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Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate
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Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate Bahman Meyghani , Mokhtar Awang , C.S. Wu PII: DOI: Reference:
S2666-3309(20)30005-4 https://doi.org/10.1016/j.jajp.2020.100007 JAJP 100007
To appear in:
Journal of Advanced Joining Processes
Received date: Revised date: Accepted date:
23 November 2019 14 January 2020 14 January 2020
Please cite this article as: Bahman Meyghani , Mokhtar Awang , C.S. Wu , Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate, Journal of Advanced Joining Processes (2020), doi: https://doi.org/10.1016/j.jajp.2020.100007
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Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate
Bahman Meyghani1, Mokhtar Awang2, , and C.S. Wu1,
1
Institute of Materials Joining, Shandong University, 17923 Jingshi Road, Jinan, 250061, China 2
Department of Mechanical Engineering, Faculty of Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak Darul Ridzuan, Malaysia Corresponding Authors Email: [email protected] and [email protected]
Abstract: For decades, Friction Stir Welding (FSW) has been used to decrease the weight of structures. In addition, the application of the curved surfaces has been extensively increasing in numerous applications like FSW, 5 axis milling computer numerical controlled (CNC) machines, and elsewhere. However, for finite element modelling of the abovementioned operations, there is trouble in defining the tool perpendicular movement on the curved surface because the basic principle of the finite element software is based on the tool single point movement. To explain the difficulty, the tool should follow a pattern and has to have a position perpendicular to the surface at each point, however because of the modelling difficulties the literature only simulated the tool single point movement. Consequently, the software should be modified for simulating an accurate representation of perpendicular movement. In this paper Altair Hyperworks® and ABAQUS® software are employed to simulate the process on a curved plate. Mathematical formulations solve the governing equations of the perpendicular tool movement (movement in X direction, Y direction and the angular movement). Then, VDISP user-defined subroutines and the optimized input parameters (from the previous part) are incorporated in the software for analyzing the curved FSW thermal behavior. It should be noted that the letter “V” shows the analysis type that is explicit and the word “DISP” indicates that this subroutine can be appropriate when complicated displacement boundary conditions should be applied to the model. The results showed that, there is a significant increase for the heat generation, resulting in the
expansion of the shear zone, which leads to the peak temperature of almost 300 °C after 3 seconds. During the dwelling step (t = 3 s to t= 5 s), the generated heat was stable and the shoulder moves the material up, because the material velocity at the upper surface is higher. In addition, a non-symmetrical temperature distribution is found at the cross section. By the end of the welding (t = 12.8 s), the temperature pattern was asymmetrical, while at the step time of 19.6 s an asymmetrical temperature was observed. Consequently, the outcomes of this paper indicate that the model has a good agreement with the literature.
Keywords: Friction Stir Welding (FSW), Curved Surfaces, Perpendicular Movement, Altair Hyperworks® and ABAQUS®, VDISP User-Defined Subroutine, Thermal Behavior.
1. Introduction Many studies [1-5] have been focused on the experimental investigation of FSW, however due to the complexity of the process, the limitations of the equipment, and the possible experimental uncertainties a deep investigation of the thermal behavior by using experiments is still challenging [6]. Therefore, to study the process in detail; finite element methods (FEM) attract enormous research interest [7]. Numerous studies [8-15] had investigated thermomechanical analysis of FSW process on flat plates by using different FE software packages. These packages are deemed as relatively capable to solve process governing equations. This formulation was applied into different software with automatic re-meshing. The results illustrated that the precision of the results in the temperature field is affected by the limitation of the software. To illustrate more, software limitations leads to simplifying the model and these simplifications increase the gap between the reality and the simulated. Johnson–Cook material law, arbitrary Lagrangian–Eulerian formulation, and Coulomb friction law to develop a three dimensional FE model [16]. The research indicated that the generation of the heat in FSW could be divided into two parts, first, the tool generates the frictional heat, and second, the heat which is generated by the material deformation [17-21]. Moreover, according to the results, compared to the plastic deformation, the friction generated heat has a greater impact on the temperature during the welding. This issue shows that the produced heat by the friction is higher than the heat which is
produced heat by the deformation of the material. As the summary of the results, it can be concluded that the position of the tool and its movement will affect the frictional behavior and also the plastic deformation. Sun et al. [22] simulated the residual stresses and the peak temperatures through the use of a stationary shoulder during the FSW with a straight welding seam. Thus, compared to the traditional form of FSW, a narrower and more consistent pattern was observed in different welding zones, because the material flow in the stationary shoulder friction stir welding (SSFSW) process is only influenced by the rotating pin. Form their observations, it can be summarized that the geometry of the tool highly affect the process thermal and mechanical behavior. Another literature done by Bussetta et al. [23] presented a thermomechanical simulation with a flat welding seam. The study compared two linear 3D models in which a trigonal pin was used. The study concluded that both formulations lead to similar findings. Jain et al. [24] proposed a 3-D model to examine the thermo-mechanical behavior. Riahi et al. [25] introduced material characteristics into a FE model. It should be noted that the welding seam was flat, and the simulation was conducted in two phases. First, the workpiece thermal behavior was studied, where the friction causes the generation of the heat, then, for thermo-mechanical modelling of FSW the work-piece thermal behavior was considered as an inlet heat. The results obtained from the abovementioned papers showed that the distribution of the temperature highly depends on the geometry of the tool, workpiece, and the contact condition (like the penetration depth, welding conditions etc.). One study [26] developed a 3-D localized FEM to predict the heat generation and the defect formation. For the methodology part, temperature dependent material properties were adopted to examine the high temperature mechanical behavior during the welding process of a 6xxx series aluminum alloy [27, 28]. The study found that the tool geometry and the process parameters highly affect the generation of the heat and the formation of the defect. It should be noted that, the highest temperature estimated by the researchers was similar to the solidus temperature of the material (583 C). The implementation of the contact condition during the process is one of the most significant issues that needs to be considered for modelling the process. A study by Zhang [29] adopted two different contact conditions to study the heat generation and the material flow. They compared the conventional and the modified Coulomb friction models as well as the Norton contact model. The study found that the welding forces and the welding temperature affect the friction
coefficient in the Norton friction model. Thus, the study stipulated the need proper rendering of the temperature profile and the accurate experimental measurements of the forces. Furthermore, it is imperative to calculate the contact surface changes caused by slight friction variations. Therefore the lack of data when the Norton law is used in the model, the results will be unrealistic and as a result, a past study [30] posited that the Coulomb friction law could provide more realistic and better results in the investigation of the thermal behavior. This is because the model considers the variable on temperature and strain rate, which makes this law suitable for solving couple temperature displacement problems. Form the abovementioned descriptions, it should be noted that, the literature proposed the modified version of the Coulomb friction law as an appropriate method model for implementing the contact condition during FSW. Additionally, some of studies considered full sliding condition but neglected the influence of the pin depth [31]. Thus, these studies claimed that the contact area is unrealistic and there is a wide gap between the experimental measurements of the temperature profile and the numerical results. Hamilton et al. [32] proposed a FSW thermal model with a straight welding seam in which a full sliding contact was used, because of the simplification of the finite element model. Studies by Ulysse [33] investigated the contact condition to measure the workpiece plastic deformation in a unique heat source condition while Heurtier et al. [34] considered full sliding and full sticking conditions. However, both models were uncoupled due to the complexity of the process and the diverse local phenomena. It should be also noted that the models based on the tool flat movement. Gerlish et al. [35] and Schmidt et al. [36] models showed that the contact condition in the FSW process has a partial sliding/sticking condition, especially for high strength aluminum alloys. Moreover, Bussetta et al. [37] Dialami et al [38, 39] and Cho et al. [40] have investigated the flat FSW accurately. Some of the literature focused on the modelling of friction stir welding on non-flat workpieces including the FSW of pipes or FSW of curved plates [41-45]. The modelling simplifications and assumptions for FSW of pipes is almost the same as the linear friction stir welding, because in modelling the pipes the FSW tool is fixed and a special kind of fixture will rotate the workpiece. The previous literature used CAM and CAD software to model the FSW of curved surfaces, however the modelling and the visualization module of that software is not high quality and an accurate prediction of the temperature or material flow in those software cannot be done.
As cited earlier most of the above-mentioned references only focused on the flat movement of the tool across the welding seam or the FSW of pipelines, while the use of curved surfaces in various engineering applications such as aerospace, automotive etc. is increasing. However, there is a significant challenge for modelling the FSW process on a curve plate. To explain the problem, in order to simplify the model, decreasing the computational time and minimizing the possibility of the error, the tool needs to be considered as a rigid body, because in comparison to the workpiece its deformations can be neglected. However, according to the limitations, only a single point movement can be defined for a rigid body, thus it is difficult to define a perpendicular tool path for a rigid body. Moreover, the consideration of the tool as a deformable part will increase the distortion of the mesh, and whereby the simulation termination. Therefore, the curved movement of the tool is still challenging and can attract enormous research interest. The main objective of this research is to develop a three dimensional finite element model for thermomechanical analysis of friction stir welding on a complicated curved surface. It should be mentioned that, due to the recommendations during the review of the literature the modified version of the Coulomb friction law in a partial sliding/sticking condition was employed. For solving the problem of the perpendicular movement of the tool, a novel method is proposed for defining the proper movement of the tool on the curved surface. Two different software (Altair Hyperworks® and ABAQUS® explicit) was used, in order to show the ability of the methodology for different software packages. Moreover, arbitrary Lagrangian-Eulerian (ALE) formulation is used in order to solve the problem of the mesh distortion. It needs to be explained that, this method has numerous benefits applications in different industries in which not linear welding is required such as aerospace, automotive, oil and gas etc.
