Metallurgy, Mechanical Testing & Materials Science
Vickers Microhardness (HV) & Tabor Yield-Strength Formula
Calculate ASTM E384 / ISO 6507 Equivalent Test Load (kgf), Vickers Diamond-Pyramid Hardness (HV), True Pyramidal Contact Pressure (MPa), and Tabor Yield-Strength Estimate (MPa).
Use 0.1891 for Newtons vs 1.8544 for kgf—mixing units inflates Vickers HV by 9.81x!
In ASTM E384 / ISO 6507 Vickers hardness testing, a 136° square-base diamond pyramid indents a polished metal surface under load F, leaving two perpendicular diagonals of mean length d (mm). Because traditional Vickers numbers (HV) are defined in kgf/mm² of sloping pyramidal surface area (2 * SIN(68°) = 1.8544), HV = 1.8544 * F_kgf / d_mm^2 = 0.1891 * F_Newtons / d_mm^2, while True Contact Pressure in MPa is H_MPa = 1.8544 * F_Newtons / d_mm^2! Under David Tabor’s (1951) plastic constraint factor C ≈ 3 for low-strain-hardening steels, Uniaxial Yield Strength is approximately sigma_y ≈ H_MPa / 3!
Verify on a Quenched-and-Tempered Alloy Steel Weld Zone—Indentation_Load F = 50.0 N (B2 -> 50 / 9.80665 = 5.10 kgf ~HV5 in E2) and Mean_Diagonal d = 0.14 mm (140 µm, B3): Vickers Hardness equals 0.1891 * 50 / 0.14^2 = 482.40 HV (E3), Pyramidal Contact Pressure is 1.8544 * 50 / 0.14^2 = 4,730.61 MPa (E4), and Tabor Estimated Yield Strength is 4,730.61 / 3 = 1,576.87 MPa (E5)!
| ASTM E384 Vickers Indent KPI (F = 50.0 N, Mean Diagonal d = 0.14 mm) | Formula | Verified Output |
|---|---|---|
| Equivalent Test Force (kgf) | Force_Newtons / 9.80665 | 5.10 kgf |
| Vickers Hardness Number (HV) | 0.1891 * Force_Newtons / (d_mm ^ 2) | 482.40 HV (120.60 HV @ 0.28 mm) |
| Pyramidal Contact Pressure (MPa) | 1.8544 * Force_Newtons / (d_mm ^ 2) | 4,730.61 MPa (1,182.65 @ 0.28) |
| Tabor Yield Strength Est. (MPa) | Contact_Pressure_MPa / 3 | 1,576.87 MPa (394.22 @ 0.28) |
Newton-Input Vickers Hardness & Tabor Yield Formula
Validate Force_Newtons > 0 and Mean_Diagonal_mm > 0!
=LET(f_nw, B2, d_mm, B3, IF(OR(f_nw <= 0, d_mm <= 0), "Invalid Vickers Indent Input", ROUND(0.1891 * f_nw / (d_mm ^ 2), 2)))Annealed Base-Metal Inverse-Square Diagonal Check (Set Diagonal d = 0.28 mm)
Double Mean_Indent_Diagonal B3 from 0.14 mm to 0.28 mm in soft annealed base metal: because d is squared, Vickers Hardness E3 drops by exactly 4x to 120.60 HV, Contact Pressure E4 falls to 1,182.65 MPa, and Tabor Yield Estimate E5 drops to 394.22 MPa!
=IF(ISTEXT(E3), E3, ROUND((1.8544 * B2 / (B3 ^ 2)) / 3, 2))Try the example
Use the original values or change them to test your understanding.