Effect of Process Variable on Temperature Distribution in the Heat-Affected Zone of Temper Bead Welds *

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1 [ 溶接学会論文集第 35 巻第 号 p. 3s-7s (7)] Effect of Process Variable on Temperature Distribution in the Heat-Affected Zone of Temper Bead Welds * by Tadayoshi Kashiyama**, Shigetaka Okano** and Masahito Mochizuki** Stress corrosion cracking (SCC) has recently been obsered in Ni-based alloy welds in nuclear power plants, despite countermeasures to preent it. In the repair welding, temper bead welding (TBW) is applicable when post weld heat treatment (PWHT) is difficult to carry out. In TBW, the welding process ariables are appropriately controlled so that the thermal cycles of the subsequent passes proide the area hardened by preious passes with the temper effect, so the hardened area size and thermal cycle tempering parameter (TCTP) are ery important. Howeer, ery few studies hae discussed the quantitatie relationships among the hardened area size, TCTP and the welding process ariables. In this study, we conducted a combined weld bead surface profile and heat conduction analysis for simulating temper bead welding with Ni-based filler metal to SQVA plate under arious welding conditions. We quantified the hardened area size and TCTP as linear functions of the welding process ariable parameter, which was deried from welding heat conduction theory with a moing heat source. Consequently, we concluded that the appropriate welding conditions in temper bead repair welding can be determined based on the welding process ariable parameter. Key Words: Temper bead welding, Process ariable, Temperature Distribution, Thermal cycle tempering parameter, Heat conduction analysis, Weld bead surface profile analysis. Introduction Stress corrosion cracking (SCC) has recently been obsered in Ni-based alloy welds in nuclear power plants, despite countermeasures to preent it. In the repair welding, temper bead welding (TBW) ) is applicable when post weld heat treatment (PWHT) is difficult to carry out. In TBW, the welding process ariables are appropriately controlled so that the thermal cycles of the subsequent passes proide the area hardened by preious passes with the temper effect, so the hardened area size and thermal cycle tempering parameter (TCTP) ) should be controlled appropriately. Howeer, ery few studies hae discussed the quantitatie relationships among the hardened area size, TCTP and the welding process ariables. In this study, through a combined weld bead surface profile and heat conduction analysis, we quantified the hardened area size and TCTP with the process ariables in temper bead welding.. Combined weld bead surface profile and heat conduction analysis In this study, we conducted a combined weld bead surface profile and heat conduction analysis to take into account the interaction between bead formation and temperature distribution during welding 3). In the profile analysis of the weld bead surface, the proposed * Receied:..7 ** Graduate school of Engineering, Osaka Uniersity cured surface equation shown in Eq. () ) was used, where x is the welding direction, z is the ertically upward direction, y is the direction perpendicular to the x-z plane and zx, zy, zxx, zyy and zxy are z/x, z/y, z/ x, z/ y and z/xy, respectiely. This equation was deried from the equilibrium of the surface tension σ, graity and arc pressure Parc by using the density ρ and graitational acceleration g. The Lagrange multiplier λl was determined by the bisection method to balance the bead olume increment with the wire supply. zy zxx zzz x y xy zx z z 3/ x y zyy gz Parc l () In the heat conduction analysis, the three-dimensional heat conduction equation shown in Eq. () was used, where t is the elapsed time, λ is the heat conductiity, H is the specific enthalpy, T is the temperature and w is the heat generation. H T T T w t x x y y z z () For the combined analysis, Gaussian distributed heat input was proided to the surface of welded plate directly from a traeling welding arc, and then the filler metal elements with enthalpy were added according to the calculated weld bead surface displacement. Then, the bead radius was determined by referring to a preious study 5). The heat radiation based on the Stefan-Boltzmann law

