PSI - Issue 42

178 7 more hydrogen concentration and =513 K). This behavior indicates an important hydrogen desorption process, and thus, an important hydrogen mobility. It can last be conjectured that, when the number of cycles increases, so does the maximal value. The impact of mechanical fields on hydrogen retention can be investigated by introducing its total amount — ̈́Ȁ̈́ ൌ ∫ ሺ͓ Ǩ ൅ ͓ ̶ ሻ™ in the DFW section; — ̈́Ȁ̈́ evolution with time is plotted in Fig. 7a for the three cases. The impact of the cooling pipes pressure is here very clear: at each cycle, — ̈́Ȁ̈́ increases continuously, exhibiting cycles corresponding the loading ones. When the DFW section is exposed to both hydrogen and temperature, — ̈́Ȁ̈́ increases. Hydrogen amount decreases as soon as hese bounda y conditions are modified, during phase 2 (no more hydrogen concentration and Ǥ ൐ǫ̷ =513 K). This behavior denotes an important hydrogen desorption process, and thus, an important hydrogen mobility. It can last be conjectured that, when the number of cycles increases, so does the maximal — ̈́Ȁ̈́ value. Shihao Bian/ Structural Integrity Procedia 00 (2019) 000 – 000 7 Fig. 5. Distribution of ̶ at the end of phase 1 ’ s last cycle (160 cycles) considering (a) water pressure only and (b-c) all thermomechanical fields at higher and lower exposition temperature ͓̈́ΨƬ respectively. The impact of mech nical fields on hydrogen retention can be investigated by intr ducing its total amount — ̈́Ȁ̈́ ൌ ∫ ሺ͓ Ǩ ൅ ͓ ̶ ሻ™ in the DFW section; — ̈́Ȁ̈́ evolution with time is plotted in Fig. 7a for the three cases. The impact of the cooling pipes pressure is here very clear: at each cycle, — ̈́Ȁ̈́ increases continuously, exhibiting cycles corresponding the loading ones. When the DFW section is exposed to both hydrogen and temperature, — ̈́Ȁ̈́ increases. Hydr gen amount decreases as soon as these oundary conditions are odified, during phase 2 (no more hydrogen concentr tion and Ǥ ൐ǫ̷ =513 K). This behavior den tes an importan hydrogen desorption pro ess, and thus, an important hydrogen mobility. It can last be conjectured that, wh n the number of cycles increases, so does the maximal — ̈́Ȁ̈́ value. Shihao Bian et al. / Procedia Structural Integrity 42 (2022) 172–179 Shihao Bian/ Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 6. (a) Temperature and (b) thermal strain fields and (c) equivalent plastic strain at the end of Phase 1’s last cycle, at the higher value. When thermal strain fields are furthermore accounted for, the extra impact on appears to be small, as previously observed: fields are indeed not that much affected by thermal strains. (c) Fig. 6. (a) Temperature and (b) thermal strain fields and (c) equivalent plastic strain at the end of Phase 1 ’ s last cycle, at the higher ͓̈́ΨƬ value. When thermal strain fields are furthermore accounted for, the extra impact on — ̈́Ȁ̈́ appears to be small, as previously observed: ͓ Ǩ fields are indeed not that much affected by thermal strains. Figure 7: (a) Temperature field at T m ax and (b) Thermal st rain fi elds at the end of Phase 1. When only the cooling pipe pressure is accounted for, it can be seen that the DFW sect ion is slight ly under dilatat ion (negat ivepressure), leading to an increase of the C L maximal value. The ext ra effect f t hermal t rains on the C L field is small, however. During the hot phase of each cycle (higher T ex po ), two oppositeeffect s are involved: while the important temperature fi eld leads to an increaseof t he t ri t ium diffusion coefficient (see the temperature field on figure 7a), thermal st rains ( fi gure 7b) induced compression st resses (posit ive P H , see fi gures 6b) which tends t o slow the t rit ium diffusion. During the cool phase of each cycle, these two cont radictory effect s are also present s; from the C L fields, it can beconclude that they neut ralize each other, leading to a small effect of the thermal st rain fields. The impact of mechanical