Effect of electron beam welding parameters on temperature and stress field of AISI P20 tool steel in vacuum roll-cladding process

Vacuum roll-cladding (VRC) is an effective method to produce high-quality ultra-heavy AISI P20 plate steel. In the process of VRC, reasonable welding process of electron beam welding (EBW) can significantly avoid welding cracks and reduce the cost. In this paper, the electron beam welding process of AISI P20 tool steel was simulated by using a combined heat source model based on finite element method, and the temperature field and stress field under different welding parameters were studied respectively. The results showed that welding parameters have a greater effect on weld penetration than that of weld width, making the aspect ratio increases with the increase of welding current, and decrease with the increase of welding speed. The weld morphologies were consistent with those of the modeling, and the measured thermal heat curves were in good agreement with those of simulated, which verified the feasibility and effectiveness of temperature fields. The results of stress fields under different welding parameters indicated that welding speed of 300mm/min and welding current of 60mA result in lower residual stress at welded joint, which means lower risk of cracking after EBW. The results of this study have been successfully applied to industrial production.


Introduction
Plastics, together with steel, wood, and cement, constitute the four basic materials of modern society in the twenty-first century. With the increasing demand of large-scale and precision plastic products, it is necessary to develop ultra-heavy and high precision steel plates. AISI P20 tool steel is commonly employed in the manufacture of molds for plastics because of its high wear and corrosion resistances and excellent machining properties [1,2]. Traditional production methods of ultra-heavy AISI P20 plate process, such as continuous casting and rolling, have many shortcomings. The microstructure and properties of the rolled ultra-heavy plates are inhomogeneous due to the center segregation, small rolling deformation, and low rate of heat transfer. These defects seriously affected the overall properties of the steel plates and generated internal cracks [3][4][5]. In recent years, with the appearance of laminated metal composites (LMC), two or more layers of pure, homogeneous, and dense thin continuous casting billets can be rolled into a high-quality extra-thick plate, which not only solved the above performance defects, but also reduced the production cost [6,7]. Vacuum roll-cladding (VRC) technology is widely used in the fabrication of high-quality ultraheavy LMC [8]. The VRC process is shown in Fig. 1; the purity of the interface is crucial to the healing of interface during hot rolling process. Thus, the layers are usually packaged by electron beam welding (EBW) under high vacuum conditions. However, the welding performance of P20 steel is poor because of its relatively high carbon content [9]. Therefore, it is necessary to guarantee the weld quality and avoid cracks after EBW process. Compared to other welding methods, such as inert gas welding (TIG) and laser beam welding (LBW), EBW has higher energy density and larger depth-width ratio, resulting in a narrower heat-affected zone (HAZ) and lower residual stress at welded joint [10][11][12][13].
Meanwhile, the weld residual stress is considered to be the main factor that affected the weld strength and welding cracks. Nevertheless, it should be realized that the welding residual stress is hard to measure by existing methods such as holedrilling method and X-ray diffraction method [14]. These experiment tests have many limitations and large error due to the complexity of welding process and expensive costs. In order to obtain accurate residual stress value, researchers solved this problem based on finite element method (FEM) during the past decades. For the past few years, more and more accurate and persuasive results were obtained with the constant optimization of the mathematical model. Moreover, it should be clear that temperature distribution has a great effect on residual stress because deformation and residual stress are generated by temperature field. The characteristics of temperature field in EBW are mainly reflected in the following aspects [15,16]: (1) High concentration of heat in EBW process causes a large temperature gradient. (2) The temperature field changed continuously with the movement of heat source. (3) The heat transfer properties inside the metal transformed because of the formation of "keyhole." Hence, the effectiveness of stress field depends on the accuracy of the temperature field. The distributions of temperature field during EBW were widely reported in recent years. For instance, Huang et al [17] proposed a three-dimensional coupling model to predict keyhole and dynamics of weld pool in EBW, which successfully obtained the temperature field around keyhole, and the results agree with the experimental data. Wang et al [18] analyzed plasma temperature during laser beam welding (LBW), which similar to EBW, and the results showed that maximum temperature can reach 13000°. Fu et al [19] studied EBW with multi-beam on high temperature titanium alloy, and the temperatures gradually lowered with the increase of the distance from weld because of the great heat gradient of EBW. They also found that the temperature uniformity of EBW can be improved by pre-heating and post heating.
Based on temperature field results, Hong et al [20] calculate residual stress and deformation of GH80A plates during EBW. With increase of distance from welding lines, the transverse stress develops to increase and always characterized as tensile stress. Lacki et al [21] calculated effective stress distribution of 30HGSA steel tube during pulsed electron beam welding, and the results indicated that maximal values of stress occur in bottom area of weld. Li et al [22] has conducted welding of Ti2AlNb alloys using electron beam. In their studies, plate produced more than 1000MPa tensile residual stress  of longitudinal direction in the fusion zone. They also found that wider weld has relatively low tensile stress in z direction, resulting in low risk for cracking. Since the temperature distribution in EBW is determined by the welding parameters, the welding parameters, especially the welding beam current and welding speed, have crucial impact on the residual stress. Therefore, it is of great significance to study the influence of different welding parameters on residual stress of EBW.
Previous studies have mainly focused on various temperature fields and stress field under a specific welding parameter [23][24][25], and there were mainly reported the microstructure and properties of AISI P20 tool steel welded joint under TIG or LBW [26,27]. Little work has been done concerning on the influence of different welding parameters on residual stress fields of AISI P20 tool steel. In this paper, a combined heat source model was used to simulate the EBW process of P20 steel. The temperature field and stress field were obtained under different EBW parameters. The thermal cycle curves at different positions were measured and weld morphologies were compared; both of them verified the accuracy of simulated results. Ultimately, the change rule of welding residual stresses under different welding parameters was analyzed.

