Blind source separation for classification and detection of flaws in impact-echo testing

This paper presents a technique for defect detection and material classification based on blind source separation by independent component analysis (ICA) for application in impact-echo testing. The transfer functions between the impact point and the defects in the material are modelled as “sources” for blind source separation. The sensors located on the material surface measure a convolutive mixture of the contribution of each of the defects. From spectral analysis the dominant resonance frequencies, varying from homogeneous to defective material, are selected. These frequencies are processed by instantaneous ICA in order to obtain more information about the defects using bootstrap resampling to analyse the stability of the solution. Results show that source estimates fit well with the theoretical response of the material. In addition, it has been found that the number of defects can be estimated by ICA in simulations and experiments with various defective parallelepiped-shape materials of aluminium alloy series 2000.     

Influence of end-conditions during tube hydroforming of aluminum extrusions

Tube hydroforming experiments were conducted to develop the forming limit diagram of AA6082-T4 by utilizing three types of end-conditions: (i) “free-end”, (ii) “pinched-end” or “fixed-end” and (iii) “forced-end”. It was found that “free-end” hydroforming gives the lowest forming limits followed by “pinched-end” and “forced-end” hydroforming. It was noticed that the tube failure occurs within 5° to the extrusion weld in the “free-end” experiments, within 7° in the “pinched-end” condition and extended up to 10° in the “forced-end” hydroforming experiments. Finite element simulations were carried out to capture the effects of the weld geometry, weld mechanical properties and the end-conditions of the extruded tube on the maximum induced stress and location of the maximum von Mises stress. It was found that the anisotropy of the weld material and the end-condition used during hydroforming experiments have the largest influence on the failure location with respect to the weld center.     

Nonlinear identification using a B-spline neural network and chaotic immune approaches

One of the important applications of B-spline neural network (BSNN) is to approximate nonlinear functions defined on a compact subset of a Euclidean space in a highly parallel manner. Recently, BSNN, a type of basis function neural network, has received increasing attention and has been applied in the field of nonlinear identification. BSNNs have the potential to “learn” the process model from input–output data or “learn” fault knowledge from past experience. BSNN can be used as function approximators to construct the analytical model for residual generation too. However, BSNN is trained by gradient-based methods that may fall into local minima during the learning procedure. When using feed-forward BSNNs, the quality of approximation depends on the control points (knots) placement of spline functions. This paper describes the application of a modified artificial immune network inspired optimization method − the opt-aiNet − combined with sequences generate by Hénon map to provide a stochastic search to adjust the control points of a BSNN. The numerical results presented here indicate that artificial immune network optimization methods are useful for building good BSNN model for the nonlinear identification of two case studies: (i) the benchmark of Box and Jenkins gas furnace, and (ii) an experimental ball-and-tube system.     

Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure

The dynamic plastic collapse of energy-absorbing structures is more difficult to understand than the corresponding quasi-static collapse, on account of two effects which may be described as the “strain-rate factor” and the “inertia factor” respectively. The first of these is a material property whereby the yield stress is raised, while the second can affect the collapse mode, etc. It has recently been discovered [6,7]that structures whose load-deflection curve falls sharply after an initial “peak” are much more “velocity sensitive” than structures whose load-deflection curve is “flat-topped” (Fig. 1a); that is, when a given amount of energy is delivered by a moving mass, the final deflection depends more strongly on the impact velocity. In this paper we investigate strain-rate and inertia effects in these two types of structure by means of some simple experiments performed in a “drop hammer” testing machine, together with some simple analysis which enables us to give a satisfactory account of the experimental observations. The work is motivated partly by difficulties which occur in small-scale model testing of energy-absorbing structures, on account of the fact that the “strain-rate” and “inertia” factors not only scale differently in general, but also affect the two distinct types of structure differently.     

Substepping algorithms with stress correction for the simulation of sheet metal forming process

The finite element analysis of the sheet metal forming process involves various nonlinearities. To predict accurately the final geometry of the sheet blank and the distribution of strain and stress and control various forming defects, such as thinning, wrinkling and springback, etc., the accurate integration of the constitutive laws over the strain path is essential. Our objective in this paper is to develop an effective and accurate stress integration scheme for the analysis of three-dimensional sheet metal forming problems. The proposed algorithm is based on the explicit “substepping” schemes incorporating with the stress correction scheme. The proposed algorithms have been implemented into ABAQUS/Explicit via User Material Subroutine (VUMAT) interface platform. The algorithms are then employed to analyze a typical deep-cup drawing process and the accuracy of these algorithms has been compared with the implicit “return” algorithm and explicit forward algorithm. The results indicate that the explicit schemes with local truncation error control, together with a subsequent check of the consistency conditions, can achieve the same or even better level of accuracy as “return” algorithm does for integrating large plastic problems like sheet metal forming process.     

