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A dynamic welding heat source model in pulsed current gas tungsten arc welding
Journal of Materials Processing Technology 213 (2013) 2329–2338
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
A dynamic welding heat source model in pulsed current gas tungsten arc welding Zhang Tong, Zheng Zhentai ∗ , Zhao Rui School of Materials Science and Engineering, Hebei University of Technology, No. 8, Duangrongdao Road, Hongqiao District, Tianjin 300130, PR China
a r t i c l e
i n f o
Article history: Received 25 January 2013 Received in revised form 9 July 2013 Accepted 11 July 2013 Keywords: Numerical simulation Welding temperature field Heat source model Pulsed current gas tungsten arc welding
a b s t r a c t A time-dependent welding heat source model, which is defined as the dynamic model, was established according to the characteristic of PCGTAW. The parabolic model was proposed to describe the heat flux distribution at the background times. The recommended Gaussian model was used at the peak times due to the bell-shaped temperature contour. The dynamic welding heat source was composed of these two models with a function of time. To assess the validity of the dynamic model, an experiment was conducted in which the pulsed current gas tungsten arc deposits on the plate. From the comparison of the experimental and the simulated values, it can be concluded that the dynamic heat source model, which uses the parabolic model at the background time, is more realistic and accurate under the same welding conditions. © 2013 Elsevier B.V. All rights reserved.
1. Introduction With the development of the computer and numerical analysis technologies, the FEM has become a powerful and reliable technique for prediction in the welding processing industry. The temperature field contains sufficient information about the quality and properties of the welded joint, and determines the distortion, residual stresses, and reduced strength of a structure in and near the welded joint. The temperature field is also the foundation of the metallurgical analysis and phase change analysis. To obtain an accurate welding temperature field, Goldak et al. (1984) reported that the importance of a good welding heat source model has been emphasized by many investigators. Many welding heat source models have been developed up to now, and the Gaussian model and the double ellipsoidal model are the most popular models among them. Some good welding heat source models can accurately predict the temperature field. However, most of these models were developed on the assumption that the heat sources are static and not varied with time in the welding processes. These models are no longer realistic for some dynamic welding processes, such as the pulsed current gas tungsten arc welding (PCGTAW). The objective of this paper is to develop a more realistic and accurate welding heat source model for PCGTAW. PCGTAW was developed in 1950s and is widely used in the manufacturing industry today. In PCGTAW, the welding current is
∗ Corresponding author. Tel.: +86 13512499764; fax: +86 13512499764. E-mail addresses: [email protected] (Z. Tong), [email protected] (Z. Zhentai). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.07.007
varied periodically from the peak current to the background current. Balasubramanian et al. (2008) indicated that the heat energy to melt the base metal is provided mainly by the peak current, while the background current is set at a low level to maintain a stable arc. Therefore, the background time can be seen as brief intervals during heating, which allow the heat to conduct and diffuse in the base metal. PCGTAW is a widely utilized welding process. Traidia et al. (2010) and Balasubramanian et al. (2008) pointed out that PCGTAW has the following advantages over the constant current gas tungsten arc welding (CCGTAW): (a) lower heat input; (b) narrower heat affected zone; (c) finer grain size; (d) less residual stresses and distortion; (e) improved mechanical properties; and (f) enhanced arc stability to avoid weld cracks and reduce porosity, etc. However, the welding parameters of PCGTAW are more complex to define than CCGTAW, and the choice of parameters with PCGTAW remains empirical. The parameters of PCGTAW were depicted by Madadi et al. (2012) in Fig. 1. A great deal of work has been conducted on the numerical simulation of PCGTAW. Fan et al. (1997) developed a two-dimensional model using the boundary fitted coordinate system to simulate the PCGTAW process. Kim and Na (1998) computed the fluid flow and heat transfer in partially penetrated weld pool under PCGTAW by the finite difference method. Traidia and Roger (2011) used the unified time-dependent model to describe the fluid flow, heat transfer and electromagnetic fields in the three regions respectively. Many investigations have been conducted, but far less work has been done on the development of the welding heat source model under PCGTAW. Several heat source models have been developed. They are classified in Table 1. Most of the current heat source models have been
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Table 1 The classification of current welding heat source models. One-dimension
Two-dimension
Three-dimension
Uniform distribution mode
Point heat source Line heat source – –
Plane heat source Circular mode Tripped heat source Square heat source
Columnar heat source – – –
Gaussian mode
– – – – – – – – –
Circular mode Oval-shaped heat source Double oval-shaped heat source Tripped heat source – – – – –
Circular disk heat source Columnar heat source Cuboid heat source Rotary body heat source Conic heat source Hemispherical heat source Semi-ellipsoidal heat source Ellipsoidal heat source Double ellipsoidal heat source
Exponential decay mode
–
–
Exponential decay heat source
developed on the geometrical shape and distribution in space, but time as an important factor, which has rarely been considered, in the model design. In fact, the heat source is varied with time in some dynamic process, e.g. in the PCGTAW. Therefore, a time-dependent heat source model, which is available for the dynamic process, is necessary to be developed. In this paper, a dynamic finite element model of welding heat source under PCGTAW is established. Then the moving, timedependent heat source was attempted to load onto the structure, and the FEM was used to compute the temperature field through the software ANSYS. 2. Theoretical formulations 2.1. Model consideration With the help of high speed CCD, Traidia and Roger (2011) used an infra-red camera to capture the characteristic of a welding arc under PCGTAW, and some good images were obtained which at the background and peak times (see Fig. 2). It is easy to see that there is significant difference between the peak time and the background time, and the arc is bell-shaped during the peak duration, but not during the background duration.
