Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld Joint Coupled Analysis of Heat Transfer Induced Thermal Stress Driven Hydrogen Diffusion

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(1)Materials Transactions, Vol. 60, No. 2 (2019) pp. 222 to 229 Special Issue on Development of Materials Integration in Structural Materials for Innovation © 2019 The Japan Institute of Metals and Materials. Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld JointCoupled Analysis of Heat Transfer Induced Thermal Stress Driven Hydrogen Diffusion A. Toshimitsu Yokobori, Jr.1,+, Go Ozeki1, Toshihito Ohmi2, Tadashi Kasuya3, Nobuyuki Ishikawa4, Satoshi Minamoto5 and Manabu Enoki3 1. Teikyo University, Tokyo 173-8605, Japan Shonan Institute of Technology, Fujisawa 251-8511, Japan 3 The University of Tokyo, Tokyo 113-8656, Japan 4 JFE Steel Corporation, Kawasaki 210-0855, Japan 5 National Institute for Materials Science, Tsukuba 305-0047, Japan 2. Hydrogen embrittlement cracking caused at a weld joint is considered to be dominated by hydrogen diffusion and concentration driven by thermal stress induced by heat transfer during cooling process. The gradient of hydrostatic stress component is considered to be a driven force of hydrogen transportation. However, this problem concerns the occurrence phenomenon during cooling process. Therefore, diffusion coefficient, yield stress and Young’s modulus are changed corresponding with temperature change. Especially, diffusion coefficient shows the space gradient corresponding with space gradient of temperature caused by heat transfer. This affects the diffusion equation of hydrogen as a driven force of hydrogen diffusion. Under these backgrounds, to clarify not only the effect of local thermal stress but also that of space gradient of diffusion coefficient on hydrogen release and trap, the hydrogen diffusion analysis based on our proposed ¡ multiplication and FEM-FDM methods was conducted by introducing the terms of gradients of diffusion coefficient and temperature into the diffusion equation. The following results were obtained. The space gradient of diffusion coefficient was found to contribute the release of hydrogen from the site of stress concentration when the gradient of local hydrogen concentration takes the same sign as that of diffusion coefficient. Concerning the prevention of hydrogen embrittlement cracking at weld joint, these results show that not only Pre-Heat Treatment (PHT) which is a mechanical factor, but also the space gradient of diffusion coefficient which is a factor of material science was found to be one of effective factor of release of hydrogen from a site of stress concentration. [doi:10.2320/matertrans.ME201716] (Received June 19, 2018; Accepted November 5, 2018; Published January 25, 2019) Keywords: weld joint, hydrogen embrittlement, thermal stress, gradient of diffusion coefficient, ¡ multiplication method, FEM-FDM method. 1.. Introduction. Hydrogen induced cracking was found to be caused by local thermal stress induced hydrogen concentration at the welded site of the structure during cooling process.110) Especially it is considered to be preferentially caused at the heat affected zone (HAZ).11,12) For such case, analyses of hydrogen diffusion and concentration are important to understand these behaviours. Concerning the analytical treatment of the differential equation of hydrogen diffusion and concentration behavior, there were many analytical treatments.1317) However, from the view point of engineering application, numerical analysis will be useful. Sofronis et al. has analyzed the hydrogen diffusion behavior using the hydrogen diffusion equation considering the stress driving term under existence of diffusive and trapped hydrogen conditions.18) However, due to some approximated treatments, this analysis closely concerns that under steady state condition such as delayed fracture.18) To clarify the time sequential transition behavior of hydrogen diffusion behaviors under the time sequential change of diffusion coefficient and thermal stress during the cooling process of weld metal, both of the time sequential effect of r·P and that of rD on hydrogen diffusion behavior should be notice as driven factors of hydrogen diffusion. Previously, Yokobori et al. have been proposed the ¡ multiplication method19,20) which magnifies stress driving term in the diffusion equation to realize the effect of local stress driven term on hydrogen +. Corresponding author, E-mail: [email protected]. diffusion. Furthermore, for the application of engineering structure, the FEM-FDM (Finite element methodFinite difference method) analytical method was proposed.21,22) In this method, stress analysis is conducted by FEM and diffusion analysis is conducted by FDM, respectively, since FEM and FDM are suitable for stress and fluid analysis respectively. Furthermore, this proposed analysis enables us to obtain more reasonable numerical solutions for such time sequential behaviors of hydrogen diffusion. In this research, to clarify both of the effect of local thermal stress and that of rD on hydrogen diffusion behaviors, the coupled analysis of heat transfer, thermal stress with hydrogen diffusion was conducted based on ¡ multiplication and FEM-FDM methods by introducing the terms of gradients of diffusion coefficient and temperature into the diffusion equation in the manner of rD and rT.2325) 2.. Method of Analysis. Analyses of hydrogen flow based on the coupled analysis of heat transfer-thermal stress-hydrogen diffusion To analyze the behaviors of hydrogen diffusion and concentration at the weld joint during cooling process, coupled analysis of Heat transfer-thermal stress-hydrogen diffusion was conducted using our original program software. However, these analytical methods and physical model have been already written in our previous researches,2325) to make sure the peculiarity of this method, it is reshown as follows and in sections from 2.2³2.6. After input initial data and 2.1.

