A robust model for rolling of thin strip and foil

A new analysis for cold rolling of thin strip and foil is developed. This model follows the approach of Fleck et al. [8], but relaxes their assumption of a central flat neutral zone. Instead of following their inverse method to obtain the pressure distribution in this neutral zone, an explicit equation for the contact pressure variation is obtained from the sticking condition in this region. This significantly simplifies the solution method, leading to a much more robust algorithm. Moreover the method treats the cases either where the roll retains its circular arc or where there is very significant roll deformation in the same way, greatly simplifying the method of obtaining solutions. This will facilitate the incorporation of other effects such as the friction models currently being developed. Results are in line with the theory of Fleck et al. [8]. The effect of entry and exit tensions on the non-dimensional load and forward slip is investigated. It is found that the effect of equal entry and exit tensions is equivalent to reducing the yield stress of the strip by this tension stress.     

A modified Hertzian foil rolling model: approximations based on perturbation methods

Fleck and Johnson (Int. J. Mech. Sci. 1987;29:507) have developed a foil rolling model, which has been used subsequently as a temper rolling model, based on a modification of the Hertzian contact problem. It removes the restrictive assumption that the rolls remain circular in profile. A perturbation approximation of the Fleck and Johnson model equations for small reductions has been developed. This enables good approximations to the roll torque and roll force to be obtained in a small fraction of the time required for the full iterative solution and has potential for use in on-line control.     

Deformation processing of metal powders: Part I—Cold isostatic pressing

Analytical and numerical techniques are used to analyze in detail the stage I Cold Isostatic Pressing (CIPing) of metal powders. Plastic yielding is considered to be the only densification mechanism and the constitutive model developed recently by Fleck, Kuhn and McMeeking [(J. Mech. Phys. Solids40, 1139 (1992)] is used to describe the elastoplastic behavior of the metal powder. It is shown that, for the case of powder consolidation in a long cylindrical tube, a change in length is not possible, unless it is accompanied by some distortion (“shape change”) of the CIPed specimen. The numerical implementation of the constitutive elastoplastic equations in a finite element program is discussed. The finite element method is used to analyze the CIPing of titanium powder. The predictions of the finite element solution agree well with available experimental data.     

Application of the singularity function method to semi-infinite orthotropic rectangular plates on an elastic foundation

The singularity function method is applied to solve the structural problems of semi-infinite orthotropic rectangular plates on a Winker-type elastic foundation. Previous application by Selek et al. (Int. J. Mech. Sci., 25 (1983) 397) of the singularity function to plates on an elastic foundation was limited only to isotropic cases. Foundation-free orthotropic plate problems have been previously solved Adewale et al. (Int. J. Mech. Sci., 31 (1989) 853). In this paper, the singularity function method technique is extended to orthotropic rectangular plate on Winkler-type foundation. The isotropic rectangular plate results of Selek et al. (Int. J. Mech. Sci., 25 (1983) 397) and the foundation-free orthotropic rectangular plate results provided by Adewale et al. (Int. J. Mech. Sci., 31 (1989) 853) are recovered as special cases.     

Numerical modelling of cold compaction of metal powder

A finite element programme has been developed for the analysis of porosity and stress distributions in a powder compact, based on rate-independent finite strain plasticity theory. The strain hardening versions of the Gurson model (J. Engng. Mater. Technol., 1977, 99, 2-15), the more recent FKM model (J. Mech. Phys. Solids, 1992, 40(5), 1139-1162), developed by Fleck, Kuhn and McMeeking, and a combination of the two models are used. The friction between the mould wall and the metal powder is modelled by a combination of Coulomb friction and a constant friction shear stress, since Coulomb friction is not realistic at high normal pressures. The finite element programme has been used to study the effects of friction, compaction method, and material parameters. Analyses for powder compacts of various geometries are presented to illustrate the method.     

Experimental measurements of load and strip profile in thin strip rolling

Experiments are described in which plasticine strips are rolled using elastomer rolls. Conditions cover the range from “thick strip” behaviour, in which roll elastic deformations are small, to “thin strip rolling”, in which elastic deformations of the rolls are very significant. Results provide the first direct experimental confirmation of the thin strip rolling model proposed by Fleck et al. (Proc. Instn Mech. Engrs B206 (1992) 119–131). Strip profiles clearly show a short region of reduction at the inlet to the bite and a central region which is relatively flat, in accord with the theory. The profiles do not however show a short region of reduction at the exit as predicted. For intermediate strip thicknesses the measured loads are in reasonable agreement with theory. For the thinnest strips, although the form of the dependence of load on reduction and inlet strip thickness is as predicted by theory, the measured loads are almost an order of magnitude lower than predicted. It is suggested that this is caused either by differences between the assumed rigid–perfectly plastic strip and the real constitutive behaviour of the plasticine, or by errors in treating the rolls as elastic half-spaces, an approximation which is accurate for industrial metal rolling, but is not good for the conditions of these experiments.     

