BIZOMAT MAKEOS · Manufacturing
Ductile-Regime Critical Depth of Cut for Brittle Materials
Below what depth of cut will a brittle material such as silicon, germanium, glass or a ceramic machine in the ductile regime instead of fracturing, and is my planned depth below it and above the depth at which the tool edge only ploughs?
The handbook’s fracture mechanics threshold for ductile-regime micromachining: critical depth of cut dc = A (E ÷ H)(Kc ÷ H)² with Young’s modulus E, surface fracture toughness Kc and surface microhardness H of the material and the constant A you enter (0.1 to 0.6 by the handbook), compared with your planned depth of cut, and the check that the depth is not less than about half the tool cutting edge radius, below which ploughing and fracture occur.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Young’s modulus E | GPa | Young’s modulus of the work material, for its crystal orientation where known. |
| Surface fracture toughness Kc | MPa·√m | Surface fracture toughness of the work material from tests or data. |
| Surface microhardness H | GPa | Surface microhardness (Knoop or Vickers) of the work material. |
| Constant A | Constant of the threshold equation; the handbook gives 0.1 to 0.6. | |
| Planned depth of cut | µm | Depth of cut you intend to take. |
| Tool cutting edge radius (0 = no check) | µm | Cutting edge radius of the diamond or other tool. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Young’s modulus E
- What it is
- Stiffness of the brittle work material in tension, Young’s modulus.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 2000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 168 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The critical depth rises in proportion.
- Get it right
- Use the value for the crystal orientation being cut where it is known.
What this means: Surface fracture toughness Kc
- What it is
- Resistance of the work surface to crack growth, its fracture toughness.
- Units and format
- Enter a number in MPa·√m: MPa·√m. The form accepts 0.000001 MPa·√m to 50 MPa·√m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 MPa·√m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The critical depth rises with its square.
- Get it right
- Take it from tests or material data, in MPa√m.
What this means: Surface microhardness H
- What it is
- Surface microhardness of the work material, Knoop or Vickers.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 200 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The critical depth falls with its cube.
- Get it right
- Use the same hardness scale for every material you compare.
What this means: Constant A
- What it is
- Constant of the plastic flow to fracture energy threshold.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.15 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The critical depth rises in proportion.
- Get it right
- The handbook gives 0.1 to 0.6 because of the uncertainty in the measured properties.
What this means: Planned depth of cut
- What it is
- Depth of cut you intend to take with the diamond or other tool.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.000001 µm to 1000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.005 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Compared with the critical depth and the edge radius.
- Get it right
- Ductile-regime cuts are usually well under a micrometre.
What this means: Tool cutting edge radius (0 = no check)
- What it is
- Radius of the rounded cutting edge of the tool.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 100 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.008 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Depths below half of it plough instead of cutting.
- Get it right
- Take it from the tool maker or an edge measurement, or 0 to skip the check.
Method and formulas
- dc = A (E ÷ H)(Kc ÷ H)² with E and H in the same units and Kc ÷ H in √m.
- The cut is in the ductile regime when the depth of cut is below dc.
- Ploughing and fracture occur when the depth is less than about half the cutting edge radius.
- Example: the critical depth of cut is 0.009072 µm.
Limitations
- A varies with the uncertainty of the measured properties; E, Kc and H depend on crystal orientation, surface condition and cutting fluid.
- True ductile-regime cutting happens only along favourable crystal orientations.
- Confirm the depth with test cuts; the threshold is an estimate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the depth of cut for diamond turning silicon, germanium or glass
- Compare brittle materials for ductile-regime machining
- Check the depth against the tool edge radius
Who it is for
- Precision machinists
- Manufacturing engineers
- Optics makers
What you get
- Critical depth of cut
- Ratio of planned to critical depth
- Whether the cut is in the ductile regime
- Edge radius check
Interpreting the result
- A larger toughness or a lower hardness raises the critical depth.
- Cutting fluid changes the surface properties and so the critical depth, as the handbook shows for germanium.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1109–1110. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
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