9.3 Creep, Stress Rupture & Short-Term Overheating

Creep and Stress Rupture Fundamentals — API RP 571 Section 3.23

1. The Physics and Metallurgy of High-Temperature Creep

Creep is defined as the time-dependent, permanent (inelastic) deformation of a metallic material subjected to sustained mechanical stress at elevated temperatures. When creep deformation continues until complete physical separation occurs, the failure mode is termed Stress Rupture.

At ambient and low temperatures, metals deform plastically only when applied stress exceeds the yield strength ($S_y$). At elevated temperatures, however, atomic thermal vibrations supply sufficient thermal activation energy for atoms and vacancies to move freely through the lattice. Consequently, metals subjected to stresses well below their yield strength undergo continuous, irreversible plastic strain over time.

2. The Homologous Temperature Threshold

The initiation of engineering creep is governed by the homologous temperature ($T_H$), defined as the ratio of operating temperature ($T$) to the material's absolute melting temperature ($T_m$), with both values expressed on an absolute temperature scale (Kelvin or Rankine): $T_H = \frac{T}{T_m} > 0.35 \text{ to } 0.40$

When operating temperatures exceed 35% to 40% of the absolute melting point, thermal activation enables three core microscopic deformation mechanisms:

1. Vacancy Diffusion: Vacancies migrate through the crystal lattice (Nabarro-Herring creep) or along grain boundaries (Coble creep), allowing grains to elongate under tensile stress.
2. Dislocation Climb: Dislocations that are pinned at internal precipitate barriers or obstacles absorb or emit vacancies, climbing out of their slip planes and resuming motion.
3. Grain Boundary Sliding: Adjacent grains slide shear-wise past one another along their boundary interfaces, leading to stress concentrations at triple points and precipitating microscopic voids.

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3. RP 571 Creep Threshold Temperatures

API RP 571 tabulates approximate threshold temperatures above which creep becomes a concern. These values are heavily tested:

Below these temperatures creep is usually not a practical concern; above them, design allowable stresses come from creep and rupture data rather than from yield and tensile strength. H-grade stainless steels (0.04 to 0.10 wt% C) are used for their higher creep strength, and cast alloys such as HK-40 and HP-modified are used for reformer tubes at still higher temperatures.

--- | :--- | :--- | :--- | | Carbon Steel | ASTM A106 Gr B, A516 Gr 70 | > 700 °F to 750 °F ($371\text{--}399\ ^\circ\text{C}$) | Below 700 °F: Yield / Tensile Strength<br/>Above 700 °F: 100,000-hr Creep / Stress Rupture | | C-0.5Mo | ASTM A335 Gr P1, A204 Gr A | > 750 °F to 800 °F ($399\text{--}427\ ^\circ\text{C}$) | Governed by creep kinetics and graphitization risks. | | 1.25Cr-0.5Mo | ASTM A387 Gr 11, A335 Gr P11 | > 800 °F ($427\ ^\circ\text{C}$) | Standard design for catalytic reformer piping and fired heater coils. | | 2.25Cr-1Mo | ASTM A387 Gr 22, A335 Gr P22 | > 800 °F ($427\ ^\circ\text{C}$) | Standard metallurgy for heavy-wall hydroprocessing reactors and coker transfer lines. | | 5Cr-0.5Mo & 9Cr-1Mo | ASTM A335 Gr P5, Gr P9 | > 900 °F ($482\ ^\circ\text{C}$) | Delayed coker furnace tubes and crude heater coils. | | 9Cr-1Mo-V (Grade 91) | ASTM A335 Gr P91 | > 1000 °F ($538\ ^\circ\text{C}$) | Advanced creep-strength enhanced ferritic (CSEF) steel; high-temperature steam lines. | | Austenitic Stainless Steels | 304H, 316H, 321H, 347H | > 1000 °F ($538\ ^\circ\text{C}$) | FCC crystal lattice provides superior creep resistance; H-grades mandate $0.04\text{--}0.10\text{ wt\% C}$. | | Nickel Alloys | Alloy 800H/HT, Alloy 625 | > 1100 °F to 1200 °F ($593\text{--}649\ ^\circ\text{C}$) | High-temperature steam-methane reformer pigtails and collection headers. | | Centrifugally Cast Alloys | HK-40, HP-40 Nb modified | > 1600 °F to 1850 °F ($871\text{--}1010\ ^\circ\text{C}$) | Primary steam-methane reformer radiant catalyst tubes. |

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The Three Classic Stages of Creep Deformation

When strain is plotted against time under constant tensile stress and elevated temperature, a classic creep curve exhibits three distinct operational regimes.