Material and procedures
The material used in this study is commercial AISI P20 tool steel, produced by Jinan Steel Group, China. The chemical composition is 0.36 C, 0.41 Si, 1.3 Mn, 1.86 Cr, 0.6 Ni, 0.44 Mo, 0.006 P, and 0.006 S, the rest being Fe, all in mass fraction. P20 steel plates with dimensions of 160×200×20mm were welded using a THDW-15EBW machine made by Guilin Shida Technology Co., Ltd. The dimensions of the vacuum chamber are 1700mm length, 650mm width, and 750mm height, and the vacuum of the chamber is less than 10 −2 Pa during welding process. The accelerating voltage is 80kV, and the electron beam focused on the top surface of the specimens. The plates were grinded using 80-800-grit SiC paper and then cleaned by acetone and alcohol within 30 min   Table 1. Welding power is expressed as Eq. (1): where P is welding power, V is accelerating voltage of EBW, which is constant at 80kV, and A is electron current.
According to the shape of plates, the models of plates were established and meshed. In order to improve calculation efficiency, symmetric model and transition grid were used in meshing (as shown in Fig.2). DC3D8 brick elements were employed in temperature field calculation. Reduced integral elements C3D8R were used in stress field calculation by sequential coupling method. The whole model was composed of 194,240 elements, with a total of 209,412 calculation nodes. The minimum size of element was 1 mm at the weld, and the maximum size of element was 10 mm at base metal. The thermophysical property parameters of AISI P20 were obtained by JMatPro material property simulation software. The high temperature mechanical parameters of AISI P20 were obtained by thermal simulation test on MMS-200 thermomechanical simulator. The material properties under different temperature are shown in Fig 3.

Mathematical model
According to previous research results [17], the fusion line morphology of actual weld shows that electron beam distribution area is not the fusion area of large aspect ratio perpendicular to the workpiece surface, but more like the weld morphology formed by the superposition of two "V" types. Besides, the opening of the upper "V" type is larger than that of the lower "V" type. Thus, based on previous EBW studies [28][29][30] and morphologies of weld profile, a Gaussian surface heat source model was used to describe the heat flux distribution in each thickness layer, and an attenuation equation in the thickness direction was employed to simulate the characteristics of deep penetration. The schematic of heat source model combined by Gaussian surface heat source and attenuation body heat source is shown in Fig. 4.
The mathematical model equation of combined heat source model can be expressed as Eq. (2), where Q s and Q v are the energy of surface heat source and the energy of body heat source, respectively, R h represents heating spot radius of the cross section at height h, C S is shape concentration factor of body heat source, and H is the depth of weld.
The heat conduction during EBW can be defined by Fourier equation and energy conservation equation (expressed as Eq. (3) and Eq. (4), respectively), where Φx; Φy; Φz; ∂t ∂x ; ∂t ∂y ; ∂t ∂z are heat flux and temperature gradient of x, y, and z directions, λ is heat conductivity coefficient, ΔQ d is net heat flow of the element, ΔQ v is formation heat in element, and ΔE is increment in internal energy.
Heat conduction equation of system can be deduced by Eq. (3) and Eq. (4). Thus, the three-dimensional heat conduction differential equation can be expressed as Eq. (5), where ρ and c are density and specific heat of workpiece, Φ is formation heat of internal heat source per unit volume per unit time, τ is unit interval, and a = λ/ρc is thermal diffusivity. Due to the EBW conducted in vacuum chamber, the surface film condition can be ignored. Heat emissivity is set to 0.75. Initial temperature is set to 293K.

