Orthogonal Path Research Articles

Effect of the plasticity model on the yield surface evolution after abrupt strain-path changes

Abrupt strain path changes without elastic unloading have been used in the literature to investigate the yield surface of sheet metals, both experimentally and theoretically. Such pioneering studies emphasized an apparent non-normality of the plastic strain rate tensor with respect to the trace of the yield surface in stress space, following such a strain-path change. They inspired numerous subsequent developments of plasticity models including non-associated flow rules. In this paper, this type of abrupt strain-path changes is investigated using state-of-the-art plasticity models. The aim is to emphasize the respective contributions of elasticity, isotropic-kinematic hardening, and rate sensitivity, to the apparent violation of the normality condition. The results show that these classical ingredients of plasticity models significantly contribute to the apparent vertex and loss of normality. These effects are quantified for typical sheet metals subject to biaxial-to-shear orthogonal strain path change.

A Bee Colony Optimization Approach for Mixed Blocking Constraints Flow Shop Scheduling Problems

The flow shop scheduling problems with mixed blocking constraints with minimization of makespan are investigated. The Taguchi orthogonal arrays and path relinking along with some efficient local search methods are used to develop a metaheuristic algorithm based on bee colony optimization. In order to compare the performance of the proposed algorithm, two well-known test problems are considered. Computational results show that the presented algorithm has comparative performance with well-known algorithms of the literature, especially for the large sized problems.

Stress update algorithm for enhanced homogeneous anisotropic hardening model

A stress integration algorithm is provided for a novel homogeneous-yield-function-based anisotropic hardening (HAH) model. The new model is an extension of the original HAH model that describes cross-hardening or softening of a sheet metal under an orthogonal strain path change. A semi-explicit integration scheme for the stress update is utilized to efficiently handle the gradient of the distorted yield surface during complex strain path changes, as originally proposed by Lee et al. (2012). Validations of the algorithm developed were conducted by comparing the predicted stress–strain curves of dual-phase (DP) 780 and extra-deep-drawing-quality (EDDQ) steels with experimental stress–strain responses observed under cross-loading conditions. Finally, the accuracy of the proposed finite element (FE) formulations was assessed by r-value prediction and preparation of iso-error maps.

Research of Layered Machining Experiment by Micro-EDM

The effect of electrode wear is significant on machining quality, in order to ensure the processing precision of micro-EDM milling, need to give reasonable compensation for the tool electrode. In this paper, based on the model of fixed length compensation method to machining the micro groove with micro-EDM by layered milling experiment, moreover, adopted the orthogonal machining path and the machine vision technology to obtain the stable end of the electrode image after processing, and then determine the reasonable path of trajectory overlap. The experimental results show that, the electrode compensation model can availably compensate the electrode wear, and the processing time is shortened by 50% with the machining method of orthogonal trajectories, and the method can make the residual cut remove obviously, gained good machining precision. We observe the bottom section linearity of micro groove is very good and the processing error of the micro groove depth is about 2 μm by the optical microscope.

Inherent and induced anisotropic finite visco-plasticity with applications to the forming of DC06 sheets

In the current work we present a finite visco-plasticity model accounting for inherent and induced plastic anisotropy as well as Bauschinger effect for the interstitial free (IF) steels and its application to a forming process simulation of DC06 sheets. The inherent plastic anisotropy uses a Hill-48 type structural tensor whereas the induced anisotropy is modeled via its evolution accounting for dynamic (active) and latent (inactive) parts. The latter appears to be an eminent requirement for predicting the qualitative effect of the evolving dislocation microstructures under orthogonal loading path changes, i.e., the cross hardening. A nonlinear isotropic and Armstrong–Frederick type kinematic hardening is also involved. Finally, the rate dependence of the plastic response is incorporated using Johnson–Cook type formulation. The model is implemented as VUMAT user defined material subroutine for ABAQUS and used in a set of sensitivity analyses to present mentioned model features. The model parameters are identified based on a set of experiments involving monotonic shear, uniaxial tension, forward to reverse shear and plane strain tension followed by shear tests. Finally, the channel forming process of a DC06 sheet is simulated. A good agreement with the experimental findings is observed, in both the tool response history curves and the extent of spring-back which is conclusive on the final product geometry.