In contrast to constant current welding, the heat input in PCGTAW is supplied mainly during the peak times, and the heating is halted periodically during the background times. Xu et al. (2009) pointed out that the characteristic of discontinuity during heating under PCGTAW is more obvious when the frequency is low. So, two heat source models must be proposed which will be available in the peak times and background times. Considering the bell-shaped temperature contour, the recommended Gaussian model was used during the peak times; the big problem at present is to propose a good heat source model which is available during the background times. Some good experience can be obtained from the proposed process of the Gaussian heat source model. The design of the experiment was made to investigate the heat and current distribution of GTAW, which consists of splitting a water cooled copper anode. Measure the heat flux to one of the sections as a function of the arc position relative to the splitting plane. The radial heat distribution can then be derived by an Abel transformation of the measured heat flux on the anode. The distribution of heat on the anode is a result of a series of collisions of electrons with ionized atoms as electrons travel from the cathode to the anode. The energy released on the anode surface carried by the electrons constitutes most of the heat, and Tsai and Eagar (1985) considered that the distribution of the heat flux on the water cooled anodes should closely approximate to the distribution across the weld pool. Similarly, regarding the PCGTAW in this paper, it can be also considered that the anodic heat flux distribution is closely approximate to the heat distribution across the weld pool. 2.2. Mathematical model Traidia and Roger (2011) obtained the numerical simulation result of the radial heat flux distribution at the anode between the pulsed current – background time and peak time – and the mean current, which are shown in Fig. 3a. The third curve which the arrow points to is the radial heat flux distribution during the background time. To simplify the problem, it can be assumed that the radial heat flux at the background time is parabolic shape, which passes through three points (0, q(0)), (Rb , 0), (−Rb , 0) in the coordinate –x plane. The function of radial heat flux distribution at the background time can be written as:
q(x, ) = q(0)
Fig. 1. Pulsed current GTAW process parameters (Madadi et al., 2012).
1−
x2 Rb2
,
− Rb ≤ x ≤ Rb
(1)
where q(0) is the maximum value of heat flux and Rb is the radius of the power density.
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Fig. 2. Infra-red camera images at the background and peak times for both first and last periods.
Substituting q(0) = 43 W/mm2 and R ≈ 2.8 mm which is corresponded with the third curve in Fig. 3a into Eq. (1):
q(x, ) = 43
x2
1−
2.82
,
− Rb ≤ x ≤ Rb
(2)
q(x, y, ) = q(0)
1−
x 2 + y2
(3)
Rb2
where q(x, y, ) is the power density (W/m2 ).
x2 + y2 which is the radial distance from the center of For r = the heat source, then Eq. (3) can be written as:
q(r) = q(0)
r2
1−
Rb2
,
r ≤ Rb
(4)
2UI
(7)
Rb2
Substituting q(0) from Eq. (7) into Eq. (4) gives: q(r) =
The function image of Eq. (2) is shown in Fig. 3b, which approximates to the third curve in Fig. 3a that represents the radial heat flux distribution at the background time, which can be clearly observed in Fig. 3c which combined Fig. 3a with Fig. 3b in the same scale. So it can be considered that the radial heat flux distribution at background time is approximate to parabolic shape, and the welding heat source is a spinning parabolic shape distribution as shown in Fig. 4. The spinning parabolic shape model of welding heat source with the center at (0, 0, 0) to coordinate axes x, y, can be written as:
q(0) =
2UI
1−
Rb2
r2
,
Rb2
r ≤ Rb
(8)
So the dynamic welding heat source model of PCGTAW in one pulse cycle can be written as: q(r) =
3p UIp Rp2
or q(r) =
exp
2b UIb Rb2
−3
1−
r2 Rp2 r
,
t ∈ [0, tp ] (at peak times)
,
t ∈ (tp , tT ] and r ≤ Rb
2
Rb2
(9) (at background times)
where q(r) is the power density (W/m2 ), p the heat source efficiency at the peak time, b the heat source efficiency at the background time, U the arc voltage (V), Ip the peak current (A), Ib the background current (A), r = (x2 + y2 )1/2 which is the radial distance from the center of the heat source (m), Rb the radius of the heat source at the background time (m), Rp the radius of the heat source at the peak time (m), tT = 1 pulse cycle time = 1/f (s), f the pulse frequency, tp the peak time (s), tb the background time (s) and tp + tb = tT . 3. Evaluation of the dynamic model of welding heat source in PCGTAW
Conservation of energy requires that:
Q = UI =
q(r)r dr d =
Rb
q(0) 0
1−
r2 Rb2
r dr
2
d (5) 0
and produces the following: Q = UI = q(0)
Rb2 2
(6)
One experiment was conducted in which the pulsed current gas tungsten arc was deposited on the plate. The thermocouple was used to measure the temperature field at the given points, then the experimental values were compared with the simulated values to assess the validity of the dynamic welding heat source model. Due to the lack of data on material properties, material modeling has always been a critical issue in the welding simulation.
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Table 2 The chemical composition of AA7075. Elements
Zn
Mg
Cu
Cr
Mn
Fe
Si
Ti
Al
Impurities
wt.%
5.1–6.1
2.1–2.9
1.2–2.0
0.18–0.28
0.30
0.50
0.40
0.20
Bal.
0.15
Sattari-Far and Javadi (2008) reported that some simplifications and approximations are usually introduced to deal with this problem, which are necessary because of the scarcity of material data and numerical problems when trying to model the actual high-temperature behaviors of the material. Here we select the Aluminum Alloy 7075 as the base metal; the chemical composition is shown in Table 2. The thermal properties of AA7075 shown
in Fig. 5 were reported by Guo et al. (2006) which are temperaturedependent, the emissivity is assumed to be 0.6, and the fusion temperature range is 477–638 ◦ C. 3.1. Experimental procedure 3.1.1. Experiment preparation The plate of Aluminum Alloy 7075 was cut to the required size of 80 mm × 80 mm × 8 mm. To measure the temperature in the welding process, the K type NiCr–NiSi thermocouple was used. The positions of the thermocouples in the plate were shown in Fig. 6. The thermocouples were glued to a depth of 4 mm, through the blind holes which were drilled from the bottom of the plate; the hot end diameter of the thermocouple was 1.5 mm, the cold end was connected to a multichannel temperature measuring instrument to acquire the thermal cycle, and the same method was introduced by Karunakaran and Balasubramanian (2011). 3.1.2. Welding Bead-on-plate welds were made using the PCGTAW on the surface of the plate along with the center line. The welding parameters are shown in Table 3. 3.2. FEM calculation 3.2.1. Finite element model Only half of the plate was selected to analysis for its symmetry. To reduce the calculation time, the zone near the welding bead has been modeled with a finer mesh, while the zone further away from the welding bead has been modeled with a coarser one. Solid70 and Surf152 were used to mesh the model; the surface has been
Fig. 3. The establishment of the parabolic distribution (a is referred to Traidia and Roger, 2011).
Fig. 4. Heat source configuration for the spinning parabolic shape.