The transition of mild to severe wear of ceramics

The transition of mild to severe wear of ceramics depends on the operating conditions (normal load, velocity and temperature) and material properties (like grain size, mechanical and thermal material properties). Adachi et al. [Wear 203-204 (1997) 291] introduced the transition of mild to severe wear of ceramics by defining a mechanical severity parameter based on the work of Hamilton [Proc. Inst. Mech. Eng. 197C (1983)] and a thermal severity parameter based on the work of Ashby et al. [Tribol. Trans. (34) (1991) 577]. Metselaar et al. [Wear 249 (2001) 962] improved the thermal severity parameter using the temperature model introduced by Bos [Frictional heating of tribological contacts, Ph.D. Thesis, University of Twente, 1995]. Better prediction of wear transition in the region where the transition is dominated by thermally induced wear was achieved. The combination of the mechanical severity parameter and the thermal severity parameter for Peclet number (Pe) higher than 2 is presented in this paper. This model is verified experimentally and gives an improved prediction of the mild to severe wear transition of ceramics.     

Three-dimensional topography of the matt surface in aluminium pack rolling

A model has been presented in a companion paper (Utsunomiya et al., Int. J. Mech. Sci., in press) to predict the generation of roughness on the matt surface in pack rolling of aluminium foil. This model was based on a two-dimensional (2D) finite element analysis using an isotropic plasticity model for the material. The spread of crystallographic grain orientations was simulated by ascribing different material properties to each grain. The predictions showed good qualitative agreement with experiments. It was found that the formation of shear bands causes roughening of the matt surface. The effect of material properties was further explored in Utsunomiya et al. (Int. J. Mech. Sci., in press).In the current study the model for evolution of the matt surface roughness is extended to a three-dimensional (3D) analysis and compared with predictions using a 2D analysis, a full crystallographic 3D model and experiments. The amplitude of the predicted roughness for the 3D model is lower than for the corresponding 2D analysis. In the 3D model, grains deform more uniformly due to the homogeneous constraint from adjacent grains. The predicted roughness shows good quantitative agreement with experiments, as well as with the predictions of the crystal plasticity model. The influences of grain shape and deformation mode are investigated. It is found that peaks or valleys running perpendicular to the first principal axis of strain are generated at the matt surface, regardless of initial grain shape.     

A densification model for mixed metal powder under cold compaction

Densification behavior of mixed copper and tool steel powder under cold compaction was investigated. By mixing the yield functions proposed by Fleck et al. and by Gurson for pure powder in terms of volume fractions of Cu powder and the fraction of contact, a new mixed yield function was employed for densification of powder composites under cold compaction. The constitutive equations were implemented into a finite element program (ABAQUS) to compare with experimental data and with results from the model of Kim et al. for densification of mixed powder under cold isostatic pressing and die compaction. Finite element calculations by using the yield functions mixed by the fraction of contact agreed better than those by volume fractions of Cu powder with experimental data.     

An Analytical Solution for Elastic and Elastic-Plastic Contact Models

In tribology often a closed form solution for calculation of contact stress and real contact area is required for the purposes of, for example, developing wear maps and temperature profiles at asperities. In assuming a Gaussian distribution of asperity heights it is not possible to obtain an analytical solution for the contact load and real contact area for many analytical models such as those developed by Greenwood and Williamson (elastic model), Chang, et al. (elastic-plastic model) and Horng (elliptic elastic-plastic model). In this paper, two exponential functions have been derived from a fitting procedure applied to the numerical results of the Gaussian height distribution thus offering an analytical expression for the above three models. It has been demonstrated that the two exponential functions (φ₂* and φ₄*) can give a fair approximation to the contact load and the real contact area in the separation of 0 to 4σ. In addition, variations in plasticity index (ψ) and effective asperity radius (γ) do not significantly affect the approximated accuracy. The results obtained by the newly derived exponential functions have been compared with the exponential function φ₁*; suggested by Greenwood and Williamson, 1966 and it has been shown that use of φ₁* invariably gives a larger error than using two exponential functions over two ranges of separation distances.     

