針對 P92 與 316LN 在 3D/5D 冷作彎管後之消除應力熱處理 (PBHT) 機制及 ASME B31.1/B31J 規範應用之深度解析研究 (In-Depth Analysis of Post-Bend Heat Treatment (PBHT) Mechanisms and ASME B31.1/B31J Code Applications for P92 and 316LN 3D/5D Cold Bends)

/ Uncategorized / 作者:

摘要/Abstract

本研究針對超臨界火力發電與先進核能系統中廣泛應用之潛變強度強化鐵素體鋼（ASTM A335 P92，ASME P-No. 15E）與低碳控氮沃斯田鐵不銹鋼（316LN，ASME P-No. 8），在經歷 3D 與 5D 大曲率半徑冷作彎管成型後之微觀金相演變、材料劣化機制，以及後續之消除應力熱處理（Post-Bend Heat Treatment, PBHT）冶金修復作用進行深度學術解析。為確保探討對象符合現代高能管線「以彎代銲」之設計趨勢，本研究專注於一體成型之 3D/5D 冷作彎管，從物理冶金、熱力學動力學及巨觀力學等多維度切入。我們深入剖析冷作變形對 P92 中 Laves 相與 Z 相異常加速析出之影響，以及對 316LN 中應變誘發馬氏體（SIM）生成與敏化（Sensitization）動力學之催化作用。同時，本研究嚴格基於 ASME B31.1 動力配管規範，解析其對 P-No. 15E 與 P-No. 8 材料成型應變極限與強制熱處理之法規邊界；並結合 ASME B31J 規範，探討 3D/5D 彎管在面內（In-Plane）與面外（Out-of-Plane）載荷下之應力強度因子（SIF）及柔性因子（Flexibility Factor）特徵。研究結果論證，精確落實 PBHT 不僅是滿足 B31.1 規範之法定基礎，更是確保 B31J 應力分析模型在工程應用中具備物理真實性之核心關鍵。This study provides an in-depth academic analysis of the microstructural evolution, material degradation mechanisms, and subsequent Post-Bend Heat Treatment (PBHT) metallurgical restoration of creep strength enhanced ferritic steel (ASTM A335 P92, ASME P-No. 15E) and low-carbon, nitrogen-controlled austenitic stainless steel (316LN, ASME P-No. 8) widely used in ultra-supercritical thermal power generation and advanced nuclear systems. To align with the modern design trend of replacing welds with bends in high-energy piping, this study focuses on integrally formed 3D/5D cold bends, examining them from the multidimensional perspectives of physical metallurgy, thermodynamic kinetics, and macroscopic mechanics. We deeply analyze the effects of cold deformation on the abnormally accelerated precipitation of Laves and Z phases in P92, as well as its catalytic effect on the formation of strain-induced martensite (SIM) and sensitization kinetics in 316LN. Furthermore, based strictly on the ASME B31.1 Power Piping Code, this study analyzes the regulatory boundaries for forming strain limits and mandatory heat treatment for P-No. 15E and P-No. 8 materials. In conjunction with the ASME B31J Code, it also explores the characteristics of stress intensification factors (SIF) and flexibility factors for 3D/5D bends under in-plane and out-of-plane loads. The findings demonstrate that accurately executing PBHT is not only the statutory foundation for meeting B31.1 code requirements but also the core key to ensuring the physical authenticity of B31J stress analysis models in engineering applications.

一、 緒論與研究背景/I. Introduction and Research Background

在現代超超臨界（Ultra-Supercritical, USC）火力發電廠以及第四代先進核反應爐（如鉛冷快中子反應爐與高溫氣冷爐）之設計中，主蒸汽管線、再熱蒸汽管線與冷卻水迴路必須承受極端的高溫、高壓及複雜的熱機疲勞（Thermo-mechanical Fatigue）循環載荷。在如此嚴苛的服役環境與工廠條件下，材料的選擇至關重要。ASTM A335 P92 鋼作為 9Cr 系潛變強度強化鐵素體鋼（Creep Strength Enhanced Ferritic Steels, CSEF）之代表，透過添加鎢（W）與硼（B）等元素，展現出優異的高溫潛變抗力與抗氧化性能，被廣泛應用於 600°C 以上之 USC 蒸汽管線1。另一方面，316LN 作為添加氮（N）的低碳沃斯田鐵不銹鋼，藉由氮元素的間隙固溶強化與穩定沃斯田鐵相之特性，具備卓越的抗晶界腐蝕、高溫機械強度以及抗輻射脆化能力，成為核能與高溫化工系統不可或缺的關鍵材料4。In the design of modern Ultra-Supercritical (USC) thermal power plants and fourth-generation advanced nuclear reactors (such as lead-cooled fast reactors and high-temperature gas-cooled reactors), main steam piping, reheat steam piping, and cooling water loops must withstand extreme high temperatures, high pressures, and complex thermo-mechanical fatigue cyclic loads. Under such severe service environments and plant conditions, material selection is critical. As a representative of 9Cr Creep Strength Enhanced Ferritic Steels (CSEF), ASTM A335 P92 steel exhibits excellent high-temperature creep resistance and oxidation resistance through the addition of elements like tungsten (W) and boron (B), and is widely used in USC steam piping operating above 600°C1. On the other hand, 316LN, a low-carbon austenitic stainless steel with added nitrogen (N), possesses outstanding resistance to intergranular corrosion, high-temperature mechanical strength, and resistance to radiation embrittlement due to the interstitial solid solution strengthening of nitrogen and its austenite-stabilizing characteristics, making it an indispensable key material for nuclear and high-temperature chemical systems4.

