It’s important to know the ultimate tensile strength of work materials and their Brinell hardness because these mechanical properties are the guidelines for selecting the cutting speed, feed per tooth, axial DOC and radial WOC when milling, and the cutting speed, DOC and feed per revolution when turning.
In milling, knowledge of a work material’s ultimate tensile strength is imperative because the calculations of the cutting force, torque and required machining power are based on this mechanical property.
Specialized laboratories perform tension testing to determine the ultimate tensile strength of materials. The obtained data determines whether or not the quality of a material satisfies the required strength specification. However, universaltesting machines with associated equipment and the need for skilled operators are costly and most fabricating shops cannot afford such testing (not to mention the cost of making the standard tension test specimens).
A hardness test, such as Brinell or Rockwell, is much less expensive to perform. Usually, workpiece suppliers provide hardness data. A problem may occur if the hardness is given in Rockwell (B or C scale) or in Scleroscope numbers. If so, these numbers should be converted into Brinell hardness numbers at a 3,000kg load. Conversion tables can be found in various handbooks. Formulas for conversion Rockwell hardness (B and C scales) into Brinell hardness, developed by the author, were published in Cutting Tool Engineering (February 2008, pages 22 to 23).
With the Brinell hardness of a given work material, the ultimate tensile strength can be calculated.
The author has developed numerous statistical and linear regression formulas for calculating ultimate tensile strength of carbon, alloy, stainless and tool steels based on their Brinell hardness numbers.
Because of space limitations, a few formulas for calculating ultimate tensile strength (σ) vs. Brinell hardness (HB) will be provided only for some grades of stainless steels.
• Austenitic stainless steel, AISI type 304
Applications include dairy equipment, valves and accessories for chemical handling equipment.
Example of calculation:
Brinell hardness is 150 HB
The linear regression formula for calculating ultimate tensile strength:
σ = 325 × HB + 35,246 (formula 1)
The ultimate tensile strength (calculated and rounded off):
σ = 325 × 150 + 35,246 = 84,000 psi, or 580 MPa (megapascals) in the metric system.
The use of this formula is limited to this grade with a hardness range from 145 to 310 HB.
• Martensitic stainless steel, AISI type 403
Applications include steam turbine blades and parts, gas turbine blades, jet engine parts, furnace and valve parts and burners operating below 1,200° F (650° C).
Example of calculation:
Brinell hardness is 150 HB
The linear regression formula for calculating ultimate tensile strength:
σ = 536 × HB – 7,792 (formula 2)
The ultimate tensile strength (calculated and rounded off):
σ = 536 × 150 – 7,792 = 72,600 psi, or 500 MPa.
The use of this formula is limited to this grade with a hardness range from 145 to 225 HB.
• Ferritic stainless steel, AISI type 405
Applications include vessel linings and rolled profiles for steam turbine parts.
Example of calculation:
Brinell hardness is 150 HB
The linear regression formula for calculating ultimate tensile strength:
σ = 410 × HB + 7,905 (formula 3)
The ultimate tensile strength (calculated and rounded off):
σ = 410 × 150 + 7,905 = 69,400 psi, or 480 MPa.
The use of this formula is limited to this grade with a hardness range from 130 to 185 HB.
• Precipitationhardening stainless steel, AISI type 630 (also known as 174 PH)
Applications include oil field valve parts, aircraft fittings, chemical process equipment, pump shafts, nuclear reactor components, gears, jet engine parts and missile fittings.
Example of calculation:
Brinell hardness is 280 HB
The linear regression formula for calculating ultimate tensile strength:
σ = 523 × HB – 18,525 (formula 4)
The ultimate tensile strength (calculated and rounded off):
σ = 523 × 280 – 18,525 = 127,900 psi, or 880 MPa.
The use of this formula is limited to this grade with a hardness range from 275 to 420 HB.
As can be seen, these formulas are the equations of straight lines. Each straight line is expressed by a general equation, such as:
y = Ax ± B, where A is the slope, and B is the intercept. In this case, x is the Brinell hardness number, and y is the ultimate tensile strength. These formulas have been developed by statistical treatment of Brinell hardness data and the respective ultimate tensile strength data, using linear regression analysis.
This analysis allows obtaining a correlation coefficient C, which indicates the relationship between the two depending variables: y and x. If the correlation coefficient C is greater than or equal to 0.9 (it cannot be greater then 1), it means that there is a strong linear relationship between these variables, and the accuracy in calculating y is 95 percent or higher (if C = 1, the accuracy is 100 percent).
In our case, the correlation coefficients are as follows:
Formula 1, C = 0.984; the accuracy of the formula is 95.5 to 99.8 percent.
Formula 2, C = 0.999; the accuracy of the formula is 99.0 to 99.7 percent.
Formula 3, C = 0.947; the accuracy of the formula is 93.7 to 99.2 percent.
Formula 4, C = 0.993; the accuracy of the formula is 97.4 to 99.9 percent. CTE
About the Author: Edmund Isakov, Ph.D., is a consultant and writer. His books include “Mechanical Properties of Work Materials” (Modern Machine Shop Publications, 2000), “Engineering Formulas for Metalcutting” (Industrial Press, 2004) and “Cutting Data for Turning of Steel” (Industrial Press, 2009). He has also developed “Advanced Metalcutting Calculators” (Industrial Press, 2005) and is a frequent contributor to Cutting Tool Engineering. He can be emailed at edmundisakov@bellsouth.net or reached at (561) 3694063.
