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Mechanical and microstructural properties prediction by artificial neural networks in FSW processes of dual phase titanium alloys
Journal of Manufacturing Processes 14 (2012) 289–296
Contents lists available at SciVerse ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Technical paper
Mechanical and microstructural properties prediction by artificial neural networks in FSW processes of dual phase titanium alloys Gianluca Buffa ∗ , Livan Fratini, Fabrizio Micari Department of Manufacturing, Production and Management Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy
a r t i c l e
i n f o
Article history: Received 21 July 2011 Received in revised form 6 October 2011 Accepted 25 October 2011 Available online 5 December 2011 Keywords: Friction Stir Welding Titanium alloys Neural networks FEM
a b s t r a c t Friction Stir Welding (FSW), as a solid state welding process, seems to be one of the most promising techniques for joining titanium alloys avoiding a large number of difficulties arising from the use of traditional fusion welding processes. In order to pursue cost savings and a time efficient design, the development of numerical simulations of the process can represent a valid choice for engineers. In the paper an artificial neural network was properly trained and linked to an existing 3D FEM model for the FSW of Ti–6Al–4V titanium alloy, with the aim to predict both the microhardness values and the microstructure of the welded butt joints at the varying of the main process parameters. A good agreement was found between experimental values and calculated results. © 2011 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction The use of titanium alloys has become a key factor to success for many aerospace, aeronautical, chemical and nuclear companies. The high mechanical resistance to weight ratio together with the significant corrosion resistance makes this alloys appealing for different applications. Welding is the most cost effective process in order to obtain the complex geometries required for specific components. Unfortunately, the joining of titanium alloys by traditional fusion welding techniques presents several drawbacks due to the peculiarities of these materials. Among the most important problems that may arise there are the formation of brittle and coarse microstructures, the elevated residual stresses after the process and the consequent large distortions, and the contamination with oxygen, hydrogen and nitrogen due to the high reactivity, especially at high temperatures, of titanium alloys. Friction Stir Welding (FSW), as a solid state welding process, seems to be one of the most promising techniques for joining titanium alloys minimizing or even avoiding the potential problems cited above. FSW is a solid state welding process, patented in 1991 by The Welding Institute (TWI), in which rotating tool is inserted into the adjoining edges of the sheets to be welded with a proper tilt angle and moved all along the joint. The composition of the tool rotation and advancing velocity vectors induces a characteristic metal flow all around the tool contact surface. The tool
∗ Corresponding author. Tel.: +39 91 23861869; fax: +39 91 6657039. E-mail addresses: [email protected], [email protected] (G. Buffa).
movement determines heat generation due to friction forces and material deformation work. The process has been demonstrated to be effective and is currently industrially utilized for materials difficult to be welded or “unweldable”, especially aluminum and magnesium alloys. As a matter of fact, the use of a solid state welding process limits the insurgence of defects, due to the presence of gas in the melting bath, and avoids the negative effects of material metallurgical transformations strictly connected to the change of phase. Finally, the reduced thermal flux – with respect to traditional fusion welding operations – results in smaller residual stress values in the joints and, consequently, in limited distortions in the final products [1,2]. Unfortunately, when titanium alloys are concerned, additional problems arise. In particular the clamping fixture must be designed in order to provide a correct positioning of the blanks to be welded, the needed back force and the proper joint cooling. Finally, a specific solution must be selected in order to avoid titanium contamination with the carbon steel of the fixture itself. The authors developed a specific fixture used for a preliminary investigation of the influence of the main process parameters on the joint mechanical properties [3]. Additionally, expensive ultra resistant materials must be used for the tool and an inert gas shield must protect the joint during the weld. In order to effectively use FSW for industrial production of titanium alloys components, a complete process engineering analysis is needed. However that implies a lot of time and cost expensive experimental tests, with the aim to find the best set of input process parameters resulting in a joint characterized by specifically required properties. Although a certain number of papers can
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be found in literature on FSW of titanium alloys, focusing on the mechanical and metallurgical properties of welded joints [4,5], no research directly relating the process input parameters with the final joint macro and micro structural properties is known to the authors. The use of numerical simulations represents a valid cost and time saving choice. It is well known that the mechanical properties of the FS welded joints are strongly influenced by the final microstructure obtained which, in turn, depends on the thermo-mechanical solicitations the material experienced during the process as it will be clearly shown in the next paragraph. The latter is a direct consequence of the main process parameters, e.g. tool geometry, rotating speed and advancing speed. It is then clear why a numerical tool able to predict the final microstructure is desirable. Although a few numerical models for the FSW of aluminum alloys can be found in literature [6,7], as known by the authors, no one specifically deals with titanium alloys. Recently the authors presented the results of a numerical approach on FSW of titanium alloys using a thermo-mechanically coupled model featuring rigidviscoplastic material description and a continuum assumption for the weld seam [8]. The proposed model is capable of predicting the effect of process parameters on process thermo-mechanics, such as the temperature, strain, strain rate as well as material flow and forces. Finally a few papers can be found in literature on the use of artificial neural networks for the prediction of the final microstructure or the flow stress during simple upsetting tests of on two-phase titanium alloys [9,10]. An interesting approach is the one followed by Kim et al. [11]: in their paper, the developed neural network is coupled with a FE model for the prediction of the variation of phase volume fraction during forging operations. In this paper a neural network based approach is presented in order to predict both the microhardness and the final microstructure observed in FS welded joints of Ti–6Al–4V titanium alloy sheets. Two neural networks were designed and properly trained on the basis of experimental data obtained at the varying of the rotational and advancing speed of the tool. The developed artificial intelligence tools were linked to the 3D FEM model of the process in order to directly utilize the main field variables as input. The results were compared to the experimentally measured ones obtaining a good agreement. 2. Experiments Ti–6Al–4V titanium alloy sheets 100 mm × 200 mm and 3 mm thick were welded together under different process conditions. In particular rotating speeds of 300, 500, 700 and 1000 rpm were selected. Fixed advancing speed equal to 50 mm/min, tilt angle equal to 2◦ and tool shoulder plunge depth of 0.2 mm were considered for all the welds. A tungsten carbide tool with a 16 mm shoulder and a 30◦ conical pin, 2.6 mm in height and 5 mm in major diameter, was utilized. Both the backplate and the tool were cooled by a 2 l/min flow of water. Details on the experimental fixture can be found in [3]. From each welded joint two specimens were cut,
Fig. 1. Specimens cut for measurements from the welded joint – 700 rpm case study.
