Input interpretation
Brinell hardness
Equation
BHN = P/(1/2 π D (D - sqrt(D^2 - d^2))) | BHN | Brinell hardness P | applied force D | diameter of indenter d | diameter of indentation
Input values
applied force | 3000 kgf (kilograms-force) diameter of indenter | 10 mm (millimeters) diameter of indentation | 2.5 mm (millimeters)
Results
Brinell hardness | 601.5 kgf/mm^2 (kilograms-force per square millimeter) = 5.898 GPa (gigapascals) = 5.898×10^9 Pa (pascals)
Possible intermediate steps
Calculate the Brinell hardness using the following information: known variables | | P | applied force | 3000 kgf D | diameter of indenter | 10 mm d | diameter of indentation | 2.5 mm Convert known variables into appropriate units using the following: 1 kgf = 9806.6 g m/s^2: 1 mm = 0.001 m: 1 mm = 0.001 m: known variables | | P | applied force | 2.942×10^7 g m/s^2 D | diameter of indenter | 1/100 m d | diameter of indentation | 0.0025 m The relevant equation that relates Brinell hardness (BHN), applied force (P), diameter of indenter (D), and diameter of indentation (d) is: BHN = P/(1/2 π D (D - sqrt(D^2 - d^2))) Substitute known variables and constants into the equation: known variables | | P | applied force | 2.942×10^7 g m/s^2 D | diameter of indenter | 1/100 m d | diameter of indentation | 0.0025 m constant | | π | pi | 3.14159 | : BHN = (2.942×10^7 g m/s^2)/(1/2×3.14159×0.01 m (0.01 m - sqrt((0.01 m)^2 - (0.0025 m)^2))) Separate the numerical part, (2.942×10^7)/(1/2×3.14159×0.01 (0.01 - sqrt((0.01)^2 - (0.0025)^2))), from the unit part, (g m/s^2)/(m (m + sqrt(m^2 + m^2))) = g/(m s^2): BHN = (2.942×10^7)/(1/2×3.14159×0.01 (0.01 - sqrt((0.01)^2 - (0.0025)^2))) g/(m s^2) Evaluate (2.942×10^7)/(1/2×3.14159×0.01 (0.01 - sqrt((0.01)^2 - (0.0025)^2))): BHN = 5.8982×10^12 g/(m s^2) Convert 5.8982×10^12 g/(m s^2) into kgf/mm^2 (kilograms-force per square millimeter) using the following: 1 g/(m s^2) = 1.0197×10^-10 kgf/mm^2: Answer: | | BHN = 601.5 kgf/mm^2
Approximate system conversions
Mohs | 5.48 Knoop | 699 gf/mm^2 scleroscope | 78.9 Vickers | 663 kgf/mm^2 Rockwell A | 81 Rockwell C | 58.5 Rockwell D | 69.8 superficial Rockwell 15N | 90 superficial Rockwell 30N | 76.5 superficial Rockwell 45N | 65.5 (based on typical comparsions; results for particular samples may differ)
Units
Hardness comparisons
harder than apatite (Mohs 5)
softer than glass (Mohs 5.5)