11.2 Preheat, Interpass and Post-Heat Calculations for Cold-Crack Prevention

Preheat, Interpass, and Post-Heating Engineering Calculations

Physical Mechanisms of Preheat

Preheat alters the welding thermal cycle through two distinct physical mechanisms:

1. Cooling Rate Retardation: Reduces the cooling rate through the critical austenite decomposition window (800°C to 500°C, denoted delta t_8/5):

   delta t_8/5 is proportional to: Q_net / [2 * pi * k * (T_interpass - T_0)]
   

   Extending delta t_8/5 promotes the transformation of austenite into benign, ductile ferrite-pearlite or upper bainite rather than hard, brittle martensite.
2. Hydrogen Effusion Acceleration: Extends the residence time between 300°C and 100°C, allowing mobile hydrogen atoms to diffuse out of the fusion zone and HAZ into the atmosphere before the steel cools to ambient temperatures where brittle cleavage occurs.

Preheat Calculation Frameworks

• AWS D1.1 Annex H (Method A - Susceptibility Index): Categorizes base metals into Susceptibility Groups (I, II, III) based on composition, combines this with Diffusible Hydrogen Level (H1, H2, H3), and cross-references joint restraint thickness to dictate minimum preheat and interpass temperatures.
• AWS D1.1 Annex H (Method B - Hardness Control Method): Uses Pcm to limit peak HAZ hardness below a specified maximum (HV_max <= 350 to 400 HV) based on critical cooling time:

  T_preheat = 1600 * Pcm - 280  (in °C)
  

• EN 1011-2 / BS 5135 Method: Uses combined thickness d_c (sum of all plate thicknesses meeting at the joint line), heat input Q (kJ/mm), carbon equivalent CET, and hydrogen scale to extract preheat from standardized nomograms:

  CET = C + (Mn + Mo)/10 + (Cr + Cu)/20 + Ni/40
  

Dehydrogenation Heat Treatment (DHT / Hydrogen Bakeout)

If a thick, highly restrained weld cannot be maintained at preheat temperature until non-destructive examination or full post-weld heat treatment (PWHT), a Dehydrogenation Heat Treatment (DHT) must be applied immediately upon arc extinction:

• Parameters: Maintain the joint at 200°C to 300°C (400°F to 600°F) for a minimum soak time of 1 to 4 hours (typically 1 hour per 25 mm of joint thickness) prior to cooling below 100°C.
• Diffusion Kinetics: The diffusion coefficient of hydrogen in ferritic iron follows the Arrhenius relationship:

  D_H = D_0 * exp(-Q_d / (R * T))
  

  At 250°C, D_H is approximately 1.5 x 10^-5 cm^2/s, which is more than two orders of magnitude faster than at room temperature (20°C, D_H approx 1.2 x 10^-7 cm^2/s). The characteristic diffusion distance x approx 2 * sqrt(D_H * t) ensures that diffusible hydrogen effuses out of the joint before brittle room-temperature conditions are reached.

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Worked Numerical Example: Carbon Equivalency & Preheat Evaluation

Problem Statement

A welding engineer is qualifying a welding procedure specification (WPS) for a critical structural offshore column connection. The joint is a complete-joint-penetration (CJP) double-V groove butt weld joining 50.0 mm thick plates of thermo-mechanically controlled processed (TMCP) structural steel. The certified mill test report (CMTR) reveals the following ladle chemical composition (all values in weight percent):

• Carbon (C): 0.09%
• Manganese (Mn): 1.45%
• Silicon (Si): 0.28%
• Chromium (Cr): 0.06%
• Molybdenum (Mo): 0.18%
• Nickel (Ni): 0.35%
• Copper (Cu): 0.22%
• Vanadium (V): 0.04%
• Boron (B): 0.0012%
• Niobium (Nb): 0.03%
• Phosphorus (P): 0.010%
• Sulfur (S): 0.003%

Calculations Required:

1. Calculate the International Institute of Welding Carbon Equivalent (CE_IIW).
2. Calculate the Ito-Bessyo Cracking Parameter (Pcm).
3. Determine which parameter (CE_IIW or Pcm) metallurgically governs this steel and justify your selection.
4. Using the empirical Ito-Bessyo minimum preheat formulation for thick, highly restrained joints:

   T_p (°C) = 1440 * P_c - 392
   

   where P_c = Pcm + [H_diff]/60 + t/600, evaluate T_p for:
   • Condition 1: Shielded Metal Arc Welding (SMAW) using improperly stored basic electrodes with H_diff = 12 mL/100g.
   • Condition 2: Flux-Cored Arc Welding (FCAW-G) using certified H4 consumables with H_diff = 3.5 mL/100g.
5. Calculate the DHT soak duration at 250°C required for hydrogen to diffuse an effective diffusion distance x = 25 mm (2.5 cm), given D_H(250°C) = 1.6 x 10^-5 cm^2/s.

Step-by-Step Solution

Step 1: Calculate CE_IIW

CE_IIW = C + Mn/6 + (Cr + Mo + V)/5 + (Ni + Cu)/15
CE_IIW = 0.09 + 1.45/6 + (0.06 + 0.18 + 0.04)/5 + (0.35 + 0.22)/15
CE_IIW = 0.09 + 0.2417 + 0.28/5 + 0.57/15
CE_IIW = 0.09 + 0.2417 + 0.0560 + 0.0380 = 0.4257%

Step 2: Calculate Pcm

Pcm = C + Si/30 + (Mn + Cu + Cr)/20 + Ni/60 + Mo/15 + V/10 + 5*B
Pcm = 0.09 + 0.28/30 + (1.45 + 0.22 + 0.06)/20 + 0.35/60 + 0.18/15 + 0.04/10 + 5*(0.0012)
Pcm = 0.09 + 0.00933 + 1.73/20 + 0.00583 + 0.0120 + 0.0040 + 0.0060
Pcm = 0.09 + 0.00933 + 0.0865 + 0.00583 + 0.0120 + 0.0040 + 0.0060 = 0.2137%

Step 3: Metallurgical Parameter Selection The carbon concentration of this steel is C = 0.09%, which is substantially below the 0.18% threshold. Applying CE_IIW to low-carbon microalloyed/TMCP steels significantly overestimates the hardenability contribution of carbon and assigns excessive weight to alloying elements like manganese. Therefore, Pcm = 0.214% is the correct governing parameter for this steel.