Temperature measurement
Temperature measurement experiment was implemented to verify the veracity of temperature field. The K-type thermocouples produced by OMEGA were selected for tests. The diameter of the thermocouple line is 0.5mm. The upper limit of instantaneous temperature measurement of this thermocouple can reach 4250 K. Five locations with a depth of 6mm, 8mm, 10mm, 12mm, and 14mm from the upper surface were selected for temperature measurement. LR8431-30 data acquisition instrument produced by HIOKI was used as temperature measuring instrument. Data was collected every 500ms during the welding process. With the increase of welding current, the width of weld and heat-affected zone extended. The maximum temperature on workpiece surface increased from 3152 K ( Fig. 5a) to 3799 K (Fig. 5c) as the welding current increased from 40 to 60mA. Meanwhile, the length of welding pool gradually heightened due to the temperature increasement of workpiece. Fig. 6 shows the weld profiles of different welding current under welding speed of 300mm/min. As shown in Fig. 6, the welds presented typically nail shape, which was agreed with the results of previous studies [22,31]. The weld morphologies became longer and narrower with the increase of welding current. Fig. 7 presents the relationship between weld width/ penetration and welding current under 3 kinds of welding speed conditions. Positive correlations were showed between weld width/penetration and welding current in 3 kinds of different welding speeds. However, there was a greater promotion of weld penetration than weld width. For welding speed of 300mm/min, as the welding current increased, the weld width heightened from 5.2mm to 6mm, while weld penetration gradually heightened from 10.6 to 18.5mm. Since the increase of weld penetration is more significant, the aspect ratio of weld heightened from 2.04 to 3.08 with the increase of welding current (shown as Fig. 7a). It is worth noting that the weld aspect ratio basically unchanged as welding current increased under welding speed of 600mm/min, indicating almost same growth rate of weld width and weld penetration under this welding speed (shown as Fig. 7c). Fig.8 shows the temperature field under different welding speed with welding current of 40mA at the same position. As morphologies of weld pool shown in Fig. 8, the weld width decreased with the increase of welding speed. The upper limit of temperature on workpiece surface lowered from 3661 K (Fig. 8a) to 2708 K (Fig. 8c). As the welding speed increased, time of heat source acting on the workpiece was shortened, which lead to the shrinkage of temperature field and the rapid decrease of weld pool length. Fig. 9 shows weld profiles under different welding speed at welding current of 50mA. The weld profiles presented nail shape and funnel shape in different   welding speed as shown in Fig. 9 a and c, respectively. The weld morphology became shorter and wider with the increase of welding speed. Meanwhile, the weld profile changed from nail shape to funnel shape as the welding speed increased. Fig.10 presents the relationship between weld width/ penetration and welding speed under 3 kinds of different welding current conditions. As shown in Fig. 10, the weld width/penetration increased as the welding speed reduced in 3 kinds of welding currents. Meanwhile, the decline of weld penetration was enhanced with the increased of welding speed, while the attenuation of weld width was much smaller. For the welding current of 60mA (Fig. 10c), as the welding speed increase from 300 to 600mm/min, the weld penetration was reduced from 18.5 to 10.5mm, which was 5.2 times to the weld width. Therefore, the weld penetration has a greater attenuation than weld width with the increase of welding speed, which lead to a diminution in the aspect ratio of the weld (as shown in Fig. 10 b and c). There was no obvious variation between the aspect ratio and welding speed under welding current of 40mA.

Validation of temperature field
Weld profiles were investigated by Leica DMIRM optical microscope to verify temperature field results. Electron beam welding experiments were employed according to the parameters in Table 1. As shown in Fig. 11, the weld morphologies of EBW under 3 different welding parameters were consistent well with the simulated results. The weld width and weld penetration were almost equal with actual weld, which means the temperature fields calculated by the current computational approach could precisely represent realistic situations. Fig. 12 shows the errors between simulated results and measured results in 9 kinds of welding parameters. As shown in Fig. 12, both errors of weld width and weld penetration were less than 10%. Fig. 13 shows the comparison between the measured thermal cycle curves and the simulated thermal cycle curves at same positions. Simulated thermal cycle curves were shown as solid lines, and measured thermal cycle curves were shown as dotted lines. The measured curves at different positions were in good agreement with the simulated results. At positions of 6mm, 8mm, 10mm, 12mm, and 14mm from the surface, the differences between simulated peak temperature and measured peak temperature were only 12.8°C, 121.5°C, 22.2°C, 48°C, and 23.5°C, respectively. Variation tendency of each thermal cycle curve was basically the same, which verified the effectiveness and reliability of the numerical computation results.

