UDK 621.791.762:004.032.26 Original scientific article/Izvirni znanstveni članek ISSN 1580-2949 MTAEC9, 48(1)33(2014) PREDICTION OF THE NUGGET SIZE IN RESISTANCE SPOT WELDING WITH A COMBINATION OF A FINITE-ELEMENT ANALYSIS AND AN ARTIFICIAL NEURAL NETWORK NAPOVEDOVANJE PODROČJA PRETALITVE PRI UPOROVNEM VARJENJU S KOMBINACIJO ANALIZE KONČNIH ELEMENTOV IN UMETNIH NEVRONSKIH MREŽ Davood Afshari1, Mohammad Sedighi1, Mohammad Reza Karimi1, Zuheir Barsoum2 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran 2Department of Aeronautical and Vehicles Engineering, KTH - Royal Institute of Technology, Stockholm, Sweden sedighi @iust.ac.ir Prejem rokopisa — received: 2013-02-20; sprejem za objavo - accepted for publication: 2013-04-15 The goal of this investigation is to predict the nugget size for a resistance spot weld of thick aluminum 6061-T6 sheets 2 mm. The quality and strength of spot welds determine the integrity of the structure, which depends thoroughly on the nugget size. In this study, the finite-element method and artificial neural network were used to predict the nugget size. Different spot welding parameters such as the welding current and the welding time were selected to be used for a coupled, thermal-electrical-structural finite-element model. In order to validate the numerical results a series of experiments were carried out and the nugget sizes were measured. The results obtained with the finite-element analysis were used to build up a back-propagation, artificial-neural-network model for the nugget-size prediction. The results revealed that a combination of these two developed models can accurately and rapidly predict the nugget size for a resistance spot weld. Keywords: resistance spot weld, nugget size, finite-element analysis, artificial neural network, aluminum alloys Cilj te preiskave je napovedati velikost področja pretalitve pri uporovno zvarjeni aluminijasti pločevini 6061-T6, debeli 2 mm. Kvaliteta in trdnost točkastega zvara določata celovitost konstrukcije, kar je odvisno predvsem od velikosti področja pretalitve. V tej študiji sta bili za napovedovanje velikosti področja pretalitve uporabljeni metoda končnih elementov in umetna nevronska mreža. Izbrani so bili različni parametri varjenja, kot sta varilni tok in čas varjenja, za skupni termično-električno-strukturni model končnih elementov. Za oceno numeričnih rezultatov je bilo izvršenih več preizkusov in izmerjena je bila velikost področja pretalitve. Rezultati, dobljeni iz analize končnih elementov, so bili uporabljeni za gradnjo modela umetne nevronske mreže za napovedovanje velikosti področja pretalitve. Rezultati so odkrili, da kombinacija teh dveh razvitih modelov lahko zanesljivo in hitro napove velikost področja pretalitve pri uporovnem točkastem zvaru. Ključne besede: uporovni točkasti zvar, velikost področja pretalitve, analiza končnih elementov, umetna nevronska mreža, zlitine aluminija 1 INTRODUCTION Resistance spot welding (RSW) is one of the most important and well-known methods of sheet joining in various industries, especially in the automobile and aerospace industries. The process is ideal for joining low-carbon steel, stainless steel, nickel, and aluminum or titanium alloy components with various thicknesses and it is, thus, used extensively. Although each material has its own particular place and special importance, today, aluminum alloys are the most widely used materials after steel. Though spot welding of aluminum alloys is more difficult than spot welding of steels because of their narrow plastic rang, low bulk resistance and greater thermal conductivity, aluminum alloys are still used for the bodies and chassis of many components due to their lightweight and relatively high strength resulting in a reduction of a vehicle structural weight, fuel consumption and exhaust emissions.12 Typically, a modern automotive vehicle contains 2000-5000 spot welds and the joint quality and perfor- mance can dramatically alter the structural performance of vehicles, having a critical role in durability and safety design of vehicles.3 During a resistance-welding operation, a workpiece is pressed between two electrodes and an electrical current is passed between the electrodes. Based on the Joule's law, the resistance in the electrode-worksheet and worksheet-worksheet interfaces generates the heat that locally melts and binds the sheets