hot mounted and polished in order to carry out the microhardness measurements and the microstructure observations (Fig. 1). In particular, microhardness measurements were performed, for each specimen, at specific locations as follows: a matrix consisting of 13 columns and 5 rows was considered thus permitting to identify 65 measurement loci for each transverse section, i.e. each case study considered. In Fig. 2 a macro image of the transverse section of a welded joint is shown together with the measurement matrix utilized. The distance between two points has been chosen equal to 1.5 mm in the x direction and 0.5 mm in the y direction. In this way an overall surface of 18 mm × 2 mm was considered to completely cover the area interested by the microstructural modifications induced by the process. As far as the analysis of the microstructure is regarded, the hot mounted and polished specimens were etched with Kroll’s reagent and observed by an optical microscope. For each point of the measurement matrix an image was acquired and the corresponding microstructure was recorded. As known, the utilized alloy, i.e. Ti–6Al–4V, is a dual phase ␣ +  alloy in which the -transus temperature – the threshold of temperature above which only the  phase, characterized by a Body Centered Cubic (BCC) structure, is found – is about 950 ◦ C [12]. The base material shows a microstructure characterized by fully equiaxed ␣ grains outlined by  phase and prior  grain boundaries (Fig. 3). A different final microstructure can be observed at the varying of the temperature levels reached in the Stir Zone (SZ), that is the area where the deformation induced by the tool action occurs. As schematically represented in Fig. 4, there are three different possibilities [13]. If the selected process parameters result in temperatures in excess of the -transus temperature, a fully lamellar ␣ +  microstructure is found; it should be observed that the dimension of the  grains containing the lamellae increases at the increasing of the heat conferred to the weld, i.e. at the increasing of
Fig. 2. Macro image of the transverse section of a welded joint and measurement matrix utilized.
G. Buffa et al. / Journal of Manufacturing Processes 14 (2012) 289–296
Fig. 3. Parent material microstructure: equiaxed ␣ grains outlined by  phase and prior  grains.
Fig. 4. Schematic representation of the possible combinations of deformation and temperature during the process.
the rotational to advancing speed ratio. Fig. 5 shows a fully lamellar structure observed in the SZ of the 1000 rpm case study specimen. On the other hand, if temperature levels are near the -transus temperature, the  phase is prevalent with respect to the Hexagonal Compact (EC) ␣ phase, and its BCC structure will endure most of the strain. This will result in the so-called duplex structure, characterized by small equiaxed ␣ grains and ␣ +  lamellae inside  grains. A typical duplex structure was observed in the SZ of the 700 rpm case study specimen (Fig. 6). Finally, if the material is deformed at temperatures well below the -transus, most of the strain is endured by the ␣ grains. In this case, only the ␣ grains and no  grain will recrystallize, resulting in an equiaxial structure that can be assimilated to the one of the parent material. The wide range of rotational velocities utilized in
Fig. 5. Fully lamellar microstructure observed in the SZ – 1000 rpm case study.
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Fig. 6. Duplex microstructure observed in the SZ – 700 rpm case study.
this work (300–1000 rpm) permitted to obtain all the above cited different macrostructures within the SZ. A different mechanical behavior of the welded joints corresponds to each different microstructure observed. It is known that the duplex structure is characterized by slightly higher yield and ultimate tensile stress along with a significantly higher elongation [13]. Accordingly, looking at the results of the tensile tests performed on the welded joints, it arises that the highest resistance is found for the 700 rpm case study that is the one in which a duplex structure is found. In Fig. 7 the UTS of the welded joints is presented as percentage of the UTS of the parent material [3]. It should be observed that both in the 300 rpm and in the 500 rpm case study a bimodal structure was found within the SZ; its extension, however, is by far smaller than the one observed in the 700 rpm case study. On the contrary, for the 1000 rpm case study a lamellar structure was found in the SZ. Based on the above observations and considerations, it clearly arises that a numerical model able to predict the final microstructure and the local micro-hardness values as a function of the combined effect of temperature, strain and strain rate, can represent a valuable tool for a proper process design. 3. Numerical approach 3.1. FE model The commercial FEA software DEFORM-3DTM, Lagrangian implicit code designed for metal forming processes, was utilized to investigate the FSW of Titanium alloys. The numerical simulation was divided into two stages: the plunge depth stage and the welding (advancing) one. During the plunge depth stage, simulated to reach a high enough temperature level for the subsequent welding process, the tool moves down vertically at 0.1 mm/s with an
Fig. 7. UTS of the welded joints as percentage of the UTS of the base material.
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Fig. 9. Sketch of the developed model.