Effects of welding parameters on stress field
Based on the results of temperature fields, the stress fields were obtained by using indirect coupling method. Fig. 14 shows the residual stress distributions of the longitudinal   Fig. 14, the values of residual stress increased with the increase of welding speeds under the same welding current. Higher welding current resulted in lower residual stress, which is presented in Fig. 14 a, d, and g. Residual stresses were basically concentrated around the weld and decreased sharply in the area far away from weld. Heads and ends of welds represented larger stresses than other locations of weld. Stress reached maximum at the surface of workpiece and lowered with the increase of weld penetration.
In order to illustrate the change rules of residual stress under different welding parameters, the stress values of different welding parameters at the same path were extracted and are shown in Fig. 15. The straight line along the thickness direction at center of weld surface was selected as the path. The residual stress under welding speed of 600mm/min had the maximum values (nearly 1730MPa at welding current of 50mA) and declined dramatically with increased of the distance from weld surface (shown as chain-dotted lines). As the welding speed decreased, residual stress reduced and no evident changes of stress values were found in different thickness directions (shown as dotted lines and solid lines). At the welding speed of 300mm/min, there was a minimum value of residual stress about 1296MPa at the welding current of 60mA (as shown in solid blue line). It should be known that the effect of phase transition was ignored in the calculation of stress field, which lead to relatively large residual stress. Nevertheless, the values of residual stress in case 4 and case 7 (shown as solid green line and solid blue line respectively) were still lower than the tensile strength of material (shown in Fig. 3b), indicating low risk of crack initiation under these two welding parameters. Fig. 16 shows the actual weld morphologies after EBW processes. Severe cracks and defects were found under most of welding parameters, while no obvious defects were found in case 4 (50mA-300mm/min) and case 7 (60mA-300mm/ min). This was consistent with the simulation results shown as solid blue line and solid green line in Fig 15, which confirmed the accuracy and reliability of the simulated residual stress.

