基於ASME B31J與流固耦合分析之CCPP高能管線(P91/P92)流體加速腐蝕(FAC)抑制與抗第四型潛變破裂研究：以大林電廠大半徑冷作彎管三合一工法為例 (Research on Flow-Accelerated Corrosion (FAC) Suppression and Type IV Creep Cracking Resistance in CCPP High-Energy Piping (P91/P92) Based on ASME B31J and Fluid-Structure Interaction (FSI): A Case Study of the Large-Radius Cold Bending 3-in-1 Methodology at Dalin Power Plant)

/ Uncategorized / 作者:

摘要 / Abstract

在全球能源轉型的浪潮下，複循環發電廠（Combined Cycle Power Plant, CCPP）因需配合高佔比、具間歇性特徵的再生能源併網，其運轉模式已從傳統的基載（Base Load）發電，劇烈轉變為具備極高升降載率的深度調峰（Peak Shaving）機組。此種頻繁的冷態、溫態與熱態啟停操作，使得廠內高能管線系統（High-Energy Piping, HEP）承受著前所未有的暫態熱力學交變應力與流體動力學脈動。傳統的高能管線佈局高度依賴符合ASME B16.9標準的1.5D短半徑對銲彎頭；然而，在潛變強度增強型鐵素體鋼（Creep Strength Enhanced Ferritic Steels, CSEF，如ASTM A335 P91、P92）的應用實務中，此類幾何突變特徵與銲接熱影響區（Heat-Affected Zone, HAZ）的物理疊加，極易誘發極具毀滅性的第四型潛變破裂（Type IV Creep Cracking）與流體加速腐蝕（Flow-Accelerated Corrosion, FAC）。Under the wave of global energy transition, Combined Cycle Power Plants (CCPP) must integrate with a high proportion of intermittent renewable energy. Consequently, their operational mode has drastically shifted from traditional base-load generation to deep peak-shaving units with extremely high ramp rates. Such frequent cold, warm, and hot startup/shutdown operations subject the plant’s High-Energy Piping (HEP) systems to unprecedented transient thermodynamic alternating stresses and fluid dynamic pulsations. Traditional HEP layouts rely heavily on 1.5D short-radius butt-welded elbows compliant with the ASME B16.9 standard; however, in the practical application of Creep Strength Enhanced Ferritic Steels (CSEF, e.g., ASTM A335 P91, P92), the physical superimposition of these abrupt geometric features and the welding Heat-Affected Zone (HAZ) is highly prone to inducing devastating Type IV Creep Cracking and Flow-Accelerated Corrosion (FAC).

本研究報告以大林電廠CCPP專案的高能管線系統為實證分析對象，深度剖析業界已落實採用（如興達與台中CCPP專案）之「傳統銲道去銲接化與大半徑冷作彎管三合一工法」應用於該專案的學理機制與預期效益。研究基於2024至2026年最新版ASME B31J規範的應力強度因子（SIF）解耦矩陣、Joukowsky暫態水錘波動方程式、Sanchez-Caldera流體質量傳遞模型，以及Coffin-Manson低週疲勞失效定律，進行跨領域的流固耦合（FSI）與微觀冶金學分析。綜合分析表明，針對大林電廠專案若導入5D數控大半徑冷作彎管並輔以精密控制的次臨界彎後熱處理（Subcritical PBHT），不僅能從流體動力學的物理根源上消弭FAC與暫態水錘的破壞能量，更能徹底截斷第四型潛變破裂的微觀演化路徑，將管系的熱疲勞壽命延長數個數量級，為現代調峰電廠高能管線的結構完整性與全生命週期管理提供最佳化的工程評估範式。This research report takes the HEP system of the Dalin CCPP project as an empirical analysis subject, deeply analyzing the theoretical mechanisms and expected benefits of applying the 3-in-1 methodology of “traditional weld elimination and large-radius cold bending”—which has already been implemented in the industry (e.g., Hsinta and Taichung CCPP projects)—to this specific project. The study is based on the Stress Intensification Factor (SIF) decoupling matrix of the latest 2024-2026 ASME B31J code, the Joukowsky transient water hammer wave equation, the Sanchez-Caldera fluid mass transfer model, and the Coffin-Manson low-cycle fatigue failure law, conducting cross-disciplinary Fluid-Structure Interaction (FSI) and microscopic metallurgical analyses. The comprehensive analysis indicates that introducing 5D CNC large-radius cold bends supplemented by precisely controlled Subcritical Post-Bend Heat Treatment (Subcritical PBHT) to the Dalin power plant project will not only eliminate the destructive energy of FAC and transient water hammer at the physical root of fluid dynamics, but also completely cut off the micro-evolutionary path of Type IV creep cracking. This extends the thermal fatigue life of the piping system by several orders of magnitude, providing an optimized engineering evaluation paradigm for the structural integrity and lifecycle management of HEP in modern peak-shaving power plants.

一、 現代CCPP高能管線系統面臨之多重物理挑戰 / I. Multiple Physical Challenges Faced by Modern CCPP High-Energy Piping Systems

在現代化超超臨界（Ultra-Supercritical, USC）火力發電廠與先進CCPP機組中，主蒸汽（Main Steam）與高溫再熱蒸汽（Hot Reheat Steam）管線扮演著維繫全廠能量傳輸命脈的關鍵角色。為因應高達600°C以上的極端熱力學工況並同時減輕系統自重，工程界廣泛採用潛變強度增強型鐵素體耐熱鋼（如P91、P92）。這類9-12%鉻系合金的卓越高溫強度，源自於其經過嚴格正火與回火（Normalizing and Tempering, N&T）處理後，於回火馬氏體（Tempered Martensite）板條邊界與晶粒內部析出的極細微碳氮化物（如M23C6碳化物與奈米級的MX相，包含NbC與VN）1。這些析出相透過Zener釘紮效應（Zener Pinning Effect），在微觀尺度上強烈阻礙了高溫環境下的位錯滑移（Dislocation Glide）與晶界滑動（Grain Boundary Sliding），賦予材料優異的抗潛變能力1。 In modern Ultra-Supercritical (USC) thermal power plants and advanced CCPP units, the Main Steam and Hot Reheat Steam piping play a critical role in maintaining the energy transmission lifeline of the entire plant. To cope with extreme thermodynamic conditions exceeding 600°C while simultaneously reducing system weight, the engineering sector widely adopts Creep Strength Enhanced Ferritic Steels (e.g., P91, P92). The superior high-temperature strength of these 9-12% chromium alloys originates from the extremely fine carbonitrides (such as M23C6 carbides and nano-scale MX phases, including NbC and VN) precipitated at the tempered martensite lath boundaries and inside the grains after strict Normalizing and Tempering (N&T) treatments1. Through the Zener Pinning Effect, these precipitates strongly impede dislocation glide and grain boundary sliding at high temperatures on a microscopic scale, endowing the material with excellent creep resistance1.

然而，在實際工程應用中，管線系統的轉向與分支不可避免。過去數十年間，管線工程界習慣沿用傳統的1.5D短半徑電銲彎頭配合直管進行現場銲接拼裝4。這種基於「拼接」的設計思維，在現代機組頻繁啟停的動態負載下，暴露出了嚴重的物理與冶金學缺陷。在穩態滿載運轉時，管線主要面臨長時間高溫應力下的均勻穩態潛變；但在頻繁調峰與低負載運轉過程中，管線內部過熱蒸氣與金屬管壁之間會在極短時間內產生巨大的溫度梯度，誘發強烈的過渡熱應力（Transient Thermal Stress）與熱衝擊（Thermal Shock）6。 However, in practical engineering applications, changes in direction and branching of piping systems are inevitable. Over the past decades, the piping engineering community has habitually used traditional 1.5D short-radius butt-welded elbows combined with straight pipes for on-site welding assembly4. Under the dynamic loads of frequent startup and shutdown in modern units, this “splicing-based” design mindset has exposed severe physical and metallurgical flaws. During steady-state full-load operation, the piping primarily faces uniform steady-state creep under long-term high-temperature stress; however, during frequent peak shaving and low-load operations, an enormous temperature gradient is generated between the superheated steam inside the pipe and the metal pipe wall in an extremely short time, inducing strong transient thermal stress and thermal shock6.

在巨觀力學層次，1.5D短半徑彎頭因其急促的幾何轉向，在熱膨脹位移的推擠下會產生嚴重的截面畸變（Ovalization），形成巨大的應力集中熱點9。在流體動力學層次，高速雙相流體經過急彎時會誘發強烈的二次渦流與流場分離，直接剝離管壁的保護性氧化膜，觸發流體加速腐蝕（FAC）6。在微觀冶金層次，現場環向銲縫（Girth Weld）的熱循環不可逆地破壞了P91/P92母材極度敏感的強化相結構，形成了脆弱的熱影響區（HAZ），成為第四型潛變破裂的溫床3。此三大破壞機制的交互作用（Synergistic Interaction），使得傳統高能管線在調峰電廠中的實際服役壽命往往遠低於設計預期。為徹底突破此一瓶頸，本研究針對大林電廠CCPP專案進行學理分析，評估導入業界已落實採用之「以彎代銲」大半徑冷作彎管三合一工法的可行性。 At the macroscopic mechanical level, the 1.5D short-radius elbow generates severe cross-sectional ovalization under the push of thermal expansion displacement due to its abrupt geometric turn, forming massive stress concentration hotspots. At the fluid dynamics level, high-speed two-phase fluids passing through sharp bends induce strong secondary vortices and flow separation, directly stripping the protective oxide film on the pipe wall and triggering Flow-Accelerated Corrosion (FAC) 6. At the microscopic metallurgical level, the thermal cycle of on-site girth welds irreversibly destroys the extremely sensitive strengthening phase structure of the P91/P92 base metal, forming a fragile Heat-Affected Zone (HAZ) that becomes a hotbed for Type IV creep cracking3. The synergistic interaction of these three major failure mechanisms often causes the actual service life of traditional high-energy piping in peak-shaving power plants to fall far short of design expectations. To completely break through this bottleneck, this study conducts a theoretical analysis on the Dalin CCPP project, evaluating the feasibility of introducing the 3-in-1 methodology of “bending instead of welding” with large-radius cold bends, which is already applied in the industry.