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Table 3 Welding parameter. Process parameter
Actual
Simulated
Welding current Peak current Background current Arc voltage Welding speed Pulse frequency % Pulse on time Electrode Electrode diameter Arc length Torch angle Shielding gas Flow rate
180 A 60 A 14 V 1.96–2.03 mm/s 1 Hz 50% W–2%Th 3.2 mm 2 mm 60◦ Argon 99.9% 15 L/min
180 A 60 A 14 V 2 mm/s 1 Hz 50% – – – – – –
“coated” with Surf152 to represent the convective heat exchange. The FEM model is shown in Fig. 7.
Fig. 5. Thermal physical properties of AA7075: (a) specific heat and density and (b) conductivity.
3.2.2. Welding heat source In this research, the APDL programming languages of ANSYS were applied to realize the moving load of the heat source. A local coordinate system was established, and the center of the heat source coincided with the original point of the local coordinate, then the heat source moved gradually under the control of the loop command in APDL. To evaluate the validity of the dynamic heat source model, two simulation tests were implemented under the same welding conditions, which are described in Table 4. The parameters in the dynamic welding heat source model are not easy to decide, so a further study is needed. 3.2.3. Initial condition and boundary conditions The ambient temperature is 28 ◦ C. Considering the moving heat source, heat losses due to convention and radiation are taken into account in the finite element models. Heat loss due to convection (qc ) is taken into account using Newton’s law: qc = hc (Ts − T0 ) where hc is the heat transfer coefficient, Ts the surface temperature of the weldment and T0 is the ambient temperature which is 28 ◦ C. Heat loss due to radiation is modeled using Stefan–Boltzmann’s law: qr = −ε · [(Ts + 273)4 − (T0 + 273)4 ] where ε is emissivity which is 0.6 and = 5.67 × 10−8 W/m2 ◦ C−4 is defined as the Stefan–Boltzmann constant. 3.2.4. Latent heat of phase transition During the welding process, melting and solidifying will occur in the welding pool, it will absorb or release latent heat in the phase transition, which is defined as “latent heat of phase transition”. Lei et al. (2006) use the enthalpy method to deal with the
Fig. 6. Schematic diagram of welded plate used in the experiment. Fig. 7. FEM model.
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Table 4 List of the simulation test. Simulation test 1
Simulation test 2
Heat source model
Dynamic Model 1
Dynamic Model 2
Model description
Use Gaussian model at peak times; use parabolic model at background times
Use Gaussian model both at peak times and background times, but different values of parameters were used, respectively
Ip = 180 A, Ib = 60 A, U = 14 V, f = 1 Hz Pulse on time = 50%, Rp ≈ 5.0 mm, Rb ≈ 2.8 mm, p ≈ 0.68, b ≈ 0.62.
Ip = 180 A, Ib = 60 A, U = 14 V, f = 1 Hz, Pulse on time = 50%, Rp ≈ 5.0 mm, Rb ≈ 2.8 mm, p ≈ 0.68, b ≈ 0.62.
Parameters in model
Notes: The parameters in heat source models are difficult to decide. To simplify the problems, the same parameters in Traidia and Roger (2011) were used for test 1 and test 2 under the same welding condition.
latent heat, and define the material’s enthalpy which varies with the temperature:
H(T ) =
T
(T )c(T ) dT 0
where (T) is the density of the material varying with temperature (kg/m3 ) and c(T) is the specific heat of the material varying with temperature (J/(kg K)). Murugan et al. (2000) reported that the release or absorption of latent heat can also be considered in the numerical analysis by an
artificial increase in the value of the specific heat over the melting temperature range. 3.2.5. Others In the meshed finite element model, the number of the Solid70 element is 848,000, the number of the Surf152 element is 46,640, and the number of nodes is 887,814 in total. The heat source defined in a local coordinate system moves with time, the former load step is deleted when the heat source moves to the next step. Considering both the calculation time and the computer’s capacity, the minimum size of element is 0.2 mm, and the cooling time is fixed to 20 s.
Fig. 8. Top view of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 1.
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Fig. 9. Top view of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 2.
Fig. 10. Longitudinal cross-section of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 1.
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Fig. 11. Longitudinal cross-section of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 2.
4. Results and discussion 4.1. Temperature field 4.1.1. Top view of temperature distribution Figs. 8 and 9 which are in the same scale, show the temperature field computed by the Dynamic Model 1 and the Dynamic Model 2, respectively, and including the time 20.3 s (peak time) and 20.8 s (background time) for each. To illustrate the difference of the temperature field between the peak time and the background time in the welding process, the same area region near the weld pool was magnified in the same scale. Comparing the two temperature fields in Fig. 8a and b, it can be seen that the high temperature region at 20.3 s is larger than that at 20.8 s. Due to the cyclic variation of the heat input, there is a thermal fluctuation in the temperature field, which corresponds to the real dynamic welding process. From Fig. 9a and b, the same conclusion above can be obtained.
Table 5 Peak temperature comparison of the experimental and simulated results. Methodsa
Peak temperature (◦ C)
Differenceb (%)
Point Ac
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
402.5 397.6 393.9
– −1.2 −2.1
Point Bc
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
285.8 276.7 272.5
– −3.2 −4.7
Point Cc
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
327.2 317.2 312.3
– −3.1 −4.6
Measuring point
a Experimental: use PCGTAW – welding parameter is shown in Table 3; base metal – AA7075, chemical composition is shown in Table 2. The description of the Dynamic Model 1 and Dynamic Model 2 are listed in Table 4. b . Difference (%) = (Calculated value − Experimental value)/Experimental value. c . The position of the measuring points is depicted in Fig. 6.