當代先進高能管線佈置為了降低系統中之銲道數量，消弭銲接熱影響區（HAZ）在長期高溫服役下極易誘發的第四型潛變破裂（Type IV Cracking）風險，逐漸傾向採用 CNC 冷作彎管技術。此工法將直管直接成型為 3D（彎曲半徑為管外徑的 3 倍）或 5D（彎曲半徑為管外徑的 5 倍）之大半徑彎管。冷作彎管本質上屬於劇烈的巨觀塑性變形過程，伴隨著龐大的成型應變與殘餘應力。彎管外側（背弧）受拉伸而減薄，內側（腹弧）受壓縮而增厚。根據幾何推導，彎管外弧的最大理論成型應變率（Forming Strain, ϵ）可近似表示為管材平均半徑與彎曲半徑之比值，即ϵ≈D/(2R)，其中 D為名義外徑，R 為彎曲中心線半徑。據此計算，3D 彎管之最大冷應變約為 16.7%，而 5D 彎管之最大冷應變約為 10.0%。To reduce the number of welds in the system and eliminate the risk of Type IV creep cracking easily induced in the Heat-Affected Zone (HAZ) under long-term high-temperature service, contemporary advanced high-energy piping layouts increasingly favor CNC cold bending technology. This construction method forms straight pipes directly into large-radius bends of 3D (bend radius equals 3 times the pipe outside diameter) or 5D (bend radius equals 5 times the pipe outside diameter). Cold bending is inherently a severe macroscopic plastic deformation process, accompanied by massive forming strains and residual stresses. The outer side (extrados) of the bend stretches and thins, while the inner side (intrados) compresses and thickens. According to geometric derivation, the maximum theoretical forming strain (ϵ) on the extrados can be approximated as the ratio of the mean pipe radius to the bend radius, i.e., ϵ≈D/(2R), where D is the nominal outside diameter and R is the centerline bend radius. Based on this calculation, the maximum cold strain for a 3D bend is approximately 16.7%, and for a 5D bend, it is approximately 10.0%.

高達 10% 至 16.7% 的冷作應變在材料微觀層面上，將轉化為位錯密度（Dislocation Density）的指數級暴增與晶格嚴重扭曲。若未經適當的消除應力熱處理（PBHT）予以修復，這些高能量的晶格缺陷將對 P92 與 316LN 之長期高溫服役壽命產生不可逆的破壞。本研究將透過冶金熱力學機制，結合 ASME B31.1 之強制性法規條文與 ASME B31J 之尖端力學評估模型，針對 3D/5D 冷作彎管之 PBHT 機理展開系統性之深度學術解析。At the microstructural level, such high cold forming strains of 10% to 16.7% translate into an exponential surge in dislocation density and severe lattice distortion. If not restored through an appropriate Post-Bend Heat Treatment (PBHT), these high-energy lattice defects will cause irreversible damage to the long-term high-temperature service life of both P92 and 316LN. Through metallurgical and thermodynamic mechanisms, combined with the mandatory regulatory provisions of ASME B31.1 and the cutting-edge mechanical assessment models of ASME B31J, this study will conduct a systematic and in-depth academic analysis of the PBHT mechanisms for 3D/5D cold bends.

二、 P92 (P-No. 15E) 鋼在 3D/5D 冷作彎管之微觀組織演變與潛變劣化機制/II. Microstructural Evolution and Creep Degradation Mechanisms of P92 (P-No. 15E) Steel in 3D/5D Cold Bending

ASTM A335 P92 鋼的微觀組織在標準正常化與回火（Normalizing and Tempering, N&T）狀態下，呈現高度均勻的回火馬氏體（Tempered Martensite）結構。其卓越的高溫潛變強度源於多重強化機制的協同作用：包含鎢（W）與鉬（Mo）的固溶強化、原沃斯田鐵晶界（PAGB）與馬氏體板條邊界上富鉻之M23C6  碳化物的晶界強化，以及散佈於晶粒內部極細小的 MX 型（如 VC, NbC, CrVN）碳氮化物所提供的次晶界釘紮（Pinning）效應1。然而，3D/5D 冷作彎管所引入的劇烈塑性變形將徹底打破此一微觀平衡。In the standard Normalized and Tempered (N&T) condition, the microstructure of ASTM A335 P92 steel presents a highly uniform tempered martensite structure. Its outstanding high-temperature creep strength stems from the synergistic effect of multiple strengthening mechanisms: solid solution strengthening from tungsten (W) and molybdenum (Mo), grain boundary strengthening from Cr-rich M23C6 carbides on prior austenite grain boundaries (PAGBs) and martensite lath boundaries, and sub-boundary pinning effects provided by extremely fine MX-type carbonitrides (e.g., VC, NbC, CrVN) dispersed within the grains1. However, the severe plastic deformation introduced by 3D/5D cold bending thoroughly disrupts this microstructural equilibrium.

2.1 應變誘發析出硬化與位錯網絡碎化/2.1 Strain-Induced Precipitation Hardening and Dislocation Network Fragmentation

在 10% 至 16.7% 的冷作應變下，P92 鋼內部會產生大量交錯的滑移帶，這些滑移帶以高能量狀態強行切割原有的馬氏體板條與次晶界網絡。巨量的位錯增殖導致顯著的應變硬化（Strain Hardening），使得彎管背弧區域的巨觀硬度與降伏強度異常攀升，同時衝擊韌性急遽下降。這種高位錯密度的非平衡狀態，為後續高溫服役期間的合金元素擴散提供了極低活化能的快速通道（Pipe Diffusion），進而徹底改變了材料的析出動力學特徵6。Under cold forming strains of 10% to 16.7%, a large number of intersecting slip bands are generated inside the P92 steel. These high-energy slip bands forcibly sever the original martensite laths and sub-boundary networks. The massive multiplication of dislocations leads to significant strain hardening, causing the macroscopic hardness and yield strength in the extrados region to spike abnormally, while impact toughness plummets. This non-equilibrium state of high dislocation density provides rapid channels with extremely low activation energy (pipe diffusion) for alloy element diffusion during subsequent high-temperature service, fundamentally altering the material’s precipitation kinetics6.