FPGA Implementation of Orthogonal 2D Digital Predistortion System for Concurrent Dual-Band Power Amplifiers Based on Time-Division Multiplexing

A concurrent dual-band digital predistortion (DPD) system is presented to compensate for the nonlinearity of the radio-frequency power amplifiers (PAs) driven by a concurrent dual-band signal. Recently, a closed-form orthogonal polynomial basis has been introduced showing stability improvement compared with the conventional polynomial. An experimental test bed employing a field-programmable gate array (FPGA) linked to two mixed-signal system boards has also been presented. Based on the FPGA, this paper focuses on the hardware implementation of the new concurrent dual-band orthogonal DPD forward path using time-division multiplexing. Performances are evaluated with an experimental test setup cascading 1-10 W peak PAs and a dual-band signal center frequency spaced by 310 MHz. The lower side band (LSB) and upper side band (USB) are centered at 1890 and at 2200 MHz, respectively. Two signal scenarios are presented combining alternatively 1-carrier wide-band code-division multiple access (WCDMA) and 10-MHz long-term evolution (LTE) signals to a 5-carrier WCDMA signal. Experimental results show that the proposed time-division-multiplexing implementation approach gives similar performance compared with the software implementation with half of the resources. Adjacent channel power ratios (ACPRs) are reduced below -50 dBc and normalized mean-square error (NMSE) close to -40 dB.

In situ atomic-scale observation of continuous and reversible lattice deformation beyond the elastic limit

The elastic strain sustainable in crystal lattices is usually limited by the onset of inelastic yielding mediated by discrete dislocation activity, displacive deformation twinning and stress-induced phase transformations, or fracture associated with flaws. Here we report a continuous and gradual lattice deformation in bending nickel nanowires to a reversible shear strain as high as 34.6%, which is approximately four times that of the theoretical elastic strain limit for unconstrained loading. The functioning deformation mechanism was revealed on the atomic scale by an in situ nanowire bending experiments inside a transmission electron microscope. The complete continuous lattice straining process of crystals has been witnessed in its entirety for the straining path, which starts from the face-centred cubic lattice, transitions through the orthogonal path to reach a body-centred tetragonal structure and finally to a re-oriented face-centred cubic structure.

Wideband Dual-Frequency Dual-Polarized Dipole-Like Antenna

A wideband dual-frequency dual-polarized printed antenna is proposed for LTE, WLAN, and UWB systems. The dual-band antenna provides wide impedance bandwidths of 74% with respect to the center frequency of 2.725 GHz, and 39% with respect to the center frequency of 7.15 GHz. An open slot in the ground plane between the feed arms provides an orthogonal path to realize an embedded circularly polarized band at 2.35 GHz with an axial-ratio bandwidth of 16%. Dual-band characteristics are achieved by an asymmetrical dipole-like element and the coupling configuration between the T-shaped feed line and the wide ground-plane slot.

Chebyshev type lattice path weight polynomials by a constant term method

We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary ‘decorated’ weights as well as an arbitrary ‘background’ weight. Our CT theorem, like Viennot's lattice path theorem from which it is derived primarily by a change of variable lemma, is expressed in terms of orthogonal polynomials which in our applications of interest often turn out to be non-classical. Hence, we also present an efficient method for finding explicit closed-form polynomial expressions for these non-classical orthogonal polynomials. Our method for finding the closed-form polynomial expressions relies on simple combinatorial manipulations of Viennot's diagrammatic representation for orthogonal polynomials. In the course of the paper we also provide a new proof of Viennot's original orthogonal polynomial lattice path theorem. The new proof is of interest because it uses diagonalization of the transfer matrix, but gets around difficulties that have arisen in past attempts to use this approach. In particular we show how to sum over a set of implicitly defined zeros of a given orthogonal polynomial, either by using properties of residues or by using partial fractions. We conclude by applying the method to two lattice path problems important in the study of polymer physics as the models of steric stabilization and sensitized flocculation.

Comparison of two different models to account for induced flow anisotropy during complex loading processes

AbstractSome metals exhibit an increase of the yield stress after orthogonal strain path changes, i.e. so–called cross hardening. Two approaches are discussed in this work which are capable of taking that effect into account in an appropriate manner. The first approach is closely related to that of Teodosiu and Hu. The second model considers besides the movement of the center of the yield surface and its proportional expansion also the change of its shape and is able to describe the induced anisotropic behavior with regard to complicated loading histories. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

MAEAM investigation of the structural stability and theoretical strength of Fe crystals under uniaxial loading