together. The section, where the two pieces of metal melt and then cool down to form one piece is called a nugget. In fact, the nugget is the area that actually joins the two pieces of metal together. The quality and strength of spot welds in a structure determine the performance quality of that structure, depending thoroughly on the nugget size. The nugget size should be larger than a certain volume to secure the strength of a welded joint. On the other hand, changing the parameters to obtain a very large nugget size leads to an explosion in the weld zone which reduces the strength of a welded joint. The nugget size is usually between 4 and 8.5 mm, completely depending on the sheet thickness. So, a control of the welding parameters is necessary to obtain a high weld quality and to increase a vehicle's life. Although there are many researches being carried out on the effects of welding parameters on the nugget size in a spot weld of steels and many approaches being developed and recommended for a nugget-size prediction, the studies on aluminum-alloy spot welds are scarce. Dar-wish et al.4-6 completed many studies on the spot welds of commercial B. S. 1050 aluminum alloys. Khan et al.7 and Fangjie et al.8 used a finite-element model (FEM) to predict the nugget size for a spot weld of an aluminum alloy. Sun et al.9 studied the failure load and the failure mode of spot welds of aluminum alloys 5182-O and 6114-T4 with a cross-tension test. Pereira et al.1 carried out studies on the effect of process parameters on the strength of spot welds in 6082-T6 aluminum alloys with a sheet thickness 1 mm under a quasi-static tensile test and recommended a model for calculating the critical nugget size to achieve the PL failure mode. Recently, Han et al.10 have studied the failure load in lap shear, cross tension and coach peel of resistance-spot-welded aluminum AA5754. The use of a finite-element analysis (FEA) decreases the main costs associated with the nugget-size measurement tests; however, due to a high complexity of a spot weld, its FEA models are very time-consuming, requiring high-speed computers. The method of artificial neural networks (ANNs) is considered as an effective approach for solving non-linear problems. A quick learning ability and high-speed solutions of ANNs have led to a more extensive use of this method.11 In recent years, the use of ANNs in modelling resistance spot welds has attracted the attention of researchers. Park12 and Martin13 employed these networks to predict the fatigue life and improvement in the quality of spot welds. Also, Cortez14 used an ANN to investigate the weldabi-lity of different metals with the spot-weld process. The joint use of an FEA and ANN can eliminate the high costs of laboratory tests and significantly shorten Figure 1: Dimensions of the samples (dimensions in millimeters, not to scale) Slika 1: Dimenzije vzorcev (dimenzije v milimetrih, ni v merilu) the time needed for a solution. This idea has been the basis of our study. In this study, a FEA model along with an ANN has been adopted to predict the nugget size for the spot welds of a thick aluminum 6061-T6 sheet 2 mm. At first, the experimental procedures utilized to prepare the spot-welded samples and the nugget-size measurement are shown. Then, the basics of the axi-symmetri-cally coupled, thermal-electrical-mechanical FEA are presented. The structure of an ANN model is provided in Section 4. The results are discussed in Section 5 and the conclusions are given in last section. 2 EXPERIMENTAL PROCEDURES The thick, heat-treatable aluminum-alloy 6061-T6 sheets 2 mm were welded as a lap joint with the dimensions of 100 mm x 25 mm x 2 mm (Figure 1). The nominal chemical composition and mechanical properties of the base material are given in Table 1. Before spot welding, each sheet was cleaned mechanically with sandpaper and the welding process was performed with a NIMAK type PMP11 DGS, AC power machine with the nominal welding power of 200 kV A and copper electrodes. Nine different series of welding parameters were Table 1: Mechanical properties and chemical composition of aluminum alloy 6061-T6 (mass fractions, w/%) Tabela 1: Mehanske lastnosti in kemijska sestava zlitine aluminija 6061-T6 (masni deleži, w/%) Yield strength Tensile strength Hardness Al Si Mn Mg Fe Cu Cr MPa MPa Vickers % % % % % % % 276.0 310.0 107.0 97.0 0.6 0.1 1.0 0.5 0.2 