2 and the heat transfer (5 - W/mm K) on the metal surface were also taken into account. 3. Heat conduction theoretical parameters controlling welding temperature profiles 3. Parameter to estimate hardened area size To estimate the hardened area size based on the process ariables in the TBW technique, the parameters associated with the process ariables were deried from welding heat conduction theory. It has been reported that at a distance from the weld zone, the theoretical solution of the temperature rise by a moing point heat source, such as that in TIG welding, is almost equal to the theoretical solution by an instantaneous line heat source ). Howeer, it was unclear whether the size of the hardened area, where the peak temperature is oer 837 C, depends on welding heat conduction theory with an instantaneous heat source or a moing heat source. To examine the dependence, we adopted two welding process ariable parameters: the parameter deried from welding heat conduction theory with an instantaneous heat source and the parameter with a moing heat source. Equation (3) shows the theoretical solution of the temperature rise T by an instantaneous line heat source. In Eq. (3), q is the heat input per unit time, is the welding speed, k is the heat diffusiity, c is the specific heat, ρ is the density, r is the distance from the welding line and t is the elapsed time. When the temperature rises to the maximum temperature Tmax, or dt/dt=, Eq. () is obtained. According to this equation, Tmax is proportional to (q/). Therefore, we adopted (q/) as the welding process ariable parameter deried from welding heat conduction theory with an instantaneous heat source. q r T exp c πkt kt r πec T max q Equation (5) shows the theoretical solution of the temperature rise T by a moing point heat source. In Eq. (5), the origin of coordinates is the arc center, x is the welding direction and r is the distance from the welding line. (3) () In a preious study 7), it was deried both experimentally and theoretically that under the condition of a constant plate thickness, the maximum temperature near the welded zone Tmax is proportional to q/, as gien in Expression (). Therefore, we adopted q/ as the welding process ariable parameter deried from welding heat conduction theory with a moing heat source. T q max () 3. Parameter to estimate the temper effect It is well known that the Larson-Miller parameter (LMP) P is generally used for predicting the temper effect during isothermal heat treatment 8). The parameter, which is a deriatie of the Arrhenius equation with an approximation deried from experimental consideration, is represented by Eq. (7), where the holding temperature is T [K] and the holding time is t [hr]. P T ( l o g t ) (7) Howeer, LMP is not directly applicable to the TBW technique because TBW is a non-isothermal process. The thermal cycle tempering parameter (TCTP) was proposed as an extended LMP and then applied to estimate the temper effect during a non-isothermal process such as the TBW technique ). The parameter was deried from the additiity rule of holding times for multiple PWHT cycles. When LMP at a holding time t and a holding temperature T is equal to LMP at another holding time t and another holding temperature T, as in Eq. (8), t is represented by Eq. (9). In multiple PWHT cycles, to calculate the cumulatie holding time, the holding times at the holding temperatures are conerted to an equialent time as shown in Eq. (9). P T (log t ) T (log t ) (8) T (logt ) T t (9) TCTP is calculated by applying the additiity rule for each efficiently short time segment Δt shown in Eq. (). n P n T n ( log( t n t ) () exp q k T c k x x r x r (5) Thus, TCTP can be applied to a non-isothermal process. In this study, we adopted TCTP to estimate the temper effect during the TBW technique.

