The Science and Engineering of Cutting

The Mechanics and Processes of Separating, Scratching and Puncturing Biomaterials, Metals and Non-metals

Tony Atkins

• Publisher: Butterworth-Heinemann
• Year: 2009
• ISBN:
  9780080942452
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

The materials mechanics of the controlled separation of a body into two or more parts – cutting – using a blade or tool or other mechanical implement is a ubiquitous process in most engineering disciplines. This is the only book available devoted to the cutting of materials generally, the mechanics of which (toughness, fracture, deformation, plasticity, tearing, grating, chewing, etc.) have wide ranging implications for engineers, medics, manufacturers, and process engineers, making this text of particular interest to a wide range of engineers and specialists.

• The only book to explain and unify the process and techniques of cutting in metals AND non-metals. The emphasis on biomaterials, plastics and non-metals will be of considerable interest to many, while the transfer of knowledge from non-metals fields offers important benefits to metal cutters
• Comprehensive, written with this well-known author's lightness of touch, the book will attract the attention of many readers in this underserved subject
• The clarity of the text is further enhanced by detailed examples and case studies, from the grating of cheese on an industrial scale to the design of scalpels

Chapter 1. Controlled and Uncontrolled Separation of Parts

Cutting, Scraping and Spreading

The design of structures and components in nature and in engineering usually aims to avoid fracture – at least during life – but there are circumstances where separation of parts is required. These range all the way from the beast of prey tearing apart its victim with teeth and claws, to the manufacture of a precision surface in metal using special cutting tools. Some processes of separation rely on pulling, bending or twisting an object at regions remote from where the object breaks; others load right at the zone of fracture and this includes cutting. Processes of ‘separation’ that are not cutting include pulling corks out of bottles. Some processes that are thought to be cutting are really not: it is a common misconception that ice breakers cut ice fields by splitting; rather, they ride up on the edge of the ice sheet and break pieces off by bending fracture.

Separation of materials is all around us: in the kitchen (e.g. carving meat, coring apples, grating cheese, peeling vegetables), when eating (on the dinner plate, in the mouth), in carpentry and building (e.g. sawing, planing and drilling wood; cutting bricks and paving stones), in the office (e.g. paper guillotining and shredding, pencil sharpening), in manufacturing (e.g. all metal-cutting operations), in agriculture (e.g. ploughing, harvesting of crops, sheep shearing), in medicine and dentistry (surgery; the drilling of teeth), in nature (hunters, raptors, their prey and defences; teeth and chewing), in shaving, in opening packaging and in war (arms and armour: a spear through ancient armour, depleted uranium missiles through modern tank armour). While, usually, the cutting tool remains undeformed, in the latter field both cutter and target are deformed. ‘Cutting’ is interpreted very broadly in this book, but even so we do not consider flame cutting, liquid jets, abrasive water jet cutting, laser cutting, plasma arc cutting, electrodischarge machining and electrochemical machining.

Different materials respond differently when cut with a knife, well illustrated by the wide variety of foodstuffs that includes mashed potatoes, boiled potatoes, uncooked potatoes; cooked and uncooked vegetables; stringy vegetables like celery; squidgy food like blancmange or tofu; boiled sweets, fudge and sugar; easy-to-chew high-quality meat, or poor-quality meat with lots of gristle; soft puddings like icecream, or hard puddings like toffee; some are mixtures of hard and soft (crème brûlée); chocolates may have a hard case with a soft inside. Properties may change with time and storage: some fruit has to be stored after picking before it becomes ripe enough to eat. Fresh food and stale food behave differently: when freshly harvested, foods such as carrot or celery are hard and stiff owing to the turgor pressure that pressurizes the composite structure from within (from the Latin for ‘to swell’); turgor pressure is a plant’s internal stressing to keep it erect, among other things. Turgor pressure decreases with time after harvesting, making fruits and vegetables flaccid (from the Latin for flabby) when they become rubbery and bendy. Loss of turgor pressure is why flowers wilt. The condition of food affects how they are dealt with on the plate, their ‘mouth feel’ and how we bite and masticate food.

A wide variety of different types of implement is found, ranging from butcher’s knives to cheese graters. Kitchen shops offer strange and ingenious gadgets with pointy bits for doing special cutting jobs in the preparation of food. One of the most exotic, perhaps, is a foie-gras cutter. The Swiss have different slicers for potatoes (to prepare roesti) and for apples (for muesli). A mandolin is a device like a wood-plane over the blade of which foodstuffs are sliced, grated or shred depending on the blade. A hachoir is a rocking device for cutting up herbs (from the French hache for axe; hence hatchet). In antique shops may be found old devices such as sugar cleavers (in Victorian times, sugar used to come in big lumps), mechanical apple peelers, nutmeg grinders and so on.

