A simple criterion for filament break-up in drop-on-demand inkjet printing

Jets from drop-on-demand inkjet print-heads consist of a main drop with a trailing filament, which either condenses into the main drop, or breaks up into satellite drops. Filament behaviour is quantitatively similar to that of larger, free symmetrical filamentscan be predicted from the aspect ratio and Ohnesorge number. Symmetrical filaments generated from inkjet print-heads show the same behaviour. A simple model, based on competition between the processes of axial shortening and radial necking, predicts the critical aspect ratio below which the jet condenses into a single drop. The success of this simple criterion supports the underlying physical model. © 2013 American Institute of Physics.

A fracture criterion for the notch strength of high strength steels in the presence of hydrogen

High strength steels can suffer from a loss of ductility when exposed to hydrogen, and this may lead to sudden failure. The hydrogen is either accommodated in the lattice or is trapped at defects, such as dislocations, grain boundaries and carbides. The challenge is to identify the effect of hydrogen located at different sites upon the drop in tensile strength of a high strength steel. For this purpose, literature data on the failure stress of notched and un-notched steel bars are re-analysed; the bars were tested over a wide range of strain rates and hydrogen concentrations. The local stress state at failure has been determined by the finite element (FE) method, and the concentration of both lattice and trapped hydrogen is predicted using Oriani's theory along with the stress-driven diffusion equation. The experimental data are rationalised in terms of a postulated failure locus of peak maximum principal stress versus lattice hydrogen concentration. This failure locus is treated as a unique material property for the given steel and heat treatment condition. We conclude that the presence of lattice hydrogen increases the susceptibility to hydrogen embrittlement whereas trapped hydrogen has only a negligible effect. It is also found that the observed failure strength of hydrogen charged un-notched bars is less than the peak local stress within the notched geometries. Weakest link statistics are used to account for this stressed volume effect. © 2013 Elsevier Ltd.

The effect of hole size upon the strength of metallic and polymeric foams

Tensile and compressive tests have been performed on centre-hole panels, made from three types of metallic foams and two polymeric foams. In compression, the foams fail in a ductile, notch-insensitive manner, in support of a "net section strength" criterion. In tension, a ductile-brittle transition is observed for some of the foams at sufficiently large specimen sizes: for a small hole diameter the net section strength criterion is obeyed, whereas for a large hole a local stress criterion applies and the net section strength is reduced. For a number of the foams, the panel size was not sufficiently large to observe this ductile-brittle switch in behaviour. The predictions of a cohesive zone model are compared with the measured strengths and are found to be in good agreement. © 2001 Elsevier Science Ltd. All rights reserved.

Mode I crack growth resistance of metallic foams

A Dugdale-type cohesive zone model is used to predict the mode I crack growth resistance (R-curve) of metallic foams, with the fracture process characterized by an idealized traction-separation law that relates the crack surface traction to crack opening displacement. A quadratic yield function, involving the von Mises effective stress and mean stress, is used to account for the plastic compressibility of metallic foams. Finite element calculations are performed for the crack growth resistance under small scale yielding and small scale bridging in plane strain, with K-field boundary conditions. The following effects upon the fracture process are quantified: material hardening, bridging strength, T-stress (the non-singular stress acting parallel to the crack plane), and the shape of yield surface. To study the failure behaviour and notch sensitivity of metallic foams in the presence of large scale yielding, a study is made for panels embedded with either a centre-crack or an open hole and subjected to tensile stressing. For the centre-cracked panel, a transition crack size is predicted for which the fracture response switches from net section yielding to elastic-brittle fracture. Likewise, for a panel containing a centre-hole, a transition hole diameter exists for which the fracture response switches from net section yielding to a local maximum stress criterion at the edge of the hole.

Surface-waves, stability, and scattering for a lined duct with flow

We consider a straight cylindrical duct with a steady subsonic axial flow and a reacting boundary (e.g. an acoustic lining). The wave modes are separated into ordinary acoustic duct modes, and surface modes confined to a small neighbourhood of the boundary. Many researchers have used a mass-spring-damper boundary model, for which one surface mode has previously been identified as a convective instability; however, we show the stability analysis used in such cases to be questionable. We investigate instead the stability of the surface modes using the Briggs-Bers criterion for a Flügge thin-shell boundary model. For modest frequencies and wavenumbers the thin-shell has an impedance which is effectively that of a mass-spring-damper, although for the large wavenumbers needed for the stability analysis the thin-shell and mass-spring-damper impedances diverge, owing to the thin shell's bending stiffness. The thin shell model may therefore be viewed as a regularization of the mass-spring-damper model which accounts for nonlocally-reacting effects. We find all modes to be stable for realistic thin-shell parameters, while absolute instabilities are demonstrated for extremely thin boundary thicknesses. The limit of vanishing bending stiffness is found to be a singular limit, yielding absolute instabilities of arbitrarily large temporal growth rate. We propose that the problems with previous stability analyses are due to the neglect of something akin to bending stiffness in the boundary model. Our conclusion is that the surface mode previously identified as a convective instability may well be stable in reality. Finally, inspired by Rienstra's recent analysis, we investigate the scattering of an acoustic mode as it encounters a sudden change from a hard-wall to a thin-shell boundary, using a Wiener-Hopf technique. The thin-shell is considered to be clamped to the hard-wall. The acoustic mode is found to scatter into transmitted and reflected acoustic modes, and surface modes strongly linked to the solid waves in the boundary, although no longitudinal or transverse waves within the boundary are excited. Examples are provided that demonstrate total transmission, total reflection, and a combination of the two. This thin-shell scattering problem is preferable to the mass-spring-damper scattering problem presented by Rienstra, since the thin-shell problem is fully determined and does not need to appeal to a Kutta-like condition or the inclusion of an instability in order to avoid a surface-streamline cusp at the boundary change.