  Total Strain (ε)
       ^
       |                                                    Tertiary Creep (Stage III)
       |                                                  / (Accelerating strain rate,
       |                                                 /   cavity link-up, rupture!)
       |                     Secondary Creep (Stage II) / 
       |                   ┌───────────────────────────┘  <-- Rupture Point
       |                  /  (Steady-state creep rate, 
       |                 /    dε/dt = constant minimum)
       |   Primary (I)  /
       |   ┌───────────┘ 
       |  / (Transient: strain hardening decelerates rate)
       | / 
       +----------------------------------------------------------> Time (t)

1. Stage I: Primary (Transient) Creep

• Kinetic Behavior: Strain rate ($d\epsilon/dt$) is initially high immediately upon load application, but continuously decelerates over time.
• Metallurgical Mechanism: The metal undergoes strain hardening (work hardening). Dislocations multiply, glide along slip planes, and form tangles or pile-ups at grain boundaries and precipitate barriers, increasing the internal resistance to further deformation.

2. Stage II: Secondary (Steady-State) Creep

• Kinetic Behavior: The creep strain rate reaches a nearly constant minimum value ($d\epsilon/dt = \dot{\epsilon}_{min} = \text{constant}$). This stage represents the vast majority (80% to 95%) of the total operating lifetime of high-temperature equipment.
• Metallurgical Mechanism: A dynamic equilibrium is established between strain hardening (dislocation accumulation) and thermal recovery (dislocation climb, cross-slip, and vacancy diffusion). The steady-state creep rate is mathematically described by Norton's Power Law: $\dot{\epsilon}_{ss} = A \cdot \sigma^n \cdot \exp\left(-\frac{Q_c}{R \cdot T}\right)$ Where $A$ is a material constant, $\sigma$ is applied stress, $n$ is the stress exponent (typically 3 to 8 for dislocation climb), $Q_c$ is activation energy for creep, $R$ is universal gas constant, and $T$ is absolute temperature.

3. Stage III: Tertiary (Accelerating) Creep

• Kinetic Behavior: The creep rate accelerates exponentially over time, terminating in catastrophic physical rupture.
• Metallurgical Mechanism: Vacancy condensation nucleates sub-micron cavities along grain boundaries that are oriented perpendicular to the maximum principal tensile stress. As cavities grow, they form rounded ($r$-type) voids on grain faces and wedge-shaped ($w$-type) cracks at triple point grain junctions. These voids coalesce into intergranular micro-cracks. The effective load-bearing cross-sectional area decreases, causing true local stress to spike. Necking develops, void link-up accelerates, and stress rupture occurs.

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Larson-Miller Parameter & Life Prediction Kinetics

In plant engineering and Fitness-For-Service evaluations (API 579-1/ASME FFS-1 Part 10), engineers use time-temperature parametric models to predict the remaining creep rupture life of equipment operating at elevated temperatures.

1. The Larson-Miller Formulation

The most widely applied relationship is the Larson-Miller Parameter (LMP): $LMP = T \cdot \left[C + \log_{10}(t_r)\right]$

Where:

• $T$ = absolute temperature in Rankine ($^\circ\text{R} = ^\circ\text{F} + 460$) or Kelvin ($\text{K} = ^\circ\text{C} + 273$).
• $t_r$ = time to stress rupture in hours.
• $C$ = material-specific constant, empirically established around $C \approx 20$ for carbon and low-alloy ferritic steels (and ranging between 15 and 25 for austenitic stainless steels and nickel alloys).

2. Practical Application: Cumulative Damage Tracking

The LMP relationship allows high-temperature, short-duration laboratory rupture tests to predict long-term operational life at lower operating temperatures. Furthermore, when equipment experiences operational temperature fluctuations, cumulative creep damage is calculated using Robinson's Linear Life Fraction Rule: $D_{\text{creep}} = \sum_{i=1}^{k} \frac{t_i}{t_{r,i}} \le 1.0$

Where $t_i$ is the actual operational time spent at temperature $T_i$ and stress $\sigma_i$, and $t_{r,i}$ is the allowable rupture time under those exact conditions. When the cumulative damage index ($D_{\text{creep}}$) approaches 1.0, stress rupture failure is imminent.

Critical Exam Rule of Thumb (RP 571): Because creep depends strongly on temperature and stress, an increase of about 25 °F (12 °C) or about 15% in stress can cut the remaining life in half or more, depending on the alloy.

