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, universal-testing 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 3,000-kg 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.
• Precipitation-hardening stainless steel, AISI type 630 (also known as 17-4 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 e-mailed at edmundisakov@bellsouth.net or reached at (561) 369-4063.
Related Glossary Terms
- Brinell hardness number ( HB)
Brinell hardness number ( HB)
Number related to the applied load (usually, 500 kgf and 3,000 kgf) and to the surface area of the permanent impression made by a 10mm ball indenter. The Brinell hardness number is a calculated value of the applied load (kgf) divided by the surface area of the indentation (mm2). Therefore, the unit of measure of a Brinell hardness number is kgf/mm2, but it is always omitted.
- Brinell hardness number ( HB)2
Brinell hardness number ( HB)
Number related to the applied load (usually, 500 kgf and 3,000 kgf) and to the surface area of the permanent impression made by a 10mm ball indenter. The Brinell hardness number is a calculated value of the applied load (kgf) divided by the surface area of the indentation (mm2). Therefore, the unit of measure of a Brinell hardness number is kgf/mm2, but it is always omitted.
- cutting force
cutting force
Engagement of a tool’s cutting edge with a workpiece generates a cutting force. Such a cutting force combines tangential, feed and radial forces, which can be measured by a dynamometer. Of the three cutting force components, tangential force is the greatest. Tangential force generates torque and accounts for more than 95 percent of the machining power. See dynamometer.
- cutting speed
cutting speed
Tangential velocity on the surface of the tool or workpiece at the cutting interface. The formula for cutting speed (sfm) is tool diameter 5 0.26 5 spindle speed (rpm). The formula for feed per tooth (fpt) is table feed (ipm)/number of flutes/spindle speed (rpm). The formula for spindle speed (rpm) is cutting speed (sfm) 5 3.82/tool diameter. The formula for table feed (ipm) is feed per tooth (ftp) 5 number of tool flutes 5 spindle speed (rpm).
- feed
feed
Rate of change of position of the tool as a whole, relative to the workpiece while cutting.
- gang cutting ( milling)
gang cutting ( milling)
Machining with several cutters mounted on a single arbor, generally for simultaneous cutting.
- hardness
hardness
Hardness is a measure of the resistance of a material to surface indentation or abrasion. There is no absolute scale for hardness. In order to express hardness quantitatively, each type of test has its own scale, which defines hardness. Indentation hardness obtained through static methods is measured by Brinell, Rockwell, Vickers and Knoop tests. Hardness without indentation is measured by a dynamic method, known as the Scleroscope test.
- mechanical properties
mechanical properties
Properties of a material that reveal its elastic and inelastic behavior when force is applied, thereby indicating its suitability for mechanical applications; for example, modulus of elasticity, tensile strength, elongation, hardness and fatigue limit.
- metalcutting ( material cutting)
metalcutting ( material cutting)
Any machining process used to part metal or other material or give a workpiece a new configuration. Conventionally applies to machining operations in which a cutting tool mechanically removes material in the form of chips; applies to any process in which metal or material is removed to create new shapes. See metalforming.
- milling
milling
Machining operation in which metal or other material is removed by applying power to a rotating cutter. In vertical milling, the cutting tool is mounted vertically on the spindle. In horizontal milling, the cutting tool is mounted horizontally, either directly on the spindle or on an arbor. Horizontal milling is further broken down into conventional milling, where the cutter rotates opposite the direction of feed, or “up” into the workpiece; and climb milling, where the cutter rotates in the direction of feed, or “down” into the workpiece. Milling operations include plane or surface milling, endmilling, facemilling, angle milling, form milling and profiling.
- stainless steels
stainless steels
Stainless steels possess high strength, heat resistance, excellent workability and erosion resistance. Four general classes have been developed to cover a range of mechanical and physical properties for particular applications. The four classes are: the austenitic types of the chromium-nickel-manganese 200 series and the chromium-nickel 300 series; the martensitic types of the chromium, hardenable 400 series; the chromium, nonhardenable 400-series ferritic types; and the precipitation-hardening type of chromium-nickel alloys with additional elements that are hardenable by solution treating and aging.
- tensile strength
tensile strength
In tensile testing, the ratio of maximum load to original cross-sectional area. Also called ultimate strength. Compare with yield strength.
- tool steels
tool steels
Group of alloy steels which, after proper heat treatment, provide the combination of properties required for cutting tool and die applications. The American Iron and Steel Institute divides tool steels into six major categories: water hardening, shock resisting, cold work, hot work, special purpose and high speed.
- turning
turning
Workpiece is held in a chuck, mounted on a face plate or secured between centers and rotated while a cutting tool, normally a single-point tool, is fed into it along its periphery or across its end or face. Takes the form of straight turning (cutting along the periphery of the workpiece); taper turning (creating a taper); step turning (turning different-size diameters on the same work); chamfering (beveling an edge or shoulder); facing (cutting on an end); turning threads (usually external but can be internal); roughing (high-volume metal removal); and finishing (final light cuts). Performed on lathes, turning centers, chucking machines, automatic screw machines and similar machines.
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