Modelling metal cutting using modern ductile fracture mechanics: Quantitative explanations for some longstanding problems

The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.

Fracture toughness and cutting

An exploratory model for cutting is presented which incorporates fracture toughness as well as the commonly considered effects of plasticity and friction. The periodic load fluctuations Been in cutting force dynamometer tests are predicted, and considerations of chatter and surface finish follow. A non-dimensional group is put forward to classify different regimes of material response to machining. It leads to tentative explanations for the difficulties of cutting materials such as ceramics and brittlo polymers, and also relates to the formation of discontinuous chips. Experiments on a range of solids with widely varying toughness/strength ratios generally agree with the analysis.

Toughness & cutting: A new way of determining ductile fracture toughness and strength

A review is given of the mechanics of cutting, ranging from the slicing of thin floppy offcuts (where there is negligible elasticity and no permanent deformation of the offcut) to the machining of ductile metals (where there is severe permanent distortion of the offcut/chip). Materials scientists employ the former conditions to determine the fracture toughness of ‘soft’ solids such as biological materials and foodstuffs. In contrast, traditional analyses of metalcutting are based on plasticity and friction only, and do not incorporate toughness. The machining theories are inadequate in a number of ways but a recent paper has shown that when ductile work of fracture is included many, if not all, of the shortcomings are removed. Support for the new analysis is given by examination of FEM simulations of metalcutting which reveal that a ‘separation criterion’ has to be employed at the tool tip. Some consideration shows that the separation criteria are versions of void-initiation-growth-and-coalescence models employed in ductile fracture mechanics. The new analysis shows that cutting forces for ductile materials depend upon the fracture toughness as well as plasticity and friction, and reveals a simple way of determining both toughness and flow stress from cutting experiments. Examples are given for a wide range of materials including metals, polymers and wood, and comparison is made with the same properties independently determined using conventional testpieces. Because cutting can be steady state, a new way is presented for simultaneously measuring toughness and flow stress at controlled speeds and strain rates.

Cutting, by 'pressing and slicing,' of thin floppy slices of materials illustrated by experiments on cheddar cheese and salami

Why it is easier to cut with even the sharpest knife when 'pressing down and sliding' than when merely 'pressing down alone' is explained. A variety of cases of cutting where the blade and workpiece have different relative motions is analysed and it is shown that the greater the 'slice/push ratio' xi given by ( blade speed parallel to the cutting edge/blade speed perpendicular to the cutting edge), the lower the cutting forces. However, friction limits the reductions attainable at the highest.. The analysis is applied to the geometry of a wheel cutting device (delicatessan slicer) and experiments with a cheddar cheese and a salami using such an instrumented device confirm the general predictions. (C) 2004 Kluwer Academic Publishers.

An investigation into the mechanics of cutting using data from orthogonally cutting Nylon 66

Cutting force data for Nylon 66 has been examined in terms of various different models of cutting. Theory that includes significant work of separation at the tool tip was found to give the best correlation with experimental data over a wide range of rake angles for derived primary shear plane angle. A fracture toughness parameter was used as the measure of the specific work of separation. Variation in toughness with rake angle determined from cutting is postulated to be caused by mixed mode separation at the tool tip. A rule of mixtures using independently determined values of toughness in tension (mode 1) and shear (mode 11) is found to describe well the variation with rake angle. The ratio of modes varies with rake angle and, in turn, with the primary shear plane angle. Previous suggestions that cutting is a means of experimentally determining fracture toughness are now seen to be extended to identify the mode of fracture toughness as well.

Effect of cutting time, temperature and calcium on curd moisture, whey fat loses and curd yield by response surface methodology

Response surface methodology was used to study the effect of temperature, cutting time, and calcium chloride addition level on curd moisture content, whey fat losses, and curd yield. Coagulation and syneresis were continuously monitored using 2 optical sensors detecting light backscatter. The effect of the factors on the sensors’ response was also examined. Retention of fat during cheese making was found to be a function of cutting time and temperature, whereas curd yield was found to be a function of those 2 factors and the level of calcium chloride addition. The main effect of temperature on curd moisture was to increase the rate at which whey was expelled. Temperature and calcium chloride addition level were also found to affect the light backscatter profile during coagulation whereas the light backscatter profile during syneresis was a function of temperature and cutting time. The results of this study suggest that there is an optimum firmness at which the gel should be cut to achieve maximum retention of fat and an optimum curd moisture content to maximize product yield and quality. It was determined that to maximize curd yield and quality, it is necessary to maximize firmness while avoiding rapid coarsening of the gel network and microsyneresis. These results could contribute to the optimization of the cheese-making process.