2. Methodology 2.1.Finite Element Model Descriptions The model has two different parts, the first part is the path (a sine function) and the second part is the tool which is set at the welding starting point. Altair Hyperworks® and ABAQUS® explicit which is known as re-mesh orphan mesh exports and implement the related governing solutions,
respectively were used for solving the complicated mesh distortion problem during large plastic deformation problems like FSW. 2.2.Material Properties Material property usually uses in the simulation to define the input parameters for the material specification, creating sections and assigning the sections to the part. In this paper, according to the solid state nature of FSW, temperature dependent material properties and constant Poisson's ratio of 0.34 were used in both software [16, 46]. 2.3.Plasticity Modelling The effect of the strain rate and the temperature are considered in terms of the plasticity modelling using Johnson-Cook material law as follows, Table 1 describes the specification of each parameter for the Johnson-Cook model
[
̇ [ ]] [ ̇
( ) ][
[
] ]
(1)
Table. 1. Johnson-Cook parameters descriptions for AA 6061-T6 material Parameter
Description
Parameter
Description
Yield stress (546 MPa)
̇
Normalized strain rate
Strain factor (678 MPa)
FSW temperature (°C)
Effective plastic strain
Melting temperature (582 °C)
Strain exponent (0.71)
Room temperature (25 °C)
Strain rate factor (0.024)
Temperature exponent (1.56)
2.4.Contact Condition In FSW process shear forces is resisting again sliding (tangential motion) of bodies, therefore the contact condition needs to be defined accurately. The first issue in defining contact problems is to find those areas which are involved in the contact condition. Secondly, calculation of the contact pressures and the shear force is crucial. Basically, two contact conditions are available in Altair Hyperworks® and ABAQUS®, node to surface and surface to surface. It should be noted
that, two surfaces need to be defined for the contact condition including the master surface and the slave surface. The node to surface approach uses a master-slave approach, in which, the slave surface nodes slides over the master-surface element faces. This means that the master surface nodes can penetrate into the slave surface nodes. It should be mentioned that, for increasing the accuracy, the master and the slave surfaces should be selected carefully, and the slave surface mesh should be better in comparison with the master surface. Hence, the tool should be defined as the master surface while the work-piece should be chosen as the slave surface, because softer material is usually selected as the slave surface [47]. 2.5. Mesh Descriptions and the Boundary Conditions Figure 1 indicates the mesh which has the ability to move with the material and deform the elements. The brick C3D8RT (8-node thermally coupled brick, trilinear displacement and temperature, reduced integration, hourglass control) elements with various sizes were applied for discretization of the parts.
Figure 1. The mesh and the boundary condition
Available data in the literature [48] suggests that the rate of the film condition for the different sides of the work-piece is in a range of lies between 10 to 30 W/m2 °C for the plate (except the bottom surface). The film coefficient has been applied in the width and the length of the work-
piece. The values of the film coefficient are set up in a range of 0 to 13.66 (W m-2 K-1), however a constant film coefficient is applied for the bottom surface. The values of the convection coefficient are in a range of 0-20 W m-2 K-1 for the work-piece and tool interfaces. It should be noted that, the coefficient highly influences the output temperature. It is reported that, the lower coefficient rises the output temperature, because in the model lower percentage of the heat would be lost due to the radiation. Moreover, the room temperature of 25 °C is assumed in the model as the initial temperature. The boundary condition was applied to clamp the work-piece like a fixture. It should be mentioned that, in all directions the work-piece clamp portions are constrained, and all work-piece bottom nodes are embarrassed in the Z direction. It needs to be described that, the FSW process contains four different phases. Plunging step in which the tool plunges gradually into the work-piece. Dwelling step that is available in some cases and it continues until the temperature of the work-piece reaches the required temperature for welding. The next step is the traverse (or traveling) step in which the tool moves along the welding seam. Finally, the tool plunges out and withdrawn from the work-piece. The tool rotational and transverse speeds of 800, 1200 and 1600 revolutions per minute (RPM) have been used in the model. Different transverse speeds of 40, 70 and 100 mm/min were applied in the model. 2.6.Governing equation for the curved model In this section the governing equations for the curved plate have been developed. Figure 2 showed the sine pattern for the curved plate.
Figure 2. The pattern for the sine function
The function for the sine pattern is described as below, (
(2)
)
The first and the second derivative for equation 2 will written as follow, (
)
(3)
(
)
(4)
Then, the component of the linear velocity for X and Y directions and the rotational velocity should be calculated. If X values incorporate in the equation the ratio for the velocities in X and Y directions should be written as follow, (5) Besides, the tangential velocity should be calculated as follow, √
(6)
By incorporating equation 5 into 6 the tangential velocity can be calculated as follow, √
(
)
(7)
By factorizing √ , the tangential velocity can be calculated as follow, √ (√
( ) )
(8)
Additionally, the velocity can be calculated by dividing the displacement over the time as follow, (9) Where the displacement (L) is defined as the spline length, hence
√ (√
( ) )
(10)
By incorporating equation 3 into equation 10 the velocity in different directions can be defined, √ (√
(
(
)) )
The values of the velocity in Y direction can be found if the values of
(11) put into equation 5.
The rotational velocity in a 2-D surface can be calculated as follow, ω=
=
(12)
where θ is the angle between the velocity and the X direction, dθ is the change in angular displacement and dt is the change in the time (t). Thus, the components for the angular velocity can be found as follow, V
=
(13)
V
=
(14)
Hence, (15) The rotational velocity acceleration vector can be calculated by finding the difference for the rotational velocity vector over a small-time step Δt as follow, =
(16)
Thus, the rotational velocity acceleration can be calculated by taking the limit as Δt→0, = The, the rotational velocity values will be written as follows,
(17)
( Where
)
is the same as (
(18) , and
is the same as
, thus
( ) )
(19)
By resolving equation 19, the rotational velocity values ( ) can be calculated.
3. Results and Discussion As mentioned earlier, based on the FSW process nature, the simulation comprises of three steps; the initial process involved plunging and dwelling which shapes the heat source. Next, the tool should move across the welding seam and consequently, the elimination of the welding tool needs to be simulated. 3.1. Cross Section Results In this regard, such observation occurred the rapid increase of the peak temperature. To illustrate, there is an approximate regular pattern for the increase of the temperature throughout the plunging stage except for the last stage where the temperature increased rapidly. During the dwelling step, it is found that the interfacial temperature is approximately stable from t = 3 s to t = 5 s in both software. This happens because the contact shear stress and the heat generated by the plastic deformation is almost stable. To elaborate, at the end of the dwelling step it is obtained that, as the process time increases the generated heat becomes stable, because the interfacial temperature at the contact interface becomes constant. During the dwelling step, it is summarized that, as process time increases, the shear zone expands, and whereby viscous dissipation caused the marginal increase of heat generated over the time. Ultimately, the highest temperature of 300 °C for ABAQUS®, and the 338°C for Altair Hyperworks® have achieved which shows the stability in the achieved temperature. As can be seen in Figure 3 the pin shape largely influences the pattern of the heat-affected zone (HAZ) area. It is also summarized that the material gets pushed upwards behind the tool due to the influence of the shoulder geometry which it produces higher material velocity at the top surface.
To illustrate, the geometry of the contact area is dependent of the material behavior. Thus, the change of in the diameter from the shoulder to the pin causes the movement of the material towards the upper region. As a result, the maximum strain rate position shifted to the right (advancing side). This shows that around the welding centerline, the temperature distribution is asymmetrical. It is also worth noted that, high temperature is observed in the region under the shoulder, with extremely high energy density. Moreover, in the welding seam, there are no significant differences between the top and the bottom surfaces while there is a non-steady-state temperature distribution in the YZ-plane, which is in line with the welding direction. Furthermore, compared to the material located at the lower region, the material near the upper region has a higher velocity and there is a difference between the behavior of the material in the welding advancing and retreating sides. To explain the issue, the velocity of the material in the advancing side is higher compared to the velocity of material on the centerline. Thus, the material located at the advancing side needs to travel further. In identifying the difference between the temperature pattern at the top and the lower surface shows that the material has different flow behaviors at different locations. Around 15% of the material thickness is influenced by the tool shoulder, while the middle region is influenced by the pin and has the highest thickness between the above-mentioned regions. This difference in the thickness confirms that at the middle region, the material stirring is contributed by the tool pin, while at the upper surface, the material is mainly stirred by the shoulder.
Figure 3. Temperature distribution at the cross section of the curved model the top view is ABAQUS® and the bottom one is Altair Hyperworks®
3.2.Top View Results Descriptions Figure 4 (top view of the dwelling step) shows that the tool shape influences the material behavior. Here, the material flowed through the retreating side and forged into the trailing edge as the material flowed around the pin. It should be noted that, the pin side has shown a skewing action which caused a vertical flow of the material, however this is insignificant and can be neglected because its motion is lower compared to the material motion in other parts.
