Temp at which rate is calculated (Tc). Usually 550°C.
Gross Heat Input (Arc Energy):–
Net Heat Input (Hnet):–
Heat Flow Mode:–
Cooling Rate (at Tc):–
Estimated t8/5 Time (Approx):–
Understanding Weld Cooling Rate
The Weld Cooling Rate is a critical parameter in welding metallurgy, particularly for carbon and low-alloy steels. It represents how fast the weld metal and the Heat Affected Zone (HAZ) cool down after the welding arc passes. The rate of cooling directly influences the microstructure that forms, which in turn dictates the mechanical properties of the joint, such as hardness, toughness, and susceptibility to cracking.
Why Calculation Matters
If a weld cools too quickly, hard and brittle microstructures like martensite may form, significantly increasing the risk of Cold Cracking (Hydrogen Induced Cracking). Conversely, if the weld cools too slowly, the grain structure may become coarse, leading to reduced toughness and strength. Engineers calculate the cooling rate to optimize welding parameters (Voltage, Current, Speed) and determine necessary preheat temperatures.
The Physics: 2D vs. 3D Heat Flow
This calculator uses Rosenthal's equations to determine the cooling rate. The physics of heat flow changes depending on the plate thickness relative to the heat input:
Thick Plates (3D Heat Flow): Heat dissipates in three directions (downwards and sideways). This typically results in faster cooling rates.
Thin Plates (2D Heat Flow): The plate becomes saturated with heat, and heat can only dissipate in two dimensions (sideways). This typically results in slower cooling rates.
The calculator automatically determines whether the heat flow is 2D or 3D based on your inputs and applies the correct formula.
Key Input Definitions
Arc Voltage (V) & Welding Current (A): The primary electrical parameters that determine the power of the arc.
Travel Speed: How fast the torch moves. Slower speeds increase heat input per unit length.
Thermal Efficiency (η): Not all electrical energy becomes heat in the plate. This factor adjusts for energy lost to the environment (e.g., MIG/MAG is ~0.8, TIG is ~0.6).
Calculation Temperature (Tc): The specific temperature at which the cooling rate is measured. For steel phase transformations, 550°C (or 540°C) is the standard reference point.
Formulas Used
The calculator derives the cooling rate ($R$) using the properties of carbon steel (Thermal Conductivity $k \approx 28$ J/m·s·°C and Volumetric Specific Heat $\rho C \approx 4.5 \times 10^6$ J/m³·°C).
Thick Plate Formula: $R = \frac{2\pi k (T_c – T_0)^2}{H_{net}}$
Thin Plate Formula: $R = 2\pi k \rho C (\frac{h}{H_{net}})^2 (T_c – T_0)^3$
Where $H_{net}$ is the net heat input per unit length.
function calculateCoolingRate() {
// 1. Get Input Values
var voltage = parseFloat(document.getElementById("voltage").value);
var current = parseFloat(document.getElementById("current").value);
var speed = parseFloat(document.getElementById("speed").value);
var efficiency = parseFloat(document.getElementById("efficiency").value);
var thickness = parseFloat(document.getElementById("thickness").value);
var preheatTemp = parseFloat(document.getElementById("preheatTemp").value);
var targetTemp = parseFloat(document.getElementById("targetTemp").value);
// 2. Validation
if (isNaN(voltage) || isNaN(current) || isNaN(speed) || isNaN(thickness) || isNaN(preheatTemp) || isNaN(targetTemp)) {
alert("Please fill in all fields with valid numbers.");
return;
}
if (speed <= 0 || thickness <= 0) {
alert("Speed and Thickness must be greater than zero.");
return;
}
if (targetTemp <= preheatTemp) {
alert("Calculation Temperature (Tc) must be higher than Preheat Temperature (T0).");
return;
}
// 3. Constants for Carbon Steel (Standard Metallurgical Values)
var k = 28; // Thermal Conductivity (J / m*s*C)
var rhoC = 4500000; // Volumetric Specific Heat (J / m^3*C) aka 4.5 MJ/m^3C
// 4. Calculate Heat Input
// Arc Power P = V * I (Watts)
// Gross Heat Input (J/mm) = (V * I * 60) / Speed(mm/min)
var grossHeatInputJmm = (voltage * current * 60) / speed;
// Net Heat Input (Hnet) considering efficiency
var netHeatInputJmm = grossHeatInputJmm * efficiency;
// Convert Net Heat Input to J/m for formulas (SI units)
var H_net = netHeatInputJmm * 1000;
// Convert Thickness to meters
var h_meters = thickness / 1000;
// Temperature Difference
var deltaT = targetTemp – preheatTemp;
// 5. Calculate Cooling Rates for both 2D and 3D scenarios
// 3D Cooling Rate (Thick Plate) Formula: R = (2 * PI * k * (Tc – T0)^2) / Hnet
var R_3D = (2 * Math.PI * k * Math.pow(deltaT, 2)) / H_net;
// 2D Cooling Rate (Thin Plate) Formula: R = 2 * PI * k * rhoC * (h/Hnet)^2 * (Tc – T0)^3
// Note: (h_meters / H_net)^2 is small, so we compute carefully
var R_2D = 2 * Math.PI * k * rhoC * Math.pow((h_meters / H_net), 2) * Math.pow(deltaT, 3);
// 6. Determine Critical Thickness / Mode
// Physically, the cooling rate is limited by the geometry.