fi elds on t rit ium retent ion can be invest igated by int roducing the total amount Q t ot of t rit ium in the DFW sect ion, which is such that Figure 7: (a) Temperature field at T m ax and (b) Thermal st rain fi elds a the end of Phase 1. hen only the cooling pipe pre sure is a counted for, it can be s en that the DFW sect ion is slight ly under dilatat ion (negat ivepre sure), leading to an increase of the C L maximal value. Theext ra effect of thermal st rains on the C L field is small, however. During the hot phase of each cycle (higher T ex po ), two o positee fect sare involved: while the important te perature fi eld leads to an increaseof the t ri t iu di fusion coefficient (see the temperature field on figure 7a), thermal st rains ( fi gure 7b) induced co pre sion st re ses (posit ive P H , s e fi gures 6b) which tends to slow the t rit ium diffusion. During the c ol phase of each cycle, these two cont radictory e fect s are also present s; fro the C L fields, it can beconclude that they neut ralize each other, leading to a small e fect of the thermal st rain fields. The impact of echanical fi elds on t rit iu retent ion can be invest igat ed by int roducing the total a ount Q t ot of t rit iu in the DFW sect ion, which is such that Shihao Bian/ Structural Integrity Procedia 00 (2019) 000 – 000 7 Phase 1 Phase 2 Phase 2 Phase 1 Fig. 6. (a) Temperature and (b) thermal strain fields and (c) equivalent plastic strain at the end of hase ’ s l st l , t t i h r ͓̈́ΨƬ l . When thermal strain fields are furthermore accounted for, the extra impact on — ̈́Ȁ̈́ appears to be small, as previously observed: ͓ Ǩ fields are inde d not that much af ected b thermal str i . (a) (b) (c) Fig. 6. (a) Temperature and (b) thermal strain fields and (c) equivalent plastic strain at the end of Phase 1 ’ s last cycle, at the higher ͓̈́ΨƬ value. When thermal strain fields are furthermore accounted for, the extra impact on — ̈́Ȁ̈́ appears to be small, as p eviously observed: ͓ Ǩ fields are i deed not that much affected by thermal strains. Figure 7: (a) Temperat ure field a T m ax and (b) Thermal st rain fi elds at t he end of Phase 1. When only t he cooling pipe pressure is account ed for, it can be seen t hat t he DFW sect ion is slight ly under dilat at ion (negat ive pressure), leadi g t o an increase of t he C L maximal value. Th ext ra effect of t hermal st rains on t h C L field is small, h wever. During t he ot phase of each cyc e (hig r T e po ), two opposit e effect s are involved: whi le t he import ant t emperat ure fi eld leads t o an increaseof t he t ri t ium di ffusion coefficient (see t he t emperat ure field on figure 7a), t hermal st rains ( fi gure 7b) induced compression st resses (posit ive P H , see fi gures 6b) which t ends t o slow t he t rit ium diffusion. During t he cool phase of each cycle, t hese two cont radict ory effect s are also present s; from t he C L fields, it can be conclude t hat t hey neut ralize each ot her, leading t o a small effect of t he t hermal st rain fields. The impact of mechanical fi elds on t rit ium retent io can be invest igat ed by int roducing t he t ot al amount Q t ot of t rit ium in t he DFW sect ion, which is such t hat Q t ot = Z ( C L + C T ) dV = X ( C i L + C i T ) V i = Q L + Q T (14) Figure 7: (a) Temperat ur field at T m ax and (b) Thermal st rain fi elds at t he end of Phase 1. hen only t he c oling pipe pre sure is a count ed for, it can be s en t hat t he DFW sect ion is slight ly und r dilat at ion (n gat ive p e sure), leadi g t o an incre se of t he C L maximal value. Th ext ra e fect of t her al st ns on t he C L field is small, however. During t he hot phase of each cycl (hig er T ex po ), two opposit ee fect s are involved: while t he import ant t emperat ure fi eld leads t o an increase of t he t ri t iu di fusion coe ficient (s e t he t e perat ure field on figure 7a), t hermal st rains ( fi gure 7b) induced co pre sion st re ses (posit ive