2.2 Laves 相與 Z 相之異常加速析出動力學/2.2 Abnormally Accelerated Precipitation Kinetics of Laves and Z Phases

P92 鋼相較於 P91 的核心改良在於將鉬含量降低並添加高達約 1.8 wt.% 的鎢，以期在高溫下獲得更持久的固溶強化效果。然而，鎢的添加同時也增加了金屬間化合物Fe2(W,Mo) Laves 相的析出傾向7。在正常服役條件下，Laves 相的成核與生長極為緩慢；但在 3D/5D 冷彎引入大量晶格缺陷後，高密度位錯成為 Laves 相極佳的非均勻成核點（Heterogeneous Nucleation Sites）。The core improvement of P92 steel over P91 lies in reducing the molybdenum content while adding up to approximately 1.8 wt.% tungsten, aiming to achieve more durable solid solution strengthening at high temperatures. However, the addition of tungsten also increases the precipitation tendency of the intermetallic compound Fe2(W,Mo) Laves phase7. Under normal service conditions, the nucleation and growth of the Laves phase are extremely slow. Yet, after 3D/5D cold bending introduces massive lattice defects, the high dislocation density serves as excellent heterogeneous nucleation sites for the Laves phase.

熱力學與動力學研究指出，冷作變形將促使 Laves 相在極短的高溫暴露時間內於晶界與變形帶上大量析出並迅速粗化，此一過程遵循 Ostwald Ripening 原理1。粗大的 Laves 相顆粒會將基體中的鎢與鉬大量抽離，導致固溶強化效應衰退；更致命的是，這些硬脆且粗大的金屬間化合物顆粒與柔性基體之間存在嚴重的變形不協調，在高溫潛變載荷下極易成為潛變空洞（Creep Cavities）的微觀成核核心，從而引發沿晶微裂紋的萌生與擴展1。此外，劇烈冷變形亦會加速 P92 晶內細小的 MX 碳氮化物向熱力學更穩定的粗大 Z 相（CrVN）轉變，這徹底摧毀了晶粒內部的潛變抗力3。Thermodynamic and kinetic studies indicate that cold deformation prompts the Laves phase to precipitate abundantly and coarsen rapidly on grain boundaries and deformation bands within a very short period of high-temperature exposure, a process governed by the Ostwald ripening principle1. Coarse Laves phase particles heavily deplete tungsten and molybdenum from the matrix, causing solid solution strengthening to decay. More fatally, severe deformation incompatibility exists between these hard, brittle intermetallic particles and the ductile matrix, easily making them micro-nucleation cores for creep cavities under high-temperature creep loads, thereby initiating the formation and propagation of intergranular microcracks1. Additionally, intense cold deformation accelerates the transformation of fine MX carbonitrides within P92 grains into the thermodynamically more stable and coarse Z phase (CrVN), completely destroying the intragranular creep resistance3.

2.3 P92 冷彎管之 PBHT 冶金修復路徑/2.3 PBHT Metallurgical Restoration Pathways for P92 Cold Bends

為逆轉由冷作應變引發的微觀組織劣化，必須依賴精確控制的 PBHT 進行冶金修復。針對 P92，PBHT 的策略取決於累積成型應變的大小，主要分為次臨界回火與完全的正常化加回火兩種路徑：To reverse the microstructural degradation induced by cold forming strains, metallurgical restoration must rely on precisely controlled PBHT. For P92, the PBHT strategy depends on the magnitude of the accumulated forming strain and is primarily divided into two pathways: subcritical tempering and full Normalizing and Tempering (N&T):

  1. 次臨界消除應力處理（Subcritical Stress Relief）：當成型應變較低（如 5D 彎管的 10% 應變）且符合規範條件時，可採用低於AC1 臨界溫度的熱處理（通常介於 730°C 至 780°C 之間）6。此過程提供熱活化能以驅動位錯滑移與攀移，產生回復（Recovery）作用，從而消解巨觀殘餘應力並穩定微觀組織。然而，若冷變形量過大，單純的次臨界處理不僅無法修復已嚴重破碎的次晶界，甚至可能反而加速 Laves 相的粗化11。Subcritical Stress Relief: When the forming strain is relatively low (e.g., 10% strain for a 5D bend) and meets code requirements, heat treatment below the AC1 critical temperature (typically between 730°C and 780°C) can be applied6. This process provides thermal activation energy to drive dislocation slip and climb, triggering recovery, which dissipates macroscopic residual stresses and stabilizes the microstructure. However, if the cold deformation is too extensive, subcritical treatment alone cannot repair the severely fragmented sub-boundaries and may even provide enough thermal energy to accelerate Laves phase coarsening11.
  2. 正常化加回火（Normalizing and Tempering, N&T）：對於應變高達16.7% 的 3D 彎管，材料的原始微觀特徵已遭徹底破壞，必須進行完全的 N&T 處理。首先，將彎管加熱至 1040°C 至 1080°C 之間的奧氏體化溫度區間並充分保溫，使破碎的馬氏體、粗化的碳化物與 Laves 相完全溶解入 γ-Fe 晶格中，實現微觀組織的完全重構（Re-austenitization）。隨後以受控速率冷卻，重新生成均勻的高密度板條馬氏體，最後再於 730°C 至 780°C 進行回火，徹底恢復材料的潛變延展性6。Normalizing and Tempering (N&T): For 3D bends with strains up to 16.7%, the material’s original microstructural features are completely destroyed, making a full N&T treatment mandatory. First, the bend is heated to the austenitizing temperature range between 1040°C and 1080°C and held to fully dissolve fragmented martensite, coarsened carbides, and Laves phases into the γ-Fe lattice, achieving a complete microstructural reconstruction (re-austenitization). It is then cooled at a controlled rate to regenerate uniform, high-density lath martensite, followed by tempering at 730°C to 780°C, thoroughly restoring the material’s creep ductility6.

