age-hardenable aluminium alloy. During ageing of 7000 series aluminium alloys,microstructure evolves from supersaturated solid solution and precipitation occurs in the followingsequence [6, 7]: Solid solution → GP zones → ′ →  (MgZn2).The strength of the alloy changes as precipitation takes places. At the early stage, GP zonesform and the yield strength increases as precipitates nucleate and grow. GP zones are then graduallyreplaced by semi-coherent ′ until a peak-age condition is reached. This is when the alloy attainsits peak strength with an optimal precipitate size and density (spacing) combination. Afterwards, ′are replaced by incoherent and stable  whilst precipitates coarsen, leading to a gradual decrease instrength (over-ageing). Throughout this process, contribution from solid solution hardening graduallydecreases. During creep-ageing, dislocation hardening also contributes to the overall strength of thematerial, especially in the early stage.12006-p.3MATEC Web of ConferencesIn order for the described behaviour of 7B04 to be modelled, the multiaxial unified constitutiveequations proposed by Zhan et al. [8] were adapted:̇cre = A1 sinh{B1[e(1 − ̄d ) − kεcy]} (1)̇age = Ca ˙̄rm1p (1 − r̄p) (2)̇sol = −Cs ˙̄r m2p |r̄p − 1| (3)̇dis = −A2 · nd · ̄ nd−1d ˙̄d (4)y = sol +√2age + 2dis (5)˙̄rp = Cr (Qr − r̄p)m3 (1 + r ̄m4d ) (6)˙̄d = A3(1 − ̄d )̇ cre − C̄msd (7)where A1, B1, kc, Ca , m1, Cs , m2, A2, nd , Cr , Qr , m3, r , m4, A3, C, m5 are material constants. Theseequations describe the inter-relationship amongst the equivalent stress (e), normalised dislocationdensity (̄d ), normalised precipitate size (r̄p) and effective creep strain (cre ), as well as the strengthcontributions from solid solution hardening (sol), age hardening (age) and dislocation hardening (dis).Eq. (1) describes the rate of creep strain accumulation, which is not only a function of stress but alsoof dislocation density and yield strength (y). Readers are referred to [8] for detailed descriptions ofEqs. (1)–(7).3.2 Determination of initial conditions and material constantsAn evolutionary algorithm based optimisation software developed by Zhang et al. [9] was used formaterial constants determination. The alloy’s yield strength evolutions and creep-ageing curves obtainedfrom the tensile creep-ageing tests were used for model calibration. This was coupled with manualconstants adjustments carried out in MATLAB to calibrate for the TEM analysis result.Table 2 presents the initial conditions used and material constants determined. Referring to the initialconditions, the as-quenched yield strength of 7B04 was 206 MPa [10]. A value of 0sol = 190 MPawas chosen for the as-recieved T651 condition. Before any creep-ageing takes place, 0age = 0y − 0sol ,where 0y = 537 MPa was obtained from the tensile tests. r̄0p = 1 was set as the material is at its peak-aged condition. The initial normalised dislocation density is significantly smaller than the maximumdislocation density and ̄0d = 1E − 5 was used.Figure 4 illustrates a comparison for each of the calibrated creep-ageing curves and yield strengthevolutions with the corresponding experimental data. After 22 h of creep-ageing, maximum deviationsof 0.29 m and 9.35 MPa are observed which represent a 5.6 and 1.8% difference respectively. Thus,characteristics of both the viscoplastic deformation and yield strength evolution of 7B04-T651 duringcreep-ageing have been captured with close agreements.12006-p.4ICNFT 2015Table 2. The initial conditions used and material constants determined for CAF of 7B04-T651 (115◦C, 22 h).Initial conditions0sol (MPa) 0age (MPa) 0y (MPa) r̄0p ̄0d190 347 537 1 1E-5CAF material constantsA1 (h−1) B1 (MPa−1) kc Ca (MPa) m1 Cs (MPa) m2 A2 (MPa) nd1.95E-6 0.042 0.16 4 0.9 0.2 0.45 260 0.7Cr (h−1) Qr m3 r m4 A3 C (h−1) m50.098 1.8 2.2 3 2 150 0.145 1.55305355405455505555600 4 8 12 16 20 2401234560 4 8 12 16 20 24Time (h)200 MPa240 MPa260 MPa280 MPa(MPa)(m)(a) (b)Time (h)200 MPa240 MPa 260 MPa280 MPa0 MPaFigure 4. Comparisons of the experimentally obtained (symbols) and calibrated (solid lines) (a) creep-ageingcurves and (b) yield strength evolutions for creep-ageing at 115◦C under the indicated stress levels.Length directionPlateWorkheads Flexible surfacesElastomeric sheet(a) (b)Figure 5. Side-view images taken at full loading of (a) a physical forming test and (b) finite element simulationwith to-scale rendering of shell thicknesses.In addition to the creep and strength evolutions, the alloy’s precipitate growth was also calibrated.This was based on the TEM analysis result which estimated an average growth in precipitate size from8.5 to 12.6 nm after 22 h of stress-free ageing.4. Application to springback prediction4.1 Finite element modelA quarter finite element (FE) model of the flexible CAF tool was constructed in Abaqus. As shown inFig. 