P H , s e fi gures 6b) which t ends t o slow t he t rit ium di fusion. During t he c ol phase of each cycle, t hese two cont radict ory e fect s are also present s; from t he C L fields, it can beconclude t hat t hey neut ralize each ot her, leading t o a small e fect of t he t her al st rain fields. The impact of m cha ical fi elds on t rit iu ret ent io can be invest igated by int roducing t he t ot al a ount Q t ot of t rit iu in t he DF sect ion, which is such t hat Q t ot = Z ( C L + C T ) dV = X ( C i L + C i T ) V i = Q L + Q T (14) Shihao Bian/ Structural Integrity Procedia 00 (2019) 000 – 000 7 P as 1 Phase 2 Phase 2 Phase 1 Shihao Bian/ Structural Integrity Procedia 00 (2019) 000 – 000 7 Shihao Bian/ Structural Integrity P ocedia 00 (2019) 0 0 – 0 7 Phase 1 Phase 2 Phase 2 Phase 1 Fig. 7. (a) temporal evolution of the amount of hydrogen = ∫( + ) per unit thickness for the three configurations, (b) temporal evolution of equivalent plastic strain (black) & hydrostatic stress (purple) at point A (see Fig. 3c) when all thermomechanical fields are resolved. (c) Evolution of the tritium permeation rate during Phase 2 through the cooling pipes. Thermal strains, last, lead to the generation, at each exposure cycle, of plastic strain, localized near the exposed surface (see Fig. 6c). A plastic strain localization can be observed near the symmetry boundary condition (lower surface) corresponding to a possible overestimated value linked to the modelling assumptions. As a consequence, the trap density is modified and increases slightly at each cycle), leading to an increase of the trapped hydrogen concentration (after phase 1, ,2 has evolved from 8.5×10 22 m − 3 to 8.9×10 22 m − 3 , see Fig. 7b for evolution with time at point A of Fig. 3c). During Phase 2, the heat is provided by the cooling pipes (imposed temperature of 513K). This facilitates hydrogen diffusion and detrapping. In a stress-free configuration, H transport is only driven by traps and gradients, while mechanical fields (and especially compression) hardly affect the global desorption process (Fig. 7c). Fig. 7. (a) temporal evolution f the amount of hydrogen ̵ Ƭ̵ Ǩ ሺ for the three configurations, (b) temporal evolution of equivalent plastic strain (black) & hydrostatic stress (purple) at point A (see Fig. 3c) when all thermomechanical fields are resolved. Thermal strains, last, leads to the generation, at each exposure cycle, of plastic strain, localized near the exposed surface (see ( The evolut ion of Q t ot is represented in Figure 8a. The impact of the cooling pipes pressure is here very clear: at each cycles, Q t ot increases cont inuously, exhibit ing cycles corresponding the loading ones. When the DFW sect ion is exposed t o bot h hydrogen and temperature, Q t ot increases. Q t ot decreases as soon as these boundary condit ions are mo dified (no more hydrogen concent rat ion and T ex po = 513 K). This behavior denotes an important hydrogen desorpt ion rocess, and thus, an im portant hydrogen mobi l ity. I t can last be conjectured that , when the number of cycles increases, so does the maximal Q t ot value. 9 The evolut ion of Q t ot is represented in Figure 8a. The impact of the cool ing pipes pre sure is here very clear: at each cycles, Q t ot increases cont inuously, exhibit ing cycles co responding the loading ones. When the DFW sect ion is exposed to bot h hydrogen and temperat ure, Q t ot increases. Q t ot decreases as soon as these b undary condit ions are mo dified (no more hydrogen concent rat ion and T ex po = 513 K). This behavior denotes n important hydrogen desorpt ion proce s, and thus, an im portant hydrogen obil ity. I t can last be conjectured that , when the number of cycles increases, so does the maximal Q t ot value. 