Brinell Hardness

HB = \frac{2 P}{π D ( D - D ^{2} - d ^{2} )}

Brinell: a hard ball of diameter D is pressed with load P; d is the indentation diameter. HB correlates empirically with tensile strength for steels (Fu ≈ 500 HB in psi if HB is in kgf/mm²). Rockwell and Vickers are other Handbook hardness scales.

$P$ (kgf): Load
$D$ (mm): Ball diameter
$d$ (mm): Indentation diameter

Step-by-step solved example

P = 3000 kgf, D = 10 mm, d = 4.0 mm. HB nearest?

Hardness tracks the strength level of the σ–ε curve.

1. Denominator
D − √(D²−d²) = 10 − √(100−16) = 10 − √84 = 10 − 9.165 = 0.835 mm.
2. HB
HB = 2×3000 / (π×10×0.835) = 6000/26.23 = 229.
$HB \approx 229$

Answer: HB ≈ 229

10 practice questions

0/10 correct

1.Harder metals show

2.For many steels Fu (psi) is roughly

3.Rockwell hardness uses

4.HB units in the classic formula are

5.If d approaches D, HB

6.Vickers uses a

7.Hardness testing is popular because it is

8.A quenched martensitic steel vs annealed: HB is

9.P = 500 kgf, D = 10 mm, very small d so D−√(D²−d²) ≈ d²/(2D). HB ≈

10.You should not convert HB to Fu for