(2) Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld Joint. 223. (a). (b). Fig. 2 Physical model of analysis.24) (a) Whole physical model of analysis. (b) Detailed of A.. Fig. 1. Flow chart of analyses.. conditions, analysis of heat transfer was conducted by finite difference method (FDM). And temperature at each grid obtained by heat transfer analysis was interpolated to each node for thermal stress analysis based on the finite element method (FEM). Then, thermal stress was calculated for each node point using the interpolated temperature. After that, thermal stress obtained by this analysis was interpolated to each grid point for the analysis of hydrogen diffusion by FDM. Using the interpolated thermal stress, the stress driven hydrogen diffusion analysis was performed. By conducting sequentially these calculations mentioned above, analyses of hydrogen diffusion and concentration behaviours during cooling process were conducted. The flow chart of this analysis is shown in Fig. 1. Validity of our proposed interpolating method was assured in this research and in our previous literatures.21,22,36) 2.2 Physical model and boundary conditions In this study, y-grooved weld joint composed of WM (Weld Metal), HAZ (Heat Affected Zone) and BM (Base Metal) was modeled as shown in Fig. 2.24,26) This analysis was performed as two-dimensional analysis. The number of nodes and elements for FEM analysis are 6144 and 11713, respectively. The material properties used are as follows. ¯ = 0.3, T¡ = 4.0 © 10¹5, Young’s modulus and yield stress were changed depend on temperature as shown in Fig. 3 and Fig. 4,27) respectively. Considering the cooling from high temperature, yield stress of martensitic structure shown in Fig. 4 was used in this analysis27) similar as previous analysis.24,25) This analysis was carried out under the conditions of eq. (1) assuming that yield stress of WM and BM is lower than that of HAZ.28) Young’s modulus, Poisson’s ratio and thermal expansion coefficient are the same for all elements independent of structure such as WM and HAZ. Stress analysis was conducted under plane strain condition. Both. Fig. 3. Temperature dependence of Young’s modulus.27). Fig. 4. Temperature dependence of yield stress.27). ends were fixed for stress analysis. Boundary conditions of heat transfer analysis and hydrogen diffusion analysis are shown in Fig. 5. The number of grid points for FDM are 1500..