Step 4: Calculate Minimum Preheat Temperature (T_p) Base plate thickness t = 50 mm. The thickness restraint term is:

t / 600 = 50 / 600 = 0.0833

• Condition 1: High Hydrogen (H_diff = 12 mL/100g)

  P_c1 = 0.2137 + 12/60 + 0.0833 = 0.2137 + 0.2000 + 0.0833 = 0.4970
  T_p1 = 1440 * (0.4970) - 392 = 715.7 - 392 = 323.7°C approx 325°C (617°F)
  

  Engineering Assessment: Requiring a 325°C preheat is excessively high, commercially impractical, and risks degrading the fine-grained TMCP microstructure through over-tempering.

• Condition 2: Certified Low Hydrogen (H_diff = 3.5 mL/100g)

  P_c2 = 0.2137 + 3.5/60 + 0.0833 = 0.2137 + 0.0583 + 0.0833 = 0.3553
  T_p2 = 1440 * (0.3553) - 392 = 511.6 - 392 = 119.6°C approx 120°C (248°F)
  

  Engineering Assessment: By switching from non-controlled electrodes to certified H4 consumables, the minimum required preheat drops by over 200°C (from 325°C down to 120°C), demonstrating the critical impact of diffusible hydrogen control on fabrication economics and joint integrity.

Step 5: Calculate Dehydrogenation Post-Heat Soak Time Using the diffusion approximation x = 2 * sqrt(D_H * t):

t = x^2 / (4 * D_H) = (2.5 cm)^2 / [4 * (1.6 x 10^-5 cm^2/s)] = 6.25 / (6.4 x 10^-5) = 97,656 seconds
t = 97,656 / 3600 approx 27.1 hours (for single-surface effusion)

In standard industrial practice where hydrogen diffuses symmetrically across both top and bottom surfaces (maximum diffusion path length to nearest surface = t/2 = 25 mm = 1.25 cm):

t_sym = (1.25 cm)^2 / [4 * (1.6 x 10^-5 cm^2/s)] = 1.5625 / (6.4 x 10^-5) = 24,414 s approx 6.78 hours

Conclusion: Specifying an immediate post-heat soak (DHT) of 250°C for 4 to 6 hours reduces the residual diffusible hydrogen concentration in the mid-thickness below the critical cracking threshold (< 1.0 mL/100g).

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Real-World Engineering Scenarios & Exam Pitfalls

Industrial Scenario: Delayed Toe Cracking in Heavy Mining Shovel Booms

A heavy equipment manufacturer fabricated mining excavator booms using 65 mm thick ASTM A514 Grade B (690 MPa minimum yield strength) quenched and tempered plates. Multipass flux-cored arc welding (FCAW-G) was performed with a preheat of 110°C. Visual and magnetic particle testing (MT) conducted 2 hours after weld completion showed complete compliance. However, after full structural blast cleaning and painting 72 hours later, 100% shear toe cracking was observed running parallel to the fusion boundary across multiple structural diaphragms.

Failure Investigation & Root Cause:

1. NDE was conducted prematurely. For high-strength Q&T steels, AWS D1.1 Clause 8 mandates an inspection hold period of at least 48 hours post-weld.
2. The FCAW wire coils were left mounted on wire feeders inside the unheated shop over a humid weekend, absorbing moisture into the seam and flux core, driving diffusible hydrogen levels from an initial H4 (3.2 mL/100g) to > 14 mL/100g.
3. The preheat temperature of 110°C was inadequate for the high weld restraint and elevated hydrogen level.

Corrective Action: The fabricator instituted climate-controlled wire storage cabinets, increased preheat to 175°C, mandated an immediate dehydrogenation bakeout at 230°C for 2 hours post-weld, and enforced a strict 48-hour hold before final MT and ultrasonic examination.

Common Exam Traps

Exam Trap 1: Misapplying IIW CE to Modern Low-Carbon TMCP Steels Certification exam questions frequently present a steel with carbon content between 0.05% and 0.12% and ask which formula to use for preheat determination. Do not use CE_IIW for steels with carbon < 0.18%. CE_IIW was calibrated on 1940s-era normalized C-Mn steels; it grossly overestimates the preheat required for modern microalloyed steels. You must select the Ito-Bessyo Pcm formula.

Exam Trap 2: Preheat Only Retards Martensite Formation A widespread misconception is that preheating only serves to slow the cooling rate to avoid martensite. In high-strength steels, preheat's equally vital role is accelerating hydrogen effusion. At 150°C to 200°C, the diffusion rate of hydrogen is hundreds of times faster than at room temperature, allowing hydrogen to safely escape before the steel transforms to martensite and reaches room-temperature embrittlement ranges.

Exam Trap 3: Timing of HICC Formation If an exam question asks when hydrogen-induced cold cracking initiates, never select "during solidification" or "immediately upon arc extinguishment." HICC is delayed cracking occurring between -100°C and +200°C, typically hours or days after the joint has reached ambient temperature.