三、 316LN (P-No. 8) 鋼在 3D/5D 冷作彎管之相變與敏化現象/III. Phase Transformation and Sensitization Phenomena of 316LN (P-No. 8) Steel in 3D/5D Cold Bending

316LN 屬於添加氮元素的低碳沃斯田鐵不銹鋼，其面心立方（FCC）晶格結構在室溫下具備極佳的延展性與韌性。氮的加入降低了材料的層錯能（Stacking Fault Energy, SFE），有效提高了固溶強度、阻礙位錯交滑移，並增強了加工硬化率5。316LN is a low-carbon austenitic stainless steel with added nitrogen. Its face-centered cubic (FCC) lattice structure provides excellent ductility and toughness at room temperature. The addition of nitrogen lowers the material’s Stacking Fault Energy (SFE), effectively enhancing solid solution strength, hindering dislocation cross-slip, and increasing the work-hardening rate5.

3.1 應變誘發馬氏體（SIM）與幾何硬化/3.1 Strain-Induced Martensite (SIM) and Geometric Hardening

儘管 316 系統擁有相對較高的沃斯田鐵穩定性（較低的Md30 溫度），但在 3D/5D 冷作彎管高達 10% 至 17% 的劇烈塑性變形下，管壁承受的複雜三軸應力態仍會強制誘發相變12。沃斯田鐵相將透過不全位錯（Partial Dislocations）的滑移產生層錯重疊，並依循γ(FCC)→ϵ(HCP)→α'(BCC) 的晶體學路徑，轉變為應變誘發馬氏體（Strain-Induced Martensite, SIM）13。此一相變現象會導致彎管背弧處的硬度顯著上升，形成明顯的幾何硬化區；然而，SIM 的生成同時也消耗了材料的塑性儲備，並可能在微觀相界處引發局部應力集中。Although the 316 series possesses relatively high austenite stability (a lower Md30 temperature), the complex triaxial stress state borne by the pipe wall under severe plastic deformations of 10% to 17% in 3D/5D cold bending still forcibly induces phase transformation12. The austenite phase undergoes stacking fault overlapping via the slip of partial dislocations, transforming into Strain-Induced Martensite (SIM) along the crystallographic path γ(FCC)→ϵ(HCP)→α'(BCC)13. This phase transformation leads to a significant increase in hardness at the extrados of the bend, forming a clear geometric hardening zone; however, the generation of SIM also consumes the material’s plasticity reserves and may trigger local stress concentrations at microscopic phase boundaries.

3.2 敏化動力學加速與晶界腐蝕（IGC）/3.2 Accelerated Sensitization Kinetics and Intergranular Corrosion (IGC)

316LN 因含碳量極低（≦0.03wt.%），在常規固溶狀態下被認為對敏化（Sensitization）具備高度免疫力。然而，3D/5D 冷作彎管徹底改變了其微觀析出動力學。冷作應變在晶內與晶界產生了密集的剪切帶（Shear Bands）、孿晶界與高密度位錯網絡14。Because of its extremely low carbon content (≦0.03wt.%), 316LN is considered highly immune to sensitization in a conventional solution-annealed state. However, 3D/5D cold bending completely alters its microstructural precipitation kinetics. The cold forming strains generate dense shear bands, twin boundaries, and high-density dislocation networks within the grains and at the grain boundaries14.

當經歷冷作變形的 316LN 於高溫環境服役，或在未妥善控制冷卻速率的過程中，鉻（Cr）與碳（C）原子將沿著位錯核心進行高速的管路擴散（Pipe Diffusion）。這導致富鉻的M23C6  碳化物在極短時間內大量析出14。碳化物的快速生長劇烈消耗了周圍的鉻元素，導致晶界附近形成鉻濃度低於鈍化極限值（約 12 wt.%）的貧鉻區（Cr-depletion Zone），進而直接引發嚴重的晶界腐蝕（Intergranular Corrosion, IGC）與沿晶應力腐蝕破裂（IGSCC）14。依據 ASTM A262 規範測試的實證數據顯示，冷作變形顯著縮短了 316LN 達到敏化狀態所需的時間，使其敏化鼻端（Nose）向低溫與短時間方向大幅偏移17。When cold-deformed 316LN is placed in high-temperature service environments, or during poorly controlled cooling, chromium (Cr) and carbon (C) atoms undergo high-speed pipe diffusion along dislocation cores. This results in the massive precipitation of Cr-rich M23C6 carbides in a very short time14. The rapid growth of carbides drastically depletes the surrounding chromium, causing the formation of a Cr-depletion zone near the grain boundaries with a concentration below the passivation limit value (about 12 wt.%), thereby directly triggering severe Intergranular Corrosion (IGC) and Intergranular Stress Corrosion Cracking (IGSCC)14. Empirical data from ASTM A262 code tests show that cold deformation significantly shortens the time required for 316LN to reach a sensitized state, shifting its sensitization nose sharply toward lower temperatures and shorter times17.