(3) 224. A.T. Yokobori et al.. Hp ¼. d· ¼ m1 c1 ð¡ þ ¾p Þm1 1 d¾p. ð3Þ. 2.5 Thermal stress induced hydrogen diffusion analysis The basic equation of hydrogen diffusion is written as eq. (4).14) @C V r· p ¼ r DrC DC ð4Þ @tC RT. Fig. 5 Boundary conditions of heat transfer and hydrogen diffusion analysis.. · ysðWM;BMÞ ¼ 0:8· ysðHAZÞ. ð1Þ. 2.3 Heat transfer analysis Heat transfer analysis was performed using eq. (2). Equation (2) was discretized and solved by SOR method.2325) 2 @T @ T @2 T µc ¼k þ ð2Þ @th @x2 @y2 Initial temperature at WM was 1500°C, and at HAZ and BM were R.T. (20°C). Boundary conditions for heat transfer analysis are shown in Fig. 5. Material properties as shown in Nomenclature used for heat transfer analysis are as follows.29) k = 0.054 J/(°C·mm·sec), a = 12.0 mm2/sec, µ·c = ¹3 3 4.5310 J/(°C·mm ), H = 2.09 © 10¹5 J/(°C·mm2·sec). Only the analysis of cooling process from 1500°C to R.T was conducted in this analysis. 2.4 Thermal stress analysis The routine of thermal stress analysis was added to the two-dimensional elastic-plastic FEM program EPIC-I.30) The elastic plastic stress-strain law corresponding to the temperature change accompanied by heat transfer was also added to this program software.2325) Therefore, the yielding and the plastic deformation laws were changed depending on the temperature change. The elastic deformation is approximated by Hooke’s law. The characteristic of work-hardening for plastic deformation Hp is approximated by eq. (3). In this analysis, linear work hardening law as m1 = 1 was used. And HP was assumed to be given by HP = 0.01 © E for steel.2325) The model was fixed at both end as shown in Fig. 2.. The first and second terms are those of hydrogen diffusion due to the concentration gradient and due to the stress gradient, respectively. Value of the stress gradient term is usually lower order than that of the concentration gradient term.19,21) For such case, the effect of concentration gradient term on hydrogen diffusion appears alone and the effect of stress gradient term on hydrogen diffusion does not appear.19,21) Under this situation, it has been shown that the effect of local stress on hydrogen concentration given by the second term of eq. (4) was found to appear by adding the weight coefficient to this term in eq. (4) in order to take the same order as that of the first term of eq. (4).19,21) This method is proposed as the ¡ multiplication method.19,21) By adding the weight coefficient to each term eq. (4), eq. (5) was obtained. In this study, the weight coefficients ¡1³3 take ¡1:¡2:¡3 = 1:1000:5.2325) And, as an initial condition, initial hydrogen concentration was assumed to be C/C0 = 3.0 in the weld metal. In the other region, initial hydrogen concentration was C/C0 = 1.0. The material properties used for hydrogen diffusion analysis are shown as follows.16,31) D0 = 5.54 © 10¹6 m/sec, Q = 26.81 © 103 J/mol,31) R = 8.314 J/K·mol and ¦V = 2.0 © 10¹6 m3/mol.16) @C DV DV rCr· p ¡3 Cr2 · p ð5Þ ¼ ¡1 Dr2 C ¡2 @tC RT RT The physical meaning of ¡i is considered to be the ratio of the entropy differences, ¦Si of diffusion coefficient in each term of eq. (5) due to the different driven potentials, ¦¤i in the diffusion process between concentration gradient, ¤1 = RTlnC which is related to ¡1 and stress gradient, ¤2 = ¹·P¦V which is related to ¡2.32) This comes from the results that diffusion coefficient is not the thermal activated process of enthalpy given by eq. (6a) but that of Gibbs free energy which is a function of enthalpy and entropy given by (6b).33) H D ¼ D0 exp (6a) RT G H T S ¼ D0 exp (6b) D ¼ D0 exp RT RT Where ¦H is enthalpy, ¦G is Gibbs free energy and ¦S is entropy. Concerning ¡3, essentially for the case of elastic stress field, r2·P is identically zero16,19,21) which corresponds with ¡3 = 0, however, for the case of plastic stress field, dissipation term, QD appears due to irreversible deformation as shown in eq. (7). For such case, hydrogen concentration in whole area decreases. However, in this case, since r2·P is not zero,21) the term of r2·P was noticed and it was used to cover the effect of QD on eq. (7).21) Usually, value of ¡3 is empirically found to be kept as 0 ¯ ¡3 ¯ 0.5¡2.21).

