Cutting science in biology and engineering

Cutting is a process in which a tool is used to create a new surface in a solid. The creation of new surfaces is a fracture process so that cutting may be regarded as fracturing. However, fracture is usually driven by forces remote from the failure point while cutting involves forces being applied locally via the tool. The crucial factor in both processes is the energy per unit area required to create the new surfaces which is the notion introduced by A.A. Griffith. An understanding of the processes involved requires an energy balance to be drawn up to include the fracture energy, Gc, and other forms of energy dissipation. These include plastic deformation and friction and the latter is particularly important in cutting when the tool, or blade, rubs on the material being cut.

The analysis will be illustrated by considering the removal of a surface layer by a sharp wedge. If all the deformation is elastic, and hence there is no permanent deformation, and there is no friction then Gc is given simply by the cutting force divided by the cut width, This is similar to the splitting of wood though friction usually occurs and must be included. If the removed layer deforms plastically chip curling and shearing occurs and there is additional dissipation. For this rather simple system there are a series of transitions from elastic bending of the chip to firstly plastic bending and then to plastic shearing as the wedge angle of the tool increases.

The fracture toughness of soft solids such as foods is often needed for correlations to important parameters such as sensory attributes or release rates of contained substances (e.g. salt) and as input in model simulations of industrial food processes or mastication. Soft solids are more difficult to test and analyse due to their high compliance and strong non-linearity as well as their strong dependence on loading rate. This behaviour makes conventional fracture tests used for structural materials unsuitable for soft solids. Cutting tests in the form of wire or blade cutting offer an attractive alternative for such materials.

Cutting tests in the form of wire and blade cutting are presented for a range of food materials including cheese, gels and pet foods. The fracture toughness calculated from the cutting test data are compared to independent fracture tests for validation purposes. Methods enabling modelling of fracture initiation and propagation in such soft solids will be presented. Possible failure criteria based on critical maximum strain and cohesive zone models are employed and their accuracy is judged by comparing with experimental data. The studies enable the effect of strain rate on fracture toughness of this class of materials to be determined.

This talk will discuss and define sharpness from a practical and scientific point of view, across all aspects of the use of sharp edge cutting technology from micro surgical cutting, to shaving, to food processing, to industrial processes. Methods of sharpness measurement, both human subjective assessment to scientific measurement and quantitative measurements will be described, including their drawbacks and implications.

The talk will explain in detail the physical and material requirements of a sharp edge, the implications on cutting performance in terms of energy consumption and quality of the resultant cut and condition of the cut item. Sharpening techniques will be described, illustrating how incorrect sharpening can lead to significantly inferior performance both in terms of how sharp a blade is, but also how long a cutting edge will last.

An overview of the instrumentation used to quantify sharpness, edge durability and cutting edge geometries will be given and how they can be used both within blade / knife manufacture and importantly in re-sharpening. The talk will describe a number of real life stories, indicating significant financial losses, some incurred by World class companies, through ignorance of the simple but essential application of sharpness technology.

Why it is easier to cut when there is motion along, as well as perpendicular to, a cutting blade is explained and the analysis is applied to optimisation of blade geometries to produce minimum damage in cut surfaces.

The formation of grooves by scratching is an example of cutting with more than one edge. The mechanics are investigated and applied to the topic of abrasive wear. It is shown that not only hardness and contact load is important, but also the fracture toughness of the surface material.

Cutting the same material at different depths of cut results in a spectrum of different forms of offcut, from ductile continuous ribbons at small depths to brittle ‘knocking lumps out’ at large. The associated forces vary from steady, through oscillating, to intermittent. Which behaviour occurs depends on the depth of cut relative to a material length parameter given by [ER/k2] = [KC/k]2 where E is Young’s modulus, R is fracture toughness, k is the shear yield strength and KC is the critical stress intensity factor. Glass has low KC/k and is normally brittle, but it can be machined with continuous chips at micrometre depths of cut; steel has high KC/k and normally machines in a ductile manner, but at metre depths of cut becomes brittle. This behaviour represents a ‘cube-square’ scale effect and supports the contention that analysis of cutting is a branch of elastoplastic fracture mechanics. Its connexion with allometry (scaling in biology) is discussed.

Most dentists pay little heed to what is actually happening at the end of their turbine but as they proceed to prepare a cavity within a tooth for restoration. However, there are many surface preparation factors that will influence how well our adhesive and non-adhesive materials will work. Many of these will relate to the methods used to prepare the cavity in the first place such as diamond, tungsten carbide and steel burs.  Cutting of the root dentine is also needed in preparation prior to endodontic treatment, with significant commercial investment for the development of flexible cutting instruments based around nickel titanium alloys.