Experiments in the kitchen can be very instructive about cutting, and the reader is encouraged to do so and get a feel for stiff/compliant, strong/weak, tough, etc., materials. For example, scrape a carrot with a knife and notice the difference depending on the angle of the blade. What controls the depth of cut in a potato peeler? Why is peeling with a knife more wasteful? Can you skin an orange with a potato peeler? Indeed, can you shave with a potato peeler? Are there differences depending on whether the fruit is hard and stiff, or soft and squidgy? What determines the ease of scraping up a portion of butter on to a knife from a block, or a scoop of icecream? What are those serrations that appear on the back of the butter after scraping? What determines the ‘spreadability’ of butter on toast? What is the best way to take the top off a boiled egg? What are those cracks that appear having scraped the back of a spoon across the surface of a table jelly? These are not flippant questions or suggestions: the answers are central to understanding of the mechanics of cutting.

When we eat with the aid of a knife, fork, spoon, chopsticks or fingers, we often separate (fracture) food into smaller pieces to fit the mouth, where further deformation and fracture takes place before swallowing. Why is it easier to cut when we ‘slice’ across the food as well as simply ‘press down’? Food on the plate will have been previously prepared from larger pieces and/or cooked to make eatable and digestible. Cooking alters the properties of food and distinguishes humans from other creatures. To tell whether potatoes or other vegetables have been cooked for the requisite time, we stab the vegetable in the saucepan with a knife and see how easy it is to pierce, or see whether it can be suspended from the knife. The altered properties revealed by the knife must connect with perception in the mouth and what, for example, al dente means. Similarly, to get food from plate into mouth, we often pierce, indent or perforate the food with the prongs of a fork, the mechanics of which are similar to nailing a piece of wood.

Cutting may concern big pieces being separated into two or more still-big pieces (sawing logs of timber into planks, slitting metal sheets off rolling mills, cutting wedges from ‘rounds’ of cheese, cutting fruit into segments). In other examples, thin slices or chips are removed from the surface of a larger piece (peeling potatoes, whittling wood, lathe cutting, carving). Sometimes the piece cut off is important (wood veneer, microtomed sections for histological examination); at other times the piece left behind is important (true of most manufacturing processes where the offcut ‘swarf’ is scrap, trimming the edges of bound books); and sometimes both are important (the division of paper sheets into smaller sizes or the slicing and dicing of semiconductor wafers). Sometimes the quality of the resulting surfaces is of particular concern (limits and fits in engineering assembly) but sometimes it does not matter (chopping firewood). Sometimes the same mechanism of cutting may be both undesirable in one situation, yet beneficial in another (erosion versus sandblasting)

Different types of cutting include:

• cutting layers or slices from the surface or edge of a body

• cutting a groove in the surface of the workpiece

• dividing a workpiece into sections by cutting through the thickness

• making profiles (e.g. round shapes on a lathe)

• making some sort of hole down into, or though, the thickness by penetration and perforation.

Some separation processes using tools are on the borderline between being under control and not (such as in cutting toenails, where offcuts sometimes fly around the bathroom; and in nut cracking, where the aim is to preserve the kernel uncrushed or unbroken, but where the fate of the shell is unimportant). The flexibility of whatever is holding both the cutter and the workpiece can be important: try spreading butter with a very springy knife; observe the deformation of a loaf of bread on cutting. Sometimes there is little control at all (in crushing/ball mills or chipping timber to make wood pulp). ‘Loose tools’ are bullets and shrapnel, or the stream of grits in erosion, abrasive cleaning and sandstorms. Cutting during fault or accident conditions is often uncontrolled. Accidental and unintentional cutting, in the form of scratching, piercing, perforating and tearing, occurs when a nail punctures a tyre, and when supermarket plastic bags are torn by sharp objects. A ship getting holed after hitting a rock is a larger scale example of the same thing, as is the defeat of armour by a weapon but where the process is intentional. An understanding of piercing, cutting and perforation enables better armour to be designed that will defeat the weapon, and vice versa.