(4) Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld Joint. In this article, ¡3 = 0.005¡2 was used. It means the target materials used for this analysis behave under the state of small scale plasticity. @C DV rCr· p ¼ ¡1 Dr2 C ¡2 @tC RT DV Cr2 · p þ QD ¡3 RT. ð7Þ. 2.6 Method of numerical analyses The equations of heat transfer and hydrogen diffusion shown in eqs. (2) and (5) were discretized using the CrankNicolson implicit method.1925) And the simultaneous equations were solved by the SOR method for eq. (2). 225. and by SUR (Successive-Under-Relaxation) method for eq. (5).19) The detailed method is as follows.2325) In order to eliminate the physical property on the basic equation and make general analysis, eqs. (2) and (5) were normalized using eqs. (8) and (9), and eqs. (10) and (11) were obtained, respectively. x y ath k : ð8Þ xþ ¼ ; y þ ¼ ; t þ a¼ h ¼ 2 ; l0 l0 µc l0 x y C D t C D0 xþ ¼ ; y þ ¼ ; C þ ¼ ; Dþ ¼ ; tþ : C ¼ l0 l0 C0 D0 l20 ð9Þ 2 @T @ T @2 T ¼ þ : ð10Þ @xþ2 @yþ2 @tþ h. 2 þ þ þ þ þ @Cþ @2 Cþ @D @C @Dþ @Cþ V C @D @· p @Dþ @· p þ @ C ¼ ¡1 D þ þ2 þ þ þ þ þ þ ¡2 R @xþ2 @y @xþ @xþ @y @yþ T @xþ @xþ @y @y @tþ C Dþ @Cþ @· p @Cþ @· p Dþ Cþ @T @· p @T @· p Dþ C þ @ 2 · p @ 2 · p þ þ þ þ þ ¡ 3 @xþ @xþ @yþ @yþ T @xþ @xþ @yþ @yþ T2 T @xþ2 @yþ2. ð11Þ. Equations (10) and (11) were discretized using Crank-Nicolson’s implicit method. And, by coordinating the left hand side as unknown term (time step n + 1) and the right hand side as known term (time step n), eqs. (12) and (14) were obtained, respectively. rx ry rx ry ð1 þ rx þ ry ÞTi;j;nþ1 Ti1;j;nþ1 Ti;j1;nþ1 Tiþ1;j;nþ1 Ti;jþ1;nþ1 2 2 2 2 rx ry rx ry ¼ ð1 rx ry ÞTi;j;nþ1 þ Ti1;j;nþ1 þ Ti;j1;nþ1 þ Tiþ1;j;nþ1 þ Ti;jþ1;nþ1 ð12Þ 2 2 2 2 tþ h tþ h ; r ¼ : ð13Þ Where, rx ¼ y 2 ðxþ Þ ðyþ Þ2 Equations (12) and (14) were determined according to the boundary conditions. Then, in order to solve the difference equation, SOR and SUR method was used for eqs. (12) and (14) respectively.2325) The general equations were given by eqs. (16) and (17).19,20) Where, Kij is coefficient matrix, xi is unknown term, fi is known term, ¢ is relaxation coefficient and m is step number of convergence calculation. Usually, for SOR method, ¢ is taken as 1 < ¢ < 2. However, since the basic equation includes the first derivative term of hydrogen concentration such as eq. (5) which leads to unstable convergence, we adopted the method of SUR (SuccessiveUnder-Relaxation) (0 < ¢ < 1) for eq. (17).19,34) To ensure not only mathematical stability but also a physically correct numerical solution, even the CrankNicolson’s method sometimes has limitations on the increment values of time and distance, that is, ¦t + and ¦rx+, ¦ry+.19,34) In order to perform accurate numerical analysis, it is necessary to satisfy the condition as shown in eq. (18).19) þ @Dþ @T @T In eqs. (15a)³(15f ), terms of @D @Xþ , @yþ and @Xþ , @yþ are found to be included in the diffusion equation of eq. (14) as space distribution functions of D+ and T, that is, D+(x, y) and T(x, y). Values of D+ and T were calculated by heat transfer analysis and they were used for the hydrogen diffusion analysis of eq. (14) based on coupled analysis of heat transfer, thermal stress with hydrogen diffusion. þ + @Dþ @T @T Therefore, the effects of @D @Xþ , @yþ and @Xþ , @yþ , that is rD on hydrogen concentration were clearly reflected by this. analysis which are the characteristic terms distinguished from other analysis.18) ð¡1 rx Dþ þ ©x A1 ÞCi1;j;nþ1 þ ð2 þ ¡1 ð2rx þ 2ry ÞDþ tBÞCi;j;nþ1 þ ð¡1 rx Dþ ©x A1 ÞCiþ1;j;nþ1 þ ð¡1 ry Dþ þ ©y A2 ÞCi;j1;nþ1 þ ð¡1 ry Dþ ©y A2 ÞCi;jþ1;nþ1 ¼ ð¡1 rx Dþ ©x A1 ÞCi1;j;n þ ð2 ¡1 ð2rx þ 2ry ÞDþ þ tBÞCi;j;n þ ð¡1 rx Dþ þ ©x A1 ÞCiþ1;j;n þ ð¡1 ry Dþ ©y A2 ÞCi;j1;n þ ð¡1 ry Dþ þ ©y A2 ÞCi;jþ1;n ð14Þ where rx ¼ ©x ¼. tþ C ; ðxþ Þ2. tþ C ; 2xþ. ry ¼. ©y ¼. tþ C ; ðyþ Þ2. tþ C ; 2yþ. @Dþ K1 Dþ @· p ; @xþ T @xþ @Dþ K1 Dþ @· p A2 ¼ ¡1 þ ; @y T @yþ V V ; K2 ¼ ¡3 ; K1 ¼ ¡2 R R A1 ¼ ¡1. (15a) (15b) (15c) (15d) (15e).