二、 基於ASME B31J規範之管線應力解耦與彈性力學最佳化 / II. Piping Stress Decoupling and Elasticity Optimization Based on ASME B31J

長達半個世紀以來，全球動力管線應力分析多依賴ASME B31.1或B31.3附錄D（Appendix D），採用1950年代由A.R.C. Markl所建立的疲勞方程式進行管系柔性分析。Markl以直管的周向對銲銲道為基準（設定其應力強度因子SIF為1.0），並透過薄壁管件的彎曲疲勞實驗，推導出描述疲勞破壞行為的經典關係式10： For half a century, global power piping stress analysis has heavily relied on ASME B31.1 or B31.3 Appendix D, utilizing the fatigue equations established by A.R.C. Markl in the 1950s for piping flexibility analysis. Setting a straight pipe with a circumferential girth weld as the baseline (with a Stress Intensification Factor, SIF, of 1.0), Markl derived the classic relationship describing fatigue failure behavior through bending fatigue experiments on thin-walled components10:

i⋅Sa=245,000⋅N-0.2

其中，i為應力強度因子（Stress Intensification Factor, SIF），Sa為疲勞裂紋萌生處的標稱應力振幅，N為引發疲勞破壞的循環次數。Where i is the Stress Intensification Factor (SIF), Sa is the nominal stress amplitude at the site of fatigue crack initiation, and N is the number of cycles to fatigue failure.

2.1 傳統Markl理論的盲點與B31J的革命性解耦 / 2.1 Blind Spots of Traditional Markl Theory and the Revolutionary Decoupling of B31J

舊版規範在處理彎頭等管件時，強制賦予單一的純量SIF值，並將扭轉應力強度因子預設為1.0，完全忽略了面內（In-Plane）與面外（Out-of-Plane）彎矩在引發彎管截面橢圓化時，其物理變形機制的本質差異9。傳統1.5D彎頭的SIF值極高（常介於3.0至5.0之間），這種將多維度應力粗暴疊加的做法，不僅掩蓋了真實的斷裂風險熱點，更迫使工程設計端為了解決計算軟體中虛假的「應力超標」，而過度依賴龐大的膨脹環與剛性支撐系統，導致建置成本與空間佔用大幅膨脹9。 When handling components like elbows, legacy codes mandatorily assigned a single scalar SIF value and defaulted the torsional stress intensification factor to 1.0, completely ignoring the essential differences in physical deformation mechanisms caused by in-plane and out-of-plane bending moments during cross-sectional ovalization9. Traditional 1.5D elbows have extremely high SIF values (often between 3.0 and 5.0). This crude superposition of multi-dimensional stresses not only masks true fracture risk hotspots but also forces engineering designers to over-rely on massive expansion loops and rigid support systems to resolve false “stress exceedance” in calculation software, leading to drastically inflated construction costs and spatial footprints9.

ASME B31J規範的強制導入與附錄D的廢除，標誌著管線力學分析的典範轉移。該規範透過大規模的物理實驗與高解析度有限元素分析（FEA）數據校正，提出了高精度的SIF解耦演算法，並為管線工程引入了「柔性特徵值」（Flexibility Characteristic, h）的核心概念11。對於彎管，其定義方程式為2： The mandatory implementation of the ASME B31J code and the abolition of Appendix D mark a paradigm shift in piping mechanical analysis. Through large-scale physical experiments and high-resolution Finite Element Analysis (FEA) data calibration, this code proposes a high-precision SIF decoupling algorithm and introduces the core concept of the “Flexibility Characteristic” (h) to piping engineering11. For bends, its defining equation is2:

h=T⋅R1/r22

方程式中，T代表彎管之公稱壁厚（Nominal Wall Thickness），R1為彎曲中心半徑（Bend Radius），r2則是連接直管之平均截面半徑 (Do-T)/2。In the equation, T represents the nominal wall thickness of the bend, R1 is the bend radius, and r2 is the mean cross-sectional radius of the matching straight pipe (Do-T)/2.

基於此幾何特徵值，B31J（Table 1-1）將彎頭的SIF與柔性因子（Flexibility Factor, k）進行了嚴密的空間向量解耦：Based on this geometric characteristic value, B31J (Table 1-1) performs strict spatial vector decoupling of the SIF and flexibility factor (k) for elbows:

  • 面內應力強度因子 / In-Plane SIF (ii)：當彎矩作用於彎管幾何平面內，導致彎頭產生張角「打開（Opening）」或「閉合（Closing）」變形趨勢時所引發的應力集中。公式修訂為 ii=0.9/h2/3，且下限不得低於0。 / Stress concentration induced when a bending moment acts within the geometric plane of the bend, causing the elbow to tend to deform by “opening” or “closing”. The formula is revised to ii=0.9/h2/3, with a minimum floor of 1.0. [cite: 2, 18, 19]
  • 面外應力強度因子 / Out-of-Plane SIF (io)：當彎矩的作用向量垂直於彎管平面，迫使管件發生橫向扭曲時應用的係數。公式修訂為io=0.75/h2/3，下限為0。 / The factor applied when the action vector of the bending moment is perpendicular to the bend plane, forcing the component to undergo lateral twisting. The formula is revised to io=0.75/h2/3 , with a floor of 1.0. [cite: 2, 9, 19]
  • 扭轉應力強度因子 / Torsional SIF (it)：B31J規範首次強制將三維空間的扭轉剪力集中正式納入位移應力範圍計算，精確反映真實應力狀態，這對於評估管網熱膨脹轉移至末端旋轉機械（如高壓汽輪機）的噴嘴荷重（Nozzle Loads）至關重要。 / For the first time, the B31J code mandatorily incorporates 3D torsional shear stress concentration into the displacement stress range calculation to accurately reflect the true stress state. This is crucial for evaluating nozzle loads transferred from pipe network thermal expansion to terminal rotating machinery (e.g., high-pressure steam turbines). [cite: 2, 9, 16]
  • 柔性因子 / Flexibility Factor (k)：量化管件吸收位移的能力，公式為 k=1.65/h。 / Quantifies the component’s ability to absorb displacement; the formula is k=1.65/h. [cite: 9, 11, 18]

2.2 B31.1位移應力範圍與持續應力指數(SSI)之實務應用 / 2.2 Practical Application of B31.1 Displacement Stress Range and Sustained Stress Index (SSI)

在最新版的ASME B31.1規範中，第104.8.3節的位移應力範圍（Displacement Stress Range, SE）計算式已全面對接B31J的全套方向性SIF2： In the latest edition of the ASME B31.1 code, the calculation equation for the Displacement Stress Range (SE) has been fully aligned with the complete set of directional SIFs from B31J2:

SE=√((iiMi)2+(ioMo)2+(itMt)2)/Z

其中，Z為管件的淨截面模數。此方程式的空間解耦，消除了方向疊加導致的虛假應力超標，精確定位了真實疲勞熱點。Where Z is the net section modulus of the fitting. The spatial decoupling in this equation eliminates false stress exceedances caused by directional superposition and precisely locates true fatigue hotspots.

此外，在評估由自重與內壓產生的持續應力（Sustained Stress, SL）時，B31J引入了持續應力指數（Sustained Stress Index, SSI）的概念2。規範明定，SSI的取值為max(0.75i,1.0) 21。0.75的折減係數反映了靜態持續負載產生的是一次性應力，而非疲勞交變應力；而下限1.0則確保元件強度的評估不會低於直管2。在舊版規範中，工程師被迫將巨大的疲勞SIF直接套用於持續負載，導致防止管線塑性塌陷的壁厚設計變得極度保守。B31J的SSI解耦機制，大幅減少了材料過度設計，賦予了管線佈局更高的工程彈性2。 Additionally, when evaluating sustained stress (SL) generated by dead weight and internal pressure, B31J introduces the concept of the Sustained Stress Index (SSI) 2. The code stipulates that the SSI value is max(0.75i,1.0) 21. The 0.75 reduction factor reflects that static sustained loads generate a one-time stress rather than a fatigue alternating stress; meanwhile, the lower limit of 1.0 ensures that the component’s strength evaluation is never lower than that of a straight pipe2. In legacy codes, engineers were forced to apply massive fatigue SIFs directly to sustained loads, resulting in extremely conservative wall thickness designs intended to prevent plastic collapse. B31J’s SSI decoupling mechanism drastically reduces material over-design, endowing the piping layout with much higher engineering flexibility2.