Tooth-cutting interactions have been examined microscopically for over twenty five years using a variety of microscopic techniques; in particular, video-rate confocal microscopy. This has given a unique insight into how many of the procedures that we take for granted are achieved in clinical practice, by showing microscopic video images of the cutting as it occurs within the tooth. Cutting techniques with high and low torque handpieces, dry and wet airbrasive applications and laser cutting have all been imaged microscopically. The influence of these preparation modalities on both sound and diseased (carious) enamel and dentine is profound: especially when the integrity of the remaining tooth surface has such a strong influence on success or failure for bonding adhesive materials. 

Surgical robotics is gaining in popularity due to the ever-increasing need for more complex, accurate, but less invasive surgery, which conventional instruments are holding back. Amongst the many embodiments at different stages of research and development, needle steering holds promise, but has yet to demonstrate real clinical impact. This minimally invasive procedure involves the insertion of a thin, flexible needle through the skin and into tissue, for application to a variety of clinical needs, including diagnostics, therapy and therapy monitoring. The ability to steer the needle enables the surgeon to avoid obstacles and counteract targeting inaccuracies due to tissue deformation (due to tool-tissue interactions) and organ motion (due to e.g. breathing and pulsatile forces), but these first need to be appropriately modelled and tracked, which remains an open challenge.

In this presentation, the complexity of tool-tissue interaction modelling will be reviewed in the context of exciting new research on a steerable needle, codenamed STING, which is inspired by the ovispotior (or egg laying channel) of parasitic wasps. The biomimetic foundations of this unique design will be discussed, followed by an overview of several unique approaches to the characterisation and modelling of the needle behaviour. These have been developed specifically for STING, with the aim of understanding and optimising its performance in surgery, but many of the results have broader implications. The talk will end with a summary of the current state of the field and an outlook of what is to come.

Insects and mammals, in general, consume each other or terrestrial plants; in other words they eat organisms with structures that resist gravity. Insects have a tough exoskeleton while mammals have an endoskeleton. The leaves and stems of vascular plants, in contrast, have tough structures around each cell. The scale, heterogeneity and temporal variability of food affect the adaptations for cutting and processing food. The requirements for processing insects as food therefore differ from those for processing relatively large animals. Herbivores face the added complication that the physical properties of plant food can vary with environmental factors.

Herbivores range from the smallest insects that can live and feed inside a single leaf to larger insects and the smallest mammals that consume individual leaves but are still small enough to be able to select parts of leaves. Cutting adaptations relate to the fine scale properties of the food. On the other hand the largest mammals process food in bulk and the implications of this are not well understood.

Grazing (grass eating) in large mammals has generally evolved from browsing (eating dicotyledonous plants). Browse is commonly assumed to be relatively easy to physically process, compared with a diet of grasses (a group of monocotyledonous plants) that are considered to be tough and fibrous. These assumptions are reviewed. Browsers are potentially faced with a highly heterogeneous diet, particularly when living in seasonal environments. Cutting adaptations appear to include clearance of fractured components of the diet away from the cutting edges. In grazers, the more complicated cutting patterns of the teeth may relate not so much to relative toughness, or even the pattern of the veins, but to the bulk processing of very long, thin and narrow leaves.

Tooth wear in mammals gradually removes features of the working surfaces of teeth vital for breaking down food particles. This loss of tooth tissue is a major factor limiting the lifespans of individuals in the wild. The threat to enamel, the main contact tissue of tooth crowns, is mainly mechanical, stemming from contacts with hard objects including silica(tes) from soils, amorphous plant silica and also perhaps woody plant tissue such as seed coats. Shallow marks have been documented extensively on worn tooth enamel in microwear studies, forming the main indication of what has transpired during wear events. The circumstances of this mechanical wear qualify as a type of cutting process in which the foreign object (siliceous particle or seed shell) can be viewed as the ‘tool’ creating change in the enamel surface. During any one contact, there are two possibilities: either the enamel surface is re-arranged via plastic deformation (thus not losing material within that single event) or a chip or ribbon of enamel is created that results in immediate tissue loss (definitive of wear).  The factors affecting what transpires are well-known to include the relative hardness of the contacting materials, angulation of the contacting surfaces and friction. Less well-known is the effect that enamel toughness plays in protecting against wear, and the critical depth to which enamel is disturbed. In collaboration with a large group of collaborators that include A.G. Atkins, we have attempted displacement-controlled cutting tests on enamel designed to simulate wear conditions accurately and discover the effective value of the toughness of enamel at this scale. From this, we suggest that the standard ‘R-curve’ approach to biological mineralized tissues, which would have toughness values building from low values upwards with increasing scale, has to be revised for enamel.