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Material Cutting

February 7, 2022

Since the time of our Stone Age ancestors, tool making has been a subtractive process in which the desired article is extracted from a material by chipping, or by more advanced cutting techniques. Our Paleolithic ancestors created spear heads by chipping away layers of flint, while a modern machinist might use a laser. As Michelangelo (1475-1564) so famously described this process,
"The sculpture is already complete within the marble block, before I start my work. It is already there, I just have to chisel away the superfluous material."[1]

Engraving of a mammoth on mammoth ivory, from Upper Paleolithic deposits at Lake Baikal, Siberia (José-Manuel Benito)

engraving of a mammoth on mammoth ivory, from Upper Paleolithic deposits at Lake Baikal, Siberia. This item is at the Hermitage Museum, Saint Petersburg, Russia

(Wikimedia Commons image by José-Manuel Benito. Click for larger image.)

A more efficient form of subtractive manufacturing is casting an item to near-net-shape, and then doing a final machining. Presently, there's a slow movement towards additive manufacturing and the use of 3D printing. In most cases, the 3D printed items are crude, and they too need to undergo a final machining step. In most cases, the 3D printed and finely machined item is used to make a cast from which multiple items are made.

One fortunate part of my college education was a segment of a physics laboratory course devoted to hands-on machine shop techniques. This course was excellent experience for an experimental physicist where I learned how to drill and tap holes and operate lathes and milling machines. In doing such subtractive manufacturing, I noticed that some cutting removed metal as long ribbons, while others took chips from the metal piece.

Material cutting proceeds by the cutting tool's making frictional contact with the material, and the tool's causing plastic deformation and fracture in the material.[2] While shear deformation, which produces the ribbons of material, gives a high-quality surface finish, chip breaking through fracture is beneficial, since it prevents the formation of too long ribbons.[2] An abrupt transition from shear to fracture occurs as the depth of cut is increased, but the physics behind this transition point were unknown.[4] A team of Danish engineers from Aarhus University (Aarhus, Denmark) and the University of Southern Denmark (Sønderborg, Denmark) have recently published an open access article in Physical Review Letters that describes their theory of cutting and its experimental verification.[2-4]

The research team developed a simple physical model to predict chip formation in a homogeneous material as a function of the material intrinsic properties, the tool geometry, and the cutting process parameters (see figure).[2] As can be seen in the figure, the forces depend on the depth of the cut, the cutting geometry, and the mechanical properties of the material; most importantly, the angle of the front edge of the cutting tool.[4] The model predicts the critical cutting depth at which the cutting mode changes from shear to fracture.[4] Quite intuitively, shallower cuts result in unbroken ribbons, while deeper cuts exert so much force that the material fractures and chips break off.[2,4]

Model for gradual chip formation by plastic shearing

Why physicists and other practitioners of classical mechanics need to remember their trigonometry.

A physical model for gradual chip formation by plastic shearing.

(Fig. 2a of ref. 2, licensed under the Creative Commons Attribution 4.0 International license.[2] Click for larger image.)

The research team validated their model by experiment, and by the use of published data for many materials and cutting conditions.[2] The cutting model gave good values for the critical depth with shallower critical depth with increasing brittleness.[4] Since mechanical properties of materials vary with temperature, a ready example being the catastrophic failure of liberty ship hulls in the cold waters of the North Atlantic Ocean during World War II, the model predicts a temperature dependence of the critical cutting depth.[4] This was experimentally demonstrated in cutting experiments with frozen butter (see figure).[2]

Cutting setup and butter cutting experiments

Left, a photograph of the cutting apparatus used in the study. Center, room temperature (17 °C) butter, and right, frozen butter at -10 ° C, in cutting experiments. Smooth cutting is observed for the room temperature specimen, while chipping behavior was observed for the frozen specimen. The cutting tool was made from S355 steel and it had a cutting angle of 45 degrees with a tip radius of 0.05 millimeter. (Right image, fig. 2S from ref. 3, and other images from fig. 1 of ref. 2, licensed under the Creative Commons Attribution 4.0 International license.[2-3] Click for larger image.)

Cutting force in polycarbonate as a function of the depth of cut

Variation of the steady-state cutting force in polycarbonate as a function of the depth of cut, showing a linear correlation between the cutting force and depth of cut.

(Graph created in Gnumeric from data in ref. 3.)[3]

The summary article in Physics[4] about this research had a link to a 2018 study that's interesting enough to mention.[5-6] As I've experienced in my own laboratory, soft metals, such as aluminum, are difficult to cut, since they exhibit a gummy texture.[5] This is a consequence of their tendency to exhibit unsteady plastic flow, have macroscopic defects on the cut surface, and large energy dissipation.[5] Scientists from Purdue University (West Lafayette, Indiana) and the University of West Florida (Pensacola, Florida) demonstrated that this cutting problem was eliminated by merely coating the metal surface with glues and inks.[5]

The coating lowers the metal's surface energy, and this results in a more brittle surface that responds to the cutting tool by cracking rather than by folding.[5-6] This mechanochemical effect is not material specific, and it has a comparable efficacy across different metal systems.[5] Acetone, paraffin wax, and water exerted no influence on cutting, presumably because they don't adhere to the surface.[6] This method will have practical application in many material cutting applications.[5-6]


  1. Michelangelo Buonarroti Quotes at Goodreads.
  2. Ramin Aghababaei, Mohammad Malekan, and Michal Budzik, "Cutting depth dictates the transition from continuous to segmented chip formation," Phys. Rev. Lett., vol. 127, no. 23 (December 3, 2021), article no. 235502, DOI:https://doi.org/10.1103/PhysRevLett.127.235502. This is an open access publication with a PDF file here.
  3. Supplementary information for ref. 2 (PDF file).
  4. Mark Buchanan, "How to Cut into a Material More Smoothly," Physics, vol. 14, no. 171 (December 3, 2021).
  5. Anirudh Udupa, Koushik Viswanathan, Mojib Saei, James B. Mann, and Srinivasan Chandrasekar, "Material-Independent Mechanochemical Effect in the Deformation of Highly-Strain-Hardening Metals, Phys. Rev. Applied, vol. 10, no. 1 (July 13, 2018), article no. 014009, DOI:https://doi.org/10.1103/PhysRevApplied.
  6. Philip Ball, "Glue or Ink Improves Soft Metal Cuts," Physics, vol. 11, no. 72 (July 13, 2018).
  7. Videos of cutting experiments for ref. 2.

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