(5) 226. A.T. Yokobori et al.. B¼. þ 2 1 @D @· p @Dþ @· p K2 Dþ @T @· p @T @· p @2 · p þ @ ·p K1 þ þ D þ þ K : 2 T @xþ @xþ @yþ @yþ @xþ @xþ @yþ @yþ T @x2þ @y2þ ½Kij fXi g ¼ fi ( !) i1 n X X ðmþ1Þ ðmÞ ðmÞ ðmþ1Þ ðmÞ 1 ¼ Xi þ ¢ Xi þ Kij fi Kij Xi Kij Xj Xi n¼1. (15f ) ð16Þ ð17Þ. j¼iþ1. ðrx ; ry Þ rc ð¼ 0:4Þ:. ð18Þ. The hydrogen diffusion and concentration analysis was conducted by the finite difference method (FDM analysis). However, various stress components obtained by stress analysis were calculated as the node values for FEM analysis. Therefore, these values are necessary to be interpolated from value at each node point for FEM analysis to that at each grid point for FDM analysis. Detailed descriptions of interpolation method were written in previous studies which carried out similar analytical method.21,22,36) 3.. Results of Analysis. Hydrogen concentration behaviors dominated by effects of r·P , rD and rT on hydrogen diffusion Numerical results of two dimensional (2D) distribution of hydrogen concentration during cooling process at the y grooved weld joint without Pre-Heat Treatment (PHT) are shown in Figs. 6(a), (b) and (c). These results showed that,. Fig. 7. 3.1. (a). (b). Experimental result of y-grooved weld cracking.35). with increase in time, at first, the maximum hydrogen concentration increases from C+ = 3.0 (0 step) to 3.39 (5 step) and after that, it decreases to C+ = 2.60 (1000 step). Furthermore, at first, hydrogen was found to concentrate along the HAZ line in the region of WM (Fig. 6(b)) and finally, the hydrogen concentrated region localizes around the central region of WM linked with groove bottom (Fig. 6(c)). The hydrogen concentrated region as shown in Fig. 6(c) is in good agreement with experimental result of y-grooved weld cracking as shown in Fig. 7.35) In Fig. 6, at HAZ region, there are some sites where distribution of hydrogen concentration shows discontinuous behavior. This will be due to the gradation of hydrostatic stress around HAZ as shown in Fig. 8 (That is, yellow, green and blue level regions of hydrostatic stress exist at HAZ). Much more fine division of FDM grids will give us more continuous distribution of hydrogen concentration. 3.2. (c). Fig. 6 Numerical results of 2D distribution of hydrogen concentration during cooling process at the y grooved weld joint. Stress analysis were conducted under plane strain and both end fixed. (a) 0 step (C+max = 3.0). (b) 5 step (0.39 sec) (C+max = 3.39). (c) 1000 step (78 sec) (C+max = 2.60).. Hydrogen concentration behaviors dominated by effects of stress driven term, r·P on hydrogen diffusion under without PHT and with PHT Numerical results of two dimensional (2D) distribution of hydrostatic stress during cooling process at the y grooved weld joint with and without PHT are shown in Figs. 8(a), (b) and (c) for the case without the effect of rD and rT on hydrogen diffusion given by eq. (19). 2 þ @Cþ @ 2 Cþ þ @ C ¼ ¡1 D þ þ2 @xþ2 @y @tþ C þ þ D @C @· p @Cþ @· p ¡2 þ T @xþ @xþ @yþ @yþ Dþ C þ @ 2 · p @ 2 · p þ ¡3 þ ð19Þ T @xþ2 @yþ2 These results showed that at first, the maximum hydrostatic stress concentrate in the region of WM along the HAZ.