Figure 4. Plunging step top view, the top one is ABAQUS® and the bottom one is Altair Hyperworks®
In addition, the pattern of the temperature field near the pin area is circular, thus there is little difference between the front and the back of the pin and also between the welding sides. The welded joint near the pin is divided into three parts: plastic flow region, plastic deformed region and non-deformed region (Figure 4). The peak temperature of the thin shear boundary layer adjacent to the pin is not significantly affected by the heat from the shoulder. The results also indicated that there is a constant heating pattern ahead of the tool which confirms the presence of a linear relationship between the travel rate and peak temperature. In this regard, it is observed that at the bottom layers around the pin, the temperature near the pin is predominantly influenced by the concentrated heat of plastic deformation. To validate the observations, other studies in which shoulder less FSW and stationary shoulder FSW [49] are employed confirmed that the plastic deformation around the pin, rather than the heat generated by the shoulder, affects the temperature of the thin shear boundary layer around the pin. 3.3. Different Steps Results From the results it is summarized that (Figure 5), the maximum displacement of the material is detected at the plunging and dwelling steps due to the creation of the keyhole. Meanwhile, a narrower HAZ around the weld line is shaped during higher welding speeds. From the results it is observed that the narrower area and the adjacent region to the HAZ exerted a greater restraint and whereby it creates greater temperature difference between the HAZ area and the nearby area.
The reason of the achieved higher temperature gradient is because of the increase in the welding forces needed to deform the higher restricted material. Figure 6, Figure 7 and Figure 8 show the results of the temperature counter during the welding step at different welding time steps. Here, the vertical movement of the tool flows the material and reduces the thickness of the upper region which illustrates the material displacement from the inception to the final deposition at the upper, middle, and lower regions. Moreover, during the early stages of the welding step there is a sharp increase in the peak temperature (around 510 °C), and subsequently, the increase becomes constant as the quasi-steady state that is dominated the process. It should be noted that, the achieved temperature is around 87% of the material melting point. As previously discussed, the material at the upper region moved from the advancing side until it reaches to the final deposition during the welding step. Besides that, the total generated heat is almost constant (from t = 5 s to t = 25 s) during the welding stage which this issue confirms the domination of the quasi-steady state condition for the heat. It should be noted that, the total time for the simulation was 25 seconds.
Figure 5. Plunging step results the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Figure 6. Welding step results (step time 8 s) the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Figure 7. Welding step (step time 12.8 s) results the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Moreover, by studying of the results of the cooling stage it is obtain that, the peak temperature was decreased rapidly as the tool pulled out from the work-piece as there is no heat generated during the cooling stage and the cooling rate is relatively higher in the initial time of the cooling stage. To explain the results, it is also obtained that, as the temperature of the plate reaches to the room temperature, a dominant pattern in the distribution of the yield stress as well as the material
softening is obtained, because of this fact that the yield stress is highly influenced by the temperature. Different sizes of the mesh is applied to the model. To explain more, smaller sizes of the mesh is applied at the weld line while a coarser mesh size for other parts has been applied. These different sizes for the mesh has been set for the model, because of the optimization of the model mesh. If a small size for the mesh selects for all of the workpiece, then the computational time for the simulation would increase. On the other hand, if a coarse size applies for the entire of the workpiece, then the accuracy of the model would not be enough. To explain more, total number of nodes was 35525 and total number of elements was 29232. In addition, during the welding process, the workpiece deformations are in a hyperbolic parabolic shape. In both models, the displacement magnitude has a “V” shape across the transverse direction, and this shape is almost constant along the longitudinal direction. As previously mentioned, the material stiffeners resist to the work-piece deformations and welding deformations caused the creation of a residual stresses. Thus, in the curved model, the moment of the inertia shows lower deformations as well as the lower longitudinal stresses. Moreover, it is observed that at the step time of t=12.8 s, the temperature distribution is still asymmetrical. This fact shows that; the asymmetrical pattern of the temperature has not changed with the increase of the process time. However, with the increase of the step time up to 19.6 s (Figure 8), the asymmetric contour in the stir zone becomes wider and higher temperatures are reached on the advancing side than on the retreating side which shows that during the welding step as the welding time increases the temperature of the advancing side also is increased.
Figure 8. The temperature contour during the welding step (step time of 19.6) the top view is ABAQUS® and the bottom one is Altair Hyperworks®
It should be mentioned that, these results are in good accordance with the literature [26]. In the meantime, it is observed that as the step time increase, the stir zone appeared to be chaotic which this results is similar to the experimental observations for the welding nugget zone as reported by Choi et al. [50]. In addition, the results indicated that at the step time of 19.6 s, the material
distribution across the imaginary line which divides the domain into two parts (in the direction of the welding velocity) is relatively symmetric. This study also found that the majority of the volume of the material is accumulated at the top surface of the stir zone. Lastly, it is observed that at each step time, the tool has a perpendicular position to the curved surface and based on the findings, this study has successfully investigated the thermal behavior of FSW with two different software Altair Hyperworks® and ABAQUS®. Therefore, the used method is able to provide a solution to the problem of the tool perpendicular movement. Thus, this study could provide a better understanding of the thermal analysis of the curved FSW.
4. Conclusions This paper presets a new method which can solve the perpendicular position of the tool for a curved FSW plate. The review of the literature indicated that there is a lack of knowledge for simulating the FSW of a curved plate, because there is a difficulty in defining and applying an accurate movement for the tool. The mathematical formulations were applied in VDISP user defined subroutine in order to precisely model the perpendicular movement of the tool at each step time. It was found from the results of the curved finite element model that, there is a marginal increment in the heat generation as the shear zone expands due to the viscous dissipation leading up to a total peak temperature value of 300 °C (ABAQUS®) and 338°C (Altair Hyperworks®) happened at time, t = 3 s at the plunge stage. Meanwhile, at the dwell stage (between t = 3 s to t= 5 s), there is a stable situation in the amount of the generated heat from the plastic deformation as well as the contact shear stress at the tool/work-piece contact interfaces, thus the interfacial temperature is found to be stable. By the end of the dwelling step, the total generated heat is stable to the maximum value of 300 °C. For the material flow, the flow was observed to move around the pin passing through the retreating side and slightly stretching towards the advancing side. The shoulder also pushes the material upwards at the back of the tool, because the velocity of the material is higher at the upper region than at the lower region. Also, due to non-uniform material flow around the tool, an asymmetrical temperature distribution is formed in the centerline of the weld. During the welding step, the temperature reached a peak value of about 531 °C at the initial welding stage before remaining steady through the quasi-steady welding stage. At time, t = 12.8 s, the temperature was asymmetrically distributed across the work-piece until the time step of 19.6 s which at that point the asymmetric
contour expanded in the stir zone. More so, higher temperatures were obtained from the advancing side compared to the retreating side as the welding time increased. Acknowledgement The authors would like to thank the fellowship of the government of China, Shandong University from the International Postdoctoral Exchange Program and professor Wallace Kaufman for his endless support.
Declaration of Competing Interest There is no conflict of interest for this paper
References ]1[
G. Rezaei and N. B. M. Arab, "Investigation on tensile strength of friction stir welded joints in pp/epdm/clay nanocomposites," International Journal of EngineeringTransactions C: Aspects, vol. 28, p. 1382, 2015.
]2[
S. Emamian, M. Awang, F. Yusof, P .Hussain, B. Meyghani, and A. Zafar, "The Effect of Pin Profiles and Process Parameters on Temperature and Tensile Strength in Friction Stir Welding of AL6061 Alloy," in The Advances in Joining Technology, ed: Springer, 2018, pp. 15-37.
]3[
R. Singh, S .A. Rizvi, and S. Tewari, "Effect of friction stir welding on the tensile properties of aa6063 under different conditions," International Journal of Engineering Transactions A: Basics, vol. 30, pp. 597-603, 2017.
]4[
G. Rezaei and N. B. M. Arab, "Investigation on tensile strength of friction stir welded joints in pp/epdm/clay nanocomposites," International Journal of EngineeringTransactions C: Aspects, vol. 28, pp. 1382-1391, 2015.
]5[
R. Hasanzadeh, T. Azdast, A. Doniavi, S. Babazadeh, R. Lee, M. Daryadel, et al., "Welding properties of polymeric nanocomposite parts containing alumina nanoparticles in friction stir welding process," International Journal of Engineering Transactions A: Basics, vol. 30, pp. 143-151, 2017.
]6[
B. Meyghani and M. B. Awang" ,Prediction of the Temperature Distribution During Friction Stir Welding (Fsw) With A Complex Curved Welding Seam: Application In The Automotive Industry," MATEC Web Conf., vol. 225, p. 01001, 2018.
]7[
X. Pan, C. Wu, W. Hu, and Y. Wu, "A momentum-consistent stabilization algorithm for Lagrangian particle methods in the thermo-mechanical friction drilling analysis," Computational Mechanics, pp. 1-20, 2019.
]8[
B. Meyghani, M. B. Awang, S. S. Emamian, M. K. B. Mohd Nor, and S. R. Pedapati, "A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)," Metals, vol. 7, p. 450, 2017.
]9[
B. Meyghani, M. Awang, and S. Emamian, "A comparative study of finite element analysis for friction stir welding application," ARPN J. Eng. Appl. Sci, vol. 11, pp. 1298412989, 2016.
]11[
N. Dialami, M. Cervera, M. Chiumenti, and C. A. de Saracibar, "A fast and accurate twostage strategy to evaluate the effect of the pin tool profile on metal flow, torque and forces in friction stir welding," International Journal of Mechanical Sciences, vol. 122, pp. 215-227, 2017.
]11[
H. Su, C. S. Wu, M. Bachmann, and M. Rethmeier, "Numerical modeling for the effect of pin profiles on thermal and material flow characteristics in friction stir welding," Materials & Design, vol. 77, pp. 114-125, 2015.
]12[
H. Su, C. S. Wu, A. Pittner, and M. Rethmeier, "Thermal energy generation and distribution in friction stir welding of aluminum alloys," Energy, vol. 77, pp. 720-731, 2014.