Fig. 8. Stress–strain curves utilized for the numerical model: (a) T = 750 ◦ C and (b) strain rate = 0.1.
assumed rotating speed. Then, during welding or advancing stage, the rotating tool moves along the welding line (seam). As far as the thermal characteristics of the considered Ti–6Al–4V alloy are regarded, constant values, taken from literature [14,15], were utilized. In particular thermal conductivity equal to 14 [W/m K] and heat capacity equal to 3400 [J/(m3 K)] were utilized. This assumption makes the thermal problem linear speeding up the numerical solution at each time increment. A temperature, strain and strain rate dependent rigidviscoplastic flow stress was used to model the plastic behavior [14,15]. In Fig. 8 the stress strain curves are shown for fixed temperature (T = 750 ◦ C) and strain rate (sr = 0.1), respectively. The tool and the components of the clamping fixture, namely the backplate and the WC insert, were modeled as rigid bodies and meshed, for the thermal analysis, with about 5000 and 15,000 and 8000 tetrahedral elements, respectively. The upper part of the clamping fixture (i.e. the actual clamping system) was modeled through proper boundary conditions given to the workpiece. A “single block” continuum model is used to model the workpiece in order to avoid contact instabilities due to the intermittent contact at the sheet–sheet interfaces. The sheet blanks were meshed with about 20,000 tetrahedral elements with single edges of about 0.75 mm; in this way about four elements were placed along the sheet thickness. A non-uniform mesh with adaptive re-meshing was adopted with smaller elements close to the tool and a re-meshing referring volume was identified all along the tool feed movement [16]. Experience in previous FEM simulation showed that a coarser mesh leads to incorrect results and a finer mesh results in unaffordable computation time without significant improvement of simulation results. In Fig. 9 a sketch of the proposed model is shown. The contact conditions at the tool–workpiece interface were modeled through a constant interface heat exchange coefficient of 11,000 [W/(m K)] and a constant shear friction factor equal to 0.3. The latter was chosen in such a way to maximize the fitting of the numerical results with experiments. Details on the contact
Fig. 10. Temperature profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
modeling can be found in [16]. As will be explained more in detail in the following paragraph, the values of the main field variables were chosen as input for the neural network. Figs. 10–12 show both the distribution and the profile of the above variables in a transverse
Fig. 11. Strain profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
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Fig. 12. Strain rate profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
section of the joint taken right at the back of the welding tool once the steady state has been reached. 3.2. Neural network development The relation between the main field variables values and the final microstructure and microhardness is nonlinear and extremely complex. It is then unlikely that an analytical expression can effectively describe it. An artificial neural network (ANN), on the contrary, can perform highly complex mappings of nonlinearly related data by inferring subtle relationships between input and output parameters without prior definitions. It is able to generalize from a limited quantity of training data to predict overall trends and functional relationships. A significant advantage of the ANN approach is that there is no need to have a well-defined process for algorithmically converting an input to an output. Rather, it needs only a collection of representative examples of the desired mapping. The ANN then adapts itself to reproduce the desired output when presented with training sample input. Based on these observations, the development of a neural network has been evaluated as the most effective for the prediction of the final microstructure and the microhardness values. In particular, two different supervised multilayer feedforward networks based on a backpropagation algorithm have been built up [17]. For the microhardness and microstructure prediction, the chosen networks architecture consists of 5 and 6 layers, respectively: the input layer is the same for both the networks, then 3 and 4 hidden layers are placed, respectively, and finally an output layer, corresponding to the desired information, is found. As the input layer is regarded, it consists of three neurons representing the three input parameters of the utilized analytical models, namely the local values of the equivalent ˙ and of the temperature (T). plastic strain (ε), of the strain rate (ε) All the data were normalized to assume values between −1 and 1. As far as the microhardness network is regarded, the three considered hidden layers have 5, 4 and 5 neurons respectively, while the output layer is represented by the neuron corresponding microhardness value. The four hidden layers of the microstructure network have 3, 3, 4 and 4 neurons, respectively, being the output layer represented by the neuron corresponding microstructure morphology. The latter was modeled using three values, −1, 0 and 1, for the three main microstructures described in the experiment paragraph and shown in Figs. 4–6, respectively. Each layer is fully connected to the next and, according to the backpropagation rule, the weights of the connections linking a neuron belonging to a certain layer to a neuron belonging to the next are
Fig. 13. Architecture of the utilized neural networks: (a) microhardness network and (b) microstructure network.
adjusted in the learning stage with the aim to minimize the error between the desired output and the calculated one [18]. In Fig. 13 the architecture of the two utilized neural networks is shown. It has to be underlined that the topology of the utilized network has been defined on the basis of an optimization procedure aimed to improve the network performances: in particular the number of the hidden layers and the number of neurons have been determined, during the training stage, on the basis of the best performance following an analytical hierarchical procedure (AHP) [18]. As a matter of fact, if the architecture is too small, the network may not have sufficient degrees of freedom to learn the process correctly. On the other hand, if the network is too large, it may over fit the data. As far as the training is regarded, it was developed providing the experimental and numerical data according to Table 1. Where the considered test is identified by the correspondent rotational speed (R), equal, during the training stage, to 300 rpm, 500 rpm and 1000 rpm; the Y coordinate ranges between 0.5 mm and 2.5 mm, with 5 different values and the X coordinate ranges between −9 mm and 9 mm with 13 different values (see again Fig. 2); finally, for given test and measurement point the numerically calculated values of temperature, strain and strain rate were given as input (as taken from the transverse sections, see again Figs. 10–12), while either the experimentally measured values of microhardness or the microstructure were given as target values to the two developed networks. In this way a total of 195 data were utilized, for each neural network, during the training stage. The error curves obtained during the training stage for the microhardness network are reported in Fig. 14; in Fig. 15 a sketch of the two developed networks based on the backpropagation algorithm, highlighting the interaction between weights and biases from one layer to the next, is shown. Finally, in Table 2 the weights
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Table 1 Training parameters for the developed networks. Test
Y [mm]
X [mm]
T [◦ C]
Strain
Strain rate [1/s]
HV
Microstr.