A characteristic feature of some of the controlled cutting considered in this book is that the cutting tool or blade is not deformed when cutting, and remains ready for reuse. The only significant deterioration may be wear and blunting; unless corrected, the quality of the cut deteriorates. Progress in production engineering from the onset of the Industrial Revolution depended on having satisfactory tool and die materials, and heavy rigid machine tools. Wilkinson’s boring machine of 1775 that made possible the manufacture of Watt’s steam engine was a vital development in the history of machine tool manufacture that encompassed lathes and machines to perform drilling, milling, boring, grinding, shaping, planing and so on. Benjamin Thompson (Count Rumford of the Holy Roman Empire) realized the connexion between mechanical work done and heat generated from observing cannon being bored in Bavaria. (Thompson was American but supported the British in the American Revolution and subsequently fled to Europe. He designed the Englische Garten in Munich.)

‘The Multifarious Perforating Machine’ is illustrated in Figure 1-1.

Figure 1-1 ‘The Multifarious Perforating Machine’ that, among other jobs, was used to punch holes in the plates making up the Britannia Tubular railway bridge to Anglesey at Conway, North Wales. Many of the plates in the bridge were 12 feet long, 2 feet 8 inches broad and ¾ inch thick and the rivets were 1 inch in diameter. The machine was highly adaptable as regards rivet pitch and punches were operated by Jacquard-loom type punched cards. According to Fothergill (1848), the operation of changing plates, weighing 6 or 7cwt each, was performed by half a dozen men in less than a minute. The machine made 11 or 12 strokes per minute, so (with a 4-inch pitch) a 12-foot plate could be punched in less than four minutes, and allowing one minute for changing plates, twelve plates could be perforated per hour. (Courtesy of IMechE)

An interesting question is how hard a tool should be to avoid itself being deformed in cutting. Mutual cutting is possible where both tool and workpiece deform (bullets and the target). When it is difficult to insert a woodscrew, the high torque will distort the blade of a poor-quality screwdriver and also cut slivers from the side of the slot in the head of the screw. Cutting tools are usually thought of as hard, stiff solid objects. But when one ship collides with another, both hollow structures deform and may fracture, and this is another example of mutual cutting.

Many tools can be resharpened and used again. What ‘sharpness’ may, or may not, mean and whether it is an absolute concept is explored later in the book. Sometimes tools are used once only (disposable scalpels) or thrown away when blunt (disposable razors, indexable tool inserts). Hollow needles that pierce the skin and through which liquids may be inserted into the body (hypodermics) or removed (cannulae) may sometimes be reused depending on conditions. Improvements in tool material qualities, and reductions in cost, mean that it is often uneconomic to resharpen tools (few craftsmen these days sharpen and ‘set’ the teeth of wood-cutting handsaws, as saws are relatively cheap at DIY shops).

Some weapons can be reused (swords, spears, cannon balls, the stones of slingshots); others not (bullets, shells). Sometimes the cutting tool is sacrificial (a bee sting). Sometimes a broken or otherwise defunct tool cannot be repaired or replaced and there must be consequences. What was the effect of their teeth being ground down by sand, picked up with food, on Ancient Egyptians? Animals who lose their teeth in combat or in old age may no longer be able to feed and they die. This raises the whole ‘chicken or egg’ question of the evolution of teeth and animal diet: which led to which?

It is possible to separate a given solid into pieces by methods not involving cutting tools, by pulling, bending, twisting and so on. A sheet of paper may be torn down the middle as well as cut with scissors. A cotton thread can be snapped in tension by jerking, or cut by scissors or even with the teeth. A plank of wood can be snapped in two by bending, or alternatively cut with a saw. Facial hair can be plucked out with tweezers, but is most often shaved off, except for women’s eyebrows. Holes are usually drilled in wood, but if a drill is not available, they can be made by burning through with a red-hot poker from the fire. Sometimes items separated by tearing will not be exactly the same as those cut into nominally the same shape. The edges of a torn sheet of paper will be rough compared with an edge cut by scissors; burrs may form along the edges of a thin sheet of metal torn into two, which will be absent when cut by shears – unless the shears are in bad condition, when the sheet may fold down between the blades even if they have sharp edges. Whether such differences are important depends on what is going to be done with the separated pieces. Many modern tin cans have ring-pull tops and may be opened simply by pulling, but food cans still exist that have to be opened with a can opener which indents, pierces and then progressively propagates the initial hole by levering around the rim of the tin, thus opening the metal lid. The quality of the edge in either case probably does not matter; its sharpness does.

