Comparison of Hardness among Abrasives, Carbides, and Oxides

This table shows the representative crystal structures and hardness values (Mohs hardness and Vickers hardness, HV) of typical abrasives, carbides, and oxides. For reference, the relative effectiveness of various abrasives is also noted by comparison with whetstones composed mainly of α-alumina (Al₂O₃) or quartz (SiO₂).

Note: Mohs and Vickers hardness values may vary depending on crystal quality, defects, and measurement conditions.
The values shown are representative approximations.

Hard-to-Sharpen (HTS) Index for Blade Steels

Although the actual ease of sharpening also depends on heat treatment and microstructure, it is often practical to estimate the hardness to sharpen from the intrinsic hardness and the total fraction of carbide-forming elements in the alloy.

Formulating HTS index

We propose the following empirical formula as a Hard-to-Sharpen (HTS) index — representing the hardness from the viewpoint of sharpening :

HTS index = (α f_C (Si + Cr + Mo) + (W + V + Nb) )^β · (1 + (H_W W + H_V V + H_Nb Nb) + γ f_C (H_Si Si + H_Cr Cr + H_Mo Mo) + δ Mo )

α = 0.6 — Soft carbide contribution compensation
β = 1.2 — Carbide volume compensation factor
γ = 0.015 — Soft carbide compensation
δ = -0.2 — Mo degeneration compensation
f_C = max(0, C_rem / C_req,sec) — Correction factor for secondary carbide formation
C_rem = min(1, max(0, C - C_req,pri)) — Residual wt% C after primary carbide formation
C_req,pri = 0.065 W + 0.236 V + 0.129 Nb — wt% C required for primary carbide-forming metals
C_req,sec = 0.428 Si + 0.099 Cr + 0.063 Mo — wt% C required for secondary carbide-forming metals
H_E — Relative (E-carbids to Diamond) hardness coefficients

Secondary carbids:
H_Si = (1100 / 9000)^2 ≃ 0.015
H_Mo = (1650 / 9000)^2 ≃ 0.034
H_Cr = (1750 / 9000)^2 ≃ 0.038
Primary carbids:
H_Nb = (2300 / 9000)^2 ≃ 0.065
H_W = (2650 / 9000)^2 ≃ 0.087
H_V = (2900 / 9000)^2 ≃ 0.104

Here, Si, Mo, W, V, Nb and Cr represent the weight percentages of each element. The max() and min() function return the larger or smaller of the given arguments, respectively.

Naturally, not all of the available carbon is strictly consumed by the primary carbide-forming elements. However, for simplicity — and to emphasize the practical influence of hard carbides on sharpening difficulty — this assumption is acceptable in the present formulation.

Note: Although Si is technically a metalloid, it is commonly treated as a carbide-forming element in metallurgical contexts.

Features of the HTS index

1. Main component: ((W + V + Nb) + αf_C (Si + Cr + Mo))^β
   • Proportional to the total amount of carbide-forming elements, with an exponent slightly above unity (β = 1.2) to reflect the empirical trend that sharpening difficulty increases more than linearly with carbide content.
2. Compensation term: (1 + (0.087 W + 0.104 V + 0.065 Nb) + γ f_C (0.015 Si + 0.038 Cr + 0.034 Mo) + δ Mo)
   • W, V and Nb promote the formation of very hard carbides and therefore contribute positively.
   • Mo tends to refine and homogenize carbides, increasing the smoothness of abrasion and making sharpening slightly easier, hence the negative correction (δ = -0.2).
   • The f_C factor represents whether sufficient carbon remains available for the formation of secondary carbides.
   • Overall, this term provides a simple, weighted adjustment based on the relative hardness contributions of each element.

HTS index of various steels

Note: The values in the table are representative or estimated. Errors may exist. Please refer to manufacturer data for accurate specifications. Formulas and parameters are subject to change without notice.

Conclusions or something like that

In short, natural whetstones are only effective for steels softer than LC200N, and for steels harder than MagnaCut, simply use diamond.