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.

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.

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.

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.

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.

Design of a biomimetic skin for an octopus-inspired robot - Part II: Development of the skin artefact

In order to develop skin artefact for an octopus-inspired robot arm, which is designed to be able to elongate 60% of its original length, silicone rubber and knitted nylon sheet were selected to manufacture an artificial skin, due to their higher elastic strain and high flexibility. Tensile and scissors cutting tests were conducted to characterise the matrix and reinforcing materials and the skin artefact. Material properties of the individual and the composite materials were compared with the measured properties of real octopus skin presented in Part I. The Young’s modulus of the skin should be below 20 MPa and the elastic strain range should be over 60%. The fracture toughness should be at least 0.9 kJ·m−2. Tubes made of the skin artefact filled with liquid were tested to study volume change under deformation. Finite element analysis model was developed to simulate the material and arm structure under tensile loading. Results show that the skin artefact developed has similar mechanical properties as the real octopus skin and satisfies all the design specifications of the OCTOPUS robot.

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.

Slicing of soft, flexible solids with industrial applications

Thin slices of soft flexible solids have negligible bending resistance and hence store negligible elastic strain energy; furthermore such offcuts are rarely permanently deformed after slicing. Cutting forces thus depend only on work of separation (toughness work) and friction. These simplifying assumptions are not as restrictive as it might seem, and the mechanics are found to apply to a wide variety of foodstuffs and biological materials. The fracture toughness of such materials may be determined from cutting experiments: the use of scissors instrumented for load and displacement is a popular method where toughness is obtained from the work areas beneath load–displacement plots. Surprisingly, there is no analysis for the variation of forces with scissor blade opening and this paper provides the theory. Comparison is made with experimental results in cutting with scissors. The analysis is generalised to cutting with blades of variable curvature and applied to a commercial food cutting device having a rotating spiral plan form blade. The strong influence of the ‘slice/push ratio’ (blade tangential speed to blade edge normal speed) on the cutting forces is revealed. Small cutting forces are important in food cutting machinery as damage to slices is minimised. How high slice/push ratios may be achieved by choice of blade profile is discussed.

Design of a biomimetic skin for an octopus-inspired robot– Part I: characterising octopus skin

Octopus skin samples were tested under quasi-static and scissor cutting conditions to measure the in-plane material properties and fracture toughness. Samples from all eight arms of one octopus were tested statically to investigate how properties vary from arm to arm. Another nine octopus skins were measured to study the influence of body mass on skin properties. Influence of specimen location on skin mechanical properties was also studied. Material properties of skin, i.e. the Young's modulus, ultimate stress, failure strain and fracture toughness have been plotted against the position of skin along the length of arm or body. Statistical studies were carried out to help analyzing experimental data obtained. Results of this work will be used as guidelines for the design and development of artificial skins for an octopus-inspired robot.

Developing skin analogues for a robotic octopus

In order to fabricate a biomimetic skin for an octopus inspired robot, a new process was developed based on mechanical properties measured from real octopus skin. Various knitted nylon textiles were tested and the one of 10-denier nylon was chosen as reinforcement. A combination of Ecoflex 0030 and 0010 silicone rubbers was used as matrix of the composite to obtain the right stiffness for the skin-analogue system. The open mould fabrication process developed allows air bubble to escape easily and the artificial skin produced was thin and waterproof. Material properties of the biomimetic skin were characterised using static tensile and instrumented scissors cutting tests. The Young’s moduli of the artificial skin are 0.08 MPa and 0.13 MPa in the longitudinal and transverse directions, which are much lower than those of the octopus skin. The strength and fracture toughness of the artificial skin, on the other hand are higher than those of real octopus skins. Conically-shaped skin prototypes to be used to cover the robotic arm unit were manufactured and tested. The biomimetic skin prototype was stiff enough to maintain it conical shape when filled with water. The driving force for elongation was reduced significantly compared with previous prototypes.