9 (a) (b) Fig 5. (a) t mporal evolution of the amount of hydrogen ̶̶͓ Ǩ ̈́ for the three configurations, (b) temporal evolution of equivalent plastic strain (black) & hydrostatic stress (purpl ) at point A (see Fig 3c) when all thermomechanical fields are resolved. While the water pressure has littl impa on the p n tration and retention of hydrogen in the structure, the thermomechanical fields strongly limit them: the penetration depth of hydrogen after 160 cycles, is thus lower (Fig 4c). The temporal evolution of the amount of hydroge is represented in Fig 5a, it saturates since two hundred days and then decreases slightly (black curve) for the case where the resolution of the thermomechanical fields is complete, whereas it remains increasing if the thermomechanical fields are not taken into account. (c) Fig. 7 (a) te ral evolution f the am unt of hydrogen ̵ Ƭ̵ Ǩ ሺ for the three configurations, (b) temporal evolution of equivalent plastic st in (black) & h drostatic stress (purple) at point A (see Fig. 3c) when all thermomec anical fields are resolved. Thermal strains, last, leads to the generation, at each exposure cycle, of plastic strain, localized near the exposed surface (see (Fig. 6c). A plastic strai localisation can be bserved near the symmetry boundary condition (lower surface) orr ponding to a possible ov restimat d valu linked to t e modelling assumption . As a consequence, the trap d ns y is modified and increases slightly at e ch cycle), leading to an increase of the trapped hydrogen concentration (after phase 1, Ƭ ̶ ǡ͸ has evolved from 8.5 × 10 22 m − 3 to 8.9 × 10 22 m − 3 , see Fig. 7b for ȗ ͓ evolution with time at point A of Fig. 3c). During Phase 2, the heat is provided by the cooling pipes (imposed temperature of 513K). This facilitates hydrogen diffusion and detrapping. In a stress-free configuration, H transport is only driven by traps and ͓ Ǩ gradients, while mechanical fields (and especially compression) can affect the global desorption process 6. Conclusion The results presented in this study show that, during the first phase of loading on the DFWs, the mechanical fields play a role of limitation of diffusion and trapping of hydrogen through the hydrostatic stress variations, which induced by the thermal expansion. Their resolution is therefore positive because they reduce the contribution of the DFWs to the maximum inventory authorized in the tokamak. However, the assumptions used are extremely restrictive mechanically (plane strain, symmetries) and will have to be adjusted in order to better take into account the real geometry of the DFWs. The influence of the loading and trapping parameters will be the subject of an in-depth study, Fig. 7. (a) temporal evolution of the amount of hydrogen ̵ Ƭ̵ Ǩ ሺ for the three configurations, (b) temporal evolution of equivalent plastic strain (black) & hydrostatic stress (purple) at point A (see Fig. 3c) when all thermomechanical fields are resolved. Thermal strains, last, leads to the generation, at each exposure cycle, of plastic strain, localized near the exposed surface (see ( The evolut ion of Q t ot is represent ed in Figure 8a. The impact of t he cool ing pipes pressure is here very clear: at each cycles, Q t ot increases cont inuously, exhibit ing cycles corresponding t he loading ones. When t he DFW sect ion is exposed t o bot h hydrogen and t emperat ure, Q t ot increases. Q t ot decreases as soon as t hese boundary condit ions are mo dified (no more hydrogen concent rat ion and T ex po = 513 K). This behavior e ot es an import ant hydrogen desorpt ion process, and t hus, an im port ant hydrogen mobil ity. I t can last be conject red t hat , when the number of cycles increases, so does t he maximal Q t ot value. 9 The evolut ion of Q t ot is represent ed in Figure 8a. The impact of t he cool ing pipes pre sure is here very clear: at each cycles, Q t ot increases cont inuously, exhibit ing cycles co responding t he loading ones. When the DFW sect ion is exposed t o bot h hydrogen and t emperat ure, Q t ot increases. Q t ot decreases as soon as t hese boundary condit ions are mo dified (no more hydrogen concent rat ion and T ex po = 513 K). This behavior denot es an import ant hydrogen desorpt ion proce s, and t hus, an im port ant hydrogen mobil ity. I t c n last be co ject ured t hat , when t he number of cycles increas s, s does t he maximal Q t ot value. 