5, only workheads of the forming pins were modelled. Detailed descriptions of the FE model andmodelling procedure are available in [5].12006-p.5MATEC Web of Conferences0.70.80.98.1 8.2SAverage plate thickness (mm)Exp. FEFigure 6. Comparisons of the experimentally measured and simulated springback of 7B04-T651 plates. Theforming tests were conducted at a single curvature bending radius of 1200 mm under 115◦C for 22 h.The plates were modelled using initially flat shell elements with their actual plate thicknesses, aYoung’s modulus of 67 GPa and a Poisson’s ratio of 0.33 assigned. Equations (1)–(7) were implementedinto Abaqus via the user-defined subroutine CREEP with the initial conditions and material constants inTable 2 assigned. The following six-step modelling procedure was employed: (I) Initiate the simulationwith temperature, boundary conditions and contact scheme defined; (II) Load the upper workheads todeform the plate whilst the lower workheads remain fixed; (III) Heat the entire configuration up to theCAF temperature; (IV) Propagate into a visco step for creep-ageing to take place; (V) Cool the entireconfiguration down to room temperature; (VI) Revert the upper workheads to allow springback occurs.Simulation of the CAF tests was carried out using the FE model under conditions that match thoseof the forming tests. Springback of the plates was modelled, calculated and compared with those of theformed plates.4.2 Springback comparisonFigure 6 illustrates the comparisons between the measured and FE-simulated springback values. Theyboth show a decrease in springback as the plate thickness increases from 8.1 to 8.2 mm. The FE-simulated springback values deviate slightly from the experimental values but they are within anacceptable range of −1.2 and +2.5% difference in springback or +0.3 and −0.6 mm difference invertical deflection. Thus, a good prediction of springback was achieved using this material model.5. SummaryA material model was presented with its constants determined for creep-age forming of aluminiumalloy 7B04-T651. In addition to viscoplastic deformation, the model also predicts the precipitate growthand yield strength evolution of the alloy. A possible application was demonstrated where springbackof creep-age formed 7B04-T651 plates was predicted to within a close range of 2.5% of experimentalresults. The findings summarised in this paper enable creep-age forming of the alloy, under variousinitial and boundary conditions, to be investigated inexpensively via computational modelling.The strong support from Aviation Industry Corporation of China (AVIC) Beijing Aeronautical ManufacturingTechnology Research Institute (BAMTRI) for this funded research is much appreciated. The research wasperformed at the AVIC Centre for Structural Design and Manufacture at Imperial College London.12006-p.6ICNFT 2015References[1] M.C. Holman, J. Mech. Work. Technol. 20, 477 (1989)[2] F. Eberl, S. Gardiner, G. Campanile, G. Surdon, M. Venmans, P. Prangnell, J. Aerospace Eng.222, 873 (2008)[3] L. Zhan, J. Lin, T.A. Dean, Int. J. Mach. Tool. Manu. 51, 1 (2011)[4] K.C. Ho, J. Lin, T.A. Dean, J. Mater. Process. Technol. 153–154, 122 (2004)[5] A.C.L. Lam, Imperial College London, PhD thesis (to be deposited)[6] R. Ferragut, A. Somoza, A. Tolley, Acta Mater. 47, 4355 (1999)[7] G. Sha, A. Cerezo, Acta Mater. 52, 4503 (2004)[8] L. Zhan, J. Lin, T.A. Dean, M. Huang, Int. J. Mech. Sci. 53, 595 (2011)[9] P. Zhang, J. Lin, D. Balint, Imperial College London, Project report (2012)[10] Z. Li, B. Xiong, Y. Zhang, B. Zhu, F. Wang, H. Liu, Trans. Nonferrous Met. Soc. China, 18, 40(2008)12006-p.7

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Material modelling for creep-age forming of aluminium alloy 7B04

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