Applications of the singularity function method to orthotropic plate problems

The singularity function method is applied to solve structural problems of orthotropic rectangular and circular plates. Except in the work of Conway (Int. J. Mech. Sci.22, 209, 1980) and Selek et al. (Int. J. Mech. Sci.25, 397, 1983), which considered the tapered circular plate, previous attempts at applying the singularity function method have always assumed material isotropy. In this work extensive results for displacements and moments are presented for material rigidities different in two orthogonal directions. In particular, Conway's isotropic plate results [7] are obtained as a special case from the present work.     

Novel combination of orientation measurements and transmission microscopy for experimental determination of grain boundary miller indices in silicon and other semiconductors

The determination of grain boundary planes in multicrystalline material has only been restricted to transmission electron microscope investigations (Jang et al., 1992; Elgat et al., 1985) or to metallograpical investigations of the grain boundary (Randle et al., 1993). The first method is expensive, and both are complex and time consuming in grain boundary preparation. This paper proposes the determination of grain boundary planes in semiconductor wafer by a combined application of Electron Back Scatter Diffraction and Infrared Transmission Microscopy. In particular, the new method is demonstrated with directional solidificated multicrystalline silicon.     

Source characterization and modeling development for monoenergetic-proton radiography experiments on OMEGA

A monoenergetic proton source has been characterized and a modeling tool developed for proton radiography experiments at the OMEGA [T. R. Boehly et al., Opt. Comm. 133, 495 (1997)] laser facility. Multiple diagnostics were fielded to measure global isotropy levels in proton fluence and images of the proton source itself provided information on local uniformity relevant to proton radiography experiments. Global fluence uniformity was assessed by multiple yield diagnostics and deviations were calculated to be ～16% and ～26% of the mean for DD and D(3)He fusion protons, respectively. From individual fluence images, it was found that the angular frequencies of ?50 rad(-1) contributed less than a few percent to local nonuniformity levels. A model was constructed using the Geant4 [S. Agostinelli et al., Nuc. Inst. Meth. A 506, 250 (2003)] framework to simulate proton radiography experiments. The simulation implements realistic source parameters and various target geometries. The model was benchmarked with the radiographs of cold-matter targets to within experimental accuracy. To validate the use of this code, the cold-matter approximation for the scattering of fusion protons in plasma is discussed using a typical laser-foil experiment as an example case. It is shown that an analytic cold-matter approximation is accurate to within ?10% of the analytic plasma model in the example scenario.     

Design of a Three-Lead Synthetic ECG Generator Using the Simplified McSharry's Model

Abstract

Recently, due to the dramatic improvement in computing capabilities and processing speed of microcontrollers and digital signal processors, many analytic algorithms for electrocardiograms (ECGs) have been developed and applied to a variety of portable electronic devices. In order to test whether the algorithms can analyze the various morphologies of electrocardiogram well, it is necessary to expend much effort collecting various ECG samples to establish an ECG database. Therefore, this paper simplifies and adopts a synthetic electrocardiogram model composed of three coupled differential equations proposed by Dr. McSharry et al. (2003), as well as utilizes an improved fourth-order Taylor series to quickly approximate the exponential function within the differential equation of a simplified synthetic ECG model so that, when studying ECG analytic algorithms, the graphical user interface (GUI) application “Synthetic Waveforms Control Panel,” developed by the author using LabVIEW, can be used to attain the desirable morphology of electrocardiogram as well as the time intervals between peaks (P, Q, R, S, T) and heart rate. The parameters of the adjusted synthetic ECG model are then sent to the memory of a synthetic ECG generator through a USB interface, and the ECG generator will generate three synthetic electrocardiograms of Einthoven's triangle for testing the electrocardiogram analytic algorithms.     

Three-dimensional reconstruction of single particles embedded in ice.

Single particles embedded in ice pose new challenges for image processing because of the intrinsically low signal-to-noise ratio of such particles in electron micrographs. We have developed new techniques that address some of these problems and have applied these techniques to electron micrographs of the Escherichia coli ribosome. Data collection and reconstruction follow the protocol of the random-conical technique of Radermacher et al. [J. Microscopy 146 (1987) 113]. A reference-free alignment algorithm has been developed to overcome the propensity of reference-based algorithms to reinforce the reference motif in very noisy situations. In addition, an iterative 3D reconstruction method based on a chi-square minimization constraint has been developed and tested. This algorithm tends to reduce the effects of the missing angular range on the reconstruction, thereby facilitating the merging of random-conical data sets obtained from differently oriented particles.     