9 (a) (b) Fig 5. (a) t mporal evolution of the amount f hydrogen ̶̶͓ Ǩ ̈́ for the thre configurations, (b) temp ral evolution of equivalent plastic strain (black) & hydrostatic stress (purpl ) at point A (see Fig 3c) when all thermomechanical fiel s are resolved. While the water pressure ha littl mpa on the penetration and retention of hydrogen in the structure, the thermomechanical fields strongly limit them: the penetration depth of hydrogen after 160 cycles, is thus lower (Fig 4c). The temporal evolution of the amount of hydroge is represented in Fig 5a, it saturates since two hundred days and then decreases slightly (black curve) for the case where the resolution of the thermomechanical fields is complete, whereas it remains increasing if the thermomechanical fields are not taken into account. (a) (b) Fig 5. (a) temporal evolution of the amount of hydrogen ̶̶͓ Ǩ ̈́ for the three configurations, (b) temporal evolution of equivalent plastic strain (black) & hydrostatic stress (purple) at point A (see Fig 3c) when all thermomechanical fields are resolved. While the water pressure has little impact on the penetration and retention of hydrogen in the structu e, the hermomechanical fields strongly limit them: the penetration depth of hydrogen after 160 cycles, is thus lower (Fig 4c). The temporal evolution of the amount of hydrogen is represented in Fig 5a, it saturates since two hundred days and hen decreases slightly (black curve) for the case where the resolution of the thermomechanical fields is complete, whereas it remains increasing if the thermomechanical fields are not taken into account. (a) (b) (a) temporal evolution of the amount of hydrogen ̶̶͓ Ǩ ̈́ for the three configurations, (b) temporal evolution of equivalent plastic stra n (bl ck) & hydrostatic ress (purple) at point A (see Fig 3c) when all thermomechanical fields are resolved. hile the water pressur has l ttle impact on the penetration and retention of hydrogen in the structure, th momechanical fields strongly limit them: the pen tration depth of hydrogen after 160 cycles, is thu lower (Fig 4c). emporal evo uti n of the amount of hydrogen is repres nted in Fig 5a, it saturates since two hundred days and d creases slight y (b ack curve) for the cas where the resoluti n of the thermomechanical fields is complete, eas it remains incr asing if the thermomechanical f elds are not taken into account. (a) (c) (b) Q t ot = where V i represent s t he volume associat ed t he each Gauss n ° i point in t he mesh. As t he problem is here 2D, V i is reduced t o a surface and Q t ot is in at omes/ m. where V i represent s t he volume a sociat ed t he each Gau s n ° i point in the esh. As t he proble is here 2D, V i is reduced t o a surface and Q t ot is in at o es/ . Z V ( C L + C T ) dV = ( C L + C T ) dV = no thermomechanical fields water pressure only all thermomechanical fields X Gau s s P oin t ( C i L + C i T ) V i = Q L + Q T i T ) V i = Q L + Q T (14) where V i represent s the volume associated the each Gauss n ° i point in the mesh. As the problem is here 2D, V i is reduced to a surface and Q t ot is in atomes/ m. where V i represent s the volume a sociated the each Gau s n ° i point in t he mesh. As the proble is here 2D, V i is reduced to a surface and Q t ot is in ato es/ m. Q t ot = Z V X Gau s P oin t ( C i L + C (14) (a) (b) V Gau s s P oi n t V Gau s P oi n t no thermomechanical fields water pressure only all thermome hanical fields no thermomechanical fields water pressure only all thermomechanical fields no thermomechanical fields water pressure only all thermomechanical fields Permeation rate (H/m/s)

Figure 12: Evolut ion of the t rit ium permeat ion rat e durin and (c-d) t he exposure edge.