In Fig. 8a and b, the maximum temperatures are 892 ◦ C and 779 ◦ C, respectively. It was found that the maximum temperature at 20.3 s (peak time) is higher than the value at 20.8 s (background time). In Fig. 9a and b, the maximum temperatures are 887 ◦ C and 849 ◦ C, respectively. The maximum temperature appears in the center of the heat source model for both Figs. 8 and 9. Comparing Fig. 8a with Fig. 9a, it can be seen that there is small difference of the maximum temperature between them, which implies that the maximum temperature is nearly the same at 20.3 s when using the Dynamic Model 1 and the Dynamic Model 2. However, the maximum temperature in Fig. 8b is much lower than that in Fig. 9b, which implies that there is much difference in the maximum temperature at 20.8 s (background time) when using the Dynamic Model 1 and the Dynamic Model 2. Supplementary Video 1 is available for readers to show the temperature field computed by the Dynamic Model 1 in PCGTAW. Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jmatprotec.2013.07.007. 4.1.2. Longitudinal cross-section of temperature distribution Along with the midline of the plate in the longitudinal direction, the cross-sections of temperature distribution which are in the same scale were obtained, as shown in Figs. 10 and 11. To demonstrate clearly, the same area region near the heat source was magnified in the same scale. From Figs. 10 and 11, the same conclusions in Section 4.1.1 can also be obtained. The difference between the calculated results by the Dynamic Model 1 and the Dynamic Model 2 is demonstrated in some extent. 4.2. Welding thermal cycles The comparison of the experimental and simulated welding thermal cycles at Point A, Point B and Point C are shown in Fig. 12a–c, respectively. As can be seen from the figures, the temperatures computed by the Dynamic Model 1 and the Dynamic Model 2 are slightly lower
Z. Tong et al. / Journal of Materials Processing Technology 213 (2013) 2329–2338
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Fig. 13. The welding thermal cycle during 5–20 s at point A.
the energy released during solidifying for aluminum alloy is much bigger than the carbon steel due to the thermal physical properties of the material in or near the weld pool. However, the latent heat become less and can be neglected for the areas far away from the weld pool.
4.3. The characteristic of the pulsed current
Fig. 12. Comparison of the experimental and simulated welding thermal cycles: (a) Point A, (b) Point B and (c) Point C.
than the experimental values. Table 4 shows the peak temperature comparison of the experimental and the simulated values. The difference value listed in Table 5 indicated that the Dynamic Model 1 is more accurate than the Dynamic Model 2, and it implies that the dynamic model which uses the parabolic model at the background time is more realistic and accurate. From Fig. 12a and b, it can be noted that the temperature is increased slightly during the cooling time while it cannot be observed in Fig. 12c. The reason for that could be attributed to the latent heat in the solidifying process. Many experiments show that
Fig. 13 is part of Fig. 12a that magnified with a proper scale. It is clearly seen that there are some fluctuations in the welding thermal cycle computed by the Dynamic Model 1 and the Dynamic Model 2, which can be attributed to the influence of pulsed current. Wang (2003) used the finite element method to compute the temperature field in molybdenum alloy under PCGTAW, the fluctuation was observed in the computed welding thermal cycle. Zheng et al. (1997) developed a three-dimensional model to demonstrate the transient behavior of temperature field and weld pool in PCGTAW, and verified that the fluctuations in the thermal cycle curve are characteristic of the pulsed current welding. Therefore, it can be concluded that the Dynamic Model 1 and the Dynamic Model 2 can successfully demonstrate the dynamic process of temperature field in pulsed current welding. However, the experiment in this paper failed to capture the characteristic of the pulsed current. This may be due to the sensitivity of the temperature measuring instrument. The thermocouple is widely used as temperature sensor for measuring instrument, which can convert a temperature gradient into electricity. For the dynamic welding process of PCGTAW, the heat input is varied periodically in a very short time, which leads to the dynamic characteristic of the process that cannot be obtained easily. This requires the thermocouples to be sensitive enough to the short-term variation and the measuring instrument immediately responsive to deal with the electronic signals from thermocouples at different measured points. Maybe an improved measuring instrument or a better measuring method is needed to be developed. Although the experiment failed to capture the temperature fluctuations in PCGTAW, the temperature values measured by the calibrated instrument are accurate and convincing. The peak temperature is obtained when the heat source surpasses the measured point. As seen from Fig. 11, the pulsing effect is more obvious for the pulses closed to the measured point, while it becomes less for the pulses further away from the measured point. It can be seen that the region in or near the welded joint has experienced several heating and cooling processes due to the pulsing current, and that the soaking time at the high temperature is shorter
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compared with CCGTAW. That is why the grain is refined under the PCGTAW process. Compared with the welding thermal cycle at different points in Fig. 12a–c, it can be concluded that the pulsed current has an significant effect on the points in or near the welded joint, but less effect on the points far away from the welded joint. 5. Conclusions (1) Most of the current heat source models are static models that do not vary with time and cannot represent the heat flux distribution in some dynamic welding processes; so a good heat source model for the dynamic welding process must be developed. (2) The FEM dynamic heat source model was used to simulate the low frequency PCGTAW, which has successfully demonstrated the dynamic temperature field in the welding process. (3) From the comparisons of the experimental and the simulated values, it can be concluded that the dynamic heat source model which uses the parabolic model at the background time is more accurate under the same welding conditions. (4) In some welding process simulation, especially for those whose dynamic characteristic is more obvious, the dynamic welding heat source model has more advantages over the static models. The static heat source model is the special case of the dynamic heat source model, which is not varied with time. References Balasubramanian, M., Jayabalan, V., Balasubramanian, V., 2008. Developing mathematical models to predict grain size and hardness of argon tungsten pulse current arc welded titanium alloy. Journal of Materials Processing Technology 196, 222–229.
