Vacuum & Torch Brazing Metallurgy, AWS C3.4 Capillary Joint Overlap & Wicking Rise
Capillary Brazing Joint Overlap & Wicking Rise Formula
Calculate AWS Required Braze Overlap Length (mm), Overlap-to-Thickness Ratio (L/t), Molten Filler Capillary Suction Pressure (kPa), and Vertical Wicking Height (mm).
Widen a furnace-braze joint clearance from 0.06 mm to a sloppy 0.45 mm and molten silver/copper filler loses 87% of its vertical capillary climb!
**Vacuum and Controlled-Atmosphere Furnace Brazing (`AWS C3.4 / Brazing Handbook`)** joins stainless heat exchangers, carbide rock bits, and rocket injectors WITHOUT melting base metal of Thickness `t` (`mm`) and Ultimate Tensile Strength `sigma_{ut}` (`MPa`). To ensure the base metal yields in tension *before* the thin filler layer (`Shear Strength tau_{braze}` MPa) shears at Safety Factor `FS` (`~3.0`), joint designers size **Minimum Lap Length `L_{lap} = (FS * sigma_{ut} * t) / tau_{braze}`** (`mm`, generalizing the shop-floor `"3t rule"`!). Crucially, molten BAg silver or BCu copper filler (`Surface Tension gamma` N/m, `Wetting Angle theta < 25°`, `Liquid Density rho` kg/m³) climbs upward into Parallel-Wall Clearance `w` (`mm`, optimal `0.025–0.10` mm!) solely by **Capillary Suction `Delta_P_c = (2 * gamma * COS(theta)) / (w / 1,000)`** (`Pa`), reaching **Maximum Vertical Wicking Height `h_{wick} = ((2 * gamma * COS(theta)) / (rho * 9.80665 * (w / 1,000))) * 1,000`** (`mm`)!
Verify on a `2.0` mm 316L Stainless Plate-Fin Vacuum Braze Joint—Base_Sheet_Gauge `t` = 2.00 mm (B2), Base_Tensile `sigma_{ut}` = 420 MPa (B3), BAg-7_Braze_Shear `tau_{braze}` = 175 MPa (B4), Safety_Factor `FS` = 3.0 (B5 -> Required Overlap `L_{lap} = 14.40` mm = `7.20 * t` in E2 & E3), Hot_Joint_Gap `w` = 0.06 mm (B6), Molten_Surface_Tension `gamma` = 1.05 N/m (B7), Fluxless_Vacuum_Wetting `theta` = 18.0° (B8), and Molten_Filler_Density `rho` = 8,600 kg/m³ (B9): Capillary Pressure reaches `33.29` kPa (E4), wicking molten silver **`394.7` mm** straight up against gravity (E5)!
| AWS Furnace Brazing KPI (t=2.0 mm, UTS=420, tau=175 MPa, FS=3.0, Gap w=0.06 vs 0.45 mm) | Formula | Verified Output |
|---|---|---|
| Required Braze Overlap L_lap (mm) | (FS * Base_UTS_MPa * Thick_mm) / Braze_Shear | 14.40 mm |
| Overlap-to-Thickness Ratio (L/t) | Required_Overlap_mm / Sheet_Thick_t_mm | 7.20 x sheet thickness |
| Capillary Suction Pressure (kPa) | ((2 * gamma * COS(rad)) / (w_mm / 1000)) / 1000 | 33.29 kPa (4.44 kPa @ sloppy 0.45 mm gap!) |
| Vertical Wicking Rise h_wick (mm) | ((2*gamma*COS(rad))/(rho*9.80665*(w/1000)))*1e3 | 394.7 mm (52.6 mm void starvation @ 0.45 mm!) |
AWS Lap-Shear Strength Balance & Parallel-Slot Capillary Wicking Formula
Validate `Thickness t > 0.1` mm, `Base_UTS > 50` MPa, `Braze_Shear > 20` MPa, `FS >= 1.0`, `Joint_Gap w` in `[0.01, 2.00]` mm, `Surface_Tension gamma` in `[0.2, 2.5]` N/m, wetting `theta` in `[0°, 75°]`, and `Molten_Density` in `[2,000, 18,000]` kg/m³!
=LET(ts_m, B2, ut_m, B3, tb_m, B4, fs_j, B5, wg_m, B6 / 1000, gm_n, B7, th_r, B8 * (PI() / 180), rm_k, B9, IF(OR(ts_m <= 0.1, ut_m <= 50, tb_m <= 20, fs_j < 1, B6 < 0.01, B6 > 2, gm_n < 0.2, gm_n > 2.5, B8 < 0, B8 > 75, rm_k < 2000, rm_k > 18000), "Invalid Braze Joint", ROUND(((2 * gm_n * COS(th_r)) / (rm_k * 9.80665 * wg_m)) * 1000, 1)))Out-of-Tolerance 0.45 mm Machined Socket Gap Void Starvation Check (Set Gap w B6 = 0.45 mm)
Machine a loose `0.45` mm slip fit (`B6 = 0.45`) instead of `0.06` mm: Capillary Suction E4 collapses from `33.29` to `4.44` kPa and Vertical Wicking Height E5 plunges from `394.7` down to **`52.6` mm**—draining molten braze out the bottom of tall heat-exchanger sleeves and leaving unbonded leak paths!
=IF(ISTEXT(E5), E5, ROUND((B5 * B3 * B2) / B4, 2))Try the example
Use the original values or change them to test your understanding.