Three-dimensional solution of concentrated forces in semi-infinite coating materials

The spatial analytical solution of concentrated forces in semi-infinite coating materials has been deduced by adopting the image point technology. The explicit fundamental solution is given in the series of the displacement functions corresponding to each image point. The displacement functions corresponding to the higher order image points can be determined from those to the lower ones by the recurrence formula presented in this paper. Numerical analysis by means of the finite element method has been carried out to verify the theoretical results. It is found that the accurate enough theoretical solution can be obtained by only taking the displacement functions corresponding to the first several image points into account.     

Damage evolution in creep bulging of thin sheet metal

The creeping motion of thin sheet metal, damaged by artificial cavities is observed in bulging tests and simulated ‘semi’-analytically. The sheet metal satisfies Norton’s Law for secondary creep and is subjected to a bi-directional stretch. The stretch is produced by creep bulging through elliptical dies with the virtue of sustaining nearly uniform background stress ratio for each aspect ratio of the die axes. In order to reach large deformations with significant shape evolution of the cavities, the tests were conducted at superplastic conditions. The sheet is double layered (only one layer is cavitated) made of Tin–Lead (50–50 Pb–Sn). The measured damage growth is compared to an approximate simulation. The simulation of the damage evolution, throughout its time history, makes repeated use of a so-called “Green-function solution” for the motion of a single isolated cavity in an infinite viscoplastic continuum. The solution is modified from Muskhelishvili’s elastic solution by replacing the elastic shear modulus by a “viscous-like” variable (“plastic shear modulus”) which depends (non-linearly) on the evolved average strain-rate. Similarly, the stresses in the ligaments between cavities were averaged to approximate the local stress concentrations. Due emphasis is given to the rotation of each elliptical cavity, beside its expansion (contraction) and elongation.     

New results for the fretting-induced stress concentration on Hertzian and flat rounded contacts

Recent work on fretting fatigue has emphasized the role of stress concentration on fretting damage, while previous work had concentrated on empirical parameters to assess influence of fretting on fatigue life. In particular, analogies with fatigue in the presence of a crack or a notch have been noticed, suggesting that the stress field induced by frictional contact per se may explain the reduction of fatigue life due to fretting.In the paper, new analytical and numerical solutions are produced for the stress concentration induced in typical fretting contacts involving the Hertzian geometry or the flat punch with rounded corners in view of application to the dovetail joints. Normal and tangential load (in the Cattaneo–Mindlin sense) is considered with “moderate” or “large” bulk stresses.     

A surface flow line model of a scratching tip: apparent and true local friction coefficients

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to a moving scratching tip. It includes a so-called “true local” friction coefficient, which is the scission at the interface between the tip and the surface being scratched, and a “geometrical” friction coefficient, which is the plough effect due to the wave front created ahead of the moving tip and depends on the shape of the tip. Like in any mechanical test, three basic types of behaviour of the material at the interface are observed: purely elastic, elastic–plastic and fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model is developed here to deduce the geometrical and true friction coefficients at the interface between a moving scratching tip and a surface from the apparent friction coefficient. Using this model, several situations may be simulated to predict the influence of the geometry of the tip on the scratch resistance of the material.     

Measurement of springback

Springback, the elastically-driven change of shape of a part after forming, has been measured under carefully-controlled laboratory conditions corresponding to those found in press-forming operations. Constitutive equations emphasizing low-strain behavior were generated for three automotive body alloys: drawing-quality silicon-killed steel; high-strength low-alloy steel; and 6022-T4 aluminum. Strip draw-bend tests were then conducted using a range of die radii (3<R/t<17), friction coefficients (0<μ<0.20), and controlled tensile forces (0.5<F_b/F_y<1.5). Springback angles and curvatures were measured for bend and bend–unbend areas of the specimen, the latter corresponding to the “sidewall curl” region, which dominates the geometric change and the dependence on process variables. Friction coefficient and R/t (die-radius-to-sheet-thickness) greater than 5 have modest but measurable effects over the ranges tested. As expected, strip tension dominates the springback sensitivity, with higher forces reducing springback. For 6022-T4, springback is dramatically reduced as the tensile stress approaches the yield stress, corresponding to the appearance of a persistent anticlastic curvature. The presence of this curvature, orthogonal to the principal curvature, violates the simple two-dimensional models of springback reported in the literature. The measured springback angles and curvatures are reported both in graphical summary and tabular form for use in assessing analytical models of springback.     