Ri
yj
xk
Tijk
Strainijk
Strain rateijk
HVijk
Microstr.ijk
Table 2 Weights and biases for the microhardness network after the training stage. Layer
Neurons per layer
Weights
Biases
1
5
3.6573 −2.9774 −0.2773 −4.5488 −0.2406
−3.0689 −1.4486 −1.1548 4.2089 −1.7534
−2.3325 −1.6683 2.4558 −2.1513 2.6760
2
4
−2.8487 −0.7498 −2.9848 0.3313
0.2479 0.1465 0.5019 −0.9840
−4.3218 −1.1891 0.0709 −0.6701
1.5120 0.0684 −1.9719 −1.0903
3
5
0.4065 0.0884 −3.8072 1.3982 −1.8441
−3.7956 1.2238 3.2063 0.0068 0.8501
1.2097 1.1045 −4.0410 1.0638 0.2096
−0.8945 −2.9211 2.4074 −1.1262 0.4322
1.8048
−1.7378
−2.9106
−0.3320
Output
1
−4.0836 −0.6824 1.7163 0.0852 2.2769 2.2319 1.6411 −0.5578 −1.8459
4.5422 −0.3161 −1.3589 −1.4877 −0.7753 1.7811 0.1389 1.2427 −2.1169
0.2546
0.7717
Fig. 16. Comparison between experimental and numerical microhardness at a distance from the bottom of the joint of 1.5 mm.
4. Results Fig. 14. Error curves for the training and validation stage of the microhardness network.
and biases obtained after training are reported. Similar trends and error values were obtained for the microstructure network. Once trained, the networks have been implemented as subroutine of the utilized FEM code and tested developing a numerical simulation of the 700 rpm case study. The calculated results have been then compared to the measured values, as shown in the next paragraph.
First, the microhardness results are presented. In Fig. 16 the comparison between the experimentally measured and the numerically calculated values is shown for the central row of the matrix (see again Fig. 2), i.e. at middle height of the transverse section, corresponding to a distance from the bottom of the joint of z = 1.5 mm. A satisfying agreement is found between numerical and experimental data. A few observations can be made on the figure. In the SZ of Ti–4Al–6V friction stir welded joints the microhardness is higher than the one of the base material, which is equal to about 365 HV [3]. This is one of the biggest differences with respect to friction
Fig. 15. Sketch of the interaction between weights and biases in the utilized supervised multilayer feedforward networks based on a backpropagation algorithm.
G. Buffa et al. / Journal of Manufacturing Processes 14 (2012) 289–296
Fig. 17. Comparison between experimental and numerical microhardness at a distance from the bottom of the joint of 2.5 mm.
stir welded aluminum alloys, for which the microhardness, in the SZ, is lower than the one of the parent material. Additionally, significant microhardness values are observed in a quite large area, accordingly with the elevated resistance observed during the tensile tests (see again Fig. 7). In a previous research [3] some of the authors showed that the microhardness maximum value measured in a FS welded joint increases at the decreasing of the specific thermal contribution conferred to the weld, that is, in this study, at the decreasing of the tool rotational speed. However, the best mechanical properties are obtained when an optimum compromise is reached between the peak value and the extension of the area where values close to the peak are found. In this way the optimal distribution is not the one that shows the largest microhardness value, but the one showing a large area characterized by values higher than the base material and limited or no area with microhardness values lower than the base material. Based on these considerations, it appears clear how the microhardness distribution plays a fundamental role in the joint mechanical performance analysis. The same comparison is shown in Fig. 17, for a distance from the bottom of the joint equal to 2.5 mm. As it can be observed, in this case the network prediction is less accurate. This is due to the fact that close to the top of the joint air and/or tool material contamination phenomena may occur, altering the measured microhardness values. The latter phenomena are not considered by the proposed model thus resulting in an increased difference between the measured and the calculated values. The one represented in Fig. 17 is therefore the worst possible condition for the neural network. Even more encouraging results came from the second neural network developed, aimed, as explained in the previous paragraphs, to the prediction of the post welding microstructure in the joints. A threshold error value was set equal to 10% for each point of the measurement matrix; in other words, a network response lower than −0.90 was considered equal to −1, a response between −0.1 and 0.1 was considered equal to 0 and a response higher than 0.9 was assimilated to 1. No value outside of these ranges was obtained from the network, so no unclear response was found. The developed network was able to exactly predict the final microstructure for 63 of the 65 measurement loci of the matrix. In Fig. 18 the comparison between numerical and experimental data is shown for the central row of the matrix (z = 1.5 mm). A duplex structure is observed over a large area and a perfect matching is obtained for the 13 points of the row. Only two network errors are found in the row corresponding to z = 2.5 mm (Fig. 19). Also in this case surface phenomena may be the cause of the failure of the network. In addition, the points
295
Fig. 18. Comparison between experimental and numerically predicted microstructure at a distance from the bottom of the joint of 1.5 mm.
Fig. 19. Comparison between experimental and numerically predicted microstructure at a distance from the bottom of the joint of 2.5 mm.
where the prediction errors occur correspond to the edges of the tool shoulder. A sort of boundary effect, visible on the surface as the chip left by the tool, may result in very local overheating not calculated by the numerical model. In this way the neural network is not able to correctly predict the formation of a duplex structure.
5. Conclusions In this paper a neural network based approach for the prediction of the mechanical and microstructural properties of friction stir welded biphasic titanium alloys has been presented. Two different neural networks for the calculation of the post welding local values of microhardness and the microstructure, respectively, have been properly trained, under different process conditions, with input numerical data coming from a preexisting FE model of the process developed by the authors. The trained networks have been linked to the FE model in order to obtain a unique tool able to provide, together with the local values of the main field variables, information on the effectiveness of the set of process parameters chosen to carry out the experiment. A satisfying agreement was found for the microhardness prediction while an excellent network prediction capability has been obtained as far as the microstructure is regarded. Based on the strong relation existing between the microhardness and microstructure of the welded joints and their mechanical performances, it can be concluded that the developed numerical analysis can represent a valuable tool for an effective and time and cost saving process design.