Discussions
In the EBW process of AISI P20 steel, there was a great difference in changes of weld width and penetration with   Fig. 6 and Fig. 7). The main reason of such a big difference came from the unique heat transfer mode of EBW. Due to the high electron beam energy density and beam concentration, the temperature of the workpiece surface exceeds the boiling point of the material. The vapor pressure of the metal overcomes the surface tension of the liquid metal and pushes the molten metal away, thus forming a beam cavity inside the workpiece called "keyhole" [32,33].The existence of the cavity changes the heat transfer properties inside the metal and forms a high temperature region in the direction of the depth of molten pool, which leads to a nail-shaped or funnel-shaped weld morphology [34,35]. In order to illustrate the temperature distribution characteristics of EBW, we extracted temperature data of nodes at different locations under welding parameter of 50mA-300mm/min and plotted thermal heat curves (as shown in Fig. 17). P1~P4 represent positions of 0mm, 2mm, 6mm, and 12mm from the weld along width direction, and P5~P8 represent the same distances from the weld along depth direction. As shown in Fig. 17a, the temperature at workpiece surface reached over 3500 K, which is much higher than the boiling point of base metal. There is a severe attenuation of temperature along the width direction, making the temperature at P4 only about 500 K. However, the attenuation of temperature along depth direction is much smaller than that of width direction, making the temperature at P8 over 1800 K (as Fig. 16 Weld morphology after EBW processes: a~c cases 1~3, d~f cases 4~6, and g~i cases 7~9 shown in Fig. 17b). For this reason, the electron beam has a greater impact on temperature along depth direction, which causes keyhole effect and nail shape or funnel shape of the weld. With the increase of welding current, the power of electron beam increases and the keyhole effect is promoted, which leads to greater promotion of weld penetration than weld width (as shown in Fig. 7).
Welding speed of EBW plays another important role in affecting weld morphologies and temperature field. The research results from Seto et al [36] showed that the welding speed has great influence on the size of keyhole. In the study of Katayama et al [37], keyhole produces a certain angle of dip with the movement of electron beam. With the increase of welding speed, the inclination of the keyhole increases, which decreases the stability of keyhole and weakens the energy transfer of electron beam. From the above analysis, the impact of keyhole effect on the weld penetration is greater than that of the weld width, making greater attenuation of weld penetration (as shown in Fig. 10). Meanwhile, with constant welding power, increasing welding speed means a decrease in welding line energy, which leads to reduction of weld penetration. On the other hand, due to the increase of welding speed, the interaction time between electron beam and base metal is shortened, and the energy input to the workpiece decreases per unit time, which leads to the difficulty of temperature penetration along the depth direction. In the meantime, the heat conduction on the surface is much faster than that in depth direction, which follows that the change of weld width is not obvious relative to that of weld penetration.
The stress field is generated from the non-uniform temperature field during EBW, which is caused by high temperature gradient of heat source and uneven heat transfer. Therefore, the magnitude and distribution range of stress under different welding parameters are strikingly different due to different weld width and penetration (as shown in Fig. 14 and Fig.  15). Fig. 18 shows the temperature and stress curve with time at the same position. As shown in Fig. 18, stress is exquisitely sensitive to temperature changes. The change process of stress can be divided into three stages. In the first stage, stress increases sharply with the increase of temperature, which seems to contradict the softening behavior of metals at high temperature. However, the base metal is subjected to thermal interaction and produces severe deformation before stage I, which causes work hardening of base metal. The effect of work hardening is greater than the effect of material softening in this temperature range, resulting in increase of stress value. In the stage II, as the temperature rises above the melting point of base material, the base metal is melted and the stress drastically drops to zero and is maintained until the temperature drops below the melting point. In the last stage, the temperature drops below melting point and continues to drop. As the metal solidifies gradually, the weld is constrained by solidification, cooling, and shrinkage, resulting in thermal stress. As the welding process continues, the thermal stress gradually increased with the decrease of temperature. In this process, Fig. 18 The relationship between temperature and stress at the same location Fig. 17 Welding heat curves at different positions: a along the width direction and b along the depth direction the cooling rate has a great influence on the residual stress. The results of Ravisankar et al [38] showed that faster cooling increases the residual stress of the welded joint, because the increase of cooling rate would increase the deformation of welded joint and thus increase the thermal stress of the metal due to cooling constraints. In Fig. 15, with the increase of welding speed, the thermal interaction time between electron beam and workpiece is shortened, resulting in rapid loss of heat and acceleration of cooling at the weld. Therefore, the maximum residual stress appears at high welding speed, which is consistent with the studies of Zhang et al [39] and Deng et al [40]. With the increase of welding current, the temperature distribution in depth direction is relatively uniform due to the effect of keyhole, which makes small temperature gradient of weld section in the post-welding cooling. The uniform temperature drop makes much lower thermal stress. Consequently, no defects are observed in case 4 and case 7 after EBW (as shown in Fig. 16 d and g).
According to the results of temperature field and stress field during EBW in VRC process, high-quality ultra-heavy AISI P20 plates with thickness of 300mm were successfully prepared in Jinan Steel Co., Ltd. With optimized EBW parameter, the edges of the slab showed good qualities, and no cracks occurred after hot rolling process (shown as Fig. 19b). Metallographic images of the interface showed that the composite interface is fully healed (shown as Fig. 19c).

Conclusions
This work was comprehensively performed the electron beam welding process of AISI P20 tool steel by using finite element method. The temperature field and stress field under different welding parameters were obtained with a combined heat source model. According to the analysis of the results, the following conclusions can be drawn: (1) There is a considerable temperature gradient around the weld due to the existence of keyhole during EBW process, and the keyhole effect leads to a nail shape or funnel shape of weld profile. The residual stress is mainly concentrated around the weld. (2) With the same acceleration voltage, weld width and weld penetration increase with the increase of welding current and decrease with the increase of welding speed. The minimum weld width and weld penetration are 3.5mm and 7.9mm, respectively, under welding parameter of 40mA-600mm/min. The variation of weld penetration is much greater than that of weld width, resulting in various of weld aspect ratio. (3) The weld morphologies are consistent with the simulated results. The errors of weld width and weld penetration are less than 10%. The thermal cycle curves of modeling are in good agreement with the measured thermal cycle curves, which verified the reliability of the simulated results. (4) At welding speed of 600mm/min, the weld has greater residual stress due to faster cooling rate, increasing welding current can be attributed to reduce residual stress. Accordingly, greater aspect ratio of weld results in low risk of cracking after EBW. Further, the optimized EBW parameter derived from this study has been successfully applied to the industrial production of ultraheavy AISI P20 plates. For further research, subsequent studies can focus on the effect of accelerating voltage on EBW of AISI P20 steels. Data availability The data sets supporting the results of this article are included within the article and its additional files Code availability Not applicable Fig. 19 Production line preparation and interface morphology: a EBW system, b composite plate prepared by VRC process, and c metallography of composite plate interface

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