Fan, H.G., Shi, Y.W., Na, S.J., 1997. Numerical analysis of the arc in pulsed current gas tungsten arc welding using a boundary-fitted coordinate. Journal of Materials Processing Technology 72, 437–445. Goldak, J., Chakravarti, A., Bibby, M., 1984. A new finite element model for welding heat sources. Metallurgical Transactions B 15B, 299–305. Guo, G.F., Chen, F.R., Li, L.H., 2006. Numerical simulation of temperature field of electron beam welding for 7075 Al alloy. China Weld 3, 28–31. Karunakaran, N., Balasubramanian, V., 2011. Effect of pulsed current on temperature distribution, weld bead profiles and characteristics of gas tungsten arc welded aluminum alloy joints. Transactions of Nonferrous Metals Society of China 21, 278–286. Kim, W.H., Na, S.J., 1998. Heat and fluid flow in pulsed current GTA weld pool. Heat and Mass Transfer 41, 3213–3227. Lei, Y.C., Yu, W.X., Li, C.H., Cheng, X.N., 2006. Simulation on temperature field of TIG welding of copper without preheating. Transactions of Nonferrous Metals Society of China 16, 838–842. Madadi, F., Ashrafizadeh, F., Shamanian, M., 2012. Optimization of pulsed TIG cladding process of satellite alloy on carbon steel using RSM. Journal of Alloys and Compounds 510, 71–77. Murugan, S., Gill, T.P.S., Kumar, P.V., Raj, B., Bose, M.S.C., 2000. Numerical modeling of temperature distribution during multipass welding of plates. Science and Technology of Welding and Joining 5 (4), 208–214. Sattari-Far, I., Javadi, Y., 2008. Influence of welding sequence on welding distortions in pipes. Pressure Vessels and Piping 85, 265–274. Traidia, A., Roger, F., 2011. Numerical and experimental study of arc and weld pool behaviour for pulsed current GTA welding. International Journal of Heat and Mass Transfer 54, 2163–2179. Traidia, A., Roger, F., Guyot, E., 2010. Optimal parameters for pulsed gas tungsten arc welding in partially and fully penetrated weld pools. International Journal of Thermal Sciences 49, 1197–1208. Tsai, N.S., Eagar, T.W., 1985. Distribution of the heat and current fluxes in gas tungsten arcs. Metallurgical Transactions 16B (12), 257–262. Wang, J.H., 2003. The Techniques and Application of Numerical Simulation in Welding. Shanghai Jiaotong University Press, Shanghai, pp. 21–23 (in Chinese). Xu, G.X., Wu, C.S., Qin, G.L., 2009. Numerical simulation of weld formation in laser + GMAW hybrid welding. III. Treatment of pulsed arc action and improvement of heat source modes. Acta Metallurgica Sinica 45 (1), 107–112. Zheng, W., Wu, C.S., Wu, L., 1997. Numerical simulation for transient behavior of fluid flow and heat transfer in pulsed current TIG weld pool. Transactions of the China Welding Institution 18 (4), 227–231.
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
A dynamic welding heat source model in pulsed current gas tungsten arc welding Zhang Tong, Zheng Zhentai ∗ , Zhao Rui School of Materials Science and Engineering, Hebei University of Technology, No. 8, Duangrongdao Road, Hongqiao District, Tianjin 300130, PR China
a r t i c l e
i n f o
Article history: Received 25 January 2013 Received in revised form 9 July 2013 Accepted 11 July 2013 Keywords: Numerical simulation Welding temperature field Heat source model Pulsed current gas tungsten arc welding
a b s t r a c t A time-dependent welding heat source model, which is defined as the dynamic model, was established according to the characteristic of PCGTAW. The parabolic model was proposed to describe the heat flux distribution at the background times. The recommended Gaussian model was used at the peak times due to the bell-shaped temperature contour. The dynamic welding heat source was composed of these two models with a function of time. To assess the validity of the dynamic model, an experiment was conducted in which the pulsed current gas tungsten arc deposits on the plate. From the comparison of the experimental and the simulated values, it can be concluded that the dynamic heat source model, which uses the parabolic model at the background time, is more realistic and accurate under the same welding conditions. © 2013 Elsevier B.V. All rights reserved.
1. Introduction With the development of the computer and numerical analysis technologies, the FEM has become a powerful and reliable technique for prediction in the welding processing industry. The temperature field contains sufficient information about the quality and properties of the welded joint, and determines the distortion, residual stresses, and reduced strength of a structure in and near the welded joint. The temperature field is also the foundation of the metallurgical analysis and phase change analysis. To obtain an accurate welding temperature field, Goldak et al. (1984) reported that the importance of a good welding heat source model has been emphasized by many investigators. Many welding heat source models have been developed up to now, and the Gaussian model and the double ellipsoidal model are the most popular models among them. Some good welding heat source models can accurately predict the temperature field. However, most of these models were developed on the assumption that the heat sources are static and not varied with time in the welding processes. These models are no longer realistic for some dynamic welding processes, such as the pulsed current gas tungsten arc welding (PCGTAW). The objective of this paper is to develop a more realistic and accurate welding heat source model for PCGTAW. PCGTAW was developed in 1950s and is widely used in the manufacturing industry today. In PCGTAW, the welding current is
∗ Corresponding author. Tel.: +86 13512499764; fax: +86 13512499764. E-mail addresses: [email protected] (Z. Tong), [email protected] (Z. Zhentai). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.07.007
varied periodically from the peak current to the background current. Balasubramanian et al. (2008) indicated that the heat energy to melt the base metal is provided mainly by the peak current, while the background current is set at a low level to maintain a stable arc. Therefore, the background time can be seen as brief intervals during heating, which allow the heat to conduct and diffuse in the base metal. PCGTAW is a widely utilized welding process. Traidia et al. (2010) and Balasubramanian et al. (2008) pointed out that PCGTAW has the following advantages over the constant current gas tungsten arc welding (CCGTAW): (a) lower heat input; (b) narrower heat affected zone; (c) finer grain size; (d) less residual stresses and distortion; (e) improved mechanical properties; and (f) enhanced arc stability to avoid weld cracks and reduce porosity, etc. However, the welding parameters of PCGTAW are more complex to define than CCGTAW, and the choice of parameters with PCGTAW remains empirical. The parameters of PCGTAW were depicted by Madadi et al. (2012) in Fig. 1. A great deal of work has been conducted on the numerical simulation of PCGTAW. Fan et al. (1997) developed a two-dimensional model using the boundary fitted coordinate system to simulate the PCGTAW process. Kim and Na (1998) computed the fluid flow and heat transfer in partially penetrated weld pool under PCGTAW by the finite difference method. Traidia and Roger (2011) used the unified time-dependent model to describe the fluid flow, heat transfer and electromagnetic fields in the three regions respectively. Many investigations have been conducted, but far less work has been done on the development of the welding heat source model under PCGTAW. Several heat source models have been developed. They are classified in Table 1. Most of the current heat source models have been
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Table 1 The classification of current welding heat source models. One-dimension
Two-dimension
Three-dimension
Uniform distribution mode
Point heat source Line heat source – –
Plane heat source Circular mode Tripped heat source Square heat source
Columnar heat source – – –
Gaussian mode
– – – – – – – – –
Circular mode Oval-shaped heat source Double oval-shaped heat source Tripped heat source – – – – –
Circular disk heat source Columnar heat source Cuboid heat source Rotary body heat source Conic heat source Hemispherical heat source Semi-ellipsoidal heat source Ellipsoidal heat source Double ellipsoidal heat source
Exponential decay mode
–
–
Exponential decay heat source
developed on the geometrical shape and distribution in space, but time as an important factor, which has rarely been considered, in the model design. In fact, the heat source is varied with time in some dynamic process, e.g. in the PCGTAW. Therefore, a time-dependent heat source model, which is available for the dynamic process, is necessary to be developed. In this paper, a dynamic finite element model of welding heat source under PCGTAW is established. Then the moving, timedependent heat source was attempted to load onto the structure, and the FEM was used to compute the temperature field through the software ANSYS. 2. Theoretical formulations 2.1. Model consideration With the help of high speed CCD, Traidia and Roger (2011) used an infra-red camera to capture the characteristic of a welding arc under PCGTAW, and some good images were obtained which at the background and peak times (see Fig. 2). It is easy to see that there is significant difference between the peak time and the background time, and the arc is bell-shaped during the peak duration, but not during the background duration.
