Architectural & Automotive Glazing Engineering, ASTM C1048 Thermal Glass Tempering
Thermal Glass Tempering Quench Stress & ASTM C1048 Formula
Calculate Half-Plate Air-Quench Biot Number Bi, Parabolic Surface Compressive Residual Stress (MPa), Mid-Plane Core Tensile Stress (MPa), and ASTM C1048 / EN 12150 Safety Glass Class.
Why 3 mm thin glass needs MORE than 2x the air-jet blower pressure of 6 mm float glass to lock in 69 MPa ASTM C1048 safety temper!
**Thermal Glass Tempering** heats soda-lime-silica float glass (`Thickness d` mm, `Thermal Conductivity k = 1.05` W/(m·K), **Thermoelastic Constant `beta = (alpha * E) / (1 - nu) ~= 0.82` MPa/K**) above its `~620°C` softening point and blasts both faces with high-velocity air-quench nozzles (`Heat-Transfer Coefficient h` W/(m²·K))! While the outer skins freeze rigid below the `~550°C` glass transition `T_g`, the hot viscoelastic core stays `Delta_T_f` (`K`) hotter; when the core finally cools to room temperature and tries to contract, the already-rigid skins resist it—locking in a **Parabolic Residual Stress Profile** with **Surface Compression `sigma_{surf} = (2 / 3) * beta * Delta_T_f`** (`MPa`, exact `2:1` equilibrium against **Mid-Plane Core Tension `sigma_{core} = sigma_{surf} / 2`** MPa)! Because `Delta_T_f` scales with **Half-Thickness Quench Biot Number `Bi = (h * (d / 2)) / k`**, halving glass thickness `d` halves `Bi` unless quench jet `h` doubles! Per **ASTM C1048**, **Fully Tempered (`FT`)** safety glass requires **`sigma_{surf} >= 69` MPa** (`10,000` psi, shattering into blunt dicing cubes instead of dagger shards)!
Verify on a `6.0` mm Automotive Side-Lite Air Quench—Glass_Thickness `d` = 6.0 mm (B2 -> half-thickness `a = 0.003` m), Quench_Blower_HTC `h` = 340 W/(m²·K) (B3), Glass_Conductivity `k` = 1.05 W/(m·K) (B4), Frozen_Surface-to-Core_Temp_Lag `Delta_T_f` = 155 K (B5), and Thermoelastic_Modulus_Factor `beta` = 0.82 MPa/K (B6): Quench Biot Number equals `0.971` (E2), Surface Compression reaches `84.73` MPa (`>= 69` MPa! E3), Balanced Mid-Plane Core Tension equals `42.37` MPa (E4), certifying `"ASTM C1048 FULLY TEMPERED"` (E5)!
| ASTM C1048 Glass Tempering KPI (6 mm Soda-Lime Float, k=1.05 W/m·K, beta=0.82 MPa/K) | Formula | Verified Output |
|---|---|---|
| Half-Plate Quench Biot Number Bi | (Quench_h * (Thickness_mm / 2000)) / Glass_k | 0.971 (0.457 weak quench @ h=160) |
| Surface Compressive Stress (MPa) | (2 / 3) * Thermoelastic_beta * Frozen_dT_K | 84.73 MPa (44.83 MPa heat-strengthened) |
| Mid-Plane Core Tension (MPa) | Surface_Compression_MPa / 2 (Parabolic 2:1) | 42.37 MPa (22.41 MPa core tension) |
| ASTM C1048 Glazing Classification | Surface_Compression >= 69 MPa FT Safety Gate | ASTM C1048 FULLY TEMPERED |
Gardon Thermoelastic Air-Quench Biot Number & Parabolic 2:1 Temper Stress Formula
Validate `Thickness d` in `[2.0, 25.0]` mm, `Quench_HTC h` in `[20, 1,500]` W/(m²·K), `Conductivity k` in `[0.5, 2.5]` W/(m·K), `Frozen dT` in `[10, 350]` K, and `beta` in `[0.3, 1.5]` MPa/K right on `E2` (checking `ISTEXT(E2)` on `E3..E4` so `E5` text stays decoupled)!
=LET(dm_m, B2, hq_w, B3, kg_w, B4, dt_k, B5, bt_m, B6, sc_m, (2 / 3) * bt_m * dt_k, IF(OR(dm_m < 2, dm_m > 25, hq_w < 20, hq_w > 1500, kg_w < 0.5, kg_w > 2.5, dt_k < 10, dt_k > 350, bt_m < 0.3, bt_m > 1.5), "Invalid Tempering Input", IF(sc_m >= 69, "ASTM C1048 FULLY TEMPERED", "BELOW 69 MPa TEMPER FLOOR")))Low-Pressure Heat-Strengthening Quench (`h = 160` W/m²·K, `dT = 82` K) Non-Safety Check
Throttle quench blower static pressure for curtain-wall spandrel **Heat-Strengthened (`HS`, `24–52` MPa)** glass (`B3 = 160`, `B5 = 82` K): Biot Number E2 drops to `0.457`, Surface Compression E3 falls to **`44.83` MPa** (`22.41` MPa core tension in E4), and E5 warns `"BELOW 69 MPa TEMPER FLOOR"`—prohibited in frameless doors or automotive glazing because break pattern reverts to large shards!
=IF(ISTEXT(E2), E2, ROUND((2 / 3) * B6 * B5, 2))Try the example
Use the original values or change them to test your understanding.