(6) Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld Joint. 227. (a). (a). (b). (b). (c). Fig. 9 Numerical results of 2D distribution of hydrogen concentration during cooling process at the y grooved weld joint dominated by term of the gradient of stress alone for without and with PHT of 100°C. Stress analysis were conducted under plane strain and both end fixed. (a) 5000 step (390 sec, C+max = 2.48, without PHT). (b) 5000 step (390 sec, C+max = 1.86, with PHT of 100°C).. (a) Fig. 8 Numerical results of 2D distribution of hydrostatic stress during cooling process at the y grooved weld joint without PHT and with PHT of 100°C. Stress analysis were conducted under plane strain and both end fixed. (a) 1 step (0.078 sec, ·p,max = 131.6 MPa, ·p,min = ¹178.4 MPa, without PHT). (b) 5000 step (390 sec, ·p,max = 1087.8 MPa, ·p,min = ¹74.7 MPa, without PHT). (c) 5000 step (390 sec, ·p,max = 1012.5 MPa, ·p,min = ¹73.5 MPa, PHT of 100°C).. (b). line (Fig. 8(a)) and with increase in time, stress concentration extends to the region of WM as shown in Fig. 8(b). Hydrostatic stress under PHT condition decreases as compared with that under without PHT condition as shown in Figs. 8(b) and (c). Correspondingly, the gradient of hydrostatic stress which is a driven force of hydrogen concentration decreases. This causes decrease in hydrogen concentration as shown in Fig. 9(a) and (b). That is, the maximum hydrogen concentration decreases from C+ = 2.45 (5000 step) to 1.86 (5000 step) by PHT. Furthermore, hydrogen concentration was found to localize in the central WM region and it was not eminent at the bottom site of WM. That is, high concentrated region of hydrogen does not extend to the groove bottom of WM which is different from that of Figs. 6(a), (b) and (c). This means that the effect of rD on hydrogen concentration plays a role of transportation of hydrogen to the site of the groove bottom of WM. This results were clearly shown in Figs. 11(a) and (b). These results showed that r·P was found to cause local hydrogen concentration at the upper central site of WM. On the other hand, rD was found to play a role of transportation of hydrogen to the site of the groove bottom of WM, since the site of maximum hydrogen concentration was found to move toward to the site of groove bottom of WM.. Fig. 10 Numerical results of 2D distribution of hydrogen concentration during cooling process at the y grooved weld joint for the case of ¡1 = 5 under without and with PHT of 100°C. Stress analysis were conducted under plane strain and both ends were fixed. (a) 5000 step (390 sec, C+max = 1.81, without PHT). (b) 5000 step (390 sec, C+max = 1.58, with PHT of 100°C).. 3.3. Hydrogen concentration behaviors dominated by effect of the multiplied diffusive term, ¡1 on hydrogen diffusion under with and without PHT Numerical results of two dimensional (2D) distribution of hydrogen concentration during cooling process at the y grooved weld joint with and without PHT for the case of multiplied diffusive term, that is, ¡1 = 5 are shown in Figs. 10(a), (b). These results showed that the effect of PHT on hydrogen concentration exists, even though the effect of rD on hydrogen concentration is included in the hydrogen diffusion equation. Furthermore, hydrogen concentration.