劣化機制 / Degradation Mechanism P92 (P-No. 15E) 鋼 / Steel 316LN (P-No. 8) 鋼 / Steel
主要相變特徵 / Main Phase Change Features 回火馬氏體碎化、Z相粗化 / Fragmentation of tempered martensite, Z-phase coarsening γ→ϵ→α’應變誘發馬氏體 (SIM) /γ→ϵ→α’ Strain-induced martensite (SIM)
有害析出物 / Harmful Precipitates Laves 相 (Fe2(W,Mo))、粗大 Z 相 / Laves phase (Fe2(W,Mo)), coarse Z-phase M23C6 碳化物、σ相、χ相 / M23C6 carbides, σ phase, χ phase
物理退化表現 / Physical Degradation Manifestation 潛變延展性喪失、高溫潛變空洞成核 / Loss of creep ductility, high-temp creep cavity nucleation 貧鉻區形成、敏化效應 (Sensitization) / Formation of Cr-depleted zones, Sensitization
最終失效模式 / Ultimate Failure Mode 類似第四型潛變破裂之沿晶微裂紋 / Intergranular microcracks resembling Type IV cracking 晶界腐蝕 (IGC)、沿晶應力腐蝕破裂 (IGSCC) / IGC, Intergranular Stress Corrosion Cracking (IGSCC)

3.3 固溶退火（Solution Annealing）作為 PBHT 之冶金必然性/3.3 The Metallurgical Necessity of Solution Annealing as PBHT

針對冷作變形後的 316LN，PBHT 並非單純的「消除應力」，而是必須進行高溫固溶退火（Solution Annealing，通常介於 1050°C 至 1150°C 之間）14。在高溫熱能的驅動下，高儲能的冷變形晶粒發生靜態再結晶（Static Recrystallization），應變誘發馬氏體（α’）發生逆轉變，恢復為均勻的 FCC 沃斯田鐵組織4。同時，已生成的 M23C6 碳化物重新溶解入基體，消除貧鉻區，徹底恢復 316LN 的抗晶界腐蝕能力4。For 316LN after cold deformation, PBHT is not merely about “stress relief” but requires high-temperature solution annealing (typically between 1050°C and 1150°C)14. Driven by high thermal energy, the highly stored-energy cold-deformed grains undergo static recrystallization, and the strain-induced martensite (α’) undergoes reverse transformation, restoring a uniform FCC austenite structure4. Simultaneously, previously formed M23C6 carbides redissolve into the matrix, eliminating Cr-depleted zones and thoroughly restoring 316LN’s resistance to intergranular corrosion4.

四、 基於 ASME B31.1 之 3D/5D 冷彎管 PBHT 規範解析/IV. Analysis of PBHT Code Requirements for 3D/5D Cold Bends Based on ASME B31.1

ASME B31.1 (Power Piping) 規範作為全球動力管線設計與施工的最高指導準則，其核心設計哲學建立在長壽命與極高可靠性之上23。針對彎曲與成型組件的熱處理要求，ASME B31.1 在第 129.3 節（Heat Treatment of Bends and Formed Components）中訂定了嚴謹且強制性的法規框架27。As the highest guiding principle for global power piping design and construction, the ASME B31.1 (Power Piping) Code roots its core design philosophy in long service life and extremely high reliability23. Regarding the heat treatment requirements for bends and formed components, ASME B31.1 establishes a rigorous and mandatory regulatory framework in Section 129.3 (Heat Treatment of Bends and Formed Components)27.

4.1 針對 P-No. 15E (P92) 之強制規範界線/4.1 Mandatory Code Boundaries for P-No. 15E (P92)

鑑於潛變強度強化鐵素體鋼（CSEF）對微觀組織的高度敏感性，ASME B31.1 第 129.3.3 段落針對 P-No. 15E 材料提出了極其嚴苛的規範要求24。若冷作成型應變大於法規設定的極限值（可能低至 10% 甚至更嚴格之折半規定24），法規嚴禁僅施以次臨界消除應力熱處理，製造商必須對整個彎曲管段執行完全的正常化與回火（N&T）。即使未達強制 N&T 上限，只要其設計溫度高於潛變影響範圍，仍必須依據 Table 129.3.2 強制進行次臨界 PBHT1。Given the high microstructural sensitivity of Creep Strength Enhanced Ferritic Steels (CSEF), ASME B31.1 paragraph 129.3.3 sets extremely stringent code requirements for P-No. 15E materials24. If the cold forming strain exceeds the code-defined limit value (which could be as low as 10% or even a stricter halved requirement24), the code strictly prohibits applying only subcritical stress relief heat treatment; manufacturers must perform a full Normalizing and Tempering (N&T) on the entire bent pipe section. Even if the strain is below the mandatory N&T limit, as long as the design temperature is within the creep range, a mandatory subcritical PBHT must still be conducted in accordance with Table 129.3.21.

4.2 針對 P-No. 8 (316LN) 之規範應用與工程實踐/4.2 Code Applications and Engineering Practices for P-No. 8 (316LN)

相較於鐵素體鋼，ASME B31.1 針對 P-No. 8 沃斯田鐵不銹鋼的 PBHT 提供較大彈性。依據 Table 129.3.2 規定，對 316LN 冷彎管，若無特殊考量通常為「不強制要求亦不禁止」24。然而，若管線服役於核能高溫水環境或具備強烈 SCC 風險，前瞻性的工程設計規範（Design Specifications）通常會超越 B31.1 最低底線，主動要求進行高溫固溶退火 PBHT，以確保長期耐腐蝕完整性34。Compared to ferritic steels, ASME B31.1 offers greater flexibility for PBHT of P-No. 8 austenitic stainless steels. According to Table 129.3.2, PBHT for 316LN cold bends is typically “neither required nor prohibited” unless special considerations apply24. However, if the piping will serve in nuclear high-temperature water environments or carries severe SCC risks, forward-looking engineering Design Specifications usually exceed the minimum B31.1 baseline and proactively mandate high-temperature solution annealing PBHT to ensure long-term corrosion resistance integrity34.

五、 ASME B31J 規範在 3D/5D 冷彎管之應力強度與柔性因子應用/V. Application of ASME B31J Code to Stress Intensification and Flexibility Factors in 3D/5D Cold Bends

ASME B31J 規範的引入全面採用基於有限元素分析（FEA）驗證與大規模疲勞實驗數據的數值模型，大幅降低了傳統經驗公式的保守性36。The introduction of the ASME B31J Code entirely adopts numerical models based on Finite Element Analysis (FEA) validations and large-scale fatigue test data, significantly reducing the conservatism of traditional empirical formulas36.