AbstractThe structural stability and theoretical strength of BCC crystal Fe under uniaxial loading have been investigated with the modified analytic embedded‐atom method (MAEAM). Even if an orthorhombic path is applied, the deformation is spontaneous along the tetragonal path till Milstein modified Born criterion B22‐B23>0 is violated at λ1=0.9064 in the compressive region. The branched orthogonal path with lower compressive stress σ1 and energy E is preferred over the conventional tetragonal Bain path. A stress‐free FCC phase with the local maximum energy of ‐4.2186eV appearing either in compressive region (orthorhombic path) at λ1=0.8923 or in tensile region (tetragonal path) at λ1=1.2619 is unstable and would slip spontaneously into its near neighbor stress‐free mBCT phase with the local minimum energy of ‐4.2270eV. The initial BCC phase with the lowest energy of ‐4.280eV is the most stable in correspondence with the actual behavior of Fe. Furthermore, the stable region ranges from ‐79.7eV/nm3 to 30.6eV/nm3 in the theoretical strength or from 0.9064 to 1.1788 in the stretch λ1 correspondingly. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Theoretical strength and structural response of Cu crystal

The theoretical strength and structural response of FCC crystal Cu under uniaxial loading along one edge of a unit cell have been investigated with MAEAM. The stability criteria of the tetragonal system are extended to the generally stressed orthogonal system. The results show that, even if an orthorhombic path is applied, the deformation is spontaneously along the tetragonal Bain path till tensile elastic limit at stretch λ1=1.085 where the Born criterion is violated. The branched orthogonal path is preferred over the conventional tetragonal Bain path from minimization of the stress σ1 or the energy E. Although a stress-free BCC phase with the local maximum energy of −3.460eV appearing either in compressive region or in tensile region is unstable and would slip spontaneously into a near neighbor stress-free mBCT phase with the local minimum energy of −3.461eV, the initial FCC phase with the lowest energy of −3.489eV is the most stable in correspondence with the actual behavior of pure Cu. Furthermore, the calculated elastic moduli of FCC phase are in good agreement with the experimental values. The stable region ranges from −2.89GPa to 7.252GPa in the theoretical strength or from 0.912 to 1.085 in the stretch λ1 correspondingly.

Elastic-plastic behaviour of dual-phase, high-strength steel under strain-path changes

Abstract The elastic-plastic behaviour of dual-phase, high-strength steel sheets under two-stage strain-path changes has been investigated. Three different loading sequences, namely monotonic, 45° tensile path changes and orthogonal tensile path changes complied by sequences of simple uniaxial tensile tests, were analysed at room temperature. From the experiments, it was found that there is a considerable reduction of the initial flow stress over the strain-path changes. The transient softening phenomenon is observed to be a function of orientation, and the period of the transient behaviour following the strain-path change is lengthened with the amount of pre-strain. A constitutive model is adopted that includes combined isotropic and kinematic hardening and is capable of describing the marked transient softening behaviour after the pre-straining. The experimental stress–strain behaviour subsequent to the strain path change is predicted with reasonable accuracy, while the model fails to accurately describe the transient, deformation-induced anisotropy in the plastic flow.

Static Recovery and the Orthogonal Strain Path Change Effect in IF Steel

Tensile tests have been carried out in the rolling and transverse directions of 'interstitialfree' (IF) steel cold rolled to a strain of εh= -0.18. Tests in the transverse direction showed the characteristic features of the orthogonal strain path change effect, with an initially increased flow stress- compared to tests in the rolling direction- followed by a transient regime of very low strain hardening. Tests were also carried out following recovery annealing of the prestrained sheet at 500°C and 600°C. Static recovery had a marked effect on the strain-induced anisotropy, but this was not eliminated even when the cell structure generated by prestraining haD condensed to one consisting of low-angle boundaries. This supports the view that the length scale, with respect to active slip systems, between boundary obstacles is a significant factor in the orthogonal path change effect.

Stress–strain responses for continuous orthogonal strain path changes with increasing sharpness

In this article a series of non-proportional orthogonal tests with continuous strain paths are presented. Mild steel was investigated on a biaxial test device that was specifically developed to examine strain path sensitivity. It is shown that a gradual strain path change shows a gradual increase in stress. However, experiments with increasing sharpness in the strain path change show an overshoot in stress which is a typical feature of stress–strain curves from discontinuous strain path changes.