3 . Analytical conditions In this study, we conducted two series of analyses: a first layer welding analysis, and a subsequent layer welding analysis. In the first layer welding analysis, TIG welding with filler metal was conducted on a low-alloy steel SQVA plate. The Ni-based alloy electrode ENiCrFe- was used for filler metal. The heat conductiity and specific heat of SQVA and ENiCrFe- are shown in Fig.. The density was 8. - kg/mm 3 for both materials. The dimensions of the SQVA plate were 5 mm 5 mm 5 mm, as shown in Fig.. The welding length was 3 mm at the center of the plate except for mm from each plate edge. Table lists the welding process ariable conditions that were prepared, and Table lists the total heat input at each welding current based on experimental data 9). In the subsequent layer welding analysis, a deposited filler metal layer with a thickness of ~3 mm was set on a SQVA plate. A total of 8 welding process ariable conditions were prepared in combination with the welding process ariable conditions used in the first layer welding analysis. The filler metal layer thicknesses were, and 3 mm. Both analyses used the appropriate TBW heat source model, which was constructed and experimentally alidated in a preious study 5). The distributions of the heat input and the arc pressure directly proided to the surface of welded plate from a traeling arc are shown in Fig. 3. Fig. Dimensions of the SQVA plate. Thermal conductiity [W/K].8 Specific heat of SQVA.7 Specific heat of ENiCrFe Thermal conductiity of SQVA Thermal conductiity of ENiCrFe- 8 Temperature [ ] Fig. Material properties. 8 Specific heat [J/(Kg K)] Intensity of heat input by arc [W/mm ] 5 3 A A A 8A 5 5 Distance from arc center [mm] 8 Fig. 3 Distributions of the weld heat input and the arc pressure (in the case of ). Arc pressure [Pa] Table Combinations of welding process ariable conditions. Welding current, I [A],,, 8 Welding speed, [mm/s].33,.,.7,3.33,. The percentage of the enthalpy of the filler metal elements to the all weld heat input [%],, Table Total heat inputs. Welding current, I [A] The percentage of the enthalpy of the filler metal elements to all weld heat input [%] Weld heat input, q [J/s] Heat input by filler metal [J/s] Heat input by arc [J/s]

4 5. Results and discussion 5. Effect of welding process ariables on hardened area in TBW technique As shown in Fig., the first layer welding indicates a good linear relationship between the hardened area depth and the welding process ariable parameter q/ for each wire supply condition. In comparison with the relationship between the hardened area depth and the welding process ariable parameter (q/), as shown in Fig. 5, the relationship between the depth and q/ indicates better linearity. Hence, the hardened area depth depends on q/ more strongly than on (q/). Likewise, this tendency was obsered in the whole area near the weld zone. Similarly, in the subsequent layer welding, a good linear relationship between the peak temperature and the welding process ariable parameter q/ was obtained. Moreoer, we found that TCTP was strongly dependent on the peak temperature, as shown in Fig.. The area where TCTP reaches at a certain alue can also be controlled by the proposed welding process ariable parameter q/. Fig. 7 shows an example of the good Hardened area depth, d [mm] 5 3 % of heat input for % of heat input for y =.38x R=.99 y =.3x R=.98 y =.x R= q/ [J/ (mm s)] Fig. Relationship between the hardened area depth and the welding process ariable parameter q/. linear relationship between the depth of area where TCTP is oer and the welding process ariable parameter. Additionally, the influence of the filler metal layer thickness on the relationship was hardly obsered. 5. Discussion about appropriate welding process ariable conditions in TBW technique The quantitatie relationships among the hardened area size, TCTP and the welding process ariable parameter are expected to be applicable to determining the appropriate welding process ariable conditions in the TBW technique. From the quantitatie relationships, the hardened area depth d873 and the depth of the area dtctp where TCTP reaches a certain alue are expressed as Eqs. () and (), where the proportionality constants are Ast_873 and Bnd, and the welding process ariable parameter is q/. To preent re-hardening in subsequent layer welding, the maximum welding process ariable parameter (q/ )max._of_nd can be determined as shown in Eq. (3) to preent the hardened areas TCTP A,.mm/s, bead height of st layer : mm A,.mm/s, bead height of st layer : mm A, 3.33mm/s, bead height of st layer : mm 8A,.33mm/s, bead height of st layer : 3mm y = 7. y = 8. y = 7.8 y = 8.3 wire supply : none Peak temperature [ ] Fig. Relationship between TCTP and the peak temperature. Hardened area depth, d [mm] 5 3 % of heat input for % of heat input for y =.x R=.9 y =.x R=.9 y =.97x R= (q/ )[ (J/mm s)] Depth of area where TCTP >, d [mm] 8 y =.7x R=.98 y =.5x R=.98 y =.x R=.97 % of heat input for Bead height of % of heat input for st layer : 3mm 5 5 q/ [J/ (mm s)] Fig. 5 Relationship between the hardened area depth and the welding process ariable parameter (q/). Fig. 7 Relationship between the depth of area where TCTP is oer and the welding process ariable parameter q/.