0.1 Table 2: Resistance-spot-welding operations for aluminum 6061-T6 Tabela 2: Parametri točkastega varjenja aluminija 6061-T6 Sample No. Electrical current Welding time Electrode force Sample No. Electrical current Welding time Electrode force (kA) (cycles) (N) (kA) (cycles) (N) 1 36 4 4033 6 37 4 4033 2 36 5 4033 7 38 4 4033 3 36 6 4033 8 39 4 4033 4 36 7 4033 9 40 4 4033 5 36 8 4033 - - - - used for the welding of 27 samples (3 samples for each series of parameters). The welding conditions were based on the recommendations by AWS15 in order to achieve the minimum nugget size and avoid an expulsion in welding. Table 2 summarizes these 9 series with the corresponding welding parameters. As seen in Table 2, very small expulsions occurred in welding Samples 5 and 9. To measure the nugget size, the samples were first cut along the center line and then mounted, polished and etched. The nugget-size measurements were done using an interaction of an optic microscope and special software developed for image processing. 3 FINITE-ELEMENT ANALYSIS Different phenomena (e.g., mechanical, thermal, electrical, metallurgical, etc.) are involved in resistance-spot-welding operations. Due to a complexity of the spot-welding process and the extensive connections between these different fields, a simulation of these operations is very difficult. In this study, an axi-symmetrically coupled, thermal-electrical-mechanical FE model was used for simulating a spot weld. To create the FE model for the simulation of spot welding of aluminum 6061-T6, the commercial ANSYS12.1 software and the APDL environment were used. To achieve high accuracy, the temperature-dependent properties were defined for the material. The solving algorithm of the finite-element model is illustrated in Figure 2. The first step of the welding process is the squeeze cycle. In this step, only the electrode force is applied to the model and the structural elements are used for the initial mechanical analysis to determine the initial deformation and the contact-area shape. In the welding cycle, the electrical current is applied to the top surface of the upper electrode and by using the thermal-electrical elements the heat generation is calculated for each increment from the fully coupled model. All the mechanical, electrical and thermal boundary conditions used in the FE model are presented in Figure 3. In the welding cycle, the rms electrical current is applied uniformly to the top surface of the upper electrode and after passing through the electrode-sheet and sheet-sheet contact areas, it reaches the bottom surface of the lower electrode, where zero electrical voltage has been applied. For all the process cycles, a constant water temperature of 25 °C was considered for the electrode's water channel. Since an exact estimation of the convection-heat-transfer coefficient for the surfaces of the sheets and electrodes that are in contact with air is very difficult as it depends on numerous factors such as the air-flow velocity and surface quality, for all the surfaces that are in contact with air, the convection-heat-transfer coefficient was determined to be constant and equal to 12 W m-2 K-1.16 The ambient room temperature was assumed as 20 °C. The electrode force, as a uniform compressive load, was applied to the upper electrode, as shown in Figure 3. All the equations in this work are based on a two-dimensional cylindrical coordinate system. Equation 1 presents the governing equation for calculating the electrical potential < for the whole model: dT ic » dr V - dr 4 ic. dr 1=0 dr I 0 dr ) r dt dz I 0 dz 1 (1) Figure 2: Flowchart of the finite-element solving algorithm Slika 2: Shema reševanja algoritma s končnimi elementi Figure 3: Axi-symmetric finite-element model used for a spot-weld simulation with boundary conditions Slika 3: Osnosimetrični model končnih elementov, uporabljen za simulacijo točkastega zvara, z robnimi pogoji where r is the radial distance, z is the distance in the axis direction and Cs is the electrical conductivity. Based on the Joule heat equation, the heat generation per unit volume, q, can be shown with equation 2: q=- < 21 R (2) where t is the time and R is the material electrical resistance. The governing equation for the transient-temperature-field distribution considering the electrical-resistance heat can be presented with equation 3: dT__df dTl kdT