Object-oriented graphical modeling of FMSs

Presented in the article is a method for constructing a graphical model of an FMS by using a new modeling tool called JR-net (Job Resource relation-net). JR-net is an object-oriented graphical tool for modeling automated manufacturing systems (AMSs), such as FMSs, FASs, and AS/RSs. As with the object-oriented modeling paradigm of Rumbaugh et al. (1991), the JR-net modeling framework supports the three stages of models: static layout model (object model); job flow model (functional model); and supervisory control model (dynamic model). In this article, the existing JR-net structure (Park 1992, Han et al., 1995) is extended further to make it a graphical tool for FMS modeling. Using the extended JR-net, a step-by-step procedure for constructing a graphical model of FMSs is presented. Also addressed are issues of classifying FMSs in terms of their generic functions and of utilizing the JR-net model of FMSs.     

Forming limits of AL 6022 sheets with material damage consideration—theory and experimental validation

Characteristics of localized necking in sheet metals are examined with anisotropic plasticity as well as anisotropic damage developed progressively after load application. The vertex theory is employed to describe basic mechanisms of localized necking. Anisotropic plasticity is accounted for by Hill's quadratic yield criterion. An anisotropic damage model based on Continuum Damage Mechanics is reviewed and expanded. The anisotropic damage model is combined with a modified vertex theory to generate damage-coupled localized necking criteria on both sides of forming limit diagram (FLD). The criteria lead to explicit expressions of critical hardening modulus on both sides of FLD. It is shown that the damage-coupled FLD model can be readily reduced and used to predict the forming limit strains of damage-free materials satisfying power hardening law given by other researchers (Hill, J. Mech. Phys. Solids. (1952)1,19; Zhu et al., ASME J. Eng. Mater. Tech. (2001) 123, 329). Critical damage value at localized necking can be computed from the damage-coupled localized necking criteria as a function of stress/strain states and strain paths. Tests on the formability and material properties of Al 6022, such as hardening and damage law, anisotropic plasticity parameter, have been performed. The measured FLD of the material are compared with the predictions based on the damage-coupled localized necking criteria for validation of the proposed FLD model. Material damage is observed to have a definite effect on the forming limits of Al 6022, thus providing a more accurate prediction than that of the conventional models.     

A three-dimensional rigid-plastic finite element analysis of bevel gear forging by using a remeshing technique

A three-dimensional remeshing scheme implemented by using a modular concept is proposed for the finite element analysis of a complicated forging process. In order to show the effectiveness of the scheme, forging of a bevel gear is simulated by using several basic modules in the general rigid-plastic finite element code (Yoon and Yang, Int. J. Mech. Sci.30, 887, 1988; Yang et al., Int. J. Mech. Sci.31, 145, 1989) developed for cold forging. Criteria for remeshing as well as a scheme for the mapping of state variables are proposed for three-dimensional remeshing. The computational results are compared with experimental data in order to check the validity of the simulation. The computational results show that the computation can be effectively carried out by using the proposed remeshing scheme and that it can be extended to other more complicated product geometry.     

Plastic mechanism analysis of circular tubes under pure bending

There are a number of solutions available to predict the response of a circular steel tube under pure bending. However, most of these solutions are based on an elasto-plastic treatment, which is complex and difficult to use in any routine design. This paper describes a theoretical treatment to predict the moment-rotation response of circular hollow steel tubes of varying D/t ratios under pure bending. The Mamalis et al. (J. Mech. Sci. 1989;203:411–7) kinematics model for a circular tube under a controlled moment gradient was modified to include the effect of ovalisation along the length of the tube. Inextensional deformation and rigid plastic material behaviour were assumed in the derivation of the deformation energy. The plasticity observed in the tests was assumed to spread linearly along the length of the tube. Two local plastic mechanisms (Star and Diamond shapes) were studied to model the behaviour observed in the tests especially during the unloading stage. The theoretical predictions are compared with the experimental results recently obtained by Elchalakani et al. (Quartral. J. Struct. Eng. 2000;3(3):1–16). Good agreement was found between the theoretical predictions and experimental moment-rotation responses, particularly for the Star shape mechanism. A closed-form solution is presented suitable for spreadsheet programming commonly used in routine design.