ASTM A255 Grossmann Steel Hardenability (DI) Formula

Carbon sets MAXIMUM martensite hardness—Cr, Mo, and Mn MULTIPLY how deep martensite hardens into thick shaft cores!

Beginner heat-treaters confuse **Hardness** (surface HRC controlled almost solely by `%C`) with **Hardenability** (how thick a round bar transforms to `>= 50%` martensite at its center before slow cooling forms soft pearlite/bainite)! Marcus Grossmann (1942, standardized in **ASTM A255**) proved that alloying elements retard diffusive pearlite nucleation **MULTIPLICATIVELY** rather than additively! Starting from Base Carbon-plus-Grain-Size Diameter `D_I0` (`mm`, e.g. `5.4` mm for `0.40% C` at ASTM Grain Size `#7`), multiplying ASTM A255 linear alloy factors `f_Mn = 1 + 3.333 * %Mn` (`<= 1.2%`), `f_Cr = 1 + 2.160 * %Cr` (`<= 1.5%`), `f_Mo = 1 + 3.000 * %Mo` (`<= 0.4%`), and `f_Ni = 1 + 0.363 * %Ni` (`<= 1.5%`) yields **Ideal Critical Diameter `D_I = D_I0 * f_Mn * f_Cr * f_Mo * f_Ni`**—the thickest round bar reaching `50%` core martensite in an infinite-severity (`H = infinity`) quench!

Compare Heat-Treated **AISI 4140 Cr-Mo Alloy Steel** Against Plain **1040 Carbon Steel** at Identical `0.40%` Carbon—Base_Carbon_Grain_Diameter `D_I0` = 5.40 mm (B2), Manganese `Mn` = 0.85% (B3 -> `f_Mn = 3.833` in E2), Chromium `Cr` = 0.95% (`f_Cr = 3.052`, B4), Molybdenum `Mo` = 0.20% (`f_Mo = 1.600`, B5), and Residual_Nickel `Ni` = 0.15% (`f_Ni = 1.054`, B6): Multiplicative Alloy Product reaches `19.74x` (E3), boosting Ideal Critical Diameter `D_I` to **`106.6` mm** (`4.20` inches in E5, vs only `18.9` mm on plain `1040` steel)!

ASTM A255 Multiplicative Grossmann Ideal Critical Diameter Formula

Validate `Base_DI0` in `(1, 15]` mm, `Mn` in `[0, 1.20]%`, `Cr` in `[0, 1.50]%`, `Mo` in `[0, 0.40]%`, and `Ni` in `[0, 1.50]%` (the linear single-slope domain of ASTM A255)!

=LET(dz_m, B2, mn_p, B3, cr_p, B4, mo_p, B5, ni_p, B6, fm_n, 1 + 3.333 * mn_p, fc_r, 1 + 2.16 * cr_p, fm_o, 1 + 3 * mo_p, fn_i, 1 + 0.363 * ni_p, di_m, dz_m * fm_n * fc_r * fm_o * fn_i, IF(OR(dz_m <= 1, dz_m > 15, mn_p < 0, mn_p > 1.2, cr_p < 0, cr_p > 1.5, mo_p < 0, mo_p > 0.4, ni_p < 0, ni_p > 1.5), "Invalid Alloy Range", ROUND(di_m / 25.4, 2)))

Plain AISI 1040 Carbon Steel Shallow-Hardening Check (Set Mn = 0.75%, Cr = 0, Mo = 0, Ni = 0)

Strip out the chromium and molybdenum to plain `1040` carbon steel (`B3 = 0.75, B4 = 0, B5 = 0, B6 = 0`): Combined Alloy Multiplier E3 collapses `5.6x` from `19.74` down to `3.50`, shrinking Ideal Critical Diameter `D_I` E4 from `106.6` mm down to `18.9` mm (`0.74` in, E5)—explaining why thick `1040` axles stay soft pearlite in the core even in agitated water quench!

=IF(ISTEXT(E5), E5, ROUND(B2 * (1 + 3.333 * B3) * (1 + 2.16 * B4) * (1 + 3 * B5) * (1 + 0.363 * B6), 1))

Further reading

• Arte Sheets Lesson — Steel Gas Carburizing Harris Case-Depth & Time Formula
• Arte Sheets Lesson — Welding Heat Input, Carbon Equivalent CEIIW & Preheat