In contrast to constant current welding, the heat input in PCGTAW is supplied mainly during the peak times, and the heating is halted periodically during the background times. Xu et al. (2009) pointed out that the characteristic of discontinuity during heating under PCGTAW is more obvious when the frequency is low. So, two heat source models must be proposed which will be available in the peak times and background times. Considering the bell-shaped temperature contour, the recommended Gaussian model was used during the peak times; the big problem at present is to propose a good heat source model which is available during the background times. Some good experience can be obtained from the proposed process of the Gaussian heat source model. The design of the experiment was made to investigate the heat and current distribution of GTAW, which consists of splitting a water cooled copper anode. Measure the heat flux to one of the sections as a function of the arc position relative to the splitting plane. The radial heat distribution can then be derived by an Abel transformation of the measured heat flux on the anode. The distribution of heat on the anode is a result of a series of collisions of electrons with ionized atoms as electrons travel from the cathode to the anode. The energy released on the anode surface carried by the electrons constitutes most of the heat, and Tsai and Eagar (1985) considered that the distribution of the heat flux on the water cooled anodes should closely approximate to the distribution across the weld pool. Similarly, regarding the PCGTAW in this paper, it can be also considered that the anodic heat flux distribution is closely approximate to the heat distribution across the weld pool. 2.2. Mathematical model Traidia and Roger (2011) obtained the numerical simulation result of the radial heat flux distribution at the anode between the pulsed current – background time and peak time – and the mean current, which are shown in Fig. 3a. The third curve which the arrow points to is the radial heat flux distribution during the background time. To simplify the problem, it can be assumed that the radial heat flux at the background time is parabolic shape, which passes through three points (0, q(0)), (Rb , 0), (−Rb , 0) in the coordinate –x plane. The function of radial heat flux distribution at the background time can be written as:
q(x, ) = q(0)
Fig. 1. Pulsed current GTAW process parameters (Madadi et al., 2012).
1−
x2 Rb2
,
− Rb ≤ x ≤ Rb
(1)
where q(0) is the maximum value of heat flux and Rb is the radius of the power density.
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Fig. 2. Infra-red camera images at the background and peak times for both first and last periods.
Substituting q(0) = 43 W/mm2 and R ≈ 2.8 mm which is corresponded with the third curve in Fig. 3a into Eq. (1):
q(x, ) = 43
x2
1−
2.82
,
− Rb ≤ x ≤ Rb
(2)
q(x, y, ) = q(0)
1−
x 2 + y2
(3)
Rb2
where q(x, y, ) is the power density (W/m2 ).
x2 + y2 which is the radial distance from the center of For r = the heat source, then Eq. (3) can be written as:
q(r) = q(0)
r2
1−
Rb2
,
r ≤ Rb
(4)
2UI
(7)
Rb2
Substituting q(0) from Eq. (7) into Eq. (4) gives: q(r) =
The function image of Eq. (2) is shown in Fig. 3b, which approximates to the third curve in Fig. 3a that represents the radial heat flux distribution at the background time, which can be clearly observed in Fig. 3c which combined Fig. 3a with Fig. 3b in the same scale. So it can be considered that the radial heat flux distribution at background time is approximate to parabolic shape, and the welding heat source is a spinning parabolic shape distribution as shown in Fig. 4. The spinning parabolic shape model of welding heat source with the center at (0, 0, 0) to coordinate axes x, y, can be written as:
q(0) =
2UI
1−
Rb2
r2
,
Rb2
r ≤ Rb
(8)
So the dynamic welding heat source model of PCGTAW in one pulse cycle can be written as: q(r) =
3p UIp Rp2
or q(r) =
exp
2b UIb Rb2
−3
1−
r2 Rp2 r
,
t ∈ [0, tp ] (at peak times)
,
t ∈ (tp , tT ] and r ≤ Rb
2
Rb2
(9) (at background times)
where q(r) is the power density (W/m2 ), p the heat source efficiency at the peak time, b the heat source efficiency at the background time, U the arc voltage (V), Ip the peak current (A), Ib the background current (A), r = (x2 + y2 )1/2 which is the radial distance from the center of the heat source (m), Rb the radius of the heat source at the background time (m), Rp the radius of the heat source at the peak time (m), tT = 1 pulse cycle time = 1/f (s), f the pulse frequency, tp the peak time (s), tb the background time (s) and tp + tb = tT . 3. Evaluation of the dynamic model of welding heat source in PCGTAW
Conservation of energy requires that:
Q = UI =
q(r)r dr d =
Rb
q(0) 0
1−
r2 Rb2
r dr
2
d (5) 0
and produces the following: Q = UI = q(0)
Rb2 2
(6)
One experiment was conducted in which the pulsed current gas tungsten arc was deposited on the plate. The thermocouple was used to measure the temperature field at the given points, then the experimental values were compared with the simulated values to assess the validity of the dynamic welding heat source model. Due to the lack of data on material properties, material modeling has always been a critical issue in the welding simulation.
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Table 2 The chemical composition of AA7075. Elements
Zn
Mg
Cu
Cr
Mn
Fe
Si
Ti
Al
Impurities
wt.%
5.1–6.1
2.1–2.9
1.2–2.0
0.18–0.28
0.30
0.50
0.40
0.20
Bal.