変形経路変化下の加工硬化挙動と破断予測

The work-hardening behavior under strain path changes for dual phase (DP) steel has been investigated by using simple shear sequences, in comparison with that for interstitial free (IF) steel. The results show that a strong hardening followed by softening in an orthogonal path change, which is normally seen in IF steel, is not significant in DP steel. Based on these results, analytical approaches to predict forming limit strain and stress in monotonic and orthogonal paths by using Hill criterion have been conducted. It is known that stress based forming limit curves are path independent, while strain based forming limit curves are strongly path dependent. For IF steel, the localized necking is started just after the second loading in orthogonal sequence, which thus shows that even stress based forming limits are path dependent in IF steel. On the other hand, DP steel exhibits localized necking at the same amount of total strain both for monotonic and orthogonal paths and thus the stress based forming limits are path independent, which reflects differences in work-hardening under strain path changes in DP and IF steels. It might be pointed out that these differences are originated in the microstructural evolution of both steels.

Singularities and Undefinitions in the Calibration Functions of Sonic Anemometers

Abstract A mathematical model of the process employed by a sonic anemometer to build up the measured wind vector in a steady flow is presented to illustrate the way the geometry of these sensors as well as the characteristics of aerodynamic disturbance on the acoustic path can lead to singularities in the transformation function that relates the measured (disturbed) wind vector with the real (corrected) wind vector, impeding the application of correction/calibration functions for some wind conditions. An implicit function theorem allows for the identification of those combinations of real wind conditions and design parameters that lead to undefined correction/ calibration functions. In general, orthogonal path sensors do not show problematic combination of parameters. However, some geometric sonic sensor designs, available in the market, with paths forming smaller angles could lead to undefined correction functions for some levels of aerodynamic disturbances and for certain wind directions. The parameters studied have a strong influence on the existence and number of singularities in the correction/ calibration function as well as on the number of singularities for some combination of parameters. Some conclusions concerning good design practices are included.

In-Plane Elastic Stability of Arches under a Central Concentrated Load

This paper is concerned with the in-plane elastic stability of arches with a symmetric cross section and subjected to a central concentrated load. The classical methods of predicting elastic buckling loads consider bifurcation from a prebuckling equilibrium path to an orthogonal buckling path. The prebuckling equilibrium path of an arch involves both axial and transverse deformations and so the arch is subjected to both axial compression and bending in the prebuckling stage. In addition, the prebuckling behavior of an arch may become nonlinear. The bending and nonlinearity are not considered in prebuckling analysis of classical methods. A virtual work formulation is used to establish both the nonlinear equilibrium conditions and the buckling equilibrium equations for shallow arches. Analytical solutions for antisymmetric bifurcation buckling and symmetric snap-through buckling loads of shallow arches subjected to this loading regime are obtained. Approximations for the symmetric buckling load of shallow arches and nonshallow fixed arches and for the antisymmetric buckling load of nonshallow pin-ended arches, and criteria that delineate shallow and nonshallow arches are proposed. Comparisons with finite element results demonstrate that the solutions and approximations are accurate. It is found that the existence of antisymmetric bifurcation buckling loads is not a sufficient condition for antisymmetric bifurcation buckling to take place.

A Contour Error Controller for High Speed Machine Tools

In this paper, PID controllers primarily control the axes of a biaxial table. A contour error controller (CEC) works simultaneously, helping them. The calculus of the orthogonal path deviation (contour error) is performed with an additional term in the equation, resulting in a more accurate value and enabling the use of this type of motion controller at higher feedrate. The response results are compared with those of common PIDs and non-corrected CEC in order to analyse the effectiveness of this controller over the system.

Non-isoparametric tool path planning by machining strip evaluation for 5-axis sculptured surface machining

Presented in this paper is a new approach to 5-axis NC tool path generation for sculptured surface machining. Techniques of feasible machining strip evaluation are used for non-isoparametric 5-axis tool path generation. A searching algorithm is proposed to find the parameter increments of adjacent cutter locations along orthogonal path intervals for optimal non-isoparametric path generation. Compared to the use of the smallest path interval by the traditional constant parametric path planning, the proposed methodology can generate efficient tool paths for sculptured surface machining by reducing the redundant overlapping between adjacent tool paths. The proposed methodology includes three steps: (1) evaluating feasible machining strip, (2) solving parameter increments (Δ u, Δ v) along orthogonal path intervals, and (3) searching for adjacent non-isoparametric cutter locations. The techniques presented in this paper can be used to improve 5-axis machined surface quality and to automate the non-isoparametric cutter path generation for CAD/CAM systems.