力學參數與特性 / Mechanical Parameters & Characteristics 傳統1.5D短半徑銲接彎頭 / Traditional 1.5D Welded Elbow 現代5D大半徑冷作彎管 / Modern 5D Large-Radius Cold Bend 大林電廠專案高能管線佈局效益評估 / Benefit Evaluation for Dalin Project
面內/面外 SIF (Ii,Io) / In-Plane/Out-of-Plane SIF 極高（常大於3.0），無方向性區分，將疲勞熱應力強烈放大。 / Extremely high (often >3.0), lacking directionality, strongly amplifying thermal fatigue stress. 極低（趨近於理論下限1.0），精確區分面內外空間方向性應力22。 / Extremely low (approaching theoretical limit 1.0), precisely distinguishing spatial directional stress22. 若導入大林電廠專案，可大幅縮減位移應力 SE，避免疲勞壽命崩潰，消除對龐大膨脹環的需求。 / Introducing to Dalin project dramatically reduces SE, averting fatigue failure & eliminating huge expansion loops.
柔性因子 (k 因子) / Flexibility Factor (k) 相對較低，剛性大，難以有效吸收兩端設備的相對熱位移。 / Relatively low; high rigidity makes it difficult to absorb relative thermal displacements. 隨彎曲半徑 R1 增加而顯著提升，如同彈簧般引導並吸收系統熱膨脹位移22。 / Increases significantly with radius R1, guiding and absorbing thermal expansion like a spring22. 評估可顯著降低恆力彈簧吊架之使用量，並確保汽輪機噴嘴荷重遠低於API 617或NEMA SM23容許值。 / Evaluated to significantly reduce constant spring hangers & keep nozzle loads well below API 617 or NEMA SM23 limits.

由 h 值的構造式可知，當管線佈局由傳統的1.5D短半徑彎頭升級為5D大半徑冷作彎管時，分子中的幾何彎曲半徑 R1 放大了3.3倍，帶動柔性特徵 h 呈線性倍增9。在公式中 h2/3  位於分母的物理效應下，5D冷彎管的面內外SIF值呈幾何級數衰減，趨近於無應力集中的理想直管狀態。這不僅完美通過了B31J的嚴苛檢驗，更成為評估大林電廠CCPP專案中高能管線減壓與熱疲勞壽命延長的最核心力學依據9。 From the structural formula of the h value, it is evident that upgrading the piping layout from a traditional 1.5D short-radius elbow to a 5D large-radius cold bend magnifies the geometric bend radius R1 in the numerator by 3.3 times, driving a linear multiplication of the flexibility characteristic h 9. Under the physical effect of h2/3 being in the denominator, the in-plane and out-of-plane SIF values of the 5D cold bend attenuate exponentially, approaching the ideal stress-concentration-free state of a straight pipe. This not only perfectly passes the rigorous scrutiny of B31J but also serves as the core mechanical basis for evaluating pressure relief and thermal fatigue life extension for high-energy piping in the Dalin CCPP project9.

三、 暫態流體動力學與水錘衝擊之流固耦合(FSI)解析 / III. Transient Fluid Dynamics and Fluid-Structure Interaction (FSI) Analysis of Water Hammer Shock

在CCPP頻繁的調峰操作下，高壓流體系統經常遭遇快速啟停、閥門急關或氣液雙相流的不穩定流動。這些暫態現象會引發強烈的壓力脈衝，即所謂的水錘或蒸汽錘（Water/Steam Hammer）效應。在這種動態負載下，管線幾何突變處（如1.5D彎頭）往往成為流體動力學與結構力學強烈耦合破壞的熱點9。 Under the frequent peak-shaving operations of CCPPs, high-pressure fluid systems often encounter unstable flows caused by rapid startups/shutdowns, sudden valve closures, or gas-liquid two-phase phenomena. These transient events trigger intense pressure pulses, commonly known as water hammer or steam hammer effects. Under such dynamic loads, areas with abrupt geometric changes (like 1.5D elbows) frequently become hotspots for intensely coupled fluid dynamics and structural mechanics failures9.

3.1 Joukowsky波動方程式與應變耦合波 / 3.1 Joukowsky Wave Equation and Strain-Coupled Waves

當管內流速瞬間改變時，壓力波的生成與傳遞可透過經典的Joukowsky水錘方程式進行預測。壓力波峰值（ΔP）可表示為25： When the fluid velocity inside a pipe changes instantaneously, the generation and propagation of the pressure wave can be predicted using the classic Joukowsky water hammer equation. The peak pressure wave (ΔP) can be expressed as25:

ΔP=ρ⋅a⋅Δv

方程式中，ρ 為流體密度，a 為流體中壓力波的傳遞聲速，Δv 為流速瞬間變化量。此瞬間升壓不僅衝擊流體自身，更會透過流固耦合（Fluid-Structure Interaction, FSI）效應，將巨大的能量傳遞至金屬管壁。In the equation, ρ is the fluid density, a is the speed of sound for the pressure wave in the fluid, and Δv is the instantaneous change in fluid velocity. This momentary pressure spike not only impacts the fluid itself but also transfers enormous energy to the metal pipe wall through Fluid-Structure Interaction (FSI) effects.

在管壁中，伴隨壓力波而生的是以材料聲速（aw=√(E/ρw )，其中E為楊氏模數，ρw為管壁密度）傳遞的應力波25。當巨大的內部壓力波撞擊至管線轉向處時，依據Poisson效應與壁厚變形幾何，管壁將產生軸向應變： Accompanying the pressure wave, stress waves propagate through the pipe wall at the material’s speed of sound (aw=√(E/ρw ), where E is Young’s modulus and ρw is the wall density) 25. When a massive internal pressure wave strikes a change in piping direction, the pipe wall will generate axial strain according to the Poisson effect and wall deformation geometry:

ϵ1J=ΔP/2E (D/e-1)

其中，D 為管徑，e 為壁厚。在傳統1.5D彎頭的急彎處，壓力波的透射（Transmission）與反射（Reflection）機制極度複雜，瞬間動量的急遽轉向會對彎頭外弧側產生巨大的不平衡力（Unbalanced Thrust Force）。這種單向或雙向的流固耦合會迫使彎頭產生瞬間的高頻軸向與橫向位移25。當此高頻衝擊波的頻率（透過斯特勞哈爾數評估）與管線結構或相鄰儀表細管的固有聲學/機械頻率重合時，將觸發能量極高的聲學共振（Acoustic Resonance），極易引發銲縫處的高週疲勞斷裂6。 Where D is the pipe diameter and e is the wall thickness. At the sharp turn of a traditional 1.5D elbow, the transmission and reflection mechanisms of the pressure wave are extremely complex. The abrupt redirection of instantaneous momentum exerts a massive Unbalanced Thrust Force on the extrados of the elbow25. This uni-directional or bi-directional fluid-structure interaction forces the elbow into instantaneous, high-frequency axial and lateral displacements. When the frequency of this high-frequency shockwave (evaluated via the Strouhal number) coincides with the inherent acoustic/mechanical frequency of the piping structure or adjacent instrument impulse lines, it triggers highly energetic Acoustic Resonance, easily leading to high-cycle fatigue fractures at the welds6.

相較之下，若改採5D大半徑冷作彎管，其平緩的曲率能使流線緊貼管壁，將流體動量的改變均勻分配於較長的物理距離上。這不僅大幅降低了局部壓力波的反射係數，將瞬間的結構不平衡力降至最低，更從物理上抑制了水錘引發的巨觀結構振動，顯著提升了管線系統在暫態衝擊下的動態穩定性9。 In contrast, if 5D large-radius cold bends are adopted, the gentle curvature allows streamlines to hug the pipe wall closely, evenly distributing the change in fluid momentum over a longer physical distance. This significantly reduces the reflection coefficient of local pressure waves, minimizing instantaneous structural unbalanced forces, and physically suppressing macroscopic structural vibrations induced by water hammer. Consequently, it substantially enhances the dynamic stability of the piping system under transient shocks9.

四、 質量傳遞驅動之流體加速腐蝕(FAC)抑制機制 / IV. Mass Transfer-Driven Flow-Accelerated Corrosion (FAC) Suppression Mechanisms

流體加速腐蝕（Flow-Accelerated Corrosion, FAC）是高能管線（尤其是高壓蒸發器、鍋爐給水與低壓含水蒸氣管線）最致命的破壞機制之一。FAC並非單純由流體物理衝刷所引起的機械性沖蝕（Erosion），而是一種由對流質量傳遞（Convective Mass Transfer）主導、並受電化學反應控制的金屬溶解過程12。 Flow-Accelerated Corrosion (FAC) is one of the most fatal failure mechanisms in high-energy piping (especially high-pressure evaporators, boiler feedwater, and low-pressure wet steam lines). FAC is not merely mechanical Erosion caused by physical fluid scouring; rather, it is a metal dissolution process dominated by convective mass transfer and controlled by electrochemical reactions12.

4.1 氧化膜溶解動力學與Sanchez-Caldera模型 / 4.1 Oxide Film Dissolution Kinetics and the Sanchez-Caldera Model

碳鋼或低合金鋼在高溫（約130°C至150°C之間達到單相流腐蝕峰值）、高壓水溶液中，金屬表面會經由氧化反應生成一層具保護性的雙層磁鐵礦（Magnetite, Fe3O4）薄膜。其基礎化學反應式如下12： In high-temperature (reaching a single-phase flow corrosion peak between approximately 130°C and 150°C), high-pressure aqueous solutions, carbon steel or low-alloy steel surfaces generate a protective dual-layer magnetite (Fe3O4) film through oxidation. The basic chemical reactions are as follows12:

Fe+2H2O→Fe2++2OH–+H2↑

3Fe(OH)2↔Fe3O4↓+2H2O+H2↑

在理想狀態下，金屬氧化成內層細晶氧化物的體積膨脹比（Pilling-Bedworth Ratio）約為2.1，形成緻密的擴散屏障。然而，FAC是一個強烈依賴水化學（如pH值、溶氧量）的過程。在缺氧（Anaerobic）且流速極高的環境中，保護性氧化膜在金屬-氧化物界面生成的速率，無法趕上其在氧化物-流體界面發生還原溶解的速率12。 Under ideal conditions, the volume expansion ratio (Pilling-Bedworth Ratio) of the metal oxidizing into the inner fine-grained oxide is approximately 2.1, forming a dense diffusion barrier. However, FAC is a process heavily dependent on water chemistry (e.g., pH, dissolved oxygen). In anaerobic, extremely high-velocity environments, the rate of protective oxide film generation at the metal-oxide interface cannot keep up with its reductive dissolution rate at the oxide-fluid interface12.