Sometimes cutting is not the preferred option (the best long bows are made by splitting the yew, even if an irregular cross-section results, in order to ensure continuity of the wood fibres; spoke-shaven bows have ‘exposed’ grain-ends from which cracks may propagate during flexure). Similarly for split-cane fishing rods: when the nodes are machined off bamboo, the fibres become discontinuous. The best rods have the nodes flattened, so fibres lie in the line of the rod (Vincent, 2008). It is possible to cut the feathers from chickens, turkeys and other birds in preparation for cooking, but that would leave parts of the rachises (Ancient Greek for the spines of feathers) in the flesh, so feathers are plucked off instead (Bonser, 2008).

In the cutting of solid bodies, the blade creates new surfaces that are exposed from within the bulk of the body. In layered materials, or glued joints or welds, interfaces already exist and, although the mechanics is the same, the specific work of separation along a pre-existing interface will be different from the bulk material. Adhesion between the pages of a book, or between the sides of plastic bags, has to be overcome to permit separation; adhesion is why gauge blocks (Johansson blocks) have to be wrung apart in the workshop. When the adhesion between a deposit and substrate is not too strong, separation is sometimes achieved by scraping (debris adhered on kitchen counter tops, ice on car windscreens, dirt removed from under the fingernails, mud on dock floors, scrapers in sewage plants and in ore dressing buddles). Errors in writing by pen on parchment or paper can, with care, be scratched off and the surface returned to its original state (it is the origin of ‘to gloss over’). Hygienists at the dentist scrape plaque from the surface of teeth. The Roman strigil was an instrument with a curved blade used to scrape sweat and dirt from skin in the bath-house. The scraper used to remove films of paint from window glass is a tool that can be used in both directions, as can a hoe when weeding. Is there a difference in performance depending on direction? When a pile of soil just sits on a concrete base, the effort of a bulldozer or scraper is principally to move soil about with little effort for soil-to-concrete separation; in contrast, more work is required when the machine digs into a pile of soil to cause soil-to-soil separation. Many processes, which may even employ cutting tools, are more processes of ‘dislodgement’ rather than cutting. Is removal of dog hair from sofas by tearing off with sticky tape, or leg hair by waxing, a cutting process? A pin extracting a winkle from its shell is dislodging it rather than cutting, but the pin does have to penetrate the winkle to give a grip. When eating snails, they are held by a plier-like clamp and then are wiggled out with a two-pronged small fork. How the interface is detached (all at once or in stages) is of interest in these situations. Is the device with rollers rotating in different directions, to split open the skins of grapes before pressing, a ‘cutting’ device? Probably not.

Is a toothbrush (or sweeping or scrubbing brush) a cutting tool? Is a wire brush a cutting tool when taking rust off a steel component? Strongly adhered debris requires more work to flick away, and this is achieved with stiffer bristles and more pressing down of the brush into the surface: the forces deflecting the bristles increase and the bristles store more elastic strain energy before the instant at which the force for detachment is attained in the deflected bristle. Is the tongue a tool when licking icecream from a cone? Certainly an icecream scoop cuts, as does the device for making whorls of butter: it is controlled chip formation.

Instead of cutting or scraping (in which material is removed), a tool may push ahead a standing wave of material, resulting in a more even spre...

Table of contents

• Cover Image
• Table of Contents
• Dedication
• Copyright
• Preface
• Acknowledgements
• Chapter 1. Controlled and Uncontrolled Separation of Parts
• Chapter 2. Fracture Mechanics and Friction
• Chapter 3. Simple Orthogonal Cutting of Floppy, Brittle and Ductile Materials
• Chapter 4. Types of Chip
• Chapter 5. Slice–Push Ratio
• Chapter 6. Cutting with More Than One Edge
• Chapter 7. Sawing, Chisels and Files
• Chapter 8. Punching Holes
• Chapter 9. Sharpness and Bluntness: Absolute or Relative?
• Chapter 10. Unrestrained and Restrained Workpieces
• Chapter 11. Cutting in Biology, Palaeontology and Medicine
• Chapter 12. Food and Food-Cutting Devices and Wire Cutting
• Chapter 13. Teeth as Cutting Tools
• Chapter 14. Burrowing in Soils, Digging and Ploughing
• Chapter 15. Unintentional and Accidental Cutting
• Appendix 1. Friction Forces on a Wedge-shaped Tool Cutting Orthogonally
• Appendix 2. Friction in Cutting
• References
• INDEX