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Contents lists available at SciVerse ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Technical paper
Mechanical and microstructural properties prediction by artificial neural networks in FSW processes of dual phase titanium alloys Gianluca Buffa ∗ , Livan Fratini, Fabrizio Micari Department of Manufacturing, Production and Management Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy
a r t i c l e
i n f o
Article history: Received 21 July 2011 Received in revised form 6 October 2011 Accepted 25 October 2011 Available online 5 December 2011 Keywords: Friction Stir Welding Titanium alloys Neural networks FEM
a b s t r a c t Friction Stir Welding (FSW), as a solid state welding process, seems to be one of the most promising techniques for joining titanium alloys avoiding a large number of difficulties arising from the use of traditional fusion welding processes. In order to pursue cost savings and a time efficient design, the development of numerical simulations of the process can represent a valid choice for engineers. In the paper an artificial neural network was properly trained and linked to an existing 3D FEM model for the FSW of Ti–6Al–4V titanium alloy, with the aim to predict both the microhardness values and the microstructure of the welded butt joints at the varying of the main process parameters. A good agreement was found between experimental values and calculated results. © 2011 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.
1. Introduction The use of titanium alloys has become a key factor to success for many aerospace, aeronautical, chemical and nuclear companies. The high mechanical resistance to weight ratio together with the significant corrosion resistance makes this alloys appealing for different applications. Welding is the most cost effective process in order to obtain the complex geometries required for specific components. Unfortunately, the joining of titanium alloys by traditional fusion welding techniques presents several drawbacks due to the peculiarities of these materials. Among the most important problems that may arise there are the formation of brittle and coarse microstructures, the elevated residual stresses after the process and the consequent large distortions, and the contamination with oxygen, hydrogen and nitrogen due to the high reactivity, especially at high temperatures, of titanium alloys. Friction Stir Welding (FSW), as a solid state welding process, seems to be one of the most promising techniques for joining titanium alloys minimizing or even avoiding the potential problems cited above. FSW is a solid state welding process, patented in 1991 by The Welding Institute (TWI), in which rotating tool is inserted into the adjoining edges of the sheets to be welded with a proper tilt angle and moved all along the joint. The composition of the tool rotation and advancing velocity vectors induces a characteristic metal flow all around the tool contact surface. The tool
∗ Corresponding author. Tel.: +39 91 23861869; fax: +39 91 6657039. E-mail addresses: [email protected], [email protected] (G. Buffa).
movement determines heat generation due to friction forces and material deformation work. The process has been demonstrated to be effective and is currently industrially utilized for materials difficult to be welded or “unweldable”, especially aluminum and magnesium alloys. As a matter of fact, the use of a solid state welding process limits the insurgence of defects, due to the presence of gas in the melting bath, and avoids the negative effects of material metallurgical transformations strictly connected to the change of phase. Finally, the reduced thermal flux – with respect to traditional fusion welding operations – results in smaller residual stress values in the joints and, consequently, in limited distortions in the final products [1,2]. Unfortunately, when titanium alloys are concerned, additional problems arise. In particular the clamping fixture must be designed in order to provide a correct positioning of the blanks to be welded, the needed back force and the proper joint cooling. Finally, a specific solution must be selected in order to avoid titanium contamination with the carbon steel of the fixture itself. The authors developed a specific fixture used for a preliminary investigation of the influence of the main process parameters on the joint mechanical properties [3]. Additionally, expensive ultra resistant materials must be used for the tool and an inert gas shield must protect the joint during the weld. In order to effectively use FSW for industrial production of titanium alloys components, a complete process engineering analysis is needed. However that implies a lot of time and cost expensive experimental tests, with the aim to find the best set of input process parameters resulting in a joint characterized by specifically required properties. Although a certain number of papers can
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be found in literature on FSW of titanium alloys, focusing on the mechanical and metallurgical properties of welded joints [4,5], no research directly relating the process input parameters with the final joint macro and micro structural properties is known to the authors. The use of numerical simulations represents a valid cost and time saving choice. It is well known that the mechanical properties of the FS welded joints are strongly influenced by the final microstructure obtained which, in turn, depends on the thermo-mechanical solicitations the material experienced during the process as it will be clearly shown in the next paragraph. The latter is a direct consequence of the main process parameters, e.g. tool geometry, rotating speed and advancing speed. It is then clear why a numerical tool able to predict the final microstructure is desirable. Although a few numerical models for the FSW of aluminum alloys can be found in literature [6,7], as known by the authors, no one specifically deals with titanium alloys. Recently the authors presented the results of a numerical approach on FSW of titanium alloys using a thermo-mechanically coupled model featuring rigidviscoplastic material description and a continuum assumption for the weld seam [8]. The proposed model is capable of predicting the effect of process parameters on process thermo-mechanics, such as the temperature, strain, strain rate as well as material flow and forces. Finally a few papers can be found in literature on the use of artificial neural networks for the prediction of the final microstructure or the flow stress during simple upsetting tests of on two-phase titanium alloys [9,10]. An interesting approach is the one followed by Kim et al. [11]: in their paper, the developed neural network is coupled with a FE model for the prediction of the variation of phase volume fraction during forging operations. In this paper a neural network based approach is presented in order to predict both the microhardness and the final microstructure observed in FS welded joints of Ti–6Al–4V titanium alloy sheets. Two neural networks were designed and properly trained on the basis of experimental data obtained at the varying of the rotational and advancing speed of the tool. The developed artificial intelligence tools were linked to the 3D FEM model of the process in order to directly utilize the main field variables as input. The results were compared to the experimentally measured ones obtaining a good agreement. 2. Experiments Ti–6Al–4V titanium alloy sheets 100 mm × 200 mm and 3 mm thick were welded together under different process conditions. In particular rotating speeds of 300, 500, 700 and 1000 rpm were selected. Fixed advancing speed equal to 50 mm/min, tilt angle equal to 2◦ and tool shoulder plunge depth of 0.2 mm were considered for all the welds. A tungsten carbide tool with a 16 mm shoulder and a 30◦ conical pin, 2.6 mm in height and 5 mm in major diameter, was utilized. Both the backplate and the tool were cooled by a 2 l/min flow of water. Details on the experimental fixture can be found in [3]. From each welded joint two specimens were cut,
Fig. 1. Specimens cut for measurements from the welded joint – 700 rpm case study.