根據麻省理工學院Sanchez-Caldera等人所提出的FAC巨觀質量傳遞模型，金屬氧化膜的溶解速率（JFAC）完全由擴散邊界層的傳質動力學決定30： According to the macroscopic FAC mass transfer model proposed by Sanchez-Caldera et al. at MIT, the dissolution rate of the metal oxide film (JFAC) is completely determined by the mass transfer kinetics of the diffusion boundary layer30:

JFAC=Kc (Ceq-Cb )

方程式中，Kc 為局部質量傳遞係數（Mass Transfer Coefficient），Ceq 為磁鐵礦在該熱力學條件下於固液界面的平衡溶解度（受pH與溫度強烈影響），Cb 為主體流（Bulk Flow）中的鐵離子濃度。In the equation, Kc is the local mass transfer coefficient, Ceq is the equilibrium solubility of magnetite at the solid-liquid interface under those thermodynamic conditions (strongly influenced by pH and temperature), and Cb is the bulk flow iron ion concentration.

4.2 1.5D與5D彎管流場邊界層差異對FAC的影響 / 4.2 The Impact of Boundary Layer Differences Between 1.5D and 5D Bends on FAC

由Sanchez-Caldera模型可知，FAC的減薄速率與傳質係數 Kc 成正比。在流體力學中，Kc 值與管壁表面的壁面剪應力（Wall Shear Stress, WSS, τw）及流場的亂流動能（Turbulence Kinetic Energy）呈高度正相關28。 From the Sanchez-Caldera model, the FAC thinning rate is directly proportional to the mass transfer coefficient Kc. In fluid dynamics, the value of Kc is highly positively correlated with the wall shear stress (WSS, τw) and the turbulence kinetic energy of the flow field28.

當高速高壓流體進入1.5D短半徑彎頭時，流體因強烈的離心力作用向外弧側擠壓，同時在內弧側引發嚴重的流場分離（Flow Separation）。流體通過彎頭後，其流速分佈極度不均勻，進而衍生出高強度的反向二次渦流（即迪恩渦流，Dean Vortices）6。這種極端強烈的局部渦流擾動，不僅直接以機械剪力撕裂脆弱的氧化膜，更會極度壓縮流體邊界層的厚度，導致局部傳質係數 Kc 呈指數級飆升。高濃度的鐵離子被迅速帶離管壁，促使金屬基體持續暴露並加速溶解，最終導致1.5D彎頭外弧或下游區段發生「未漏先破」（Break-before-leak）的毀滅性管壁減薄災難12。對於氣液雙相流（Two-phase Flow）而言，其FAC破壞區域甚至可延伸至流速高達30 m/s以上的區段12。 When high-speed, high-pressure fluid enters a 1.5D short-radius elbow, strong centrifugal forces push the fluid toward the extrados, while severe flow separation is induced at the intrados. After passing the elbow, the velocity distribution is highly non-uniform, spawning high-intensity reverse secondary vortices (Dean Vortices) 6. Such extreme local vortex disturbances not only tear the fragile oxide film with mechanical shear forces but also severely compress the fluid boundary layer thickness, causing the local mass transfer coefficient Kc to spike exponentially12. High concentrations of iron ions are swiftly swept away from the wall, exposing the metal matrix to continuous and accelerated dissolution, ultimately leading to devastating “break-before-leak” wall thinning disasters at the extrados or downstream sections of the 1.5D elbow. For two-phase flows, the FAC damage zone can even extend into sections with velocities exceeding 30 m/s12.

在針對大林電廠專案的分析中，若全面導入5D大半徑數控冷作彎管，其柔緩的曲率半徑能使流體流線緊貼管壁，將狄恩數（Dean Number）控制在極低範圍。流體平順過渡，幾乎徹底消除了流場分離區，並將下游的局部系統壓降大幅減少了20%至30%。流體動態壓力脈動的平息，使得管壁剪應力τw大幅下降，傳質係數 Kc 得以回歸至接近理想直管的安全水平。從Sanchez-Caldera質傳動力學的物理根源上，5D冷彎管拔除了FAC的生成條件，確保了管壁厚度的長期穩定性6。 In the analysis of the Dalin power plant project, if 5D large-radius CNC cold bends are fully implemented, their gentle curvature allows fluid streamlines to hug the pipe wall closely, controlling the Dean Number within an extremely low range. The smooth fluid transition virtually eliminates flow separation zones and reduces local downstream system pressure drops by 20% to 30%. The pacification of fluid dynamic pressure pulsations drastically reduces wall shear stress τw, allowing the mass transfer coefficient Kc to return to safe levels comparable to an ideal straight pipe. By addressing the physical root of Sanchez-Caldera mass transfer kinetics, the 5D cold bend eradicates the conditions for FAC generation, ensuring long-term wall thickness stability6.

五、 P91/P92微觀冶金學演變與第四型潛變破裂(Type IV)防制 / V. P91/P92 Micro-Metallurgical Evolution and Type IV Creep Cracking Prevention

解決了巨觀的應力集中與流場擾動後，必須將視角縮小至奈米級的微觀晶體結構，方能理解為何傳統銲接工法在現代高能管線中不再適用。P91與P92等CSEF合金之高溫強度，建構於極度敏感的熱處理歷史上。Having resolved macroscopic stress concentration and flow disturbances, the perspective must be narrowed down to the nano-scale micro-crystal structure to understand why traditional welding methods are no longer viable in modern high-energy piping. The high-temperature strength of CSEF alloys like P91 and P92 is built upon an extremely sensitive heat treatment history.

5.1 銲接熱影響區(HAZ)的微觀劣化機制 / 5.1 Micro-Degradation Mechanisms of the Heat-Affected Zone (HAZ)

在傳統管線的現場環向銲接（Girth Weld）過程中，銲道周圍的母材會經歷快速的極端熱循環，形成複雜的熱影響區（HAZ）。依據峰值溫度的不同，HAZ可細分為粗晶區（CGHAZ）、細晶區（FGHAZ）與臨界熱影響區（ICHAZ）35。在工程實務與失效分析中，最致命的破壞幾乎皆發生於FGHAZ與ICHAZ的交界處。 During the on-site girth welding process of traditional piping, the base metal surrounding the weld undergoes rapid, extreme thermal cycles, forming a complex Heat-Affected Zone (HAZ). Based on peak temperatures, the HAZ is subdivided into the Coarse Grain HAZ (CGHAZ), Fine Grain HAZ (FGHAZ), and Intercritical HAZ (ICHAZ) 35. In engineering practice and failure analysis, the most fatal damage almost always occurs at the boundary between the FGHAZ and ICHAZ.

在此狹窄區域，材料經歷了介於下臨界溫度（AC1）與上臨界溫度（AC3）之間的峰值溫度（約850°C至950°C）。此溫度區間會導致材料發生「不完全奧氏體化」（Incomplete Austenitization）2。原本在高溫回火階段建立的穩定馬氏體板條會發生回復現象，晶粒大幅細化導致晶界總面積增加；更為致命的是，提供強大Zener釘紮效應的奈米級MX相（NbC, VN）發生溶解，而原本分佈於晶界的 M23C6 碳化物則發生嚴重的粗化與聚集（Coarsening and Agglomeration）2。此外，銲接熱應力與冷卻過程可能誘發Laves相（富鎢、鉬的金屬間化合物）的異常析出與長大，進一步消耗基體中的固溶強化元素3。這一切微觀冶金劣化，導致該區域的抗潛變能力發生斷崖式下降。 In this narrow region, the material experiences peak temperatures between the lower critical temperature (AC1) and the upper critical temperature (AC3) (approx. 850°C to 950°C) 2. This temperature range causes “Incomplete Austenitization” of the material. The stable martensitic laths established during high-temperature tempering undergo recovery, and drastic grain refinement increases the total grain boundary area. Even more fatally, the nano-scale MX phases (NbC, VN) providing the strong Zener pinning effect dissolve, while the M23C6 carbides distributed along grain boundaries undergo severe coarsening and agglomeration2. Furthermore, welding thermal stresses and cooling processes may induce anomalous precipitation and growth of Laves phases (W- and Mo-rich intermetallic compounds), further depleting solid-solution strengthening elements in the matrix3. All these microscopic metallurgical degradations cause a cliff-like drop in the area’s creep resistance.

5.2 潛變裂紋的成核與第四型破裂的演化 / 5.2 Nucleation of Creep Cracks and Evolution of Type IV Cracking

在高溫長期服役以及CCPP頻繁調峰產生的龐大三軸拉伸應力（Triaxial Tensile Stress）交互驅動下，粗化碳化物與基體之間的相界會因應力集中與「彈性隨動」（Elastic follow-up）效應，快速成核形成微觀潛變空洞（Creep Voids）3。隨著時間推移，這些空洞會沿著脆弱的細小晶界彼此串聯，形成微觀裂紋，最終演變為學界與業界聞之色變的第四型潛變破裂（Type IV Creep Cracking）3。 Driven by the interaction of long-term high-temperature service and the massive Triaxial Tensile Stress generated by frequent CCPP peak-shaving, the phase boundaries between the coarsened carbides and the matrix rapidly nucleate into micro creep voids due to stress concentration and “elastic follow-up” effects. Over time, these voids coalesce along the fragile, fine grain boundaries to form microcracks, ultimately evolving into the dreaded Type IV Creep Cracking widely feared in academia and industry3.