C–H local modes in cyclobutene. II. Laser photoacoustic studies 10 000–17 000 cm−1. Vibrational structure and C–H local mode dynamics

In part I of this study [Baggott, Clase, and Mills, Spectrochim. Acta Part A 42, 319 (1986)] we presented FTIR spectra of gas phase cyclobutene and modeled the v=1–3 stretching states of both olefinic and methylenic C–H bonds in terms of a local mode model. In this paper we present some improvements to our original model and make use of recently derived ‘‘x,K relations’’ to find the equivalent normal mode descriptions. The use of both the local mode and normal mode approaches to modeling the vibrational structure is described in some detail. We present evidence for Fermi resonance interactions between the methylenic C–H stretch overtones and ring C–C stretch vibrations, revealed in laser photoacoustic spectra in the v=4–6 region. An approximate model vibrational Hamiltonian is proposed to explain the observed structure and is used to calculate the dynamics of the C–H stretch local mode decay resulting from interaction with lower frequency ring modes. The implications of our experimental and theoretical studies for mode‐selective photochemistry are discussed briefly.

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).

Structural and magnetic studies of Schiff base complexes of nickel(ii) nitrite: change in crystalline state, ligand rearrangement and a very rare μ-nitrito-1κO:2κN:3κO′ bridging mode

Four new nickel(II) complexes, [Ni2L2(NO2)2]·CH2Cl2·C2H5OH, 2H2O (1), [Ni2L2(DMF)2(m-NO2)]ClO4·DMF (2a), [Ni2L2(DMF)2(m-NO2)]ClO4 (2b) and [Ni3L¢2(m3-NO2)2(CH2Cl2)]n·1.5H2O (3) where HL = 2-[(3-amino-propylimino)-methyl]-phenol, H2L¢ = 2-({3-[(2-hydroxy-benzylidene)-amino]-propylimino}-methyl)-phenol and DMF = N,N-dimethylformamide, have been synthesized starting with the precursor complex [NiL2]·2H2O, nickel(II) perchlorate and sodium nitrite and characterized structurally and magnetically. The structural analyses reveal that in all the complexes, NiII ions possess a distorted octahedral geometry. Complex 1 is a dinuclear di-m2-phenoxo bridged species in which nitrite ion acts as chelating co-ligand. Complexes 2a and 2b also consist of dinuclear entities, but in these two compounds a cis-(m-nitrito-1kO:2kN) bridge is present in addition to the di-m2-phenoxo bridge. The molecular structures of 2a and 2b are equivalent; they differ only in that 2a contains an additional solvated DMF molecule. Complex 3 is formed by ligand rearrangement and is a one-dimensional polymer in which double phenoxo as well as m-nitrito-1kO:2kN bridged trinuclear units are linked through a very rare m3-nitrito-1kO:2kN:3kO¢ bridge. Analysis of variable-temperature magnetic susceptibility data indicates that there is a global weak antiferromagnetic interaction between the nickel(II) ions in four complexes, with exchange parameters J of -5.26, -11.45, -10.66 and -5.99 cm-1 for 1, 2a, 2b and 3, respectively

Southern annular mode dynamics in observations and models, Part II: Eddy feedbacks

Many global climate models (GCMs) have trouble simulating Southern Annular Mode (SAM) variability correctly, particularly in the Southern Hemisphere summer season where it tends to be too persistent. In this two part study, a suite of experiments with the Canadian Middle Atmosphere Model (CMAM) is analyzed to improve our understanding of the dynamics of SAM variability and its deficiencies in GCMs. Here, an examination of the eddy-mean flow feedbacks is presented by quantification of the feedback strength as a function of zonal scale and season using a new methodology that accounts for intraseasonal forcing of the SAM. In the observed atmosphere, in the summer season, a strong negative feedback by planetary scale waves, in particular zonal wavenumber 3, is found in a localized region in the south west Pacific. It cancels a large proportion of the positive feedback by synoptic and smaller scale eddies in the zonal mean, resulting in a very weak overall eddy feedback on the SAM. CMAM is deficient in this negative feedback by planetary scale waves, making a substantial contribution to its bias in summertime SAM persistence. Furthermore, this bias is not alleviated by artificially improving the climatological circulation, suggesting that climatological circulation biases are not the cause of the planetary wave feedback deficiency in the model. Analysis of the summertime eddy feedbacks in the CMIP-5 models confirms that this is indeed a common problem among GCMs, suggesting that understanding this planetary wave feedback and the reason for its deficiency in GCMs is key to improving the fidelity of simulated SAM variability in the summer season.