An analytical framework for modelling intermetallic compound ( IMC ) formation and optimising bond strength in aluminium‐steel welds
2019; Wiley; Volume: 1; Issue: 3 Linguagem: Inglês
10.1002/mdp2.57
ISSN2577-6576
AutoresØystein Grong, Lise Sandnes, Tina Bergh, Per Erik Vullum, Randi Holmestad, Filippo Berto,
Tópico(s)Aluminum Alloy Microstructure Properties
ResumoMaterial Design & Processing CommunicationsVolume 1, Issue 3 e57 REPORTFree Access An analytical framework for modelling intermetallic compound (IMC) formation and optimising bond strength in aluminium-steel welds Øystein Grong, Øystein Grong Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway HyBond AS, NAPIC, Trondheim, NorwaySearch for more papers by this authorLise Sandnes, Corresponding Author Lise Sandnes lise.sandnes@ntnu.no orcid.org/0000-0002-9967-4528 Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway Correspondence Lise Sandnes, Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Richard Birkelands vei 2B, NO-7491 Trondheim, Norway. Email: lise.sandnes@ntnu.noSearch for more papers by this authorTina Bergh, Tina Bergh Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorPer Erik Vullum, Per Erik Vullum Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorRandi Holmestad, Randi Holmestad Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorFilippo Berto, Filippo Berto orcid.org/0000-0001-9676-9970 Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this author Øystein Grong, Øystein Grong Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway HyBond AS, NAPIC, Trondheim, NorwaySearch for more papers by this authorLise Sandnes, Corresponding Author Lise Sandnes lise.sandnes@ntnu.no orcid.org/0000-0002-9967-4528 Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, Norway Correspondence Lise Sandnes, Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Richard Birkelands vei 2B, NO-7491 Trondheim, Norway. Email: lise.sandnes@ntnu.noSearch for more papers by this authorTina Bergh, Tina Bergh Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorPer Erik Vullum, Per Erik Vullum Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorRandi Holmestad, Randi Holmestad Department of Physics, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this authorFilippo Berto, Filippo Berto orcid.org/0000-0001-9676-9970 Department of Mechanical and Industrial Engineering, Norwegian University of Science and Technology, Trondheim, NorwaySearch for more papers by this author First published: 15 March 2019 https://doi.org/10.1002/mdp2.57Citations: 13AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract In aluminium-steel welding bonding occurs via intermetallic compound (IMC) formation. Therefore, the reaction layer thickness X is a key parameter controlling the bond strength. To enable prediction of the layer thickness in a real welding situation, a simple diffusion model has been developed. The model, which is isokinetic in nature, allows X to be calculated via the Scheil integral from knowledge of the weld thermal cycle. Its relevance to solid state butt welding of aluminium to steel is illustrated in two different case studies, representing best practice for friction stir welding (FSW) and hybrid metal extrusion and bonding (HYB), respectively. 1 INTRODUCTION In dissimilar aluminium-steel welding, where bonding occurs via intermetallic compound (IMC) formation, control of the IMC evolution is essential.1 This is because both a thick continuous reaction layer in the micrometre range and a thin discontinuous film will be detrimental to joint properties owing to the risk of interfacial cracking and inadequate bonding, respectively.1, 2 Based on the binary Al-Fe phase diagram it can be argued that a wide range of IMCs may form during aluminium-steel welding. Which of these compounds that eventually develops into a reaction layer depends, in turn, on the kinetics. However, matters concerning the underlying nucleation and growth mechanisms involved will not be dealt with here because, in a process modelling context, it is sufficient to assume that the growth is controlled by diffusion of one of the elements participating in the IMC formation, say, aluminium.3 In that case the problem can be solved using Fick's first law of diffusion, which following integration yields a closed analytical solution for the variation of the layer thickness with time and temperature. This is a prerequisite for developing a more general isokinetic solution to handle IMC layer growth under nonisothermal conditions, as in welding.3, 4 Because the reaction layer thickness is a key parameter controlling the Al-Fe bond strength, its value needs to be optimised in each case to obtain a mechanically sound weld. Illustrations of how this can be done in a real welding situation are provided in two different case studies towards the end of the paper. 