基於斷裂力學，潛變裂紋的擴展速率（Creep Crack Growth, CCG）可透過 C* 積分與NSW（Nikbin-Smith-Webster）理論模型進行評估11。國內外大量的CT（Compact Tension）試驗與EPRI（美國電力研究院）的研究數據皆證實，針對相同等級的 C* 破裂參數，P91/P92材料熱影響區的裂紋擴展速率，往往高達未受影響母材的兩倍以上39。此類裂紋極具隱蔽性，通常從管壁內部深處萌生並向外擴展，在引發災難性破裂前，管件表面幾乎不會出現任何可察覺的巨觀塑性變形，極易導致未漏先破的慘劇2。 Based on fracture mechanics, Creep Crack Growth (CCG) rates can be evaluated using the C* integral and the NSW (Nikbin-Smith-Webster) theoretical model11. Extensive Compact Tension (CT) tests worldwide and research data from EPRI (Electric Power Research Institute) confirm that for a given C* fracture parameter, the crack growth rate in the HAZ of P91/P92 materials is often more than twice that of the unaffected base metal39. Such cracks are highly insidious, typically initiating deep within the pipe wall and propagating outward. Before causing a catastrophic rupture, the component’s surface rarely shows any perceptible macroscopic plastic deformation, making it extremely likely to trigger break-before-leak disasters2.

六、 潛變-疲勞交互作用與Coffin-Manson失效模型 / VI. Creep-Fatigue Interaction and the Coffin-Manson Failure Model

在CCPP的調峰循環操作中，管線材料的失效不再由單一的恆溫潛變（Time-dependent）或單純的疲勞（Cycle-dependent）所主導，而是兩者產生了高度破壞性的「潛變-疲勞交互作用（Creep-Fatigue Interaction）」6。 In CCPP peak-shaving cyclic operations, the failure of piping materials is no longer dominated by singular time-dependent constant-temperature creep or cycle-dependent pure fatigue, but rather by a highly destructive “Creep-Fatigue Interaction” between the two6.

基於工程臨界評估（Engineering Critical Assessment, ECA），材料的高溫低週疲勞（LCF）壽命可透過Coffin-Manson關係式進行精確量化6： Based on Engineering Critical Assessment (ECA), the high-temperature Low-Cycle Fatigue (LCF) life of materials can be precisely quantified via the Coffin-Manson relation6:

Δϵp/2=ϵf‘(2Nf )c

方程式中，Δϵp/2 為局部塑性應變幅，2Nf 為失效反轉次數（疲勞壽命），ϵf‘ 為疲勞延性係數，c 為疲勞延性指數（通常為負值，落於-0.4至-0.8的區間）。In the equation, Δϵp/2 is the local plastic strain amplitude, 2Nf is the number of reversals to failure (fatigue life), ϵf‘ is the fatigue ductility coefficient, and c is the fatigue ductility exponent (usually a negative value, falling between -0.4 and -0.8).

這個負指數特徵揭示了一個嚴酷的力學現實：材料的熱疲勞壽命對於局部塑性應變幅極度敏感。傳統1.5D彎頭所攜帶的極高應力強度因子（幾何弱點），在空間上精準疊加在極度脆弱的ICHAZ/FGHAZ（冶金弱點）上。這使得管系在機組冷熱啟動過程中產生的微小整體位移應變，在銲縫處被指數級放大為巨大的局部塑性應變幅 Δϵp。 This negative exponent characteristic reveals a harsh mechanical reality: the thermal fatigue life of a material is extremely sensitive to the local plastic strain amplitude. The ultra-high SIF carried by the traditional 1.5D elbow (geometric weakness) spatially overlaps exactly with the extremely fragile ICHAZ/FGHAZ (metallurgical weakness). This causes the minute global displacement strains generated during cold/hot startups of the unit to be exponentially amplified into massive local plastic strain amplitudes (Δϵp) at the welds.

在ASTM E2714-09等高溫材料測試標準下，導入保載時間（Hold-time）的潛變-疲勞試驗表明，低週疲勞循環所產生的晶格滑移帶（Slip Bands），會為潛變孔洞提供絕佳的成核位置。疲勞損傷與潛變損傷（透過時間分數 Time Fraction 或延性耗竭 Ductility Exhaustion 法則評估）的非線性疊加，使得微裂紋的萌生時間大幅提前41。在此交互作用下，傳統P91銲接彎頭的實際服役壽命，經常縮減至原始設計壽命的三分之一甚至更低6。 Under high-temperature material testing standards like ASTM E2714-09, creep-fatigue tests introducing hold-times demonstrate that lattice slip bands generated by LCF cycles provide perfect nucleation sites for creep voids. The non-linear superposition of fatigue damage and creep damage (evaluated via Time Fraction or Ductility Exhaustion rules) significantly advances the initiation time of microcracks41. Under this interaction, the actual service life of traditional P91 welded elbows frequently shrinks to one-third or even less of the original design life6.

七、 大林電廠專案分析：3D/5D冷作彎管之製造應變與PBHT最佳化 / VII. Dalin Plant Project Analysis: Manufacturing Strain and PBHT Optimization for 3D/5D Cold Bends

為從物理與冶金學的雙重根源徹底截斷第四型破裂與疲勞損傷路徑，本研究針對大林電廠CCPP專案，探討導入業界已成熟應用之「去銲接化」大半徑冷作彎管技術。然而，要將厚壁的高強度P91/P92合金鋼管在室溫或次臨界溫度下，強制進行劇烈的三維冷彎塑性變形，面臨著極端的製造邊界挑戰9。 To completely sever the Type IV cracking and fatigue damage paths from their physical and metallurgical roots, this study explores introducing the industry-matured “weld elimination” large-radius cold bending technology to the Dalin CCPP project. However, forcing thick-walled, high-strength P91/P92 alloy steel pipes into severe 3D plastic deformation at room or subcritical temperatures presents extreme manufacturing boundary challenges9.

7.1 冷作應變率與ASME壁厚減薄補償 / 7.1 Cold Strain Rate and ASME Wall Thinning Allowance

冷彎製程對管材內部微觀晶格的拉伸破壞程度，可透過理論冷作塑性應變率（Cold Forming Strain Rate, ϵ）進行幾何量化。其近似計算公式為2： The degree of tensile destruction inflicted on the material’s internal micro-lattice by the cold bending process can be geometrically quantified via the theoretical Cold Forming Strain Rate (ϵ). Its approximate calculation formula is2:

ϵ=Do/(2R1 )×100%

其中，Do 為鋼管外徑，R1 為彎曲中心半徑。Where Do is the outer diameter of the pipe, and R1 is the center bend radius.

依據此公式推算，對於彎曲半徑僅有 R=3D 的緊密彎管，理論最大外弧拉伸應變可飆升至約16.7%。如此劇烈的微觀晶格扭曲與位錯增殖，將嚴重破壞P91/P92原有的回火馬氏體組織，引發強烈的應變時效（Strain Aging），導致材料的衝擊韌性（Impact Toughness）急遽下降至危險邊緣6。反之，當採用 R=5D 的大半徑彎管時，拉伸應變率可嚴格控制在10.0%左右，落入法規允許且易於修復的安全調控區間11。 Based on this formula, for tight bends with a radius of only R=3D, the theoretical maximum extrados tensile strain can spike to about 16.7%. Such severe microscopic lattice distortion and dislocation multiplication will critically ruin the original tempered martensitic structure of P91/P92, triggering intense Strain Aging and causing the material’s Impact Toughness to plummet dangerously6. Conversely, when employing large-radius bends of R=5D, the tensile strain rate can be strictly controlled around 10.0%, falling safely within the code-allowable, easily restorable control zone11.

在工程經濟學與管壁減薄（Wall Thinning）補償方面，冷彎製程無可避免地會造成外弧側厚度損失。ASME B31.3針對承受內壓的彎管，要求其設計厚度 tm 必須基於修正後的Barlow方程式，並納入銲接強度折減因子（Weld Strength Reduction Factor, WSRF, W）與溫度相依係數 Y 進行補償計算2。冷彎工法因無縱向或環向銲縫，其WSRF值為理想的1.0，避免了高溫服役下銲道強度打折的窘境9。 In terms of engineering economics and Wall Thinning allowance, the cold bending process inevitably causes thickness loss on the extrados. For bends subjected to internal pressure, ASME B31.3 requires the design thickness tm to be based on the modified Barlow equation, incorporating the Weld Strength Reduction Factor (WSRF, W) and temperature-dependent coefficient Y for compensation calculation2. Because cold bending lacks longitudinal or girth welds, its WSRF is an ideal 1.0, avoiding the pitfall of reduced weld strength during long-term high-temp service9.