0.15
Sattari-Far and Javadi (2008) reported that some simplifications and approximations are usually introduced to deal with this problem, which are necessary because of the scarcity of material data and numerical problems when trying to model the actual high-temperature behaviors of the material. Here we select the Aluminum Alloy 7075 as the base metal; the chemical composition is shown in Table 2. The thermal properties of AA7075 shown
in Fig. 5 were reported by Guo et al. (2006) which are temperaturedependent, the emissivity is assumed to be 0.6, and the fusion temperature range is 477–638 ◦ C. 3.1. Experimental procedure 3.1.1. Experiment preparation The plate of Aluminum Alloy 7075 was cut to the required size of 80 mm × 80 mm × 8 mm. To measure the temperature in the welding process, the K type NiCr–NiSi thermocouple was used. The positions of the thermocouples in the plate were shown in Fig. 6. The thermocouples were glued to a depth of 4 mm, through the blind holes which were drilled from the bottom of the plate; the hot end diameter of the thermocouple was 1.5 mm, the cold end was connected to a multichannel temperature measuring instrument to acquire the thermal cycle, and the same method was introduced by Karunakaran and Balasubramanian (2011). 3.1.2. Welding Bead-on-plate welds were made using the PCGTAW on the surface of the plate along with the center line. The welding parameters are shown in Table 3. 3.2. FEM calculation 3.2.1. Finite element model Only half of the plate was selected to analysis for its symmetry. To reduce the calculation time, the zone near the welding bead has been modeled with a finer mesh, while the zone further away from the welding bead has been modeled with a coarser one. Solid70 and Surf152 were used to mesh the model; the surface has been
Fig. 3. The establishment of the parabolic distribution (a is referred to Traidia and Roger, 2011).
Fig. 4. Heat source configuration for the spinning parabolic shape.
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Table 3 Welding parameter. Process parameter
Actual
Simulated
Welding current Peak current Background current Arc voltage Welding speed Pulse frequency % Pulse on time Electrode Electrode diameter Arc length Torch angle Shielding gas Flow rate
180 A 60 A 14 V 1.96–2.03 mm/s 1 Hz 50% W–2%Th 3.2 mm 2 mm 60◦ Argon 99.9% 15 L/min
180 A 60 A 14 V 2 mm/s 1 Hz 50% – – – – – –
“coated” with Surf152 to represent the convective heat exchange. The FEM model is shown in Fig. 7.
Fig. 5. Thermal physical properties of AA7075: (a) specific heat and density and (b) conductivity.
3.2.2. Welding heat source In this research, the APDL programming languages of ANSYS were applied to realize the moving load of the heat source. A local coordinate system was established, and the center of the heat source coincided with the original point of the local coordinate, then the heat source moved gradually under the control of the loop command in APDL. To evaluate the validity of the dynamic heat source model, two simulation tests were implemented under the same welding conditions, which are described in Table 4. The parameters in the dynamic welding heat source model are not easy to decide, so a further study is needed. 3.2.3. Initial condition and boundary conditions The ambient temperature is 28 ◦ C. Considering the moving heat source, heat losses due to convention and radiation are taken into account in the finite element models. Heat loss due to convection (qc ) is taken into account using Newton’s law: qc = hc (Ts − T0 ) where hc is the heat transfer coefficient, Ts the surface temperature of the weldment and T0 is the ambient temperature which is 28 ◦ C. Heat loss due to radiation is modeled using Stefan–Boltzmann’s law: qr = −ε · [(Ts + 273)4 − (T0 + 273)4 ] where ε is emissivity which is 0.6 and = 5.67 × 10−8 W/m2 ◦ C−4 is defined as the Stefan–Boltzmann constant. 3.2.4. Latent heat of phase transition During the welding process, melting and solidifying will occur in the welding pool, it will absorb or release latent heat in the phase transition, which is defined as “latent heat of phase transition”. Lei et al. (2006) use the enthalpy method to deal with the
Fig. 6. Schematic diagram of welded plate used in the experiment. Fig. 7. FEM model.
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Table 4 List of the simulation test. Simulation test 1
Simulation test 2
Heat source model
Dynamic Model 1
Dynamic Model 2
Model description
Use Gaussian model at peak times; use parabolic model at background times
Use Gaussian model both at peak times and background times, but different values of parameters were used, respectively
Ip = 180 A, Ib = 60 A, U = 14 V, f = 1 Hz Pulse on time = 50%, Rp ≈ 5.0 mm, Rb ≈ 2.8 mm, p ≈ 0.68, b ≈ 0.62.
Ip = 180 A, Ib = 60 A, U = 14 V, f = 1 Hz, Pulse on time = 50%, Rp ≈ 5.0 mm, Rb ≈ 2.8 mm, p ≈ 0.68, b ≈ 0.62.
Parameters in model
Notes: The parameters in heat source models are difficult to decide. To simplify the problems, the same parameters in Traidia and Roger (2011) were used for test 1 and test 2 under the same welding condition.
latent heat, and define the material’s enthalpy which varies with the temperature:
H(T ) =
T
(T )c(T ) dT 0
where (T) is the density of the material varying with temperature (kg/m3 ) and c(T) is the specific heat of the material varying with temperature (J/(kg K)). Murugan et al. (2000) reported that the release or absorption of latent heat can also be considered in the numerical analysis by an
artificial increase in the value of the specific heat over the melting temperature range. 3.2.5. Others In the meshed finite element model, the number of the Solid70 element is 848,000, the number of the Surf152 element is 46,640, and the number of nodes is 887,814 in total. The heat source defined in a local coordinate system moves with time, the former load step is deleted when the heat source moves to the next step. Considering both the calculation time and the computer’s capacity, the minimum size of element is 0.2 mm, and the cooling time is fixed to 20 s.
Fig. 8. Top view of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 1.
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Fig. 9. Top view of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 2.
Fig. 10. Longitudinal cross-section of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 1.
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Fig. 11. Longitudinal cross-section of temperature distribution: (a) at 20.3 s (peak time) and (b) at 20.8 s (background time) computed by the Dynamic Model 2.
4. Results and discussion 4.1. Temperature field 4.1.1. Top view of temperature distribution Figs. 8 and 9 which are in the same scale, show the temperature field computed by the Dynamic Model 1 and the Dynamic Model 2, respectively, and including the time 20.3 s (peak time) and 20.8 s (background time) for each. To illustrate the difference of the temperature field between the peak time and the background time in the welding process, the same area region near the weld pool was magnified in the same scale. Comparing the two temperature fields in Fig. 8a and b, it can be seen that the high temperature region at 20.3 s is larger than that at 20.8 s. Due to the cyclic variation of the heat input, there is a thermal fluctuation in the temperature field, which corresponds to the real dynamic welding process. From Fig. 9a and b, the same conclusion above can be obtained.
