Resistance Spot Welding Joule Heat & Nugget Size Formula

Let a copper spot-weld electrode cap mushroom from 6.0 to 8.5 mm on galvanized steel and current density halves—producing cold "stuck" welds at full kA!

Robotic automotive Body-in-White (`BIW`) **Resistance Spot Welding (`RSW`)** clamps overlapping steel stampings of Governing Sheet Thickness `t` (`mm`) between water-cooled CuCrZr electrode caps of Contact Face Diameter `d_{cap}` (`mm`) and pulses RMS Secondary Current `I` (`kA` = `1,000` A) across Dynamic Faying-Surface Resistance `R` (`uOhm` = `10^{-6}` Ohm) for `N_{cyc}` `60`-Hz cycles (**Weld Time `t_w = N_{cyc} / 60`** s). Under **Joule’s First Law `Q = I^2 * R * t_w`** (`Joules`), interfacial melting must grow a fused button exceeding **AWS D8.1 Minimum Weld Nugget Diameter `d_{min} = 4 * SQRT(t)`** (`mm`, `5 * SQRT(t)` shop setup target)! Crucially, as hundreds of zinc-coated welds alloy and flatten ("mushroom") `d_{cap}`, **Electrode Current Density `J = (I * 1,000) / ((PI() / 4) * d_{cap}^2)`** (`A/mm²`) drops as `1 / d_{cap}^2`—causing sudden cold-weld peel failures unless automatic tip-dressing milling cutters or stepper-current tables intervene!

Verify on a `1.44` mm Dual-Phase `DP600` Galvanized BIW Spot Weld—Sheet_Thickness `t` = 1.44 mm (B2 -> AWS Minimum Button `d_{min} = 4.80` mm in E2), Secondary_Weld_Current `I` = 9.50 kA (B3), Dynamic_Stack_Resistance `R` = 160 uOhm (B4), `60`-Hz_Weld_Duration = 12 cycles (B5 -> `0.200` s in E3), and Dressed_Electrode_Cap_Face `d_{cap}` = 6.00 mm (B6): Joule Weld Energy delivers `2,888.0` J (E4) at a crisp `336.0` A/mm² Cap Current Density (E5)!

Joule I²Rt Spot-Weld Energy, AWS 4*SQRT(t) Button & Cap Current Density Formula

Validate `Sheet_Gauge t` in `[0.4, 6.0]` mm, `Current I` in `[2.0, 35.0]` kA, `Resistance R` in `[20, 1,000]` uOhm, `Cycles >= 1`, and `Cap_Face d_{cap}` in `[3.0, 16.0]` mm!

=LET(ts_m, B2, ik_a, B3, ru_o, B4, nc_y, B5, dc_m, B6, ac_m, (PI() / 4) * (dc_m ^ 2), IF(OR(ts_m < 0.4, ts_m > 6, ik_a < 2, ik_a > 35, ru_o < 20, ru_o > 1000, nc_y < 1, dc_m < 3, dc_m > 16), "Invalid Spot-Weld Input", ROUND((ik_a * 1000) / ac_m, 1)))

Un-Dressed Mushroomed 8.5 mm Copper Cap Cold-Weld Failure Check (Set Cap Face B6 = 8.5 mm)

Skip robotic tip dressing for `400` galvanized spots until the copper cap mushrooms from `6.0` to `8.5` mm (`B6 = 8.5`): Nominal Current stays `9.50` kA, yet Electrode Current Density E5 **halves from `336.0` down to `167.4` A/mm²**—dropping below the galvanized fusion threshold and leaving brittle interfacial "stuck" welds that pop open under chisel testing!

=IF(ISTEXT(E5), E5, ROUND(((B3 * 1000) ^ 2) * (B4 * 0.000001) * (B5 / 60), 1))

Further reading

• Arte Sheets Lesson — Ultrasonic Angle-Beam Weld Inspection Skip Distance & Depth
• Arte Sheets Lesson — Friction Stir Welding (FSW) Pitch, Heat Index & Power Formula