// If the plate behaves as "Thick" (3D), heat flows away faster (downward + sideways).
// If the plate behaves as "Thin" (2D), heat saturates the thickness and flows only sideways (slower).
// The actual cooling rate is governed by the limiting factor.
// Standard approach: The true cooling rate is the MINIMUM of the two calculated rates.
// Why? Because you cannot cool faster than the 3D rate (infinite thickness),
// and you cannot cool faster than the 2D rate allows given the lack of material.
// Actually, in transition, it's complex, but for calculations:
// If R_2D R_3D, the plate is "Thick" (thickness doesn't matter, behaves like infinite block).
var finalRate = 0;
var mode = "";
if (R_2D < R_3D) {
finalRate = R_2D;
mode = "2D (Thin Plate Behavior)";
} else {
finalRate = R_3D;
mode = "3D (Thick Plate Behavior)";
}
// 7. Calculate t8/5 Estimate (Time to cool from 800C to 500C)
// This is a rough approximation derived from the cooling rate at approx 650C or integrated.
// Simplified formula based on Hnet:
// t8/5 (3D) = (4550 – 5*To) * Q / 10^5 ??? No, let's use the rate inverse approximation.
// Average Rate roughly between 800 and 500 (avg 650).
// Let's use the explicit t8/5 formulas from EN 1011-2 for accuracy if possible, or approximate via Rate.
// Approx: t8/5 = 300 / Rate_at_avg_temp. But Rate varies.
// Better to use EN 1011-2 Formulas:
// F1 (3D) = (6700 – 5 * preheatTemp) * netHeatInputJmm / 100000; // Q in kJ/mm? No, formula varies.
// Let's stick to converting the specific rate calculated to a readable format.
// We will calculate t8/5 using the specific EN1011-2 3D/2D eq for display.
// Q is in kJ/mm for these standard approx formulas
var Q_kJmm = netHeatInputJmm / 1000;
var t85_3D = (6700 – 5 * preheatTemp) * Q_kJmm;
// Note: Standard approx often cited as t8/5 = (6700 – 5*T0)*Q*…
// Let's rely on the cooling rate calculated (User requested Cooling Rate).
// We will just label the rate clearly.
// 8. Output Results
document.getElementById("grossHeatResult").innerHTML = grossHeatInputJmm.toFixed(2) + " J/mm (" + (grossHeatInputJmm/1000).toFixed(2) + " kJ/mm)";
document.getElementById("netHeatResult").innerHTML = netHeatInputJmm.toFixed(2) + " J/mm";
document.getElementById("flowModeResult").innerHTML = mode;
document.getElementById("coolingRateResult").innerHTML = finalRate.toFixed(2) + " °C/s";
// Simple t8/5 estimation based on rate: 300 deg diff / rate. (Very rough, but gives context)
var estimatedTime = 300 / finalRate;
document.getElementById("t85Result").innerHTML = "~" + estimatedTime.toFixed(1) + " seconds (800°C to 500°C)";
document.getElementById("resultBox").style.display = "block";
}