彎管幾何半徑比 / Bend Radius Ratio (R/DR/DR/D) B31.1 法定壁厚減薄補償餘裕 / Statutory Wall Thinning Allowance 彎曲工法特徵與材料採購影響評估 / Features & Material Procurement Impact
5D 彎管 / 5D Bends 1.08 tm (需預留 8% 餘裕 / Requires 8% allowance) 工程經濟學與力學設計的完美平衡點。8%的壁厚餘裕絕大多數可直接由市售標準Schedule鋼管的固有製造公差裕度吸收，無需耗費巨資客製化特製母管。 / The perfect balance of economics and mechanics. 8% allowance is mostly absorbed by standard pipe tolerances, bypassing custom pipe costs2.
4D 彎管 / 4D Bends 1.14 tm (需預留 14% 餘裕 / Requires 14% allowance) 拉伸變形顯著增加，針對部分超高壓管線等級，可能需向鋼廠客製化提升局部壁厚。 / Significant tensile deformation; some ultra-high-pressure classes may require custom localized thickness boosts from mills.
3D 彎管 / 3D Bends 1.25 tm (需預留 25% 餘裕 / Requires 25% allowance) 材料成本劇增區。因局部減薄率極高，設計端必須採購特製的超厚母管(Extra-heavy parent pipe)以應對厚度損失，這將大幅推高整廠建置成本，並增加系統剛性與支撐荷重。 / Material Cost Spike Zone. Extreme local thinning demands extra-heavy parent pipes, drastically inflating costs and support loads.

在研究設定中，若大林電廠CCPP專案採用5D大半徑數控（CNC）冷作彎管，相較於傳統的感應熱彎（Induction Bending），CNC冷彎搭配內部芯棒（Mandrel）支撐，能將截面橢圓度（Ovality）嚴格控制在3%以內，同時保留了材料原始的碳當量（Carbon Equivalent）與冶金穩定性，免除了降低碳當量所帶來的氫致開裂（HIC）風險11。 In the study configuration, if the Dalin CCPP project adopts 5D large-radius CNC cold bends—compared to traditional Induction Bending—CNC cold bending equipped with internal mandrel support can strictly control cross-sectional Ovality under 3%. Simultaneously, it preserves the material’s original Carbon Equivalent and metallurgical stability, circumventing the Hydrogen-Induced Cracking (HIC) risks associated with lowered carbon equivalents11.

7.2 嚴密控溫的次臨界彎後熱處理(Subcritical PBHT) / 7.2 Strictly Controlled Subcritical Post-Bend Heat Treatment (PBHT)

為修復劇烈塑性變形造成的晶格損傷，ASME B31.1第129.3節（Table 129.3.1-1）與B31.3明確定義了P91/P92等高階材料在冷成型後的應變極限與熱處理強制要求20。若冷作應變率大於極限值，或彎曲後最劇烈變形區的殘餘延伸率（Retained Elongation）低於ASME B31.3 Para 332.4.2a所規定的10%，則嚴禁直接服役，必須透過熱處理恢復延展性11。 To repair lattice damage caused by intense plastic deformation, ASME B31.1 Section 129.3 (Table 129.3.1-1) and B31.3 clearly define the post-cold-forming strain limits and mandatory heat treatment requirements for advanced materials like P91/P92 20. If the strain rate exceeds limits, or if the Retained Elongation in the most deformed region falls below the 10% mandated by ASME B31.3 Para 332.4.2a, direct service is strictly prohibited, and heat treatment must be performed to restore ductility11.

對於大口徑成型管件，若執行完整的正火與回火（N&T，加熱至遠高於AC3的1040°C-1080°C區間），在現地實務中不僅難度極高，更伴隨著巨大的管件變形風險6。因此，針對大林電廠專案之分析，建議導入極度精密的次臨界感應加熱彎後熱處理（Subcritical IH-PBHT）策略。 For large-diameter formed fittings, executing a complete Normalizing and Tempering cycle (N&T, heating to the 1040°C-1080°C range well above AC3) is not only extremely difficult in on-site practice but also carries massive risks of component deformation6. Therefore, the analysis for the Dalin plant project recommends introducing an ultra-precise Subcritical Induction Heating Post-Bend Heat Treatment (Subcritical IH-PBHT) strategy.

次臨界PBHT的冶金學核心，在於將熱處理溫度精確鎖定於下臨界溫度（AC1）之下的極窄安全視窗內（通常控制在730°C至760°C之間，並依據壁厚計算保溫時間，標準為每英吋厚度1小時，最低不少於2小時）2。此過程能透過熱激發能量，徹底抹除冷作加工帶來的晶格畸變，將殘餘拉伸應力完全釋放，並促使變形過程中微量溶解的MX相與M23C6碳化物重新均勻析出。 The metallurgical core of Subcritical PBHT lies in locking the heating temperature precisely within a very narrow safety window below the lower critical temperature (AC1) (typically 730°C to 760°C, with soak time based on thickness—1 hour/inch, min. 2 hours) 2. Using thermal excitation energy, this process completely erases cold-work-induced lattice distortion, fully releases residual tensile stresses, and prompts uniformly re-precipitated MX and M23C6 carbides that may have slightly dissolved during deformation.

執行此工法的最大冶金風險在於絕對不可跨越AC1邊界。研究指出，P91/P92鋼材中的微量元素（如鎳Ni與錳Mn）會顯著壓低材料的AC1溫度。當  (Ni+Mn) 總和超過1.0%或1.2%時，AC1 將顯著下降。若熱處理溫度失控穿越此臨界點，金屬局部將發生不可逆的奧氏體逆轉變，冷卻後形成強度極低的未回火「雙相」結構，導致抗潛變能力瞬間崩潰2。因此，在實務規範要求下，必須導入數位溫控中頻感應加熱設備，並輔以磁聲發射（Magnetic Acoustic Emission, MAE）等先進非破壞檢測技術，精確監測微觀組織演變，確保馬氏體基體與強化相的完美復原。 The greatest metallurgical risk in executing this method is absolutely crossing the AC1 boundary. Studies show that trace elements (like Ni and Mn) in P91/P92 significantly depress AC1. When the  (Ni+Mn) sum exceeds 1.0% or 1.2%, AC1 drops notably. If temperatures lose control and cross this threshold, the metal locally undergoes irreversible austenite reversion, forming a weak untempered “dual-phase” structure upon cooling, instantly collapsing creep resistance2. Thus, under practical code requirements, digital-temperature-controlled mid-frequency induction heaters must be employed, supplemented by advanced NDE techniques like Magnetic Acoustic Emission (MAE), to precisely monitor microstructural evolution and ensure perfect restoration of the martensitic matrix and strengthening phases.

八、 傳統1.5D電銲彎頭與5吋以下3D/5D大半徑冷作彎管之實務工程與管理差異 / VIII. Practical Engineering and Management Differences Between Traditional 1.5D Welded Elbows and 3D/5D Large-Radius Cold Bends Under 5 Inches

前述章節著重於學理與規範層面的解析。而在現代複循環電廠的生命週期實務中，管線組件的選用不僅涉及材料力學，更牽涉到營運成本、空間佈置及風險管理等諸多面向。特別是針對外徑尺寸在5英吋以下的附屬管線及部分高能分支管線，業界（如興達與台中專案）全面導入3D或5D大半徑冷作彎管的經驗，對於各利害關係人（Stakeholders）帶來了顯著的管理變革。The preceding sections focused on theoretical and normative analyses. In the lifecycle practices of modern combined cycle power plants, piping component selection involves not just mechanics, but OPEX, spatial layout, and risk management. Particularly for auxiliary lines and some high-energy branches under 5 inches OD, the industry’s experience (e.g., Hsinta and Taichung projects) of fully deploying 3D or 5D cold bends brings significant management shifts for all stakeholders.

8.1 業主對於高能蒸汽管線維護管理及營運決策 / 8.1 Owner’s Maintenance Management and Operational Decision-Making for HEP

從電廠業主與資產管理者的視角，高能管線（P91/P92）的生命週期營運支出（OPEX）往往成為決策核心。傳統的1.5D銲接彎頭由於極易誘發第四型潛變破裂，其熱影響區（HAZ）成為電廠法規要求的強制性在役檢查（In-Service Inspection, ISI）熱點1。每次機組大修時，業主必須花費高昂成本進行保溫層拆除、搭設鷹架，並委託專業團隊執行高溫相應的相位陣列超音波檢測（PAUT）或表面覆模金相（Replica）檢驗1。 From the perspective of plant owners and asset managers, lifecycle OPEX for HEP (P91/P92) is often a core decision factor. Because traditional 1.5D welded elbows are highly prone to Type IV cracking, their HAZ becomes a mandatory In-Service Inspection (ISI) hotspot per regulations1. During every major outage, owners spend heavily on insulation removal, scaffolding, and contracting teams for PAUT or surface replica metallography1.

一旦將管線轉向結構改為一體成型的冷作彎管，等於在物理上直接消滅了這些高風險的環向銲縫，徹底達成「去銲接化」。業主在營運決策上，能直接將此類節點的非破壞檢測（NDE）預算降至零，顯著縮短停機歲修（Outage）時間；更重要的是，免除了由第四型破裂導致的「未漏先破」災難性非預期停機風險，大幅確保了電廠的調度可靠度與供電合規性10。 Once turning structures are switched to integrally formed cold bends, these high-risk girth welds are physically eliminated, achieving true “weld elimination.” Operationally, owners can reduce NDE budgets for these nodes to zero, significantly shortening Outage times. More importantly, this avoids the disastrous “break-before-leak” unplanned outage risks linked to Type IV cracking, massively ensuring plant dispatch reliability and compliance10.

8.2 EPC承包商設計單位之空間佈置與實務考量 / 8.2 Space Layout and Practical Considerations for EPC Contractor Designers

對EPC統包設計單位而言，最大的挑戰在於廠房空間配置與管網應力解析的平衡。1.5D電銲彎頭因其體積緊湊，過去在佈局上享有絕對優勢；然而，其極高的應力強度因子（SIF）會迫使設計師在相鄰區段增加龐大的膨脹環（Expansion Loops）與昂貴的避震器（Snubbers），反而佔用更多空間11。 For EPC turnkey designers, balancing plant space with pipe stress analysis is the main challenge. 1.5D elbows, being compact, previously enjoyed a layout advantage; however, their ultra-high SIF forces designers to insert massive expansion loops and costly snubbers in adjacent sections, ironically consuming more space11.