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1, - ∞ < x < ∞ with mean flow Mach number M > 0 and a hard wall along x < 0 and a wall of impedance Z along x > 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t), no more singular than h = Ο(x1/2) for x ↓ 0. A mode, incident from x < 0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = Ο(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z (ω) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ω → 0, the modulus fends to |R001| → (1 + M)/(1 -M) without and to 1 with Kutta condition, while the end correction tends to ∞ without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow.

Changes of mind in decision-making.

A decision is a commitment to a proposition or plan of action based on evidence and the expected costs and benefits associated with the outcome. Progress in a variety of fields has led to a quantitative understanding of the mechanisms that evaluate evidence and reach a decision. Several formalisms propose that a representation of noisy evidence is evaluated against a criterion to produce a decision. Without additional evidence, however, these formalisms fail to explain why a decision-maker would change their mind. Here we extend a model, developed to account for both the timing and the accuracy of the initial decision, to explain subsequent changes of mind. Subjects made decisions about a noisy visual stimulus, which they indicated by moving a handle. Although they received no additional information after initiating their movement, their hand trajectories betrayed a change of mind in some trials. We propose that noisy evidence is accumulated over time until it reaches a criterion level, or bound, which determines the initial decision, and that the brain exploits information that is in the processing pipeline when the initial decision is made to subsequently either reverse or reaffirm the initial decision. The model explains both the frequency of changes of mind as well as their dependence on both task difficulty and whether the initial decision was accurate or erroneous. The theoretical and experimental findings advance the understanding of decision-making to the highly flexible and cognitive acts of vacillation and self-correction.

Recurrent input transformations for Hidden Markov models

This paper presents a new architecture which integrates recurrent input transformations (RIT) and continuous density HMMs. The basic HMM structure is extended to accommodate recurrent neural networks which transform the input observations before they enter the Gaussian output distributions associated with the states of the HMM. During training the parameters of both HMM and RIT are simultaneously optimized according to the Maximum Mutual Information (MMI) criterion. Results are presented for the E-set recognition task which demonstrate the ability of recurrent input transformations to exploit longer term correlations in the speech signal and to give improved discrimination.

Road damage due to dynamic tyre forces measured on a public road

This paper describes a series of tests conducted on a UK trunk road, in which the dynamic tyre forces generated by over 1500 heavy goods vehicles (HGVs) were measured using a load measuring mat containing 144 capacitive strip sensors. The data was used to investigate the relative road damaging potential of the various classes of vehicles, and the degree of spatial repeatability of tyre forces present in a typical highway fleet. Approximately half the vehicles tested were found to contribute to a spatially repeatable pattern of pavement loading. On average, air suspended vehicles were found to generate lower dynamic load coefficients than steel suspended vehicles. However, air suspended vehicles also generated higher mean levels of theoretical road damage (aggregate force) than steel suspended vehicles, indicating that the ranking of suspensions depends on the pavement damage criterion used.

Probabilistic fault identification using vibration data and neural networks

Bayesian formulated neural networks are implemented using hybrid Monte Carlo method for probabilistic fault identification in cylindrical shells. Each of the 20 nominally identical cylindrical shells is divided into three substructures. Holes of (12±2) mm in diameter are introduced in each of the substructures and vibration data are measured. Modal properties and the Coordinate Modal Assurance Criterion (COMAC) are utilized to train the two modal-property-neural-networks. These COMAC are calculated by taking the natural-frequency-vector to be an additional mode. Modal energies are calculated by determining the integrals of the real and imaginary components of the frequency response functions over bandwidths of 12% of the natural frequencies. The modal energies and the Coordinate Modal Energy Assurance Criterion (COMEAC) are used to train the two frequency-response-function-neural-networks. The averages of the two sets of trained-networks (COMAC and COMEAC as well as modal properties and modal energies) form two committees of networks. The COMEAC and the COMAC are found to be better identification data than using modal properties and modal energies directly. The committee approach is observed to give lower standard deviations than the individual methods. The main advantage of the Bayesian formulation is that it gives identities of damage and their respective confidence intervals.