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.

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.

Fracture incidence in relation to the pattern of use of hormone therapy in postmenopausal women

Context: Evidence is limited on the effects of different patterns of use of postmenopausal hormone therapy on fracture incidence and particularly on the effects of ceasing use. Objective: To investigate the effect of different patterns of hormone therapy use on fracture incidence. Design, Setting, and Participants: Prospective study of 138737 postmenopausal women aged 50 to 69 years recruited from the UK general population in 19961998 (the Million Women Study) and followed up for 1.9 to 3.9 years (average, 2.8 years) for fracture incidence. Main Outcome Measure: Adjusted relative risk (RR) for incident fracture (except fracture of the fingers, toes, and ribs) in hormone therapy users compared with never users at baseline. Results: A total of 5197 women (3.7%) reported 1 or more fractures, 79% resulting from falls. Current users of hormone therapy at baseline had a significantly reduced incidence of fracture (RR, 0.62; 95% confidence interval [CI], 0.58-0.66; P<.001). This protection was evident soon after hormone therapy began, and the RR decreased with increasing duration of use (P=.001). Among current users at baseline the RR of fracture did not vary significantly according to whether estrogen-only, estrogen-progestin, or other types of hormones were used (RR [95% CI], 0.64 [0.58-0.71], 0.58 [0.53-0.64], and 0.67 [0.56-0.80], respectively; P=19), nor did it vary significantly according to estrogen dose or estrogen or progestin constituents. The RR associated with current use of hormone therapy did not vary significantly according to 11 personal characteristics of study participants, including their age at menopause, body mass index, and physical activity. Past users of hormone therapy at baseline experienced no significant protection against fractures (RR, 1.07; 95% CI, 0.99-1.15); incidence rates returned to those of never-users within about a year of ceasing use. Conclusions: All types of hormone therapy studied confer substantial protection against fracture while they are used. This protection appears rapidly after use commences and wears off rapidly after use ceases. The older women are, the greater is their absolute reduction in fracture incidence while using hormone therapy.

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.

Measuring toughness and the cohesive stress-displacement relationship by the essential work of fracture concept

The complete fracture behaviour of ductile double edge notched tension (DENT) specimen is analysed with an approximate model, which is then used to discuss the essential work of fracture (EWF) concept. The model results are compared with the experimental results for an aluminium alloy 6082-O. The restrictions on the ligament size for valid application of the EWF method are discussed with the aid of the model. The model is used to suggest an improved method of obtaining the cohesive stress-displacement relationship for the fracture process zone (FPZ).

Mode I fracture of sheet metal

The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I “bath-tub”, i.e. “cup & cup”, fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5–5 mm). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the “fracture” work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of 1 mm, both fracture and necking contributions have the same order of magnitude in most of the metals investigated. A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing and the plate thickness, and (ii) the flow properties of the material. Each term can dominate depending on the properties of the material which explains the different behaviours reported in the literature about thin plate fracture toughness and its dependence with thickness.

Investigation of the fracture mode for hard and soft wheat endosperm using the loading-unloading bending test

Investigation of the fracture mode for hard and soft wheat endosperm was aimed at gaining a better understanding of the fragmentation process. Fracture mechanical characterization was based on the three-point bending test which enables stable crack propagation to take place in small rectangular pieces of wheat endosperm. The crack length can be measured in situ by using an optical microscope with light illumination from the side of the specimen or from the back of the specimen. Two new techniques were developed and used to estimate the fracture toughness of wheat endosperm, a geometric approach and a compliance method. The geometric approach gave average fracture toughness values of 53.10 and 27.0 J m(-2) for hard and soft endosperm, respectively. Fracture toughness estimated using the compliance method gave values of 49.9 and 29.7 J m(-2) for hard and soft endosperm, respectively. Compressive properties of the endosperm in three mutually perpendicular axes revealed that the hard and soft endosperms are isotropic composites. Scanning electron microscopy (SEM) observation of the fracture surfaces and the energy-time curves of loading-unloading cycles revealed that there was a plastic flow during crack propagation for both the hard and soft endosperms, and confirmed that the fracture mode is significantly related to the adhesion level between starch granules and the protein matrix.

Rate-dependent fracture toughness of polycrystalline ice

A series of three-point bend tests using single edge notched testpieces of pure polycrystalline ice have been performed at three different temperatures (–20°C, –30°C and –40°C). The displacement rate was varied from 1 mm/min to 100 mm/min, producing the crack tip strain rates from about 10–3 to 10–1 s–1. The results show that (a) the fracture toughness of pure polycrystalline ice given by the critical stress intensity factor (K IC) is much lower than that measured from the J—integral under identical conditions; (b) from the determination of K IC, the fracture toughness of pure polycrystalline ice decreases with increasing strain rate and there is good power law relationship between them; (c) from the measurement of the J—integral, a different tendency was appeared: when the crack tip strain rate exceeds a critical value of 6 × 10–3 s–1, the fracture toughness is almost constant but when the crack tip strain rate is less than this value, the fracture toughness increases with decreasing crack tip strain rate. Re-examination of the mechanisms of rate-dependent fracture toughness of pure polycrystalline ice shows that the effect of strain rate is related not only to the blunting of crack tips due to plasticity, creep and stress relaxation but also to the nucleation and growth of microcracks in the specimen.