Influence of curd cutting programme and stirring speed on the prediction of syneresis indices in cheese-making using NIR light backscatter

An NIR reflectance sensor, with a large field of view and a fibre-optic connection to a spectrometer for measuring light backscatter at 980 nm, was used to monitor the syneresis process online during cheese-making with the goal of predicting syneresis indices (curd moisture content, yield of whey and fat losses to whey) over a range of curd cutting programmes and stirring speeds. A series of trials were carried out in an 11 L cheese vat using recombined whole milk. A factorial experimental design consisting of three curd stirring speeds and three cutting programmes, was undertaken. Milk was coagulated under constant conditions and the casein gel was cut when the elastic modulus reached 35 Pa. Among the syneresis indices investigated, the most accurate and most parsimonious multivariate model developed was for predicting yield of whey involving three terms, namely light backscatter, milk fat content and cutting intensity (R2 = 0.83, SEy = 6.13 g/100 g), while the best simple model also predicted this syneresis index using the light backscatter alone (R2 = 0.80, SEy = 6.53 g/100 g). In this model the main predictor was the light backscatter response from the NIR light back scatter sensor. The sensor also predicted curd moisture with a similar accuracy.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

Perennial legumes native to Australia: a preliminary investigation of nutritive value and response to cutting

Six Australian native herbaceous perennial legumes (Lotus australis, Swainsona colutoides, Swainsona swainsonioides, Cullen tenax, Glycine tabacina and Kennedia prorepens) were assessed in the glasshouse for nutritive value, soluble condensed tannins and production of herbage in response to three cutting treatments (regrowth harvested every 4 and 6 weeks and plants left uncut for 12 weeks). The Mediterranean perennial legumes Medicago sativa and Lotus corniculatus were also included. Dry matter (DM) yield of some native legumes was comparable to L. corniculatus, but M. sativa produced more DM than all species except S. swainsonioides after 12 weeks of regrowth. Dry matter yield of all native legumes decreased with increased cutting frequency, indicating a susceptibility to frequent defoliation. Shoot in vitro dry matter digestibility (DMD) was high (>70%) in most native legumes, except G. tabacina (65%) and K. prorepens (55%). Crude protein ranged from 21-28% for all legumes except K. prorepens (12%). More frequent cutting resulted in higher DMD and crude protein in all species, except for the DMD of C. tenax and L. australis, which did not change. Concentrations of soluble condensed tannins were 2-9 g/kg DM in the Lotus spp., 10-18 g/kg DM in K. prorepens and negligible (<1 g/kg) in the other legumes. Of the native species, C. tenax, S. swainsonioides and L. australis showed the most promise for use as forage plants and further evaluation under field conditions is now warranted.

Trophallaxis in Dehydrated Leaf Cutting Colonies of Atta sexdens rubropilosa (Hymenoptera: Formicidae)

Trophallaxis, the transfer of liquid among individuals by oral regurgitation or anal deposition, occurs in many insect groups including ants. The first indication that trophallaxis could occur in leaf cutting ants (Atta sexdens rubropilosa) was made by Autuori in 1942. He reported water collection by this ant species, and highlighted what in those days was an undescribed behavior for this species. In 2005, Da-Silva and Ribeiro presented preliminary results suggesting the existence of trophallaxis in A. sexdens rubropilosa. Here we report on a formal test of the hypothesis of trophallaxis in that species. Our approach was to test ant pairs in which only one individual (Group I) had access to blue-dyed water and the other individual (Group II), a nest-mate, came from a colony dehydrated by offering dry crushed corn for fungal growth. Positive results for trophallaxis were obtained in ants from four colonies and accounted for 33%-46% of all tests in which ants from Group I drank dyed water. These results indicate that trophallaxis occurs in this species.

Colony dehydration and water collection by specialized caste in the leaf-cutting ant Atta sexdens rubropilosa

Social organization enables leaf-cutting ants to keep appropriate micro-ecological nest conditions for the fungus garden (their main food), eggs, larvae and adults. To maintain stability while facing changing conditions, individual ants must perceive destabilising factors and produce a proper behavioral response. We investigated behavioral responses to experimental dehydration in leaf-cutting ants to verify if task specialization exists, and to quantify the ability of ant sub-colonies for water management. Our setup consisted of fourteen sub-colonies, ten of which were randomly assigned to different levels of experimental dehydration with silica gel, whereas the remaining four were controls. The ten experimental sub-colonies were split into two groups, so that five of them had access to water. Diverse ant morphs searched for water in dehydrated colonies, but mainly a caste of small ants collected water after sources had been discovered. Size specialization for water collection was replicable in shorter experiments with three additional colonies. Ants of dehydrated colonies accumulated leaf-fragments on the nest entrance, and covering the fungus garden. Behaviors that may enhance humidity within the nests were common to all dehydration treatments. Water availability increased the life span of dehydrated colonies.