(7) 228. A.T. Yokobori et al.. (a) Gradient of D, T and σp Only stress gradient α1=5. Air. Weld Metal Air. Base Metal. 0. 0.5. 1 1.5 2 2.5 3 3.5 Hydrogen concentration, C/C0. 4 Fig. 12 Time sequential change of hydrostatic stress distribution at x = 62.24). (b) Gradient of D, T and σp Only stress gradient α1=5. Air. hydrogen release, that is, flow out from WM when the gradient of local hydrogen concentration takes the same sign as that of diffusion coefficient which corresponds with increase in ¡1. Therefore, when the value of diffusive term of eq. (11) multiplied by ¡1 increases, for example, ¡1 = 5, hydrogen was found to be typically flowed out from WM which results in decrease in hydrogen concentration in the region of WM as shown in Fig. 11. Therefore, hydrogen concentration can be decreased not only by decrease in residual thermal stress due to PHT but also by selecting hydrogen diffusion coefficient,25) that is increase in diffusion coefficient which results in existence of rD.. Weld Metal Air. Base Metal. 5. 0. 0.5. 1 1.5 2 2.5 3 3.5 Hydrogen concentration, C/C0. 4. Fig. 11 Hydrogen distribution in the y direction at x+ = 62 without PHT. (a) 1000 step (78 sec). (b) 5000 step (390 sec).. typically decreases as compared with that of ¡1 = 1. This means that promotion of diffusive term of hydrogen by ¡1 causes flow out of hydrogen from WM which results in the release of hydrogen from the region of WM. 4.. Discussions. Results of Figs. 11(a) and (b) showed that the effect of r·P was found to cause local hydrogen concentration at the maximum site of hydrostatic stress due to the driven force of r·P as shown in Fig. 11 and 12. That is, the site of maximum hydrostatic stress as shown in Fig. 12 is in good agreement with that of maximum hydrogen concentration dominated by r·P alone as shown in Fig. 11. However, since the original hydrogen diffusion equation of eq. (11) includes the term of rD, it causes release of hydrogen from WM by rD. Results of Fig. 11 showed that the effect of rD on hydrogen concentration shifts the site of maximum hydrogen concentration toward the groove bottom direction, that is, it causes. Conclusion. (1) The effect of rD on hydrogen concentration plays an important role of release, that is, flow out of hydrogen from the site of the maximum hydrostatic stress. Therefore, the space gradient of hydrogen diffusion coefficient between BM and WM is also effective on the release of hydrogen from the WM in the manner of rD. rD is caused by temperature gradient during cooling process or selecting different diffusion coefficients between BM and WM. (2) PHT was also found to decrease the residual thermal stress, that is the gradient of thermal residual stress which results in decrease in hydrogen concentration. (3) From these results mentioned above, to prevent hydrogen embrittlement cracking at the weld joint, however, PHT contributes the decrease in the gradient of thermal residual stress which results in decrease in hydrogen concentration, the space distribution of diffusion coefficient, rD was found to be an alternative effective factor of decrease in hydrogen concentration by release of hydrogen from WM. Acknowledgments This work was supported by Council for Science,.