5 of the first layer welding and the subsequent layer welding from oerlapping; that is, the parameter is determined so that the depth of the area where the temperature is oer Ac3 of SQVA in subsequent layer welding dnd_873 does not exceed the filler metal layer thickness h (dnd_873 < h), as illustrated in Fig. 8. Meanwhile, to proide the area hardened by preious passes with a sufficient temper effect, the minimum welding process ariable parameter (q/ )min._of_nd can be determined as shown in Eq. () to proide the area hardened by preious passes with a sufficient TCTP; that is, the parameter is determined so that the d 873 A 873 q d TCTP B TCTP q st nd q max._of_nd h/a 873 q (A873q h)/btctp min._of_nd st. Conclusion () () (3) () depth of the area where TCTP reaches at a certain alue dnd_tctp exceeds the sum of the filler metal layer thickness h and the depth of area hardened by preious passes dst_873 (dnd_tctp > h+dst_873), as illustrated in Fig. 9. Fig. shows an example of the range of the appropriate welding process ariable parameter. Although the requirements are assumed, the appropriate welding process ariable conditions in the TBW technique can be determined based on the welding process ariable parameter proposed in this study. Through the combined temperature and bead surface profile analyses of the TBW technique, we quantified the hardened area size and TCTP, as linear functions of the welding process ariables parameter, which was deried from welding heat conduction theory with a moing heat source. Consequently, in the TBW technique, we established a methodology for estimating the appropriate welding conditions based on the welding process ariable parameter. Reference Fig. 8 Schematic iew of fulfilling the upper limit of the welding process ariable parameter. Fig. 9 Schematic iew of fulfilling the lower limit of the welding process ariable parameter. q/ of nd layer welding 5 5 Bead height of st layer : 3mm % of heat input of nd layer TCTP=5 TCTP= TCTP=3 Maximum limit to preent re-hardening 8 q/ of st layer welding Fig. Range of the appropriate welding process ariable parameter fulfilling the requirement. ) S. Hirano, T. Sera, N. Chigusa, K. Okimura and K. Nishimoto: R/D and implement of temper bead welding as newly deeloped maintenance technique in nuclear power plant, Maintenology, 9- (), ) L. Yu, Y. Nakabayashi, K. Saida, M. Mochizuki, K. Nishimoto, M. Kameyama, S. Hirano and N. Chigusa: Quantitatie Consideration for the Tempering Effect during Multi-pass Thermal Cycle in HAZ of Low-Alloy Steel, QUARTERLY JOURNAL OF THE JAPAN WELDING SOCIETY, 9- (), ) H. Murakami, S. Okano, M. Kameyama, T. Sera and M. Mochizuki: Numerical Model of Multi-pass Repair Process by Temper Bead Welding, QUARTERLY JOURNAL OF THE JAPAN WELDING SOCIETY, 3- (3), 3-7. ) T. Ohji and K. Nishiguchi: Mathematical Modelling of a Molten Pool in Arc Welding of Thin Plate, Technol. Repts. Osaka Uni., 33 (983), ) S. Okano, F. Miyasaka, M. Tanaka and M, Mochizuki: Deelopment and Validation of Predictie Simulation Model of Multi-layer Repair Welding Process by Temper Bead Technique, Journal of High Pressure Institute of Japan, 53- (5), ) T. Terasaki, T. Akiyama, T. Kitamura and M. Nakatani: On Application Conditions of Instantaneous Source for Welding Heat Conduction, QUARTERLY JOURNAL OF THE JAPAN WELDING SOCIETY, 3- (5), ) M. Watanabe, K. Satoh: Prediction of Penetration in Welded Joints by Welding Conditions (Part II), JOURNAL OF THE JAPAN WELDING SOCIETY, 5- (95), ) F. R. Larson and J. Miller: A Time-temperature Relationship for Rupture and Creep Stresses, Trans. ASME, 7 (95), ) S. Okano, M. Mochizuki: Dominant factors influencing weld angular distortion from a iewpoint of generation characteristics of inherent strain, Transactions of the JSME, 8-8 (5), 5-8.