5.1 柔性特徵值 (h) 與柔性因子 (k) 之演算法/5.1 Algorithms for Flexibility Characteristic (h) and Flexibility Factor (k)

在 B31J 體系中，彎管的柔性特徵值定義為： h=tR/r22 ，其中 t 為壁厚，R 為彎曲半徑，r2 為平均截面半徑38。彎管的柔性因子 k 與 h 成反比（k≈1.65/h）38。當採用 3D 或 5D 大彎曲半徑時，h 值顯著提升，進而導致 k 值急遽下降，代表 5D 彎管在力學表現上較 3D 更為「僵硬（Stiff）」37。In the B31J system, the flexibility characteristic of a bend is defined as: h=tR/r22, where t is the wall thickness, R is the bend radius, and r2 is the mean cross-sectional radius38. The bend’s flexibility factor k is inversely proportional to h (k≈1.65/h)38. When using large bend radii like 3D or 5D, the h value increases significantly, leading to a sharp decrease in the k value, meaning that a 5D bend is mechanically “stiffer” than a 3D bend37.

5.2 應力強度因子（SIF）之面內與面外精確解耦/5.2 Precise Decoupling of In-Plane and Out-of-Plane Stress Intensification Factors (SIF)

ASME B31J 將 SIF 進行了精確的力學解耦37：ASME B31J provides precise mechanical decoupling of the SIF37:

  • 面內 SIF（In-Plane SIF）：ii=0.9/h2/3 [cite: 24, 27]
  • 面外 SIF（Out-of-Plane SIF）：io=0.75/h2/3 [cite: 24, 27]

這揭示了 3D/5D 大半徑冷彎管的核心優勢：大曲率半徑使其擁有極低的疲勞應力集中效應。This reveals the core advantage of 3D/5D large-radius cold bends: their large radius of curvature results in extremely low fatigue stress concentration effects.

六、 PBHT 冶金修復與 B31J 力學模型之深層耦合機制/VI. Deep Coupling Mechanism Between PBHT Metallurgical Restoration and B31J Mechanical Models

ASME B31J 規範的所有精確公式，皆建立在一個物理預設之上：管件材料必須是巨觀均質且各向同性的，且內部不存在巨量殘餘應力。若省略 PBHT，冷作彎管的高度非均質狀態與殘餘應力將導致 B31J 預測模型嚴重失真。唯有嚴格落實高溫 PBHT 消除殘餘應力並恢復材料均質性，B31J 的分析模型方能真實安全地反映管線疲勞行為。All precise formulas in the ASME B31J Code are built upon a physical premise: the piping material must be macroscopically homogeneous and isotropic, with no massive internal residual stresses. If PBHT is omitted, the highly heterogeneous state and residual stresses of the cold bend will cause severe distortion in B31J predictive models. Only by strictly implementing high-temperature PBHT to eliminate residual stresses and restore material homogeneity can B31J’s analytical models truly and safely reflect the fatigue behavior of the piping.

七、 業主（台電）對於 P91/P92 蒸氣管線選取 3D/5D 彎徑與 PBHT 決策思維/VII. Owner’s (Taipower) Decision-Making Process for Selecting 3D/5D Bend Radii and PBHT for P91/P92 Steam Piping

在面對複循環發電廠高頻啟停需求時，為消弭傳統工法中銲接熱影響區極易誘發的第四型潛變破裂風險，業主端明確傾向採用「以彎代銲」的大半徑冷作彎管。業主結合冶金學實證，將 PBHT 的目標溫度確立為 760°C，此一精確熱處理不僅釋放巨觀殘餘應力，更防止應變誘發析出硬化，確保全生命週期之運轉可靠度。Faced with the high-frequency start-stop demands of combined cycle power plants, to eliminate the risk of Type IV creep cracking easily induced in the weld heat-affected zone of traditional construction methods, owners clearly favor the use of large-radius cold bends to “replace welds with bends”. Integrating metallurgical evidence, owners have established the target PBHT temperature at 760°C. This precise heat treatment not only relieves macroscopic residual stresses but also prevents strain-induced precipitation hardening, ensuring operational reliability throughout the entire lifecycle.

八、 EPC 承包商對於 P91/P92 蒸氣管線選擇 3D/5D 彎徑與 PBHT 之工法考量/VIII. EPC Contractors’ Construction Considerations for Selecting 3D/5D Bend Radii and PBHT for P91/P92 Steam Piping

對於 EPC 統包商而言，採用冷作彎管省去了冗長的彎頭元件訂製期與二次防腐塗裝工序。在施工安全與 ESG 指標上，冷作工法排除了明火熱工作業，大幅降低工安隱患。此外，銲口數量的減少直接縮減了非破壞性檢測（NDE）的時程，為試車階段的合規驗收提供了極高的移交效率。For EPC contractors, adopting cold bends eliminates lengthy procurement cycles for elbow components and secondary anti-corrosion coating processes. Regarding construction safety and ESG metrics, the cold forming method eliminates open-flame hot work, vastly reducing safety hazards. Furthermore, the reduction in weld seams directly shortens the schedule for Non-Destructive Examination (NDE), providing extremely high handover efficiency for compliance sign-offs during the commissioning phase.

九、 CCPP 3D/5D 彎徑在潁璋工程三合一工法實務效益/IX. Practical Benefits of 3D/5D Bend Radii in CCPP Using the Ying Zhang Engineering Three-in-One Method

針對 CCPP 高能管線需求，潁璋工程所提出之「CNC冷彎 + IH-PBHT + 數位履歷」三合一工法展現了卓越效益42。Addressing the demands of high-energy piping in CCPP, the “Three-in-One Method” (CNC Cold Bending + IH-PBHT + Digital Resume) proposed by Ying Zhang Engineering demonstrates outstanding practical benefits42.