Table 5 Peak temperature comparison of the experimental and simulated results. Methodsa
Peak temperature (◦ C)
Differenceb (%)
Point Ac
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
402.5 397.6 393.9
– −1.2 −2.1
Point Bc
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
285.8 276.7 272.5
– −3.2 −4.7
Point Cc
Experimental FEM (Dynamic Model 1) FEM (Dynamic Model 2)
327.2 317.2 312.3
– −3.1 −4.6
Measuring point
a Experimental: use PCGTAW – welding parameter is shown in Table 3; base metal – AA7075, chemical composition is shown in Table 2. The description of the Dynamic Model 1 and Dynamic Model 2 are listed in Table 4. b . Difference (%) = (Calculated value − Experimental value)/Experimental value. c . The position of the measuring points is depicted in Fig. 6.
In Fig. 8a and b, the maximum temperatures are 892 ◦ C and 779 ◦ C, respectively. It was found that the maximum temperature at 20.3 s (peak time) is higher than the value at 20.8 s (background time). In Fig. 9a and b, the maximum temperatures are 887 ◦ C and 849 ◦ C, respectively. The maximum temperature appears in the center of the heat source model for both Figs. 8 and 9. Comparing Fig. 8a with Fig. 9a, it can be seen that there is small difference of the maximum temperature between them, which implies that the maximum temperature is nearly the same at 20.3 s when using the Dynamic Model 1 and the Dynamic Model 2. However, the maximum temperature in Fig. 8b is much lower than that in Fig. 9b, which implies that there is much difference in the maximum temperature at 20.8 s (background time) when using the Dynamic Model 1 and the Dynamic Model 2. Supplementary Video 1 is available for readers to show the temperature field computed by the Dynamic Model 1 in PCGTAW. Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jmatprotec.2013.07.007. 4.1.2. Longitudinal cross-section of temperature distribution Along with the midline of the plate in the longitudinal direction, the cross-sections of temperature distribution which are in the same scale were obtained, as shown in Figs. 10 and 11. To demonstrate clearly, the same area region near the heat source was magnified in the same scale. From Figs. 10 and 11, the same conclusions in Section 4.1.1 can also be obtained. The difference between the calculated results by the Dynamic Model 1 and the Dynamic Model 2 is demonstrated in some extent. 4.2. Welding thermal cycles The comparison of the experimental and simulated welding thermal cycles at Point A, Point B and Point C are shown in Fig. 12a–c, respectively. As can be seen from the figures, the temperatures computed by the Dynamic Model 1 and the Dynamic Model 2 are slightly lower
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Fig. 13. The welding thermal cycle during 5–20 s at point A.
the energy released during solidifying for aluminum alloy is much bigger than the carbon steel due to the thermal physical properties of the material in or near the weld pool. However, the latent heat become less and can be neglected for the areas far away from the weld pool.
4.3. The characteristic of the pulsed current
Fig. 12. Comparison of the experimental and simulated welding thermal cycles: (a) Point A, (b) Point B and (c) Point C.
than the experimental values. Table 4 shows the peak temperature comparison of the experimental and the simulated values. The difference value listed in Table 5 indicated that the Dynamic Model 1 is more accurate than the Dynamic Model 2, and it implies that the dynamic model which uses the parabolic model at the background time is more realistic and accurate. From Fig. 12a and b, it can be noted that the temperature is increased slightly during the cooling time while it cannot be observed in Fig. 12c. The reason for that could be attributed to the latent heat in the solidifying process. Many experiments show that
Fig. 13 is part of Fig. 12a that magnified with a proper scale. It is clearly seen that there are some fluctuations in the welding thermal cycle computed by the Dynamic Model 1 and the Dynamic Model 2, which can be attributed to the influence of pulsed current. Wang (2003) used the finite element method to compute the temperature field in molybdenum alloy under PCGTAW, the fluctuation was observed in the computed welding thermal cycle. Zheng et al. (1997) developed a three-dimensional model to demonstrate the transient behavior of temperature field and weld pool in PCGTAW, and verified that the fluctuations in the thermal cycle curve are characteristic of the pulsed current welding. Therefore, it can be concluded that the Dynamic Model 1 and the Dynamic Model 2 can successfully demonstrate the dynamic process of temperature field in pulsed current welding. However, the experiment in this paper failed to capture the characteristic of the pulsed current. This may be due to the sensitivity of the temperature measuring instrument. The thermocouple is widely used as temperature sensor for measuring instrument, which can convert a temperature gradient into electricity. For the dynamic welding process of PCGTAW, the heat input is varied periodically in a very short time, which leads to the dynamic characteristic of the process that cannot be obtained easily. This requires the thermocouples to be sensitive enough to the short-term variation and the measuring instrument immediately responsive to deal with the electronic signals from thermocouples at different measured points. Maybe an improved measuring instrument or a better measuring method is needed to be developed. Although the experiment failed to capture the temperature fluctuations in PCGTAW, the temperature values measured by the calibrated instrument are accurate and convincing. The peak temperature is obtained when the heat source surpasses the measured point. As seen from Fig. 11, the pulsing effect is more obvious for the pulses closed to the measured point, while it becomes less for the pulses further away from the measured point. It can be seen that the region in or near the welded joint has experienced several heating and cooling processes due to the pulsing current, and that the soaking time at the high temperature is shorter
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compared with CCGTAW. That is why the grain is refined under the PCGTAW process. Compared with the welding thermal cycle at different points in Fig. 12a–c, it can be concluded that the pulsed current has an significant effect on the points in or near the welded joint, but less effect on the points far away from the welded joint. 5. Conclusions (1) Most of the current heat source models are static models that do not vary with time and cannot represent the heat flux distribution in some dynamic welding processes; so a good heat source model for the dynamic welding process must be developed. (2) The FEM dynamic heat source model was used to simulate the low frequency PCGTAW, which has successfully demonstrated the dynamic temperature field in the welding process. (3) From the comparisons of the experimental and the simulated values, it can be concluded that the dynamic heat source model which uses the parabolic model at the background time is more accurate under the same welding conditions. (4) In some welding process simulation, especially for those whose dynamic characteristic is more obvious, the dynamic welding heat source model has more advantages over the static models. The static heat source model is the special case of the dynamic heat source model, which is not varied with time. References Balasubramanian, M., Jayabalan, V., Balasubramanian, V., 2008. Developing mathematical models to predict grain size and hardness of argon tungsten pulse current arc welded titanium alloy. Journal of Materials Processing Technology 196, 222–229.
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