]13[
C.-s. WU, W.-b. ZHANG, S. Lei, and M.-a. CHEN, "Visualization and simulation of plastic material flow in friction stir welding of 2024 aluminium alloy plates," Transactions of Nonferrous Metals Society of China, vol. 22, pp. 1445-1451, 2012.
]14[
B. Meyghani, M. B. Awang ,R. G. M. Poshteh, M. Momeni, S. Kakooei, and Z. Hamdi, "The Effect of Friction Coefficient in Thermal Analysis of Friction Stir Welding (FSW)," in IOP Conference Series: Materials Science and Engineering, 2019, p. 012102.
]15[
B. Meyghani, M. B. Awang, M .Momeni, and M. Rynkovskaya, "Development of a Finite Element Model for Thermal Analysis of Friction Stir Welding (FSW)," in IOP Conference Series: Materials Science and Engineering, 2019, p. 012101.
]16[
B. Meyghani, M. Awang, S. Emamian, and N. M. Khalid, "Developing a Finite Element Model for Thermal Analysis of Friction Stir Welding by Calculating Temperature Dependent Friction Coefficient," in 2nd International Conference on Mechanical, Manufacturing and Process Plant Engineering, 2017, pp. 107-126.
]17[
S. Kumar, C. Wu, S. Zhen, and W. Ding, "Effect of ultrasonic vibration on welding load, macrostructure, and mechanical properties of Al/Mg alloy joints fabricated by friction stir lap welding," The International Journal of Advanced Manufacturing Technology, vol. 100, pp. 1787-1799, 2019.
]18[
S. Kumar and C. Wu, "Review: Mg and its alloy—scope, future perspectives and recent advancements in welding and processing," J Harbin Inst Technol (New Ed), vol. 24, pp. 1-37, 2017.
]19[
H. S. Chuansong WU, Lei SHI, "Numerical Simulation of Heat Generation, Heat Transfer and Material Flow in Friction Stir Welding," Acta Metall, vol. 54, pp. 265-277, 2018-02-20 2018.
]21[
N. Dialami, M. Chiumenti, M. Cervera, and C. A. de Saracibar, "Challenges in Thermomechanical Analysis of Friction Stir Welding Processes," Archives of Computational Methods in Engineering, pp. 1-37, 2015.
]21[
N. Dialami, M. Chiumenti, M. Cervera, A. Segatori, and W. Osikowicz, "Enhanced friction model for Friction Stir Welding (FSW) analysis :Simulation and experimental validation," International Journal of Mechanical Sciences, vol. 133, pp. 555-567, 2017/11/01/ 2017.
]22[
T. Sun, M. Roy, D. Strong, P. J. Withers, and P. B. Prangnell, "Comparison of residual stress distributions in conventional and stationary shoulder high-strength aluminum alloy friction stir welds," Journal of Materials Processing Technology, vol. 242, pp. 92-100, 2017.
]23[
P. Bussetta, É. Feulvarch, A. Tongne, R. Boman, J.-M. Bergheau, and J.-P. Ponthot, "Two 3D thermomechanical numerical models of friction stir welding processes with a trigonal pin," Numerical Heat Transfer, Part A: Applications, vol. 70, pp. 995-1008, 2016.
]24[
R. Jain, S. K. Pal, and S. B. Singh, "Finite Element Simulation of Temperature and Strain Distribution during Friction Stir Welding of AA2024 Aluminum Alloy," Journal of The Institution of Engineers (India): Series C, pp. 1-7, 2016.
]25[
M. Riahi and H. Nazari, "Analysis of transient temperature and residual thermal stresses in friction stir welding of aluminum alloy 6061-T6 via numerical simulation," The International Journal of Advanced Manufacturing Technology, vol. 55, pp. 143-152, 2011.
]26[
F. Al-Badour, N. Merah, A. Shuaib, and A. Bazoune, "Coupled Eulerian Lagrangian finite element modeling of friction stir welding processes," Journal of Materials Processing Technology, vol. 213, pp. 1433-1439, 2013.
]27[
B. Meyghani, M. B. Awang, S. Emamian, and E. T. Akinlabi, "A comparison between temperature dependent and constant Young's modulus values in investigating the effect of the process parameters on thermal behaviour during friction stir welding," Materialwissenschaft und Werkstofftechnik, vol. 49, pp. 427-434.
]28[
B. Meyghani, M. Awang, S. Emamian, and M. K. B. M. Nor, "Thermal Modelling of Friction Stir Welding (FSW) Using Calculated Young’s Modulus Values," in The Advances in Joining Technology, ed: Springer, 2018, pp. 1-13.
]29[
Z. Zhang, "Comparison of two contact models in the simulation of friction stir welding process," Journal of Materials Science, vol. 43, pp. 5867-5877, 2008.
]31[
B. Meyghani, M. Awang, and S. Emamian, "A Mathematical Formulation for Calculating Temperature Dependent Friction Coefficient Values: Application in Friction Stir Welding (FSW)," in Defect and Diffusion Forum, 2017, pp. 73-82.
]31[
S. Emamian, M. Awang, P. Hussai, B. Meyghani, and A. Zafar, "INFLUENCES OF TOOL PIN PROFILE ON THE FRICTION STIR WELDING OF AA6061," 2006.
]32[
C. Hamilton, A. Sommers, and S. Dymek, "A thermal model of friction stir welding applied to Sc-modified Al–Zn–Mg–Cu alloy extrusions," International Journal of Machine Tools and Manufacture, vol. 49, pp. 230-238, 2009.
]33[
P. Ulysse, "Three-dimensional modeling of the friction stir-welding process," International Journal of Machine Tools and Manufacture, vol. 42, pp. 1549-1557, 2002.
]34[
P. Heurtier, M. Jones, C. Desrayaud, J. H. Driver, F. Montheillet, and D. Allehaux, "Mechanical and thermal modelling of friction stir welding," Journal of Materials Processing Technology, vol. 17 ,1pp. 348-357, 2006.
]35[
A. Gerlich, M. Yamamoto, and T. North, "Strain rates and grain growth in Al 5754 and Al 6061 friction stir spot welds," Metallurgical and materials transactions A, vol. 38, pp. 1291-1302, 2007.
]36[
H. N. B. Schmidt, T. Dickerson, and J. H. Hattel, "Material flow in butt friction stir welds in AA2024-T3," Acta Materialia, vol. 54, pp. 1199-1209, 2006.
]37[
P. Bussetta, N. Dialami, M. Chiumenti, C. A. de Saracibar, M. Cervera, R. Boman, et al., "3D numerical models using a fluid or a solid formulation of FSW processes with a noncylindrical pin," Advanced Modeling and Simulation in Engineering Sciences, vol. 2, p. 27, 2015.
]38[
N. Dialami, M. Cervera, and M. Chiumenti, "Numerical Modelling of Microstructure Evolution in Friction Stir Welding (FSW)," Metals, vol. 8, p. 183, 2018.
]39[
N. Dialami, M. Cervera, M. Chiumenti, and C. A. de Saracibar, "Speed-up strategy for the analysis of FSW pin profile effect on torque and forces".
]41[
H.-H. Cho, S.-T. Hong, J.-H. Roh, H.-S. Choi ,S. H. Kang, R. J. Steel, et al., "Threedimensional numerical and experimental investigation on friction stir welding processes of ferritic stainless steel," Acta Materialia, vol. 61, pp. 2649-2661, 2013.
]41[
M. Chiumenti, M. Cervera, A. Salmi, C. A. De Saracibar, N. Dialami, and K. Matsui, "Finite element modeling of multi-pass welding and shaped metal deposition processes," Computer methods in applied mechanics and engineering, vol. 199, pp. 2343-2359, 2010.
]42[
A. Kumar, D. Fairchild, M. Macia, T. Anderson, H. Jin, R. Ayer, et al., "Research progress on friction stir welding of pipeline steels," in Proceedings of the 8th International Pipeline Conference, 2010.
]43[
M. Monreal and C. A. Rodriguez, "Influence of tool path strategy on the cycle time of high-speed milling," Computer-Aided Design, vol. 35, pp. 395-401, 2003.
]44[
B. H. Kim and B. K. Choi, "Machining efficiency comparison direction-parallel tool path with contour-parallel tool path," Computer-Aided Design, vol. 34, pp. 89-95, 2002.
]45[
Z .Yin, "Rough and finish tool-path generation for NC machining of freeform surfaces based on a multiresolution method," Computer-Aided Design, vol. 36, pp. 1231-1239, 2004.
]46[
B. Meyghani and M. Awang, "A Comparison Between the Flat and the Curved Friction Stir Welding (FSW) Thermomechanical Behaviour," Archives of Computational Methods in Engineering, pp. 1-14, 2019.
]47[
H. Su and C. Wu, "Determination of the traverse force in friction stir welding with different tool pin profiles," Science and Technology of Welding and Joining, pp. 1-9, 2018.
]48[
P. Prasanna, B. S. Rao, and G. K. M. Rao, "Finite element modeling for maximum temperature in friction stir welding and its validation," The International Journal of Advanced Manufacturing Technology, vol ,51 .pp. 925-933, 2010.
]49[
J. Li and H. Liu, "Effects of tool rotation speed on microstructures and mechanical properties of AA2219-T6 welded by the external non-rotational shoulder assisted friction stir welding," Materials & Design, vol. 43, pp. 299-30.2113 ,6
]51[
D.-H. Choi, B.-W. Ahn, C.-Y. Lee, Y.-M. Yeon, K. Song, and S.-B. Jung, "Formation of intermetallic compounds in Al and Mg alloy interface during friction stir spot welding," Intermetallics, vol. 19, pp. 125-130, 2011.
Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate Bahman Meyghani , Mokhtar Awang , C.S. Wu PII: DOI: Reference:
S2666-3309(20)30005-4 https://doi.org/10.1016/j.jajp.2020.100007 JAJP 100007
To appear in:
Journal of Advanced Joining Processes
Received date: Revised date: Accepted date:
23 November 2019 14 January 2020 14 January 2020
Please cite this article as: Bahman Meyghani , Mokhtar Awang , C.S. Wu , Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate, Journal of Advanced Joining Processes (2020), doi: https://doi.org/10.1016/j.jajp.2020.100007
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Finite Element Modelling of Friction Stir Welding (FSW) on a Complex Curved Plate
Bahman Meyghani1, Mokhtar Awang2, , and C.S. Wu1,
1
Institute of Materials Joining, Shandong University, 17923 Jingshi Road, Jinan, 250061, China 2
Department of Mechanical Engineering, Faculty of Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610, Perak Darul Ridzuan, Malaysia Corresponding Authors Email: [email protected] and [email protected]
Abstract: For decades, Friction Stir Welding (FSW) has been used to decrease the weight of structures. In addition, the application of the curved surfaces has been extensively increasing in numerous applications like FSW, 5 axis milling computer numerical controlled (CNC) machines, and elsewhere. However, for finite element modelling of the abovementioned operations, there is trouble in defining the tool perpendicular movement on the curved surface because the basic principle of the finite element software is based on the tool single point movement. To explain the difficulty, the tool should follow a pattern and has to have a position perpendicular to the surface at each point, however because of the modelling difficulties the literature only simulated the tool single point movement. Consequently, the software should be modified for simulating an accurate representation of perpendicular movement. In this paper Altair Hyperworks® and ABAQUS® software are employed to simulate the process on a curved plate. Mathematical formulations solve the governing equations of the perpendicular tool movement (movement in X direction, Y direction and the angular movement). Then, VDISP user-defined subroutines and the optimized input parameters (from the previous part) are incorporated in the software for analyzing the curved FSW thermal behavior. It should be noted that the letter “V” shows the analysis type that is explicit and the word “DISP” indicates that this subroutine can be appropriate when complicated displacement boundary conditions should be applied to the model. The results showed that, there is a significant increase for the heat generation, resulting in the
expansion of the shear zone, which leads to the peak temperature of almost 300 °C after 3 seconds. During the dwelling step (t = 3 s to t= 5 s), the generated heat was stable and the shoulder moves the material up, because the material velocity at the upper surface is higher. In addition, a non-symmetrical temperature distribution is found at the cross section. By the end of the welding (t = 12.8 s), the temperature pattern was asymmetrical, while at the step time of 19.6 s an asymmetrical temperature was observed. Consequently, the outcomes of this paper indicate that the model has a good agreement with the literature.
Keywords: Friction Stir Welding (FSW), Curved Surfaces, Perpendicular Movement, Altair Hyperworks® and ABAQUS®, VDISP User-Defined Subroutine, Thermal Behavior.
1. Introduction Many studies [1-5] have been focused on the experimental investigation of FSW, however due to the complexity of the process, the limitations of the equipment, and the possible experimental uncertainties a deep investigation of the thermal behavior by using experiments is still challenging [6]. Therefore, to study the process in detail; finite element methods (FEM) attract enormous research interest [7]. Numerous studies [8-15] had investigated thermomechanical analysis of FSW process on flat plates by using different FE software packages. These packages are deemed as relatively capable to solve process governing equations. This formulation was applied into different software with automatic re-meshing. The results illustrated that the precision of the results in the temperature field is affected by the limitation of the software. To illustrate more, software limitations leads to simplifying the model and these simplifications increase the gap between the reality and the simulated. Johnson–Cook material law, arbitrary Lagrangian–Eulerian formulation, and Coulomb friction law to develop a three dimensional FE model [16]. The research indicated that the generation of the heat in FSW could be divided into two parts, first, the tool generates the frictional heat, and second, the heat which is generated by the material deformation [17-21]. Moreover, according to the results, compared to the plastic deformation, the friction generated heat has a greater impact on the temperature during the welding. This issue shows that the produced heat by the friction is higher than the heat which is
produced heat by the deformation of the material. As the summary of the results, it can be concluded that the position of the tool and its movement will affect the frictional behavior and also the plastic deformation. Sun et al. [22] simulated the residual stresses and the peak temperatures through the use of a stationary shoulder during the FSW with a straight welding seam. Thus, compared to the traditional form of FSW, a narrower and more consistent pattern was observed in different welding zones, because the material flow in the stationary shoulder friction stir welding (SSFSW) process is only influenced by the rotating pin. Form their observations, it can be summarized that the geometry of the tool highly affect the process thermal and mechanical behavior. Another literature done by Bussetta et al. [23] presented a thermomechanical simulation with a flat welding seam. The study compared two linear 3D models in which a trigonal pin was used. The study concluded that both formulations lead to similar findings. Jain et al. [24] proposed a 3-D model to examine the thermo-mechanical behavior. Riahi et al. [25] introduced material characteristics into a FE model. It should be noted that the welding seam was flat, and the simulation was conducted in two phases. First, the workpiece thermal behavior was studied, where the friction causes the generation of the heat, then, for thermo-mechanical modelling of FSW the work-piece thermal behavior was considered as an inlet heat. The results obtained from the abovementioned papers showed that the distribution of the temperature highly depends on the geometry of the tool, workpiece, and the contact condition (like the penetration depth, welding conditions etc.). One study [26] developed a 3-D localized FEM to predict the heat generation and the defect formation. For the methodology part, temperature dependent material properties were adopted to examine the high temperature mechanical behavior during the welding process of a 6xxx series aluminum alloy [27, 28]. The study found that the tool geometry and the process parameters highly affect the generation of the heat and the formation of the defect. It should be noted that, the highest temperature estimated by the researchers was similar to the solidus temperature of the material (583 C). The implementation of the contact condition during the process is one of the most significant issues that needs to be considered for modelling the process. A study by Zhang [29] adopted two different contact conditions to study the heat generation and the material flow. They compared the conventional and the modified Coulomb friction models as well as the Norton contact model. The study found that the welding forces and the welding temperature affect the friction
coefficient in the Norton friction model. Thus, the study stipulated the need proper rendering of the temperature profile and the accurate experimental measurements of the forces. Furthermore, it is imperative to calculate the contact surface changes caused by slight friction variations. Therefore the lack of data when the Norton law is used in the model, the results will be unrealistic and as a result, a past study [30] posited that the Coulomb friction law could provide more realistic and better results in the investigation of the thermal behavior. This is because the model considers the variable on temperature and strain rate, which makes this law suitable for solving couple temperature displacement problems. Form the abovementioned descriptions, it should be noted that, the literature proposed the modified version of the Coulomb friction law as an appropriate method model for implementing the contact condition during FSW. Additionally, some of studies considered full sliding condition but neglected the influence of the pin depth [31]. Thus, these studies claimed that the contact area is unrealistic and there is a wide gap between the experimental measurements of the temperature profile and the numerical results. Hamilton et al. [32] proposed a FSW thermal model with a straight welding seam in which a full sliding contact was used, because of the simplification of the finite element model. Studies by Ulysse [33] investigated the contact condition to measure the workpiece plastic deformation in a unique heat source condition while Heurtier et al. [34] considered full sliding and full sticking conditions. However, both models were uncoupled due to the complexity of the process and the diverse local phenomena. It should be also noted that the models based on the tool flat movement. Gerlish et al. [35] and Schmidt et al. [36] models showed that the contact condition in the FSW process has a partial sliding/sticking condition, especially for high strength aluminum alloys. Moreover, Bussetta et al. [37] Dialami et al [38, 39] and Cho et al. [40] have investigated the flat FSW accurately. Some of the literature focused on the modelling of friction stir welding on non-flat workpieces including the FSW of pipes or FSW of curved plates [41-45]. The modelling simplifications and assumptions for FSW of pipes is almost the same as the linear friction stir welding, because in modelling the pipes the FSW tool is fixed and a special kind of fixture will rotate the workpiece. The previous literature used CAM and CAD software to model the FSW of curved surfaces, however the modelling and the visualization module of that software is not high quality and an accurate prediction of the temperature or material flow in those software cannot be done.
As cited earlier most of the above-mentioned references only focused on the flat movement of the tool across the welding seam or the FSW of pipelines, while the use of curved surfaces in various engineering applications such as aerospace, automotive etc. is increasing. However, there is a significant challenge for modelling the FSW process on a curve plate. To explain the problem, in order to simplify the model, decreasing the computational time and minimizing the possibility of the error, the tool needs to be considered as a rigid body, because in comparison to the workpiece its deformations can be neglected. However, according to the limitations, only a single point movement can be defined for a rigid body, thus it is difficult to define a perpendicular tool path for a rigid body. Moreover, the consideration of the tool as a deformable part will increase the distortion of the mesh, and whereby the simulation termination. Therefore, the curved movement of the tool is still challenging and can attract enormous research interest. The main objective of this research is to develop a three dimensional finite element model for thermomechanical analysis of friction stir welding on a complicated curved surface. It should be mentioned that, due to the recommendations during the review of the literature the modified version of the Coulomb friction law in a partial sliding/sticking condition was employed. For solving the problem of the perpendicular movement of the tool, a novel method is proposed for defining the proper movement of the tool on the curved surface. Two different software (Altair Hyperworks® and ABAQUS® explicit) was used, in order to show the ability of the methodology for different software packages. Moreover, arbitrary Lagrangian-Eulerian (ALE) formulation is used in order to solve the problem of the mesh distortion. It needs to be explained that, this method has numerous benefits applications in different industries in which not linear welding is required such as aerospace, automotive, oil and gas etc.