Upper bounds on plastic strains for elastic-perfectly plastic solids subjected to variable loads

The paper considers shakedown analysis problems for elastic-perfectly plastic solids subjected to quasi-static loads which vary arbitrarily within a given domain. It gives a general inequality which is able to generate Melan's theorem for shakedown, as well as bounds on plastic strains at any point of the solid. These bounds can be made the most stringent by solving a “perturbed” shakedown problem in “finite” or “holonomic” terms. The results presented in this paper are a generalization of those given in a previous paper by the present author[10].     

A new way to manage displacements in zones of active faults

The objective of this paper was to perform the complex study of features of force and deformation response of interfaces between structural tectonic blocks in the Earth's crust (active faults), which are under complex stress. The research was based on consideration of contacting geoblocks as typical friction pairs. This allowed authors to suggest investigation of influence of vibrations and also of lubrication induced change of physico-mechanical properties of the contact zone (this was realized by watering) on the maximum value of sliding resistance force and regime of relative tangential block displacement (slip). It was found that combined use of watering and “high-frequency” vibration fundamentally changes response regime of interface region and can initiate extensive but seismically safe “smooth” displacements of geo-blocks along the fault. Analysis of investigation results on the basis of Tomlinson model shown that revealed change of response character (including sliding regime) of boundaries between structural elements is general for friction pairs of various natures. Analysis of research results allows authors to propose the new approach to manmade control of displacements along seismically active faults. This approach seems to be an important tool in the management of seismic hazards in the future.     

Asymptotic analysis of extrusion of porous metals

Plane strain extrusion of fully dense and porous metals is analysed using asymptotic techniques. The extrusion die is assumed to taper gradually down the extrusion axis. The asymptotic expansions are based on a small parameter ε which is defined as the ratio of the total reduction of the original cross-section to the length of the reduction region. Coulomb's law is used to model the frictional forces that develop along the metal-die interface and the coefficient of friction is assumed to be of order ε. Analytical solutions for the first two terms in the expansions are obtained. In the case of the fully dense metals, it is shown that the leading order [O(1)] solution involves “slab flow.” It is also shown that the next term in the expansion of the solution is O(ε²), and this provides a theoretical justification for the use of the so-called “slab methods” of analysis for dies of moderate slope. An asymptotic analysis of the extrusion of porous metals with dilute concentration of voids is also carried out. Gurson's plasticity model is used to describe the constitutive behavior of the material. The leading order solution is the same as that of the fully dense material and the effects of porosity enter as an O(ε) correction. In order to verify the asymptotic solutions developed, detailed finite element calculations are carried out for both the fully dense and the porous material. The asymptotic solutions agree well with the results of the finite element calculations.     

Pressure between elastic bodies having a slender area of contact and arbitrary profiles

A numerical method is presented for calculating the pressure distribution and contact area shape between two elastic bodies of arbitrary profile which make contact over a slender contact area, i.e. where the relative curvature of the two profiles is much smaller in the longitudinal direction than in the transverse. The pressure distribution is assumed to be piecewise-linear in the longitudinal direction and semi-elliptical in the transverse. No a priori relationship is assumed between the shape of the contact area and the longitudinal variation in pressure; they are found simultaneously from dual integral equations for the compatibility of (a) the normal displacement and (b) the transverse curvature along the longitudinal axis of the contact zone.In cases where the profiles of the contacting bodies are smooth and continuous up to, and beyond, the ends of the contact area, the method gives a very reliable measure of the contact pressure distribution. Where discontinuities in profile are present, at roller ends for example, stress singularities are to be expected and like any numerical method, only approximate values of the stress concentration can be found. In the cases studied, the concentration of pressure associated with a “sharp” edge of contact is found to be very local.The method has been applied to both cylindrical and variously “crowned” rollers, also to a ball “over-riding” the edge of a closely conforming groove.     