Short-Term Overheating — Stress Rupture (API RP 571 Section 3.55)

1. Mechanism and Process Driving Forces

Short-Term Overheating—Stress Rupture is a catastrophic tensile overload failure occurring over an operational timeframe of seconds, minutes, or a few hours. It is triggered when metallic components experience severe, unpredicted temperature spikes that exceed design limits by 100 °F to 300+ °F (56 °C to 167+ °C), frequently pushing metal temperatures above 1,300 °F to 1,500 °F (704 °C to 815 °C).

Primary Root Causes in Industrial Fired Heaters and Boilers:

1. Loss of Internal Flow: Tripping of a boiler feed pump, plugged burner passes, or sudden valve closure stops process fluid flow, eliminating internal convective cooling while radiant heat flux continues unabated.
2. Internal Coking & Fouling: In crude vacuum furnaces and delayed coker heaters, heavy hydrocarbon coking forms an insulating carbonaceous layer on the tube inner diameter. Because coke has very low thermal conductivity, heat transfer into the process fluid is throttled. The tube wall skin temperature spikes dramatically to conduct the heat into the fluid.
3. Steam Blanketing: In boiler water wall tubes, high heat flux combined with inadequate water circulation causes departure from nucleate boiling (DNB). A stagnant layer of steam insulates the tube wall, driving wall temperatures to near-flame levels.
4. Flame Impingement: Damaged, tilted, or un-adjusted burners allow radiant burner flames to directly strike tube surfaces, creating intense localized hot spots.

2. Failure Physics: Tensile Overload Collapse

At temperatures above 1,300 °F (704 °C), the yield and ultimate tensile strength of carbon steel and low-alloy steels collapse to a tiny fraction of their ambient values (dropping from >60 ksi down to <5 to 10 ksi). Because the internal process pressure remains elevated, the operating hoop stress immediately exceeds the metal's high-temperature ultimate tensile strength. The tube wall experiences rapid, unconstrained plastic necking and ballooning, terminating in instantaneous ductile tensile blowout.

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Diagnostic Contrast: Creep Rupture (3.23) vs Short-Term Overheating (3.55)

The API 571 examination heavily tests the ability to distinguish between long-term creep rupture and short-term overheating through visual morphology and metallographic examination.

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Prevention, Mitigation & High-Temperature Inspection Strategies

1. Operational & Process Controls

• Skin Thermocouple Monitoring: Install high-reliability tube-skin thermocouples on radiant fired heater tubes. Thermocouple leads must feature expansion loops and weld pads shielded from radiant flame to prevent false high readings.
• Infrared (IR) Thermography: Conduct routine optical pyrometer and thermal imaging surveys through fired heater sight doors to detect localized hot spots, flame impingement, and internal coking patterns.
• Combustion Management: Maintain balanced burner flame patterns and proper draft controls to ensure flames do not impinge upon tube bundles.
• Decoking Protocols: Implement routine scheduled decoking—either automated steam-air decoking or mechanical pigging—before internal coke layers reach thicknesses that elevate tube skin temperatures above metallurgy thresholds.

2. Materials Upgrading for High-Temperature Service

• H-Grade Austenitic Stainless Steels: In fired heater radiant sections and high-temperature catalytic reforming coils, specify H-grade stainless steels (304H, 316H, 321H, 347H). The "H" designation mandates a controlled carbon content of 0.04 to 0.10 wt%, ensuring robust carbide precipitation that impedes dislocation movement and enhances creep strength.
• Centrifugally Cast Radiant Tubes: Steam-methane reformer furnaces utilize thick-walled centrifugally cast alloys such as HP-40 modified (25Cr-35Ni with additions of Niobium [Nb], Titanium [Ti], and micro-alloying additions). These alloys retain high creep rupture strength at temperatures exceeding 1,750 °F to 1,850 °F (954 °C to 1,010 °C).

3. Non-Destructive Examination (NDE) Methodologies

• Diametral Strapping and Go/No-Go Gauging: During furnace turnarounds, measure tube outside diameter using strapping tapes or calipers. Diameter swelling exceeding 2% to 3% in ferritic tubes (or 3% to 5% in austenitic tubes) can indicate advanced creep; owners set tube retirement criteria (API RP 573 discusses heater tube inspection and retirement).
• Automated Laser Profilometry: Laser crawler tools traveling through or around radiant tubes provide 360-degree high-density mapping of tube diameter, ovality, and localized bulging.
• In-Situ Metallographic Replication: Applied to the hottest tube sections during outages to detect grain boundary creep cavity formation ($r$-type voids and $w$-type triple point cracks) and evaluate carbide spheroidization.
• Ultrasonic Shear Wave and TOFD: Inspect high-stress welded joints, nozzle connections, and dissimilar metal welds (DMWs) to detect sub-surface reheat cracking and creep-fatigue fissures.