2. Methodology 2.1.Finite Element Model Descriptions The model has two different parts, the first part is the path (a sine function) and the second part is the tool which is set at the welding starting point. Altair Hyperworks® and ABAQUS® explicit which is known as re-mesh orphan mesh exports and implement the related governing solutions,
respectively were used for solving the complicated mesh distortion problem during large plastic deformation problems like FSW. 2.2.Material Properties Material property usually uses in the simulation to define the input parameters for the material specification, creating sections and assigning the sections to the part. In this paper, according to the solid state nature of FSW, temperature dependent material properties and constant Poisson's ratio of 0.34 were used in both software [16, 46]. 2.3.Plasticity Modelling The effect of the strain rate and the temperature are considered in terms of the plasticity modelling using Johnson-Cook material law as follows, Table 1 describes the specification of each parameter for the Johnson-Cook model
[
̇ [ ]] [ ̇
( ) ][
[
] ]
(1)
Table. 1. Johnson-Cook parameters descriptions for AA 6061-T6 material Parameter
Description
Parameter
Description
Yield stress (546 MPa)
̇
Normalized strain rate
Strain factor (678 MPa)
FSW temperature (°C)
Effective plastic strain
Melting temperature (582 °C)
Strain exponent (0.71)
Room temperature (25 °C)
Strain rate factor (0.024)
Temperature exponent (1.56)
2.4.Contact Condition In FSW process shear forces is resisting again sliding (tangential motion) of bodies, therefore the contact condition needs to be defined accurately. The first issue in defining contact problems is to find those areas which are involved in the contact condition. Secondly, calculation of the contact pressures and the shear force is crucial. Basically, two contact conditions are available in Altair Hyperworks® and ABAQUS®, node to surface and surface to surface. It should be noted
that, two surfaces need to be defined for the contact condition including the master surface and the slave surface. The node to surface approach uses a master-slave approach, in which, the slave surface nodes slides over the master-surface element faces. This means that the master surface nodes can penetrate into the slave surface nodes. It should be mentioned that, for increasing the accuracy, the master and the slave surfaces should be selected carefully, and the slave surface mesh should be better in comparison with the master surface. Hence, the tool should be defined as the master surface while the work-piece should be chosen as the slave surface, because softer material is usually selected as the slave surface [47]. 2.5. Mesh Descriptions and the Boundary Conditions Figure 1 indicates the mesh which has the ability to move with the material and deform the elements. The brick C3D8RT (8-node thermally coupled brick, trilinear displacement and temperature, reduced integration, hourglass control) elements with various sizes were applied for discretization of the parts.
Figure 1. The mesh and the boundary condition
Available data in the literature [48] suggests that the rate of the film condition for the different sides of the work-piece is in a range of lies between 10 to 30 W/m2 °C for the plate (except the bottom surface). The film coefficient has been applied in the width and the length of the work-
piece. The values of the film coefficient are set up in a range of 0 to 13.66 (W m-2 K-1), however a constant film coefficient is applied for the bottom surface. The values of the convection coefficient are in a range of 0-20 W m-2 K-1 for the work-piece and tool interfaces. It should be noted that, the coefficient highly influences the output temperature. It is reported that, the lower coefficient rises the output temperature, because in the model lower percentage of the heat would be lost due to the radiation. Moreover, the room temperature of 25 °C is assumed in the model as the initial temperature. The boundary condition was applied to clamp the work-piece like a fixture. It should be mentioned that, in all directions the work-piece clamp portions are constrained, and all work-piece bottom nodes are embarrassed in the Z direction. It needs to be described that, the FSW process contains four different phases. Plunging step in which the tool plunges gradually into the work-piece. Dwelling step that is available in some cases and it continues until the temperature of the work-piece reaches the required temperature for welding. The next step is the traverse (or traveling) step in which the tool moves along the welding seam. Finally, the tool plunges out and withdrawn from the work-piece. The tool rotational and transverse speeds of 800, 1200 and 1600 revolutions per minute (RPM) have been used in the model. Different transverse speeds of 40, 70 and 100 mm/min were applied in the model. 2.6.Governing equation for the curved model In this section the governing equations for the curved plate have been developed. Figure 2 showed the sine pattern for the curved plate.
Figure 2. The pattern for the sine function
The function for the sine pattern is described as below, (
(2)
)
The first and the second derivative for equation 2 will written as follow, (
)
(3)
(
)
(4)
Then, the component of the linear velocity for X and Y directions and the rotational velocity should be calculated. If X values incorporate in the equation the ratio for the velocities in X and Y directions should be written as follow, (5) Besides, the tangential velocity should be calculated as follow, √
(6)
By incorporating equation 5 into 6 the tangential velocity can be calculated as follow, √
(
)
(7)
By factorizing √ , the tangential velocity can be calculated as follow, √ (√
( ) )
(8)
Additionally, the velocity can be calculated by dividing the displacement over the time as follow, (9) Where the displacement (L) is defined as the spline length, hence
√ (√
( ) )
(10)
By incorporating equation 3 into equation 10 the velocity in different directions can be defined, √ (√
(
(
)) )
The values of the velocity in Y direction can be found if the values of
(11) put into equation 5.
The rotational velocity in a 2-D surface can be calculated as follow, ω=
=
(12)
where θ is the angle between the velocity and the X direction, dθ is the change in angular displacement and dt is the change in the time (t). Thus, the components for the angular velocity can be found as follow, V
=
(13)
V
=
(14)
Hence, (15) The rotational velocity acceleration vector can be calculated by finding the difference for the rotational velocity vector over a small-time step Δt as follow, =
(16)
Thus, the rotational velocity acceleration can be calculated by taking the limit as Δt→0, = The, the rotational velocity values will be written as follows,
(17)
( Where
)
is the same as (
(18) , and
is the same as
, thus
( ) )
(19)
By resolving equation 19, the rotational velocity values ( ) can be calculated.
3. Results and Discussion As mentioned earlier, based on the FSW process nature, the simulation comprises of three steps; the initial process involved plunging and dwelling which shapes the heat source. Next, the tool should move across the welding seam and consequently, the elimination of the welding tool needs to be simulated. 3.1. Cross Section Results In this regard, such observation occurred the rapid increase of the peak temperature. To illustrate, there is an approximate regular pattern for the increase of the temperature throughout the plunging stage except for the last stage where the temperature increased rapidly. During the dwelling step, it is found that the interfacial temperature is approximately stable from t = 3 s to t = 5 s in both software. This happens because the contact shear stress and the heat generated by the plastic deformation is almost stable. To elaborate, at the end of the dwelling step it is obtained that, as the process time increases the generated heat becomes stable, because the interfacial temperature at the contact interface becomes constant. During the dwelling step, it is summarized that, as process time increases, the shear zone expands, and whereby viscous dissipation caused the marginal increase of heat generated over the time. Ultimately, the highest temperature of 300 °C for ABAQUS®, and the 338°C for Altair Hyperworks® have achieved which shows the stability in the achieved temperature. As can be seen in Figure 3 the pin shape largely influences the pattern of the heat-affected zone (HAZ) area. It is also summarized that the material gets pushed upwards behind the tool due to the influence of the shoulder geometry which it produces higher material velocity at the top surface.
To illustrate, the geometry of the contact area is dependent of the material behavior. Thus, the change of in the diameter from the shoulder to the pin causes the movement of the material towards the upper region. As a result, the maximum strain rate position shifted to the right (advancing side). This shows that around the welding centerline, the temperature distribution is asymmetrical. It is also worth noted that, high temperature is observed in the region under the shoulder, with extremely high energy density. Moreover, in the welding seam, there are no significant differences between the top and the bottom surfaces while there is a non-steady-state temperature distribution in the YZ-plane, which is in line with the welding direction. Furthermore, compared to the material located at the lower region, the material near the upper region has a higher velocity and there is a difference between the behavior of the material in the welding advancing and retreating sides. To explain the issue, the velocity of the material in the advancing side is higher compared to the velocity of material on the centerline. Thus, the material located at the advancing side needs to travel further. In identifying the difference between the temperature pattern at the top and the lower surface shows that the material has different flow behaviors at different locations. Around 15% of the material thickness is influenced by the tool shoulder, while the middle region is influenced by the pin and has the highest thickness between the above-mentioned regions. This difference in the thickness confirms that at the middle region, the material stirring is contributed by the tool pin, while at the upper surface, the material is mainly stirred by the shoulder.
Figure 3. Temperature distribution at the cross section of the curved model the top view is ABAQUS® and the bottom one is Altair Hyperworks®
3.2.Top View Results Descriptions Figure 4 (top view of the dwelling step) shows that the tool shape influences the material behavior. Here, the material flowed through the retreating side and forged into the trailing edge as the material flowed around the pin. It should be noted that, the pin side has shown a skewing action which caused a vertical flow of the material, however this is insignificant and can be neglected because its motion is lower compared to the material motion in other parts.