  1. CNC 冷作彎曲成型：嚴密監控成型應變率與橢圓度，平順引導熱膨脹位移並降低 20%~30% 的流體壓降42。CNC Cold Bending: Forming strain rates and ovality are strictly monitored, smoothly guiding thermal expansion displacement and reducing fluid pressure drop by 20% to 30%42.
  2. 亞臨界彎後熱處理（IH-PBHT）：精準實施 760°C 的感應加熱，並透過處理後的硬度確證防範相變不足或過度回火風險42。Subcritical Induction Heating PBHT (IH-PBHT): Induction heating at exactly 760°C is implemented, with post-treatment hardness verification preventing the risks of incomplete phase transformation or over-tempering42.
  3. 數位化履歷建檔：將製程參數全面數位化並綁定 QR Code，達成高度製程追溯性，完美契合 ASME 規範的高標準驗收要求42。Digital Resume Archiving: All process parameters are comprehensively digitized and linked with QR codes to achieve a high degree of process traceability, perfectly aligning with the stringent acceptance requirements of ASME codes42.

十、 結論/X. Conclusion

本研究確立了 ASME B31.1 PBHT 強制法規與 B31J 應力評估模型之間的深層耦合關係，核心結論如下：This study establishes the deep coupling relationship between the ASME B31.1 mandatory PBHT codes and B31J stress evaluation models. The core conclusions are:

  1. P92 冷彎劣化與修復：3D/5D 冷作劇烈應變會摧毀次晶界網絡並加速 Laves 相粗化。必須依據規範執行次臨界熱處理或完全的正常化與回火（N&T），以重構回火馬氏體並恢復潛變強度。P92 Cold Bending Degradation and Restoration: The severe strain of 3D/5D cold bending destroys sub-boundary networks and accelerates Laves phase coarsening. Subcritical heat treatment or full N&T must be executed according to codes to reconstruct tempered martensite and restore creep strength.
  2. 316LN 敏化與固溶退火：冷作誘發的馬氏體與滑移帶導致鉻原子快速擴散並引發晶界腐蝕。為確保完整性，實施 1050°C 以上的固溶退火 PBHT 具有絕對的冶金必要性。316LN Sensitization and Solution Annealing: Cold-induced martensite and slip bands cause rapid diffusion of chromium atoms, triggering intergranular corrosion. To ensure integrity, performing solution annealing PBHT above 1050°C is an absolute metallurgical necessity.
  3. B31J 力學模型優勢與限制：大半徑彎管具備極低的疲勞應力集中效應，但也揭示了其柔性因子較低、剛性較大的特徵，設計者需充分考量熱膨脹推力效應。Advantages and Limitations of B31J Mechanical Models: Large-radius bends feature extremely low fatigue stress concentration effects but also exhibit lower flexibility factors and higher rigidity. Designers must fully account for the effects of thermal expansion thrusts.
  4. 冶金與力學之深層統一：嚴格遵照 ASME B31.1 執行 PBHT，不僅是滿足冶金法規底線，更是確保 B31J 應力分析演算法在工程實務中具備物理真實性之唯一途徑。Deep Unification of Metallurgy and Mechanics: Strictly executing PBHT in compliance with ASME B31.1 is not only the regulatory baseline for metallurgy but also the sole pathway to ensuring the physical authenticity of B31J stress analysis algorithms in engineering practice.