hot mounted and polished in order to carry out the microhardness measurements and the microstructure observations (Fig. 1). In particular, microhardness measurements were performed, for each specimen, at specific locations as follows: a matrix consisting of 13 columns and 5 rows was considered thus permitting to identify 65 measurement loci for each transverse section, i.e. each case study considered. In Fig. 2 a macro image of the transverse section of a welded joint is shown together with the measurement matrix utilized. The distance between two points has been chosen equal to 1.5 mm in the x direction and 0.5 mm in the y direction. In this way an overall surface of 18 mm × 2 mm was considered to completely cover the area interested by the microstructural modifications induced by the process. As far as the analysis of the microstructure is regarded, the hot mounted and polished specimens were etched with Kroll’s reagent and observed by an optical microscope. For each point of the measurement matrix an image was acquired and the corresponding microstructure was recorded. As known, the utilized alloy, i.e. Ti–6Al–4V, is a dual phase ␣ +  alloy in which the -transus temperature – the threshold of temperature above which only the  phase, characterized by a Body Centered Cubic (BCC) structure, is found – is about 950 ◦ C [12]. The base material shows a microstructure characterized by fully equiaxed ␣ grains outlined by  phase and prior  grain boundaries (Fig. 3). A different final microstructure can be observed at the varying of the temperature levels reached in the Stir Zone (SZ), that is the area where the deformation induced by the tool action occurs. As schematically represented in Fig. 4, there are three different possibilities [13]. If the selected process parameters result in temperatures in excess of the -transus temperature, a fully lamellar ␣ +  microstructure is found; it should be observed that the dimension of the  grains containing the lamellae increases at the increasing of the heat conferred to the weld, i.e. at the increasing of
Fig. 2. Macro image of the transverse section of a welded joint and measurement matrix utilized.
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Fig. 3. Parent material microstructure: equiaxed ␣ grains outlined by  phase and prior  grains.
Fig. 4. Schematic representation of the possible combinations of deformation and temperature during the process.
the rotational to advancing speed ratio. Fig. 5 shows a fully lamellar structure observed in the SZ of the 1000 rpm case study specimen. On the other hand, if temperature levels are near the -transus temperature, the  phase is prevalent with respect to the Hexagonal Compact (EC) ␣ phase, and its BCC structure will endure most of the strain. This will result in the so-called duplex structure, characterized by small equiaxed ␣ grains and ␣ +  lamellae inside  grains. A typical duplex structure was observed in the SZ of the 700 rpm case study specimen (Fig. 6). Finally, if the material is deformed at temperatures well below the -transus, most of the strain is endured by the ␣ grains. In this case, only the ␣ grains and no  grain will recrystallize, resulting in an equiaxial structure that can be assimilated to the one of the parent material. The wide range of rotational velocities utilized in
Fig. 5. Fully lamellar microstructure observed in the SZ – 1000 rpm case study.
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Fig. 6. Duplex microstructure observed in the SZ – 700 rpm case study.
this work (300–1000 rpm) permitted to obtain all the above cited different macrostructures within the SZ. A different mechanical behavior of the welded joints corresponds to each different microstructure observed. It is known that the duplex structure is characterized by slightly higher yield and ultimate tensile stress along with a significantly higher elongation [13]. Accordingly, looking at the results of the tensile tests performed on the welded joints, it arises that the highest resistance is found for the 700 rpm case study that is the one in which a duplex structure is found. In Fig. 7 the UTS of the welded joints is presented as percentage of the UTS of the parent material [3]. It should be observed that both in the 300 rpm and in the 500 rpm case study a bimodal structure was found within the SZ; its extension, however, is by far smaller than the one observed in the 700 rpm case study. On the contrary, for the 1000 rpm case study a lamellar structure was found in the SZ. Based on the above observations and considerations, it clearly arises that a numerical model able to predict the final microstructure and the local micro-hardness values as a function of the combined effect of temperature, strain and strain rate, can represent a valuable tool for a proper process design. 3. Numerical approach 3.1. FE model The commercial FEA software DEFORM-3DTM, Lagrangian implicit code designed for metal forming processes, was utilized to investigate the FSW of Titanium alloys. The numerical simulation was divided into two stages: the plunge depth stage and the welding (advancing) one. During the plunge depth stage, simulated to reach a high enough temperature level for the subsequent welding process, the tool moves down vertically at 0.1 mm/s with an
Fig. 7. UTS of the welded joints as percentage of the UTS of the base material.
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Fig. 9. Sketch of the developed model.
