Let's break down the problem: ### **Step 1: Calculate the Heat Input (Q)** The formula for heat input per unit length is: \[ Q = \frac{V \cdot I \cdot 60}{S} \cdot \eta \] Where: - \( V \) = Voltage (25 V) - \( I \) = Current (200 A) - \( S \) = Travel speed (24 in/min) - \( \eta \) = Heat transfer efficiency (0.7) - 60 = to convert from minutes to seconds (since current and voltage are in seconds, but travel speed is in min) So, \[ Q = \frac{25 \times 200 \times 60}{24} \times 0.7 \] \[ Q = \frac{300,000}{24} \times 0.7 \] \[ Q = 12,500 \times 0.7 \] \[ Q = 8,750 \text{ J/in} \] --- ### **Step 2: Calculate the Cooling Rate or Time at 540°C (1000°F)** For thick plates, the relevant parameter is the time it takes the weld to cool from 800°C to 500°C (or from 1470°F to 930°F), commonly called \( t_{8/5} \). A commonly used formula for thick plate cooling time is: \[ t_{8/5} = K \frac{Q}{(T_{plate} - T_0)} \] But we need to use the Time-Temperature-Transformation (TTT) diagram to avoid martensite formation (brittle phase). --- ### **Step 3: Avoiding Martensite** From the TTT diagram, to avoid martensite, the cooling curve should not intersect the "martensite start" line (Ms line) before it crosses into the ferrite + carbide region. - **Ms temperature** (martensite start): ~350°C (660°F) - To avoid martensite, the weld should cool slowly enough so that transformation to ferrite + carbide occurs before reaching Ms. --- ### **Step 4: Determine Preheat Temperature** Preheating slows the cooling rate, so a higher preheat helps avoid martensite. #### **Empirical Preheat Calculation:** A typical empirical formula for required preheat (°C or °F) is: \[ \text{Preheat} = \text{A function of } Q, \text{ plate thickness, interpass temperature, and steel composition} \] But **without composition info**, we use the TTT diagram and welding heat input. #### **Using the TTT Diagram:** 1. Calculate the time for the weld to cool from 800°C to 500°C with the given welding parameters. 2. Use the TTT diagram to check if this time is sufficient to avoid martensite. 3. If not, increase preheat until the cooling rate matches the safe region. **For thick plates:** - Cooling time is long, so preheat may not be strictly necessary unless the composition is highly hardenable. - However, you can estimate **minimum preheat** by ensuring the cooling curve avoids the martensite region. --- ### **Step 5: Approximate Preheat Recommendation** A common quick rule for structural steels and the given heat input is: - For **heat input ~8,750 J/in**, and thick plate, preheat is often **100°C–150°C (210°F–300°F)** as a starting point. - Check TTT: At this preheat, the cooling curve should avoid entering the martensite zone (Ms). --- ## **Summary Table** | Parameter | Value | |--------------------------|--------------| | Heat Input (Q) | 8,750 J/in | | Suggested Preheat | 100–150°C | | Avoid martensite (Ms) | >350°C | --- ## **Typical Answer** **With the given welding parameters (E = 25 V, I = 200 A, S = 24 in/min, η = 0.7), the required preheat temperature for a thick plate is approximately 100–150°C (210–300°F) to avoid martensite formation, as indicated by the TTT diagram.** > **Note**: For precise results, you need the steel's composition and should calculate the exact cooling time and compare it directly to the TTT diagram. For most low-alloy structural steels, this rule will be safe. --- If you have the chemical composition, I can give a more precise preheat temperature using formulas like the Carbon Equivalent (CE). Let me know if you want to see this approach!