2 MODELLING OF IMC GROWTH IN Al-Fe WELDS The symbols and units used throughout the paper are defined in Table 1. Table 1. Nomenclature Symbols and Units C: concentration, mol/m3 t*: time constant, s D: diffusion coefficient, m2/s T: temperature, °C or K E: gross heat input during welding, kJ/mm Tr: reference temperature, °C or K J: molar flux, mol/m2 s v: welding speed, mm/s kp: rate constant, m2/s vw: wire feed rate, mm/s reference value of kp, m2/s x: distance, m M: molar mass, g/mol xi: interface position, m Ns: rotational speed, RPM X: reaction layer thickness, m Qd: activation energy for diffusion, J/mol Xr: reference value of X, m R: universal gas constant, 8.314 J/K mol y: stochiometric factor t: time, s ρ: density, g/m3 tr: reference time, s σb: bond strength, MPa The first step in the model development is to generalise the IMC composition to FexAly and then assume that the rate controlling step during growth is diffusion of Al atoms through the FexAly lattice, as shown in Figure 1. Both approximations largely simplify the mathematical treatment of the problem and are justified, provided that the model later is calibrated against experimental data.3, 4 Figure 1Open in figure viewerPowerPoint Assumed concentration profile across the Al-Fe interface during IMC layer growth 2.1 Isothermal solution The next step is to invoke Fick's first law of diffusion and calculate the molar flux of Al atoms diffusing through the crystal lattice. Then, by assuming that the bulk concentration of Al is much larger than the corresponding interface concentration (using the linear concentration profile approximation), we get the following3, 4: (1)At the interface it is assumed that the following reaction occurs between Al and Fe: (2)Hence, by taking advantage of the stoichiometry of the reaction the flux balance can be rewritten as 3, 4: (3)This is a first order separable differential equation that can be integrated as follows: (4)After integration, we obtain the following variant of the parabolic growth law: (5)where (6) 2.2 Calibration to experimental data The experimental data reported by Jindal et al5 for the evolution of the reaction layer in Al-Fe diffusion couples provide a basis for calibrating the rate constant in the diffusion model. This calibration is necessary to ensure that the model exhibits a minimum degree of predictive power. In the study of Jindal et al,5 the average IMC composition is well described by the reaction: (7)Then, the best fit of Equations 5 and 6 to the experimental data gives the following values for k0 and Qd in the expression for the rate constant kp: (8) 2.3 Isokinetic solution It follows from the treatment of Christian6 that a diffusion-controlled reaction will be isokinetic if the increments of transformation in infinitesimal isothermal time steps are additive. This condition is met in the present case.3, 4 In order to arrive at the isokinetic solution, we first introduce the reference state, defined as: (9)which allows Equation 5 to be rewritten in a scaled form: (10)where (11)Then, the isokinetic solution is obtained by replacing the t/t* term in Equation 10 with the more general Scheil integral,3, 4 which can be integrated numerically in temperature–time space for an arbitrary thermal cycle: (12) Because Equation 12, as opposed to Equation 5, also is valid under nonisothermal conditions, it can be used to predict IMC growth during aluminium-steel welding as well when the weld thermal programme is known. In the case studies below the following input data for the fixed parameters in the model are employed: Tr = 550°C, tr = 10 s, and Xr = 1.242 μm. These input data have been obtained by first selecting sensible values for Tr and tr, which then allow Xr to be back-calculated via Equations 5, 8, and 9. 3 CASE STUDIES The case studies are concerned with solid state butt welding of aluminium to steel. Note that the experimental conditions and joint properties summarised in Tables 2 and 3 represent the best practice for friction stir welding (FSW)1 and hybrid metal extrusion and bonding (HYB), respectively at the time these joining trials were conducted. Further background information on the HYB process and how it works can be found elsewhere.7, 8 Table 2. Materials combinations and welding parameters used in the FSW and the HYB trials Process Material Combinations Welding Parameters Ns, RPM v, mm/s E, kJ/mm FSW1 BM1:AA5052-H32 (plate thickness: 3 mm) BM2: HSLA steel (plate thickness: 3 mm) 450 0.75 3.26a HYB BM1: AA6082-T6 (plate thickness: 4 mm) BM2: S355 steel (plate thickness: 4 mm) FM: AA6082 (wire diameter: 1.2 mm) Wire feed rate vw: 144 mm/s 400 6 0.25 a The value is based on an estimate of the power input during FSW, using the appropriate formula9, and a mean value for the friction coefficient between steel and aluminium of 0.3. Table 3. Measured tensile strength of the two Al-Fe joints referred to in the case studies Process Measured Tensile Strength, MPa Comments FSW1 196 (94% of the BM1 strength) Fracture in the aluminium on the retreating side (RS) adjacent to the stir zone HYB 240 (74% of the BM1 strength) Fracture in the aluminium on the retreating side (RS) adjacent to the extrusion zone 3.1 Outline of the experimental set-ups Figure 2 shows schematic drawings of the experimental set-ups during the two butt welding trials, based on the information provided by Ramachandran et al1 and HyBond AS. In the FSW case the aluminium-steel plates are firmly pressed together during the joining operation. At the same time the tungsten carbide (WC) tool pin is forced to machine the steel plate, as illustrated in Figure 2A. This is the main reason why the welding speed must be kept low and the weld heat input becomes correspondingly high during the operation. Still, the combination of welding parameters listed in Table 2 results in a bond strength σb that exceeds the local aluminium tensile strength in the weld region (i.e., σb > 196 MPa, according to the data presented in Table 3). This joint strength is impressing for an Al-Fe butt weld. Figure 2Open in figure viewerPowerPoint Overview of the experimental set-up used in A, the FSW trial and B, the HYB trial. AS: advancing side, RS: retreating side In the HYB case the situation is different, as shown in Figure 2B. Here the aluminium and the steel plates are separated from each other by a groove to enable filler metal addition. Hence, there is no need for the tool pin to machine the steel. This is why welding can be carried out at a much higher speed compared to FSW, leading to a corresponding reduction in the heat input, as shown by the data in Table 2. Apparently, the contact pressure at the Al-Fe interface during groove filling is high enough to create a very strong bond, where σb exceeds the local aluminium tensile strength in the weld region of 240 MPa (see Table 3). 3.2 Evaluation of the predictive power of the process model In general, the predictive power of a physical-based model will partly depend on the simplifying assumptions on which it is based and partly on the reliability of the input data used for the different model parameters in the calculations. Therefore, also a high-hierarchic process model of this kind would be expected to exhibit a certain degree of predictive power, provided that it is properly calibrated against experimental data.3, 4 Obviously, the pertinent differences in the plate thickness, the process temperature, and the heat input between the two welds will affect the thermal programme at the Al-Fe interface and thus the extent of IMC layer growth, which occurs during welding. Unfortunately, no in-situ thermocouple measurements are available for an unbiased comparison, but some likely T-t curves are presented in Figure 3, based on the authors' own knowledge of the processes.7-9 The curves reflect the real differences in the process temperature (which affects the peak temperature of the thermal cycles) and the heat input (which affects the heating and cooling legs of the thermal cycles) between FSW and HYB. Then, after numerical integration of Equation 12 over these thermal cycles, the following values are obtained for the reaction layer thickness X in the two cases: Figure 3Open in figure viewerPowerPoint Assumed thermal programmes at the Al-Fe interface in the FSW and the HYB trials A comparison with the measured reaction layer thicknesses in Figure 4 reveals a good agreement between predictions and measurements for the friction stir weld. However, the model largely overestimates the layer thickness in the HYB case, which in this image is seen to be in the nanometre range (i.e., between 20 and 30 nm thick), as determined from high-resolution transmission electron microscope (TEM) examinations of the Al-Fe interface.10 Figure 4Open in figure viewerPowerPoint Images of the reaction layers which form at the Al-Fe interface during A, FSW1 and B, HYB,10 as observed in SEM and TEM, respectively. Experimental conditions as in Table 2 The discrepancy can partly be explained by the fact that the IMC layer, in practice, first starts to grow when full contact is reached between aluminium and steel in the extrusion zone behind the tool pin, as illustrated previously in Figure 2B. As a result, the numerical integration of Equation 12 should be confined to the cooling leg of the HYB thermal cycle, i.e., from, say, 300°C and down to room temperature, since growth will not occur as long as the two base plates are separated from each other by a groove. When this is realised, the following adjusted value is obtained for the reaction layer thickness X in the HYB case: Although the size of the rounded Al-Fe-Si nanocrystals constituting the HYB IMC layer varies along the interface and may exceed 40 nm,10 the predicted value for X is still nearly twice as large than the measured one. In spite of this discrepancy, the present modelling exercise clearly illustrates the potentials of the approach and shows how even complex problems can be treated by means of relatively simple analytical models and used for welding process control