參考文獻

  1. Coal Power Plant Materials And Life Assessment – VDOC.PUB, https://vdoc.pub/documents/coal-power-plant-materials-and-life-assessment-developments-and-applications-5c5poetuu6n0
  2. Mono3 2001 | PDF | Steel | Fusion Power – Scribd, https://www.scribd.com/document/577478625/MONO3-2001
  3. high-strength martensitic steel: Topics by Science.gov, https://www.science.gov/topicpages/h/high-strength+martensitic+steel
  4. Effects of sensitization on intergranular corrosion and mechanical, https://www.researchgate.net/publication/392178378_Effects_of_sensitization_on_intergranular_corrosion_and_mechanical_properties_of_316LN_stainless_steel
  5. Relationship between Pitting and Intergranular Corrosion … – J-Stage, https://www.jstage.jst.go.jp/article/isijinternational1989/36/7/36_7_799/_article
  6. Homogenization of P91 weldments using varying normalizing and, https://www.researchgate.net/publication/320621164_Homogenization_of_P91_weldments_using_varying_normalizing_and_tempering_treatment
  7. (EngineeringEBookspdf) Failure Investigation of Bolier PDF – Scribd, https://www.scribd.com/document/441765921/EngineeringEBookspdf-Failure-Investigation-of-Bolier-1-pdf
  8. The effect of aging on the microstructure and mechanical behavior of, https://www.researchgate.net/publication/273288374_The_effect_of_aging_on_the_microstructure_and_mechanical_behavior_of_the_alumina-forming_austenitic_stainless_steel_Fe-20Cr-30Ni-2Nb-5Al
  9. dynamic creep test: Topics by Science.gov, https://www.science.gov/topicpages/d/dynamic+creep+test
  10. Effects of cooling rates on δ-ferrite/γ-austenite formation and, https://www.researchgate.net/publication/317260587_Effects_of_cooling_rates_on_d-ferriteg-austenite_formation_and_martensitic_transformation_in_modified_ferritic_heat_resistant_steel
  11. The Use of Portable Hardness Testing in Field | PDF – Scribd, https://www.scribd.com/document/508599387/The-Use-of-Portable-Hardness-Testing-in-Field
  12. Effect of Cold Deformation on Microstructures and Mechanical, https://www.mdpi.com/2075-4701/8/7/522
  13. Deformation induced martensite in AISI 316 stainless steel, https://pdfs.semanticscholar.org/8e9f/a0dac87d22f207a72035face410aa93b8540.pdf
  14. Influence of 40% Cold Working and Annealing on Precipitation in, https://pmc.ncbi.nlm.nih.gov/articles/PMC9505488/
  15. Influence of 40% Cold Working and Annealing on Precipitation in, https://www.researchgate.net/publication/363674213_Influence_of_40_Cold_Working_and_Annealing_on_Precipitation_in_AISI_316L_Austenitic_Stainless_Steel
  16. (PDF) Intergranular corrosion of deformed SS304 – Academia.edu, https://www.academia.edu/96319576/Intergranular_corrosion_of_deformed_SS304
  17. Stabilization and sensitization of stainless steels (Book) | OSTI.GOV, https://www.osti.gov/biblio/548573
  18. (PDF) Assessment of intergranular corrosion in AISI Type 316L, https://www.researchgate.net/publication/233697652_Assessment_of_intergranular_corrosion_in_AISI_Type_316L_stainless_steel_weldments
  19. EPR Method versus ASTM A262 Practice E for Measuring DOS in, https://discovery.researcher.life/article/epr-method-versus-astm-a262-practice-e-for-measuring-dos-in-austenitic-stainless-steels/01e0221b6d403b99928f59748d3a67e9
  20. The Effects of Cold Working on Sensitization and Intergranular, https://www.researchgate.net/publication/225699294_The_Effects_of_Cold_Working_on_Sensitization_and_Intergranular_Corrosion_Behavior_of_AlSl_304_Stainless_Steel
  21. Effect of Sigma Phase on Fracture Behavior of Steels and Weld, https://www.intechopen.com/chapters/57563
  22. Influence of Thermal Cycling Temperature on the Recrystallization of, https://www.researchgate.net/publication/346189347_Influence_of_Thermal_Cycling_Temperature_on_the_Recrystallization_of_Cold_Rolled_Stainless_Steel_316L
  23. 1, POWER PIPING – ASME Digital Collection, https://asmedigitalcollection.asme.org/ebooks/book/chapter-pdf/2793221/802183_ch16.pdf
  24. ASME B31.1-2016 – Standards Michigan, https://standardsmichigan.com/wp-content/uploads/2018/01/Proposed-Revision-of-B31.X-Power-Piping-Public-Review-Draft-2346.pdf
  25. Power Piping ASME Code for Pressure Piping, B31 – Academia.edu, https://www.academia.edu/32405461/Power_Piping_ASME_Code_for_Pressure_Piping_B31
  26. Power Piping ASME Code for Pressure Piping, B31 – pdfcoffee.com, https://pdfcoffee.com/power-piping-asme-code-for-pressure-piping-b31-2-pdf-free.html
  27. Power Piping ASME Code for Pressure Piping, B31 – pdfcoffee.com, https://pdfcoffee.com/power-piping-asme-code-for-pressure-piping-b31-pdf-free.html
  28. ANSI/ASME B31.1, “Power Piping” American National Standard, https://www.nrc.gov/docs/ML0314/ML031470592.pdf
  29. ASME B31.1-2020 Power Piping Code – Studylib, https://studylib.net/doc/25824675/asme-b31.1-2020-power-piping
  30. ASME B31.1-2016 Power Piping Code – studylib.net, https://studylib.net/doc/26181325/asme—asme-b31.1-power-piping–2016-
  31. ASME B31.1 Power Piping Code 2024: Design & Standards – Studylib, https://studylib.net/doc/27709358/asme-b31-1-2024year
  32. ASME BPVC Code Cases 2025: Boiler & Pressure Vessel Standards, https://studylib.net/doc/28045423/asme-bpvc-code-cases-2025–bpvc.cc.bpv-2025
  33. ASME Boiler & Pressure Vessel Code Cases 2023 – Studylib, https://studylib.net/doc/27155445/asme-code-case-2023
  34. ASME B31.1-2022 Power Piping Code – studylib.net, https://studylib.net/doc/28370349/asme-b31.1
  35. Low Temperature Sensitization in Stainless Steel | PDF – Scribd, https://www.scribd.com/document/490564780/11-6
  36. Stress Intensity Factor (SIF), Flexibility Factor: ASME B31.3 vs ASME, https://whatispiping.com/stress-intensity-factor-sif-flexibility-factor-asme-b-31j/
  37. Mastering ASME B31J Piping Stress Analysis for Plant Integrity, https://epcland.com/asme-b31j-piping-stress-analysis/
  38. Welding Tee SIF Calculator — ASME B31.3 Appendix D / B31J, https://pipingtoolset.com/calculators/welding-tee-sif/
  39. SIF and Flexibility Factors per ASME B31.3 | PDF – Scribd, https://pt.scribd.com/document/48457026/SIF-B31-3
  40. Stress Intensification & Flexibility Factor Calculator (B31.3 Appendix D), https://pipingtoolset.com/calculators/b313-stress-intensification-factors/
  41. Alignment of Stress Intensification and Flexibility Factors for the B31, https://asmedigitalcollection.asme.org/HTTPHandlers/ArticlePdfHandler.ashx?journal=PVP2012&multimediaId=4436288
  42. https://yz-pipe-bending.com.tw/%E5%9F%BA%E6%96%BC-asme-b31j-%E8%A6%8F%E7%AF%84%E4%B9%8B-p91-p92-%E9%AB%98%E5%BC%B7%E5%BA%A6%E5%90%88%E9%87%91%E5%86%B7%E4%BD%9C%E5%BD%8E%E7%AE%A1%E5%B7%A5%E6%B3%95%E6%87%89%E5%8A%9B%E8%A7%A3%E6%9E%90/
購物車