Anterior cingulate activity and level of cognitive conflict: explicit comparisons

The role of anterior cingulate cortex (ACC) in attention is a matter of debate. One hypothesis suggests that its role is to monitor response-level conflict, but explicit evidence is somewhat lacking. In this study, the activation of ACC was compared in (a) color and number standard Stroop tasks in which response preparation and interference shared modality (response-level conflict) and (b) color and number matching Stroop tasks in which response preparation and interference did not share modality (non-response-level conflict). In the congruent conditions, there was no effect of task type. In the interference conditions, anterior cingulate activity in the matching tasks was less than that in the standard tasks. These results support the hypothesis that ACC specifically mediates generalized modality-independent selection processes invoked by response competition.

Anticipatory activation in the amygdala and anterior cingulate in generalized anxiety disorder and prediction of treatment response

OBJECTIVE: The anticipation of adverse outcomes, or worry, is a cardinal symptom of generalized anxiety disorder. Prior work with healthy subjects has shown that anticipating aversive events recruits a network of brain regions, including the amygdala and anterior cingulate cortex. This study tested whether patients with generalized anxiety disorder have alterations in anticipatory amygdala function and whether anticipatory activity in the anterior cingulate cortex predicts treatment response. METHOD: Functional magnetic resonance imaging (fMRI) was employed with 14 generalized anxiety disorder patients and 12 healthy comparison subjects matched for age, sex, and education. The event-related fMRI paradigm was composed of one warning cue that preceded aversive pictures and a second cue that preceded neutral pictures. Following the fMRI session, patients received 8 weeks of treatment with extended-release venlafaxine. RESULTS: Patients with generalized anxiety disorder showed greater anticipatory activity than healthy comparison subjects in the bilateral dorsal amygdala preceding both aversive and neutral pictures. Building on prior reports of pretreatment anterior cingulate cortex activity predicting treatment response, anticipatory activity in that area was associated with clinical outcome 8 weeks later following treatment with venlafaxine. Higher levels of pretreatment anterior cingulate cortex activity in anticipation of both aversive and neutral pictures were associated with greater reductions in anxiety and worry symptoms. CONCLUSIONS: These findings of heightened and indiscriminate amygdala responses to anticipatory signals in generalized anxiety disorder and of anterior cingulate cortex associations with treatment response provide neurobiological support for the role of anticipatory processes in the pathophysiology of generalized anxiety disorder.

Altered anterior insula activation during anticipation and experience of painful stimuli in expert meditators.

Experientially opening oneself to pain rather than avoiding it is said to reduce the mind's tendency toward avoidance or anxiety which can further exacerbate the experience of pain. This is a central feature of mindfulness-based therapies. Little is known about the neural mechanisms of mindfulness on pain. During a meditation practice similar to mindfulness, functional magnetic resonance imaging was used in expert meditators (> 10,000 h of practice) to dissociate neural activation patterns associated with pain, its anticipation, and habituation. Compared to novices, expert meditators reported equal pain intensity, but less unpleasantness. This difference was associated with enhanced activity in the dorsal anterior insula (aI), and the anterior mid-cingulate (aMCC) the so-called ‘salience network’, for experts during pain. This enhanced activity during pain was associated with reduced baseline activity before pain in these regions and the amygdala for experts only. The reduced baseline activation in left aI correlated with lifetime meditation experience. This pattern of low baseline activity coupled with high response in aIns and aMCC was associated with enhanced neural habituation in amygdala and pain-related regions before painful stimulation and in the pain-related regions during painful stimulation. These findings suggest that cultivating experiential openness down-regulates anticipatory representation of aversive events, and increases the recruitment of attentional resources during pain, which is associated with faster neural habituation.

In-situ spatio-temporal measurements of the detailed azimuthal substructure of the substorm current wedge

The substorm current wedge (SCW) is a fundamental component of geomagnetic substorms. Models tend to describe the SCW as a simple line current flowing into the ionosphere towards dawn and out of the ionosphere towards dusk, linked by a westward electrojet. We use multi-spacecraft observations from perigee passes of the Cluster 1 and 4 spacecraft during a substorm on 15 Jan 2010, in conjunction with ground-based observations, to examine the spatial structuring and temporal variability of the SCW. At this time, the spacecraft travelled east-west azimuthally above the auroral region. We show that the SCW has significant azimuthal sub-structure on scales of 100~km at altitudes of 4,000-7,000~km. We identify 26 individual current sheets in the Cluster 4 data and 34 individual current sheets in the Cluster 1 data, with Cluster 1 passing through the SCW 120-240~s after Cluster 4 at 1,300-2,000~km higher altitude. Both spacecraft observed large-scale regions of net upward and downward field-aligned current, consistent with the large-scale characteristics of the SCW, although sheets of oppositely directed currents were observed within both regions. We show that the majority of these current sheets were closely aligned to a north-south direction, in contrast to the expected east-west orientation of the pre-onset aurora. Comparing our results with observations of the field-aligned current associated with bursty bulk flows (BBFs) we conclude that significant questions remain for the explanation of SCW structuring by BBF driven ``wedgelets". Our results therefore represent constraints on future modelling and theoretical frameworks on the generation of the SCW.