Fig. 8. Stress–strain curves utilized for the numerical model: (a) T = 750 ◦ C and (b) strain rate = 0.1.
assumed rotating speed. Then, during welding or advancing stage, the rotating tool moves along the welding line (seam). As far as the thermal characteristics of the considered Ti–6Al–4V alloy are regarded, constant values, taken from literature [14,15], were utilized. In particular thermal conductivity equal to 14 [W/m K] and heat capacity equal to 3400 [J/(m3 K)] were utilized. This assumption makes the thermal problem linear speeding up the numerical solution at each time increment. A temperature, strain and strain rate dependent rigidviscoplastic flow stress was used to model the plastic behavior [14,15]. In Fig. 8 the stress strain curves are shown for fixed temperature (T = 750 ◦ C) and strain rate (sr = 0.1), respectively. The tool and the components of the clamping fixture, namely the backplate and the WC insert, were modeled as rigid bodies and meshed, for the thermal analysis, with about 5000 and 15,000 and 8000 tetrahedral elements, respectively. The upper part of the clamping fixture (i.e. the actual clamping system) was modeled through proper boundary conditions given to the workpiece. A “single block” continuum model is used to model the workpiece in order to avoid contact instabilities due to the intermittent contact at the sheet–sheet interfaces. The sheet blanks were meshed with about 20,000 tetrahedral elements with single edges of about 0.75 mm; in this way about four elements were placed along the sheet thickness. A non-uniform mesh with adaptive re-meshing was adopted with smaller elements close to the tool and a re-meshing referring volume was identified all along the tool feed movement [16]. Experience in previous FEM simulation showed that a coarser mesh leads to incorrect results and a finer mesh results in unaffordable computation time without significant improvement of simulation results. In Fig. 9 a sketch of the proposed model is shown. The contact conditions at the tool–workpiece interface were modeled through a constant interface heat exchange coefficient of 11,000 [W/(m K)] and a constant shear friction factor equal to 0.3. The latter was chosen in such a way to maximize the fitting of the numerical results with experiments. Details on the contact
Fig. 10. Temperature profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
modeling can be found in [16]. As will be explained more in detail in the following paragraph, the values of the main field variables were chosen as input for the neural network. Figs. 10–12 show both the distribution and the profile of the above variables in a transverse
Fig. 11. Strain profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
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Fig. 12. Strain rate profile and distribution in a transverse section right at the back of the tool – 700 rpm case study.
section of the joint taken right at the back of the welding tool once the steady state has been reached. 3.2. Neural network development The relation between the main field variables values and the final microstructure and microhardness is nonlinear and extremely complex. It is then unlikely that an analytical expression can effectively describe it. An artificial neural network (ANN), on the contrary, can perform highly complex mappings of nonlinearly related data by inferring subtle relationships between input and output parameters without prior definitions. It is able to generalize from a limited quantity of training data to predict overall trends and functional relationships. A significant advantage of the ANN approach is that there is no need to have a well-defined process for algorithmically converting an input to an output. Rather, it needs only a collection of representative examples of the desired mapping. The ANN then adapts itself to reproduce the desired output when presented with training sample input. Based on these observations, the development of a neural network has been evaluated as the most effective for the prediction of the final microstructure and the microhardness values. In particular, two different supervised multilayer feedforward networks based on a backpropagation algorithm have been built up [17]. For the microhardness and microstructure prediction, the chosen networks architecture consists of 5 and 6 layers, respectively: the input layer is the same for both the networks, then 3 and 4 hidden layers are placed, respectively, and finally an output layer, corresponding to the desired information, is found. As the input layer is regarded, it consists of three neurons representing the three input parameters of the utilized analytical models, namely the local values of the equivalent ˙ and of the temperature (T). plastic strain (ε), of the strain rate (ε) All the data were normalized to assume values between −1 and 1. As far as the microhardness network is regarded, the three considered hidden layers have 5, 4 and 5 neurons respectively, while the output layer is represented by the neuron corresponding microhardness value. The four hidden layers of the microstructure network have 3, 3, 4 and 4 neurons, respectively, being the output layer represented by the neuron corresponding microstructure morphology. The latter was modeled using three values, −1, 0 and 1, for the three main microstructures described in the experiment paragraph and shown in Figs. 4–6, respectively. Each layer is fully connected to the next and, according to the backpropagation rule, the weights of the connections linking a neuron belonging to a certain layer to a neuron belonging to the next are
Fig. 13. Architecture of the utilized neural networks: (a) microhardness network and (b) microstructure network.
adjusted in the learning stage with the aim to minimize the error between the desired output and the calculated one [18]. In Fig. 13 the architecture of the two utilized neural networks is shown. It has to be underlined that the topology of the utilized network has been defined on the basis of an optimization procedure aimed to improve the network performances: in particular the number of the hidden layers and the number of neurons have been determined, during the training stage, on the basis of the best performance following an analytical hierarchical procedure (AHP) [18]. As a matter of fact, if the architecture is too small, the network may not have sufficient degrees of freedom to learn the process correctly. On the other hand, if the network is too large, it may over fit the data. As far as the training is regarded, it was developed providing the experimental and numerical data according to Table 1. Where the considered test is identified by the correspondent rotational speed (R), equal, during the training stage, to 300 rpm, 500 rpm and 1000 rpm; the Y coordinate ranges between 0.5 mm and 2.5 mm, with 5 different values and the X coordinate ranges between −9 mm and 9 mm with 13 different values (see again Fig. 2); finally, for given test and measurement point the numerically calculated values of temperature, strain and strain rate were given as input (as taken from the transverse sections, see again Figs. 10–12), while either the experimentally measured values of microhardness or the microstructure were given as target values to the two developed networks. In this way a total of 195 data were utilized, for each neural network, during the training stage. The error curves obtained during the training stage for the microhardness network are reported in Fig. 14; in Fig. 15 a sketch of the two developed networks based on the backpropagation algorithm, highlighting the interaction between weights and biases from one layer to the next, is shown. Finally, in Table 2 the weights
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Table 1 Training parameters for the developed networks. Test
Y [mm]
X [mm]
T [◦ C]
Strain
Strain rate [1/s]
HV
Microstr.