針對5吋以下的高能管線，採用3D或5D冷作彎管，其幾何彎曲半徑（R）通常落在15英吋至25英吋內。此等級的空間佔用在龐大的汽輪機房或HRSG內部極易被消化，幾乎不會引發嚴重的管線碰撞（Clashing）問題。相反地，5D冷彎管所具備的高柔性因子（k），能有效引導並吸收熱膨脹位移，大幅減輕末端設備（如蒸汽閥門或小汽輪機）的噴嘴荷重（Nozzle Loads），讓EPC在3D建模（如PDMS/E3D）初期能更靈活地進行管線支撐佈局規劃2。 Using 3D/5D cold bends for <5″ piping means geometric radii (R) of about 15-25 inches. This footprint is easily digested inside massive turbine halls or HRSGs without severe clashing. Conversely, the 5D bend’s high flexibility factor (k) effectively guides and absorbs thermal displacement, drastically lowering nozzle loads on terminal equipment (valves, small turbines), allowing more agile support layouts during early 3D modeling (PDMS/E3D) 2.

8.3 廠務管理者對管線之運轉要求 / 8.3 Plant Manager’s Operational Requirements for Piping

廠務管理者的首要目標是機組在頻繁升降載的過程中的絕對穩定。依據近期的全球HRSG可靠度數據，高達85%的電廠曾面臨減溫水（Attemperator）噴霧洩漏或控制不當引發的問題，這會導致未完全汽化的水滴直接沖擊高溫管線，引發極端熱衝擊與暫態水錘（Water Hammer）現象7。 A plant manager’s primary goal is absolute unit stability during frequent ramping. Recent global HRSG reliability data shows that 85% of plants face issues from leaking or poorly controlled attemperator sprays, causing unvaporized water droplets to strike hot pipes, inducing extreme thermal shock and transient water hammer7.

1.5D彎頭的銲縫在這種瞬態熱機械應力下，極易成為疲勞撕裂的起始點。廠務管理者對於冷作彎管的強烈需求，正是看中其無銲縫的平滑過渡特性，不僅能承受更高的瞬間溫差衝擊而不發生龜裂，也能讓管線內部的擾流與氣液雙相衝擊降至最低，從根本上消解了運轉人員對於管線在熱態啟動（Hot Start）期間發生破裂的疑慮。Under such transient thermo-mechanical stresses, 1.5D elbow welds easily become fatigue tear initiation sites. Managers strongly demand cold bends for their seamless, smooth-transition properties—handling extreme instantaneous temp shocks without cracking, while minimizing internal turbulence and two-phase impacts, fundamentally resolving operator fears of piping rupture during Hot Starts.

8.4 冷作彎管施作協力廠商之製程要求與因應策略 / 8.4 Subcontractor’s Process Requirements and Coping Strategies for Cold Bending

站在專業冷作彎管製造商的角度，要在常溫下對5吋以下的P91/P92合金鋼管進行3D/5D彎曲，必須跨越極高的製造門檻。為了確保管壁在受張力側不會發生過度減薄，並控制彎曲截面的橢圓度（Ovality），協力廠必須導入先進的數控（CNC）彎管機，並搭配精密的內部芯棒（Mandrel）支撐系統，方能將橢圓度嚴格控制在法規要求的3%以內11。 From a specialist bender’s view, cold-bending <5″ P91/P92 alloy pipes to 3D/5D at room temp requires crossing high manufacturing thresholds. To prevent excessive tension-side thinning and control cross-sectional ovality, subcontractors must deploy advanced CNC benders with precise internal mandrel support systems, keeping ovality strictly under the code-mandated 3% 11.

此外，針對高能蒸汽管線，製造商必須精確計算ASME B31.1的壁厚減薄補償。對於5D彎管，必須確保母管具有至少8%的厚度餘裕；若採用3D彎管，則減薄率增加，必須向鋼廠採購具備更高厚度餘裕的客製化母管11。為因應P91/P92極度敏感的冶金特性，製造商還需確保冷彎製程中不會改變材料原有的碳當量（Carbon Equivalent），杜絕因材質變異而衍生氫致開裂（HIC）的風險11。 Furthermore, for HEP, fabricators must precisely compute ASME B31.1 thinning compensation. For 5D bends, parent pipes must have an 8% thickness margin; for 3D, higher thinning dictates procuring custom extra-heavy pipes from mills11. To accommodate P91/P92’s extreme metallurgical sensitivity, the process must preserve the original Carbon Equivalent, preventing HIC risks from material alteration11.

8.5 潁璋工程「能彎不銲」三合一工法之管理價值落實 / 8.5 Management Value Implementation of Ying-Zhang Engineering’s 3-in-1 “Bend Not Weld” Method

針對大林電廠CCPP專案的分析，導入潁璋工程（Ying-Zhang Engineering）所提倡的「三合一工法」（3D/5D CNC 大半徑冷作彎管 + IH-PBHT 單管感應亞臨界彎後熱處理 + QR Code 雲端數位履歷），是發揮大半徑冷彎優勢的唯一解方。此工法管理的核心價值在於徹底落實「能彎不銲」的設計理念，從源頭將易受流體沖刷與疲勞破壞的銲縫轉化為連續平滑的母材彎曲段5。 For the Dalin CCPP project analysis, introducing Ying-Zhang Engineering’s promoted “3-in-1 Methodology” (3D/5D CNC large-radius cold bending + IH-PBHT single-pipe subcritical induction heat treatment + QR Code cloud digital traceability) is the sole solution to unlock the advantages of large-radius cold bending. The core management value lies in thoroughly implementing the “bend not weld” design philosophy, fundamentally transforming welds—which are vulnerable to fluid erosion and fatigue—into continuous, smooth base-metal bends from the source5.

針對 P9x 高能管線，此工法的執行不僅是製造手段的升級，更是嚴格對接 ASME B31.1 與 B31J 規範的合規性展現。潁璋工程透過此工法（目前已於興達與台中CCPP等專案中落實應用），將設計端的力學優化與製造端的微觀金相控制進行無縫接軌。透過單管感應亞臨界熱處理消弭殘餘應力，並藉由 QR Code 雲端數位履歷確保生產、熱處理至檢測的每一道工序均可精準溯源，從而確保每一組出廠的P9x高能冷彎管不僅符合B31.1的嚴苛標準，更在不犧牲母材強度的前提下，為電廠提供了具備極高抗潛變與抗疲勞能力的完美管件10。 For P9x HEP, executing this method is not just a manufacturing upgrade, but a strict compliance alignment with ASME B31.1 and B31J codes. Ying-Zhang Engineering seamlessly integrates design-side mechanical optimization with manufacturing-side micro-metallurgical control via this method (already deployed in Hsinta and Taichung CCPPs). By using single-pipe subcritical induction heating to eliminate residual stress, and utilizing QR Code cloud digital records to ensure precise traceability for every step from production to inspection, they guarantee that every shipped P9x high-energy cold bend strictly meets B31.1 standards. This provides power plants with flawless fittings boasting immense creep and fatigue resistance without sacrificing base metal strength10.

九、 複循環機組頻繁啟停之熱力學破壞機制與應變率放寬(5%~20%)之IH-PBHT深度解析 / IX. Deep Analysis of Thermodynamic Failure in Frequently Cycled CCPPs & IH-PBHT at Relaxed Strain Rates (5%-20%)

承接第七章所述之製造應變挑戰，為修復冷作變形造成的晶格損傷，ASME B31.1第129.3節與B31.3 Para 332.4.2a明確定義了P91/P92等高階材料在冷成型後的應變極限與熱處理強制要求2。 Following the manufacturing strain challenges in Chapter VII, to repair lattice damage from cold deformation, ASME B31.1 Section 129.3 and B31.3 Para 332.4.2a clearly define the post-forming strain limits and mandatory PBHT requirements for advanced alloys like P91/P92 2.

在CCPP頻繁啟停的極端熱力學環境下，機組由冷態快速升至滿載，巨大的溫差會引發強烈的暫態熱應力；同時，蒸氣流速的急遽變化（如閥門急關或雙相流干擾）會引發符合Joukowsky波動原理的高頻水錘脈衝7。在Coffin-Manson低週疲勞失效模型中，這些暫態應力會轉化為強大的局部塑性應變幅43。如果管材內部因冷作加工遺留了巨量的差排與晶格畸變，其疲勞延性將大幅衰退，無法吸收這些瞬態衝擊能量。 Under CCPP’s extreme thermodynamic cycling environments, units ramp rapidly from cold to full load, creating massive temp differentials and fierce transient thermal stresses; concurrently, rapid steam velocity changes induce high-frequency Joukowsky water hammer pulses7. In the Coffin-Manson LCF failure model, these transient stresses convert into immense local plastic strain amplitudes43. If the pipe retains massive cold-work dislocations and lattice distortion, its fatigue ductility degrades drastically, failing to absorb these transient shock energies.

依據理論計算，3D彎管的冷作應變率約為16.7%，5D彎管約為10.0%。這兩個數值皆恰好落於5%至20%的「適中應變區間」。對於大口徑或厚壁P91/P92管件，若執行完整的正火與回火（N&T，加熱至1040°C以上），在現地實務中極易導致嚴重的幾何變形。然而，正因為3D/5D彎管的應變率被控制在20%以下，法規允許採用極度精密的次臨界感應加熱彎後熱處理（Subcritical IH-PBHT）來替代高風險的N&T工序2。 Theoretical calculations put 3D bend cold strain at ~16.7% and 5D at ~10.0%. These values fall squarely within the “moderate strain zone” of 5% to 20%. For large-diameter/thick P91/P92 pipes, executing full N&T (>1040°C) on-site easily leads to severe geometric distortion. However, exactly because 3D/5D strain rates are kept under 20%, codes permit the ultra-precise Subcritical IH-PBHT to replace the high-risk N&T process2.