Figure 4. Plunging step top view, the top one is ABAQUS® and the bottom one is Altair Hyperworks®
In addition, the pattern of the temperature field near the pin area is circular, thus there is little difference between the front and the back of the pin and also between the welding sides. The welded joint near the pin is divided into three parts: plastic flow region, plastic deformed region and non-deformed region (Figure 4). The peak temperature of the thin shear boundary layer adjacent to the pin is not significantly affected by the heat from the shoulder. The results also indicated that there is a constant heating pattern ahead of the tool which confirms the presence of a linear relationship between the travel rate and peak temperature. In this regard, it is observed that at the bottom layers around the pin, the temperature near the pin is predominantly influenced by the concentrated heat of plastic deformation. To validate the observations, other studies in which shoulder less FSW and stationary shoulder FSW [49] are employed confirmed that the plastic deformation around the pin, rather than the heat generated by the shoulder, affects the temperature of the thin shear boundary layer around the pin. 3.3. Different Steps Results From the results it is summarized that (Figure 5), the maximum displacement of the material is detected at the plunging and dwelling steps due to the creation of the keyhole. Meanwhile, a narrower HAZ around the weld line is shaped during higher welding speeds. From the results it is observed that the narrower area and the adjacent region to the HAZ exerted a greater restraint and whereby it creates greater temperature difference between the HAZ area and the nearby area.
The reason of the achieved higher temperature gradient is because of the increase in the welding forces needed to deform the higher restricted material. Figure 6, Figure 7 and Figure 8 show the results of the temperature counter during the welding step at different welding time steps. Here, the vertical movement of the tool flows the material and reduces the thickness of the upper region which illustrates the material displacement from the inception to the final deposition at the upper, middle, and lower regions. Moreover, during the early stages of the welding step there is a sharp increase in the peak temperature (around 510 °C), and subsequently, the increase becomes constant as the quasi-steady state that is dominated the process. It should be noted that, the achieved temperature is around 87% of the material melting point. As previously discussed, the material at the upper region moved from the advancing side until it reaches to the final deposition during the welding step. Besides that, the total generated heat is almost constant (from t = 5 s to t = 25 s) during the welding stage which this issue confirms the domination of the quasi-steady state condition for the heat. It should be noted that, the total time for the simulation was 25 seconds.
Figure 5. Plunging step results the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Figure 6. Welding step results (step time 8 s) the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Figure 7. Welding step (step time 12.8 s) results the top view is ABAQUS® and the bottom one is Altair Hyperworks®
Moreover, by studying of the results of the cooling stage it is obtain that, the peak temperature was decreased rapidly as the tool pulled out from the work-piece as there is no heat generated during the cooling stage and the cooling rate is relatively higher in the initial time of the cooling stage. To explain the results, it is also obtained that, as the temperature of the plate reaches to the room temperature, a dominant pattern in the distribution of the yield stress as well as the material
softening is obtained, because of this fact that the yield stress is highly influenced by the temperature. Different sizes of the mesh is applied to the model. To explain more, smaller sizes of the mesh is applied at the weld line while a coarser mesh size for other parts has been applied. These different sizes for the mesh has been set for the model, because of the optimization of the model mesh. If a small size for the mesh selects for all of the workpiece, then the computational time for the simulation would increase. On the other hand, if a coarse size applies for the entire of the workpiece, then the accuracy of the model would not be enough. To explain more, total number of nodes was 35525 and total number of elements was 29232. In addition, during the welding process, the workpiece deformations are in a hyperbolic parabolic shape. In both models, the displacement magnitude has a “V” shape across the transverse direction, and this shape is almost constant along the longitudinal direction. As previously mentioned, the material stiffeners resist to the work-piece deformations and welding deformations caused the creation of a residual stresses. Thus, in the curved model, the moment of the inertia shows lower deformations as well as the lower longitudinal stresses. Moreover, it is observed that at the step time of t=12.8 s, the temperature distribution is still asymmetrical. This fact shows that; the asymmetrical pattern of the temperature has not changed with the increase of the process time. However, with the increase of the step time up to 19.6 s (Figure 8), the asymmetric contour in the stir zone becomes wider and higher temperatures are reached on the advancing side than on the retreating side which shows that during the welding step as the welding time increases the temperature of the advancing side also is increased.
Figure 8. The temperature contour during the welding step (step time of 19.6) the top view is ABAQUS® and the bottom one is Altair Hyperworks®
It should be mentioned that, these results are in good accordance with the literature [26]. In the meantime, it is observed that as the step time increase, the stir zone appeared to be chaotic which this results is similar to the experimental observations for the welding nugget zone as reported by Choi et al. [50]. In addition, the results indicated that at the step time of 19.6 s, the material
distribution across the imaginary line which divides the domain into two parts (in the direction of the welding velocity) is relatively symmetric. This study also found that the majority of the volume of the material is accumulated at the top surface of the stir zone. Lastly, it is observed that at each step time, the tool has a perpendicular position to the curved surface and based on the findings, this study has successfully investigated the thermal behavior of FSW with two different software Altair Hyperworks® and ABAQUS®. Therefore, the used method is able to provide a solution to the problem of the tool perpendicular movement. Thus, this study could provide a better understanding of the thermal analysis of the curved FSW.
4. Conclusions This paper presets a new method which can solve the perpendicular position of the tool for a curved FSW plate. The review of the literature indicated that there is a lack of knowledge for simulating the FSW of a curved plate, because there is a difficulty in defining and applying an accurate movement for the tool. The mathematical formulations were applied in VDISP user defined subroutine in order to precisely model the perpendicular movement of the tool at each step time. It was found from the results of the curved finite element model that, there is a marginal increment in the heat generation as the shear zone expands due to the viscous dissipation leading up to a total peak temperature value of 300 °C (ABAQUS®) and 338°C (Altair Hyperworks®) happened at time, t = 3 s at the plunge stage. Meanwhile, at the dwell stage (between t = 3 s to t= 5 s), there is a stable situation in the amount of the generated heat from the plastic deformation as well as the contact shear stress at the tool/work-piece contact interfaces, thus the interfacial temperature is found to be stable. By the end of the dwelling step, the total generated heat is stable to the maximum value of 300 °C. For the material flow, the flow was observed to move around the pin passing through the retreating side and slightly stretching towards the advancing side. The shoulder also pushes the material upwards at the back of the tool, because the velocity of the material is higher at the upper region than at the lower region. Also, due to non-uniform material flow around the tool, an asymmetrical temperature distribution is formed in the centerline of the weld. During the welding step, the temperature reached a peak value of about 531 °C at the initial welding stage before remaining steady through the quasi-steady welding stage. At time, t = 12.8 s, the temperature was asymmetrically distributed across the work-piece until the time step of 19.6 s which at that point the asymmetric
contour expanded in the stir zone. More so, higher temperatures were obtained from the advancing side compared to the retreating side as the welding time increased. Acknowledgement The authors would like to thank the fellowship of the government of China, Shandong University from the International Postdoctoral Exchange Program and professor Wallace Kaufman for his endless support.
Declaration of Competing Interest There is no conflict of interest for this paper
References ]1[
G. Rezaei and N. B. M. Arab, "Investigation on tensile strength of friction stir welded joints in pp/epdm/clay nanocomposites," International Journal of EngineeringTransactions C: Aspects, vol. 28, p. 1382, 2015.
]2[
S. Emamian, M. Awang, F. Yusof, P .Hussain, B. Meyghani, and A. Zafar, "The Effect of Pin Profiles and Process Parameters on Temperature and Tensile Strength in Friction Stir Welding of AL6061 Alloy," in The Advances in Joining Technology, ed: Springer, 2018, pp. 15-37.
]3[
R. Singh, S .A. Rizvi, and S. Tewari, "Effect of friction stir welding on the tensile properties of aa6063 under different conditions," International Journal of Engineering Transactions A: Basics, vol. 30, pp. 597-603, 2017.
]4[
G. Rezaei and N. B. M. Arab, "Investigation on tensile strength of friction stir welded joints in pp/epdm/clay nanocomposites," International Journal of EngineeringTransactions C: Aspects, vol. 28, pp. 1382-1391, 2015.
]5[
R. Hasanzadeh, T. Azdast, A. Doniavi, S. Babazadeh, R. Lee, M. Daryadel, et al., "Welding properties of polymeric nanocomposite parts containing alumina nanoparticles in friction stir welding process," International Journal of Engineering Transactions A: Basics, vol. 30, pp. 143-151, 2017.
]6[
B. Meyghani and M. B. Awang" ,Prediction of the Temperature Distribution During Friction Stir Welding (Fsw) With A Complex Curved Welding Seam: Application In The Automotive Industry," MATEC Web Conf., vol. 225, p. 01001, 2018.
]7[
X. Pan, C. Wu, W. Hu, and Y. Wu, "A momentum-consistent stabilization algorithm for Lagrangian particle methods in the thermo-mechanical friction drilling analysis," Computational Mechanics, pp. 1-20, 2019.
]8[
B. Meyghani, M. B. Awang, S. S. Emamian, M. K. B. Mohd Nor, and S. R. Pedapati, "A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)," Metals, vol. 7, p. 450, 2017.
]9[
B. Meyghani, M. Awang, and S. Emamian, "A comparative study of finite element analysis for friction stir welding application," ARPN J. Eng. Appl. Sci, vol. 11, pp. 1298412989, 2016.
]11[
N. Dialami, M. Cervera, M. Chiumenti, and C. A. de Saracibar, "A fast and accurate twostage strategy to evaluate the effect of the pin tool profile on metal flow, torque and forces in friction stir welding," International Journal of Mechanical Sciences, vol. 122, pp. 215-227, 2017.
]11[
H. Su, C. S. Wu, M. Bachmann, and M. Rethmeier, "Numerical modeling for the effect of pin profiles on thermal and material flow characteristics in friction stir welding," Materials & Design, vol. 77, pp. 114-125, 2015.
]12[
H. Su, C. S. Wu, A. Pittner, and M. Rethmeier, "Thermal energy generation and distribution in friction stir welding of aluminum alloys," Energy, vol. 77, pp. 720-731, 2014.