Ri
yj
xk
Tijk
Strainijk
Strain rateijk
HVijk
Microstr.ijk
Table 2 Weights and biases for the microhardness network after the training stage. Layer
Neurons per layer
Weights
Biases
1
5
3.6573 −2.9774 −0.2773 −4.5488 −0.2406
−3.0689 −1.4486 −1.1548 4.2089 −1.7534
−2.3325 −1.6683 2.4558 −2.1513 2.6760
2
4
−2.8487 −0.7498 −2.9848 0.3313
0.2479 0.1465 0.5019 −0.9840
−4.3218 −1.1891 0.0709 −0.6701
1.5120 0.0684 −1.9719 −1.0903
3
5
0.4065 0.0884 −3.8072 1.3982 −1.8441
−3.7956 1.2238 3.2063 0.0068 0.8501
1.2097 1.1045 −4.0410 1.0638 0.2096
−0.8945 −2.9211 2.4074 −1.1262 0.4322
1.8048
−1.7378
−2.9106
−0.3320
Output
1
−4.0836 −0.6824 1.7163 0.0852 2.2769 2.2319 1.6411 −0.5578 −1.8459
4.5422 −0.3161 −1.3589 −1.4877 −0.7753 1.7811 0.1389 1.2427 −2.1169
0.2546
0.7717
Fig. 16. Comparison between experimental and numerical microhardness at a distance from the bottom of the joint of 1.5 mm.
4. Results Fig. 14. Error curves for the training and validation stage of the microhardness network.
and biases obtained after training are reported. Similar trends and error values were obtained for the microstructure network. Once trained, the networks have been implemented as subroutine of the utilized FEM code and tested developing a numerical simulation of the 700 rpm case study. The calculated results have been then compared to the measured values, as shown in the next paragraph.
First, the microhardness results are presented. In Fig. 16 the comparison between the experimentally measured and the numerically calculated values is shown for the central row of the matrix (see again Fig. 2), i.e. at middle height of the transverse section, corresponding to a distance from the bottom of the joint of z = 1.5 mm. A satisfying agreement is found between numerical and experimental data. A few observations can be made on the figure. In the SZ of Ti–4Al–6V friction stir welded joints the microhardness is higher than the one of the base material, which is equal to about 365 HV [3]. This is one of the biggest differences with respect to friction
Fig. 15. Sketch of the interaction between weights and biases in the utilized supervised multilayer feedforward networks based on a backpropagation algorithm.
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Fig. 17. Comparison between experimental and numerical microhardness at a distance from the bottom of the joint of 2.5 mm.
stir welded aluminum alloys, for which the microhardness, in the SZ, is lower than the one of the parent material. Additionally, significant microhardness values are observed in a quite large area, accordingly with the elevated resistance observed during the tensile tests (see again Fig. 7). In a previous research [3] some of the authors showed that the microhardness maximum value measured in a FS welded joint increases at the decreasing of the specific thermal contribution conferred to the weld, that is, in this study, at the decreasing of the tool rotational speed. However, the best mechanical properties are obtained when an optimum compromise is reached between the peak value and the extension of the area where values close to the peak are found. In this way the optimal distribution is not the one that shows the largest microhardness value, but the one showing a large area characterized by values higher than the base material and limited or no area with microhardness values lower than the base material. Based on these considerations, it appears clear how the microhardness distribution plays a fundamental role in the joint mechanical performance analysis. The same comparison is shown in Fig. 17, for a distance from the bottom of the joint equal to 2.5 mm. As it can be observed, in this case the network prediction is less accurate. This is due to the fact that close to the top of the joint air and/or tool material contamination phenomena may occur, altering the measured microhardness values. The latter phenomena are not considered by the proposed model thus resulting in an increased difference between the measured and the calculated values. The one represented in Fig. 17 is therefore the worst possible condition for the neural network. Even more encouraging results came from the second neural network developed, aimed, as explained in the previous paragraphs, to the prediction of the post welding microstructure in the joints. A threshold error value was set equal to 10% for each point of the measurement matrix; in other words, a network response lower than −0.90 was considered equal to −1, a response between −0.1 and 0.1 was considered equal to 0 and a response higher than 0.9 was assimilated to 1. No value outside of these ranges was obtained from the network, so no unclear response was found. The developed network was able to exactly predict the final microstructure for 63 of the 65 measurement loci of the matrix. In Fig. 18 the comparison between numerical and experimental data is shown for the central row of the matrix (z = 1.5 mm). A duplex structure is observed over a large area and a perfect matching is obtained for the 13 points of the row. Only two network errors are found in the row corresponding to z = 2.5 mm (Fig. 19). Also in this case surface phenomena may be the cause of the failure of the network. In addition, the points
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Fig. 18. Comparison between experimental and numerically predicted microstructure at a distance from the bottom of the joint of 1.5 mm.
Fig. 19. Comparison between experimental and numerically predicted microstructure at a distance from the bottom of the joint of 2.5 mm.
where the prediction errors occur correspond to the edges of the tool shoulder. A sort of boundary effect, visible on the surface as the chip left by the tool, may result in very local overheating not calculated by the numerical model. In this way the neural network is not able to correctly predict the formation of a duplex structure.
5. Conclusions In this paper a neural network based approach for the prediction of the mechanical and microstructural properties of friction stir welded biphasic titanium alloys has been presented. Two different neural networks for the calculation of the post welding local values of microhardness and the microstructure, respectively, have been properly trained, under different process conditions, with input numerical data coming from a preexisting FE model of the process developed by the authors. The trained networks have been linked to the FE model in order to obtain a unique tool able to provide, together with the local values of the main field variables, information on the effectiveness of the set of process parameters chosen to carry out the experiment. A satisfying agreement was found for the microhardness prediction while an excellent network prediction capability has been obtained as far as the microstructure is regarded. Based on the strong relation existing between the microhardness and microstructure of the welded joints and their mechanical performances, it can be concluded that the developed numerical analysis can represent a valuable tool for an effective and time and cost saving process design.
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