(8) Dominating Driven Factors of Hydrogen Diffusion and Concentration for the Weld Joint. Technology and Innovation (CSTI), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Structural Materials for Innovation S” (Funding agency: JST). REFERENCES 1) F. Watkinson, R.G. Baker and H.F. Tremlette: Brit. Weld. J. 10 (1963) 5362. 2) T. Boniszewski and R.G. Baker: Brit. Weld. J. 12 (1965) 345362. 3) H. Suzuki and M. Inagaki: IIW Doc. IX-408-64. 4) C.D. Beachem: Metall. Trans. 3 (1972) 437451. 5) H. Sasaki, K. Watanabe, S. Kirihara and I. Sejima: IIW Doc. IX-78472. 6) N. Yurioka and T. Yatake: J. JWS 45 (1976) 521527. 7) T. Terasaki, H. Harasawa, M. Sakaguchi, M. Sakashita and S. Kunihiko: J. JWS 50 (1981) 11711178. 8) J.F. Lancaster: Metallurgy of Welding, 5th ed., (Chapman & Hall, London, 1993). 9) N. Yurioka and T. Kasuya: Q. JWS 13 (1995) 347357. 10) T. Wada, T. Terasaki and S. Igi: Q. J. Japan Weld. Soc. 15 (1997) 314 320. 11) M. Hayashi, M. Ishiwata, Y. Morii and N. Minakawa: J. Soc. Mater. Sci., Japan 45 (1996) 772778. 12) M. Mochizuki, N. Saito, S. Sakata and H. Uozumi: Trans. Jpn. Soc. Mech. Eng. A 61 (1996) 808813. 13) J.G. Morlet, H.H. Johnson and A.R. Troiano: J. Iron Steel Inst. 189 (1958) 3744. 14) R.A. Oriani: Stress Corrosion Cracking and Hydrogen Embrittlement of Iron Base Alloys, NACE-5, (1973) pp. 351358. 15) H.W. Liu: J. Bas. Eng. 92 (1970) 633. 16) H.P. Van Leewen: Corrosion 31 (1975) 4250. 17) M. Iino: Eng. Fract. Mech. 10 (1978) 113. 18) P. Sofronis and R.M. McMeeking: J. Mech. Phys. Solids 37 (1989) 317350. 19) A.T. Yokobori, Jr., T. Nemoto, K. Satoh and T. Yamada: Eng. Fract. Mech. 55 (1996) 4760. 20) A.T. Yokobori, Jr., Y. Chinda, T. Nemoto, K. Satoh and T. Yamada: Corros. Sci. 44 (2002) 407424. 21) A.T. Yokobori, Jr., T. Ohmi, T. Murakawa, T. Nemoto, T. Uesugi and R. Sugiura: Strength Fract. Complexity 7 (2011) 215233. 22) T. Ohmi, A.T. Yokobori, Jr. and K. Takei: Defect Diffus. Forum 326 328 (2012), 626631. 23) A.T. Yokobori, Jr., T. Ohmi, G. Ozeki, T. Kasuya, N. Ishikawa, S. Minamoto and M. Enoki: Proc. of ICF14 Rhodes, ed. by E.E. Gdoutos, (2017). 24) G. Ozeki, A.T. Yokobori, Jr., T. Ohmi, T. Kasuya, N. Ishikawa, S. Minamoto and M. Enoki: submitted to ASMEPVP 2018-84178, (2018). 25) T. Ohmi, A.T. Yokobori, Jr., G. Ozeki, A.T. Kasuya, N. Ishikawa, S. Minamoto and M. Enoki: submitted to ASMEPVP 2018-84192, (2018). 26) JIS Z 3158, Method of y-groove weld cracking test, (2016). 27) Y. Mikami, N. Kawabe, N. Ishikawa and M. Mochizuki: Q. J. Japan Weld. Soc. 34 (2016) 6780 (in Japanese).. 229. 28) K. Satoh, T. Terasaki and Y. Yamashita: J. Japan Weld. Soc. 48 (1979) 504509 (in Japanese). 29) T. Kasuya, Y. Hashoba, H. Inoue, S. Nakamura and T. Takai: Weld. World 57 (2013) 581. 30) Y. Yamada: Sosei - Nendansei, (Baifu-kan Pub., 1980) pp. 180219 (in Japanese). 31) T. Kasuya and N. Yurioka: Weld. J. 72 (1993) 107. 32) A.T. Yokobori, Jr. and T. Ohmi: Strength Fract. Complexity 8 (2014) 117124. 33) S. Kohda: Introduction of Physics of Metals, (Corona Pub, Tokyo, 1973) pp. 116117 (in Japanese). 34) S.V. Patankar: Numerical Heat Transfer and Fluid Flow, transl. Y. Mizutani and M. Katsuki, (Morikita Pub., 1985) p. 70 (in Japanese). 35) N. Ishikawa: SIP meeting at the University of Tokyo, (2017). 36) M. Ishikawa, T. Ohmi, A.T. Yokobori, Jr. and M. Nishikawa: M&M Conference of Materials and Mechanics Division, (2014) CDrom.. Nomenclature l0 C C0 D D0 T Tout Q R "V ·p E ¯ ·ys · Hp ¾p c1, ¡*, m1 H tc th µ C K A H hT T¡. Length of analytical model 0.15 m Hydrogen concentration Hydrogen concentration in atmosphere Diffusion coefficient (= D0 exp(¹Q/RT )) Diffusion constant independent of temperature Absolute temperature Temperature in atmosphere Activation energy of hydrogen diffusion Gas constant Volume change due to accommodation of a hydrogen Hydrostatic stress Young’s modulus Poisson’s ratio Yield stress Equivalent stress Work hardening coefficient Equivalent plastic strain Constant Hydrogen transfer coefficient Time of hydrogen diffusion Time of heat transfer Density Specific heat Heat conductivity (= µ·c·a) Thermal diffusion coefficient surface coefficient of heat transfer = H/k Thermal expansion coefficient.

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