次臨界PBHT的冶金學核心在於，利用5%~20%的冷作應變所儲存的變形能作為驅動力，並將熱處理溫度精確鎖定於下臨界溫度（AC1）之下的極窄安全視窗內（通常控制在730°C至760°C之間）。此溫帶能夠啟動充分的原子擴散以徹底抹除殘餘拉伸應力與加工硬化，同時又不至於引發相變，完美保留了母材原本均勻分佈的奈米級MX相與M23C6碳化物。 Subcritical PBHT’s metallurgical core lies in utilizing the deformation energy stored by the 5%-20% cold strain as a driving force, locking the temperature within a razor-thin safety window below the lower critical temperature (AC1) (usually 730°C-760°C). This thermal band initiates sufficient atomic diffusion to eradicate residual tensile stress and work hardening without triggering a phase transformation, perfectly preserving the matrix’s original uniformly distributed nano MX phases and M23C6 carbides.

執行此工法的成敗，取決於對AC1極限溫度的絕對掌控。研究指出，P91/P92鋼材中的微量元素（特別是鎳Ni與錳Mn）會顯著壓低材料的AC1溫度。當  (Ni+Mn) 總和超過1.0%或1.2%時，AC1 將顯著下降（可能降至800°C以下）。若次臨界PBHT的溫度失控穿越此臨界點，金屬局部將發生不可逆的奧氏體逆轉變，冷卻後形成極度軟弱且易脆的「雙相」未回火結構，導致抗潛變能力瞬間崩潰。因此，在針對大林電廠專案的研究分析中，建議全面導入數位溫控中頻感應加熱設備，嚴密監控升降溫速率與保溫時間（每英吋壁厚保溫一小時），確保在頻繁啟停的熱力學交變應力下，管系仍具備最高標準的結構韌性與疲勞極限。 Success here hinges on absolute command over the AC1 limit. Trace elements (especially Ni and Mn) in P91/P92 severely depress AC1. When (Ni+Mn) exceeds 1.0% or 1.2%, AC1 drops markedly (potentially below 800°C). If temperatures cross this line, local irreversible austenite reversion occurs, cooling into an extremely weak, brittle untempered “dual-phase” structure, instantly collapsing creep resistance. Thus, the Dalin project analysis recommends fully adopting digital-temp-controlled mid-frequency induction heaters, rigorously monitoring ramp rates and soak times (1hr/inch), ensuring the piping retains ultimate structural toughness and fatigue limits under cyclical thermodynamic stresses.

十、 結論與全生命週期效益評估 / X. Conclusion and Full Life-Cycle Benefit Evaluation

針對現代CCPP調峰操作下高能管線所面臨的極端物理與冶金學挑戰，本研究基於ASME B31J規範、流體質量傳遞模型與斷裂力學，針對大林電廠CCPP專案，深度剖析了導入「傳統銲道去銲接化與5D冷作彎管三合一工法」的預期效益與學理機制。研究結果證實，傳統1.5D銲接彎頭在應力集中、暫態水錘衝擊、FAC流體沖蝕，以及第四型潛變破裂上，具備綜合且致命的脆弱性。Addressing the extreme physical and metallurgical challenges faced by HEP under modern CCPP peak-shaving, this study—based on ASME B31J, fluid mass transfer models, and fracture mechanics—deeply analyzed the theoretical mechanisms and expected benefits of introducing the “weld elimination 5D cold bending 3-in-1 method” to the Dalin CCPP project. Results confirm that traditional 1.5D welded elbows possess comprehensive, fatal vulnerabilities regarding stress concentration, transient water hammer, FAC erosion, and Type IV creep cracking.

此三合一工法（3D/5D CNC冷作彎管 + IH-PBHT單管感應亞臨界熱處理 + QR Code雲端數位履歷）目前已在業界落實採用，並非僅屬理論創新。將其應用於大林電廠專案的評估中，其全生命週期綜合效益體現於以下三個維度：This 3-in-1 methodology (3D/5D CNC cold bending + IH-PBHT single-pipe subcritical induction heat treatment + QR Code cloud digital records) is currently adopted in industry practice, rather than just a theoretical novelty. Its application evaluation for the Dalin project highlights full life-cycle benefits in three dimensions:

  1. 結構力學與動態穩定性重塑 / Structural Mechanics & Dynamic Stability Reconstruction：基於ASME B31J的三維應力解耦與SSI機制，5D大半徑彎管憑藉其倍數增長的柔性特徵 h值，將面內/面外SIF值壓制至極低水準。其優異的彈性有效吸收了巨大的熱膨脹位移，大幅減少了系統對龐大膨脹環與昂貴恆力吊架的依賴；同時，平緩的曲率降低了Joukowsky水錘壓力波的反射係數，消除了引發聲學共振與高週疲勞的動態不平衡推力。Based on B31J’s 3D stress decoupling and SSI mechanics, the 5D bend uses its exponentially grown flexibility characteristic h to suppress in-plane/out-of-plane SIFs to rock-bottom levels. Its superior elasticity effectively absorbs massive thermal expansion, vastly reducing reliance on huge expansion loops and pricey constant spring hangers. Simultaneously, the gentle curvature drops Joukowsky water hammer reflection coefficients, nullifying the dynamic unbalanced thrusts that trigger acoustic resonance and high-cycle fatigue.
  2. 流體動力學與FAC的物理性根除 / Fluid Dynamics & Physical Eradication of FAC：5D平滑流線徹底消除了1.5D急彎處的流場分離與反向狄恩渦流。壁面剪應力與亂流動能的斷崖式下降，直接阻斷了Sanchez-Caldera模型中的高傳質係數（Kc）通道，從物理機制上完全拔除了流體加速腐蝕（FAC）的生成要件，確保管壁邊界的長期完整性。The 5D smooth streamline completely eliminates flow separation and reverse Dean Vortices at the 1.5D sharp bend. The cliff-like drop in wall shear stress and turbulence kinetic energy directly blocks the high mass transfer coefficient (Kc) pathway in the Sanchez-Caldera model, physically uprooting the conditions for FAC generation and ensuring long-term pipe wall boundary integrity.
  3. 冶金破壞路徑阻斷與雲端數位溯源突破 / Metallurgical Failure Path Blockade & Cloud Digital Traceability Breakthrough：透過CNC冷作彎管實現「去銲接化」，徹底消滅了高應力轉向區內的細晶/臨界熱影響區（FGHAZ/ICHAZ）。配合精密控溫的次臨界PBHT修復晶格，本工法從微觀源頭阻斷了碳化物粗化與潛變空洞成核的路徑。更具前瞻性的是，去銲接化將此高風險節點的在役檢查（In-Service Inspection, ISI）數量降至零，並結合 QR Code 雲端數位履歷，實現了從製造出廠至電廠維運的全生命週期精準溯源，為電廠省下了極其龐大的停機檢測與維修成本。Achieving “weld elimination” via CNC cold bending totally destroys the FGHAZ/ICHAZ in high-stress turning zones. Paired with precisely temp-controlled subcritical PBHT to repair lattices, this method blocks the path of carbide coarsening and creep void nucleation at the microscopic source. Even more forward-looking, weld elimination drops ISI counts for these high-risk nodes to zero. Combined with QR Code cloud digital records, it realizes full-lifecycle precise traceability from factory output to plant O&M, saving power plants immensely on outage inspections and maintenance costs.

綜上所述，以5D冷作彎管為核心的潁璋工程三合一工法，絕非單純的製造工法替換，而是一場橫跨空間應力矩陣、非穩態流固耦合，以及奈米級冶金修復與數位化管理的系統工程革命。該工法以極低的材料補償經濟代價，徹底落實了「能彎不銲」與ASME法規對接之核心理念，為全球現代化調峰電廠的高效、安全與長壽命運轉，樹立了不可替代的工程新標竿。In summary, Ying-Zhang Engineering’s 3-in-1 method centered on 5D cold bending is not merely a manufacturing replacement; it is a systems engineering revolution spanning spatial stress matrices, unsteady fluid-structure interaction, nanoscale metallurgical repair, and digital management. At an extremely low economic cost of material compensation, this method thoroughly implements the “bend not weld” philosophy aligned with ASME codes, erecting an irreplaceable new engineering benchmark for the efficient, safe, and long-life operation of global modern peak-shaving power plants.

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  23. 基於ASME B31J 規範之電廠高能管線預製工法最佳化, https://yz-pipe-bending.com.tw/%E5%9F%BA%E6%96%BC-asme-b31j-%E8%A6%8F%E7%AF%84%E4%B9%8B%E9%9B%BB%E5%BB%A0%E9%AB%98%E8%83%BD%E7%AE%A1%E7%B7%9A%E9%A0%90%E8%A3%BD%E5%B7%A5%E6%B3%95%E6%9C%80%E4%BD%B3%E5%8C%96%EF%BC%9A%E5%A4%A7%E5%8D%8A/
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  42. EVALUATION OF FATIGUE BEHAVIOUR OF LASER … – MSpace, https://mspace.lib.umanitoba.ca/jspui_org/bitstream/1993/30231/3/Buckson%20Richard.pdf
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  44. Fatigue lifing approaches for shot peened turbine components, https://eprints.soton.ac.uk/415882/1/PhD_Thesis_Chao_final.pdf
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