Some observations on the CLNA model in fretting fatigue

Using the Atzori–Lazzarin criterion, the author has recently proposed a unified model for Fretting Fatigue denominated Crack-Like Notch Analogue—CLNA model, considering only two possible behaviours: either “crack-like” or “large blunt notch”. In a general FF condition, the former condition is treated with a single contact problem corresponding to the MIT Crack Analogue (CA) improved in some details also by the author. The latter, with a simple peak stress condition, i.e. a simple Notch Analogue model, simply stating that below the fatigue limit, infinite life is predicted for any size of contact. In the typical condition of constant normal load and in phase oscillating tangential and bulk loads, both limiting conditions are immediately written, and the CLNA model permits to collapse the effect of the contact loads on a single closed form equation (differently from many other models which do not permit this flexibility). For not too large contact areas (“crack-like” contact) no dependence at all on geometry is predicted, but only on 3 load factors (bulk stress, tangential load and average pressure) and size of the contact. Only in the “large blunt notch” region occurring typically only at very large sizes of contact does size-effect disappear, but the dependence on all other factors including geometry remains. The model compares favourably with some experimental results in the literature. In this paper, some aspects of the CLNA model are further elucidated.     

Contact force measurement using acoustic emission analysis and system identification methods

Acoustic emission (AE) signals were used to investigate the contact force occurring at the head/disk interface of a computer hard drive. The AE sensor was calibrated directly using the “ball drop method” and indirectly using system identification. For the indirect calibration, a high bandwidth laser Doppler vibrometer (LDV) was used. The transfer function was established from the harmonic response derived at different vibration modes and frequencies. A finite element method based transient response simulation of impact was used to estimate the velocity and stress response of the slider. In our experiments, contact forces were found to be in the range of 5–25 mN for nano sliders and 2–10 mN for pico sliders.     

Surface geometry of slide bearings after percussive burnishing

A review of literature about the effect of oil pockets on improvement of sliding elements tribological performance as well as about the changes of surface topography during “zero-wear” process is shown. The paper presents also the results of experimental investigations done in the Department of Manufacturing Processes and Production Organisation of Rzeszow University of Technology, connected with the creation of oil pockets on sliding surfaces. In order to simulate a deterministic surface a program for the visualisation of pits was written. The procedures for assessment of the oil pocket size of specific shape and oil pockets coverage are presented. The tendencies of changes of surface topography and oil pockets dimensions during “zero-wear” process are also described.     

Buckling phenomena related to rolling and levelling of sheet metal

The paper deals with analytical and numerical considerations of buckling phenomena in thin plates or strips under in-plane loads which typically appear during rolling and levelling, i.e. straightening by stretching, of sheet metal. Buckling due to self-equilibrating residual stresses, caused by the rolling process, in eventual conjunction with global tensile stresses (denoted as “rolling buckling”) as well as buckling during the levelling process (denoted as “stretching buckling” or “towel buckling”) are considered. Analytical estimates are derived and compared against results of numerical simulations and field observations. Mode jumping by varying the global strip tension is explained on the basis of the derived analytical solutions. It is shown how from the waves, i.e. height and length, observed on the strip sliding over or lying on a rigid plane one can provide information about the distribution of the differences in the plastic strains over the width of the strip which lead to the buckled configuration. And, vice versa, knowledge of the plastic strain distribution can be used for estimating the expected wave heights representing a measure for the geometrical quality of the rolled product. The influence of the dead weight of the strip on the post-buckling pattern is also discussed on the basis of non-linear analyses.     

A simple approach to estimate failure surface of polymer and aluminum foams under multiaxial loads

From mechanical point of view, it is required to have a criterion for evaluating the failure of cellular solids (foams) under multiaxial loads. Well-documented experimental results in the literature show foams could fail by several mechanisms, e.g., elastic buckling, plastic yielding, brittle crushing or brittle fracture. In the previous years, both theoretical and phenomenological approaches have been applied to obtain the failure surface of various foams. The purpose of this paper is to present a simple approach to estimate the complete failure surface of “non-textured” foams. The predicted results of polymer and aluminum foams are compared with the experimental results reported in the literature. It is found that three selected tests will be sufficient to estimate the complete failure surface of a foam. The recommended testing stress states are σ₁=σ₂=σ₃>0, σ₁=σ₂=σ₃<0, and σ₁=−σ₂=−σ₃ (or σ₁=−σ₂, σ₃=0).