]13[
C.-s. WU, W.-b. ZHANG, S. Lei, and M.-a. CHEN, "Visualization and simulation of plastic material flow in friction stir welding of 2024 aluminium alloy plates," Transactions of Nonferrous Metals Society of China, vol. 22, pp. 1445-1451, 2012.
]14[
B. Meyghani, M. B. Awang ,R. G. M. Poshteh, M. Momeni, S. Kakooei, and Z. Hamdi, "The Effect of Friction Coefficient in Thermal Analysis of Friction Stir Welding (FSW)," in IOP Conference Series: Materials Science and Engineering, 2019, p. 012102.
]15[
B. Meyghani, M. B. Awang, M .Momeni, and M. Rynkovskaya, "Development of a Finite Element Model for Thermal Analysis of Friction Stir Welding (FSW)," in IOP Conference Series: Materials Science and Engineering, 2019, p. 012101.
]16[
B. Meyghani, M. Awang, S. Emamian, and N. M. Khalid, "Developing a Finite Element Model for Thermal Analysis of Friction Stir Welding by Calculating Temperature Dependent Friction Coefficient," in 2nd International Conference on Mechanical, Manufacturing and Process Plant Engineering, 2017, pp. 107-126.
]17[
S. Kumar, C. Wu, S. Zhen, and W. Ding, "Effect of ultrasonic vibration on welding load, macrostructure, and mechanical properties of Al/Mg alloy joints fabricated by friction stir lap welding," The International Journal of Advanced Manufacturing Technology, vol. 100, pp. 1787-1799, 2019.
]18[
S. Kumar and C. Wu, "Review: Mg and its alloy—scope, future perspectives and recent advancements in welding and processing," J Harbin Inst Technol (New Ed), vol. 24, pp. 1-37, 2017.
]19[
H. S. Chuansong WU, Lei SHI, "Numerical Simulation of Heat Generation, Heat Transfer and Material Flow in Friction Stir Welding," Acta Metall, vol. 54, pp. 265-277, 2018-02-20 2018.
]21[
N. Dialami, M. Chiumenti, M. Cervera, and C. A. de Saracibar, "Challenges in Thermomechanical Analysis of Friction Stir Welding Processes," Archives of Computational Methods in Engineering, pp. 1-37, 2015.
]21[
N. Dialami, M. Chiumenti, M. Cervera, A. Segatori, and W. Osikowicz, "Enhanced friction model for Friction Stir Welding (FSW) analysis :Simulation and experimental validation," International Journal of Mechanical Sciences, vol. 133, pp. 555-567, 2017/11/01/ 2017.
]22[
T. Sun, M. Roy, D. Strong, P. J. Withers, and P. B. Prangnell, "Comparison of residual stress distributions in conventional and stationary shoulder high-strength aluminum alloy friction stir welds," Journal of Materials Processing Technology, vol. 242, pp. 92-100, 2017.
]23[
P. Bussetta, É. Feulvarch, A. Tongne, R. Boman, J.-M. Bergheau, and J.-P. Ponthot, "Two 3D thermomechanical numerical models of friction stir welding processes with a trigonal pin," Numerical Heat Transfer, Part A: Applications, vol. 70, pp. 995-1008, 2016.
]24[
R. Jain, S. K. Pal, and S. B. Singh, "Finite Element Simulation of Temperature and Strain Distribution during Friction Stir Welding of AA2024 Aluminum Alloy," Journal of The Institution of Engineers (India): Series C, pp. 1-7, 2016.
]25[
M. Riahi and H. Nazari, "Analysis of transient temperature and residual thermal stresses in friction stir welding of aluminum alloy 6061-T6 via numerical simulation," The International Journal of Advanced Manufacturing Technology, vol. 55, pp. 143-152, 2011.
]26[
F. Al-Badour, N. Merah, A. Shuaib, and A. Bazoune, "Coupled Eulerian Lagrangian finite element modeling of friction stir welding processes," Journal of Materials Processing Technology, vol. 213, pp. 1433-1439, 2013.
]27[
B. Meyghani, M. B. Awang, S. Emamian, and E. T. Akinlabi, "A comparison between temperature dependent and constant Young's modulus values in investigating the effect of the process parameters on thermal behaviour during friction stir welding," Materialwissenschaft und Werkstofftechnik, vol. 49, pp. 427-434.
]28[
B. Meyghani, M. Awang, S. Emamian, and M. K. B. M. Nor, "Thermal Modelling of Friction Stir Welding (FSW) Using Calculated Young’s Modulus Values," in The Advances in Joining Technology, ed: Springer, 2018, pp. 1-13.
]29[
Z. Zhang, "Comparison of two contact models in the simulation of friction stir welding process," Journal of Materials Science, vol. 43, pp. 5867-5877, 2008.
]31[
B. Meyghani, M. Awang, and S. Emamian, "A Mathematical Formulation for Calculating Temperature Dependent Friction Coefficient Values: Application in Friction Stir Welding (FSW)," in Defect and Diffusion Forum, 2017, pp. 73-82.
]31[
S. Emamian, M. Awang, P. Hussai, B. Meyghani, and A. Zafar, "INFLUENCES OF TOOL PIN PROFILE ON THE FRICTION STIR WELDING OF AA6061," 2006.
]32[
C. Hamilton, A. Sommers, and S. Dymek, "A thermal model of friction stir welding applied to Sc-modified Al–Zn–Mg–Cu alloy extrusions," International Journal of Machine Tools and Manufacture, vol. 49, pp. 230-238, 2009.
]33[
P. Ulysse, "Three-dimensional modeling of the friction stir-welding process," International Journal of Machine Tools and Manufacture, vol. 42, pp. 1549-1557, 2002.
]34[
P. Heurtier, M. Jones, C. Desrayaud, J. H. Driver, F. Montheillet, and D. Allehaux, "Mechanical and thermal modelling of friction stir welding," Journal of Materials Processing Technology, vol. 17 ,1pp. 348-357, 2006.
]35[
A. Gerlich, M. Yamamoto, and T. North, "Strain rates and grain growth in Al 5754 and Al 6061 friction stir spot welds," Metallurgical and materials transactions A, vol. 38, pp. 1291-1302, 2007.
]36[
H. N. B. Schmidt, T. Dickerson, and J. H. Hattel, "Material flow in butt friction stir welds in AA2024-T3," Acta Materialia, vol. 54, pp. 1199-1209, 2006.
]37[
P. Bussetta, N. Dialami, M. Chiumenti, C. A. de Saracibar, M. Cervera, R. Boman, et al., "3D numerical models using a fluid or a solid formulation of FSW processes with a noncylindrical pin," Advanced Modeling and Simulation in Engineering Sciences, vol. 2, p. 27, 2015.
]38[
N. Dialami, M. Cervera, and M. Chiumenti, "Numerical Modelling of Microstructure Evolution in Friction Stir Welding (FSW)," Metals, vol. 8, p. 183, 2018.
]39[
N. Dialami, M. Cervera, M. Chiumenti, and C. A. de Saracibar, "Speed-up strategy for the analysis of FSW pin profile effect on torque and forces".
]41[
H.-H. Cho, S.-T. Hong, J.-H. Roh, H.-S. Choi ,S. H. Kang, R. J. Steel, et al., "Threedimensional numerical and experimental investigation on friction stir welding processes of ferritic stainless steel," Acta Materialia, vol. 61, pp. 2649-2661, 2013.
]41[
M. Chiumenti, M. Cervera, A. Salmi, C. A. De Saracibar, N. Dialami, and K. Matsui, "Finite element modeling of multi-pass welding and shaped metal deposition processes," Computer methods in applied mechanics and engineering, vol. 199, pp. 2343-2359, 2010.
]42[
A. Kumar, D. Fairchild, M. Macia, T. Anderson, H. Jin, R. Ayer, et al., "Research progress on friction stir welding of pipeline steels," in Proceedings of the 8th International Pipeline Conference, 2010.
]43[
M. Monreal and C. A. Rodriguez, "Influence of tool path strategy on the cycle time of high-speed milling," Computer-Aided Design, vol. 35, pp. 395-401, 2003.
]44[
B. H. Kim and B. K. Choi, "Machining efficiency comparison direction-parallel tool path with contour-parallel tool path," Computer-Aided Design, vol. 34, pp. 89-95, 2002.
]45[
Z .Yin, "Rough and finish tool-path generation for NC machining of freeform surfaces based on a multiresolution method," Computer-Aided Design, vol. 36, pp. 1231-1239, 2004.
]46[
B. Meyghani and M. Awang, "A Comparison Between the Flat and the Curved Friction Stir Welding (FSW) Thermomechanical Behaviour," Archives of Computational Methods in Engineering, pp. 1-14, 2019.
]47[
H. Su and C. Wu, "Determination of the traverse force in friction stir welding with different tool pin profiles," Science and Technology of Welding and Joining, pp. 1-9, 2018.
]48[
P. Prasanna, B. S. Rao, and G. K. M. Rao, "Finite element modeling for maximum temperature in friction stir welding and its validation," The International Journal of Advanced Manufacturing Technology, vol ,51 .pp. 925-933, 2010.
]49[
J. Li and H. Liu, "Effects of tool rotation speed on microstructures and mechanical properties of AA2219-T6 welded by the external non-rotational shoulder assisted friction stir welding," Materials & Design, vol. 43, pp. 299-30.2113 ,6
]51[
D.-H. Choi, B.-W. Ahn, C.-Y. Lee, Y.-M. Yeon, K. Song, and S.-B. Jung, "Formation of intermetallic compounds in Al and Mg alloy interface during friction stir spot welding," Intermetallics, vol. 19, pp. 125-130, 2011.