and optimisation of joint properties. As a matter of fact, because the approach is generic in nature it should be applicable to all metal combinations where bonding occurs via IMC formation, including the six dissimilar (Al-Ti-Cu-Fe) welds described in the accompanying paper on the multimaterial joining capabilities of the HYB process.8 3.3 The influence of the IMC layer thickness on the bond strength It must not be forgotten that also the friction stir weld, with its one micrometre thick reaction layer, displays excellent tensile properties. Still, a thin continuous IMC layer in the nanometre range is preferable. This is because a thin film will be more crack-resistant than a thick one under otherwise identical conditions and thus exhibit a higher bond strength.11 Obviously, the HYB nanolayer film is thick enough to create a very strong bond and at the same time thin enough to prevent it from cracking during tensile loading. 4 CONCLUDING REMARKS In dissimilar aluminium-steel welds, where bonding occurs via intermetallic compound (IMC) formation, control of the IMC evolution is essential. By invoking the related concepts of an isokinetic reaction and the kinetic strength of the thermal cycle, an analytical diffusion model has been developed which captures the thermal history of the welding process with respect to the IMC evolution in one computational step. This allows the IMC layer thickness to be calculated via the Scheil integral from knowledge of the weld thermal cycle. Because the reaction layer thickness is a key parameter controlling the Al-Fe bond strength, the model provides a basis for optimising the experimental conditions in a real welding situation. The results presented for the HYB process show that a thin continuous IMC layer in the nanometre range will be most crack-resistant and thus provide the highest joint strength following welding. Obviously, this nanolayer film is thick enough to create a very strong bond and at the same time thin enough to prevent it from cracking during tensile loading. ACKNOWLEDGEMENTS The authors acknowledge the financial support from HyBond AS, NTNU, NAPIC (NTNU Aluminium Product Innovation Center), and the Norwegian Research Council through SFI Manufacturing (237900), the NORTEM project (197405), and the NorFab facility (245963/F50). AUTHOR CONTRIBUTIONS Øystein Grong is responsible for most of the model development and the analyses of the results and has also prepared the draft manuscript. Lise Sandnes is responsible for all communication between the co-authors and external partners and has also been an important discussion partner during the course of the work. Tina Bergh is responsible for TEM examination of the HYB IMC layer. Per Erik Vullum, Randi Holmestad, and Filippo Berto have been discussion partners during the progress of the work and also supervisors for the two PhD students (Lise Sandnes and Tina Bergh) being co-authors of this paper. CONFLICTS OF INTEREST The authors declare that there are no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. REFERENCES 1Ramachandran KK, Murugan N, Shashi Kumar S. Friction stir welding of aluminium alloy AA5052 and HSLA steel. Weld J. 2015; 94: 291 s- 300 s. 2Arbo SM, Bergh T, Solhaug H, Westermann I, Holmedal B. Influence of thermomechanical processing sequence on properties of AA6082-IF steel cold roll bonded composite sheet. Procedia Manuf. 2018; 15: 152- 160. 3Grong Ø, Shercliff H. Microstructural modelling in metals processing. Prog Mater Sci. 2002; 47(2): 163- 282. 4Grong Ø. Metallurgical Modelling of Welding. UK: The Institute of Materials; 1997. 5Jindal V, Srivastava VC, Das A, Ghosh RN. Reactive diffusion in the roll bonded iron-aluminium system. Mater Lett. 2006; 60(13-14): 1758- 1761. 6Christian JW. The theory of phase transformations in metals and alloys. UK: Pergamon Press; 1975. 7Sandnes L, Grong Ø, Torgersen J, Welo T, Berto F. Exploring the hybrid metal extrusion & bonding process for butt welding of Al–Mg–Si alloys. Int J Adv Manuf Technol. 2018; 98(5-8): 1059- 1065. 8Grong Ø, Sandnes L, Berto F. A status report on the hybrid metal extrusion & bonding (HYB) process and its applications. Mat Design Process Comm. 2019; 1: e41. https://doi.org/10.1002/mdp2.41 9Frigaard Ø, Grong Ø, Midling OT. A process model for friction stir welding of age hardening aluminium alloys. Metall Mater Trans A. 2001; 32(5): 1189- 1200. 10Bergh T, Arbo SM, Westermann I, Holmestad R, Vullum PE. The interface between aluminium and steel joined by cold roll bonding and by hybrid metal extrusion and bonding. Proceedings of 19th International Microscopy Congress, Sidney: Austral. Microscopy and Microanalysis Soc.; 2018: 1– 5. 11Abdolrahim N, Zbib HM, Bahr DF. Multiscale modelling and simulation of deformation in nanoscale metallic multilayer systems. Int J Plast. 2014; 52: 33- 50. Citing Literature Volume1, Issue3June 2019e57 FiguresReferencesRelatedInformation
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