Step Reduction Method Research Articles

The hysteresis loop on the near-threshold fatigue crack growth curves generated by stepped load reduction and constant-amplitude loading methods in a Ni-based superalloy

Fatigue crack growth (FCG) tests were conducted on compact tension specimens made of a Ni-based superalloy to investigate the near-threshold FCG behaviors using both the stepped load reduction method (LRM) and the constant-amplitude loading method (CALM) at three stress ratios (R = 0.05, 0.5 and 0.7) under ambient condition. It is found that after the FCG threshold being approached by the LRM, a remarkable hysteresis plateau occurs on the subsequent FCG curve generated by the CALM for R ≤ 0.5, resulting a hysteresis loop on the near-threshold region, but the situation becomes complicated at R = 0.7. In the appearance of hysteresis plateau, the FCG life to fracture can be over 107 cycles longer than that without hysteresis plateau. For FCG rate faster than 10−8 m/cycle, the fractography is dominated by transgranular feature which is insensitive to the microstructure of the alloy. In the hysteresis plateau region where FCG rate is lower than 10−9 m/cycle, fractography shows a wide optical dark zone where microstructure-sensitive crystallographic facet feature dominates, while when no hysteresis at R = 0.7, the optical dark zone is too narrow for the fracture feature transition so that crystallographic facet, transgranular as well as mosaic features can be observed simultaneously. As FCG in the hysteresis plateau under the CALM can be significantly slower than that under the stepped LRM, it is recommend that the stepped LRM should be used to generate the material basic FCG curves for fatigue life prediction of high durability structures.

Difunctional AuNPs@PVP with oxidase-like activity for SERRS detection of total antioxidant capacity

Assessing the total antioxidant capacity (TAC) of foods plays a significant role in dietary guidance and disease risk reduction. Therefore, building a simple, rapid, and sensitive sensing method for detecting TAC possesses broad application prospects. Herein, we constructed a novel nanozyme catalyzed‒surface-enhanced Raman resonance scattering (SERRS) sensing strategy for analysis of TAC based on polyvinylpyrrolidone coated gold nanoparticles (AuNPs@PVP) that was synthesized by one step reduction method. AuNPs@PVP not only served as the SERRS substrate but also possessed high oxidase activity which can catalyze 3,3′,5,5′-tetramethylbenzidine (TMB) oxidation by generating hydroxyl radicals (•OH) and superoxide anion free radical (•O2−). According to the inhibiting effect of antioxidants, ascorbic acid (AA) was selected as the representative for TAC detection. The linear range and limit of detection (LOD) were determined to be 10−8‒10−5 M and 0.6 nM, respectively. More importantly, the proposed nanozyme catalyzed‒SERRS strategy has been successfully applied to the detection of TAC in fruit juices, demonstrating promising potential in the field of food supervision and healthcare applications.

Cu-Ag bimetallic nano-catalyst anchored on polyvinyl alcohol sponge for catalytic reduction of 4-nitrophenol

With increasing interest and demand for treating organic wastewater, fabricating a heterogeneous catalyst combining low-cost, excellent catalytic efficiency, and good recyclability is necessary but remains challenging. In this work, we developed a kind of low-cost Cu-Ag bimetallic nano-catalyst anchored on polyvinyl alcohol sponge (Cu-Ag/PVA) via step impregnation and reduction method, which demonstrated excellent catalytic efficiency and good recyclability for the reduction of the organic pollutant 4-nitrophenol (4-NP). The compositional and microstructural results confirmed that Cu-Ag bimetallic nanoparticles with an average size of tens of nanometers were uniformly anchored on the porous PVA sponge. The catalytic results showed that the prepared Cu-Ag/PVA exhibited an appealing catalytic performance and recyclability compared with monometallic Cu or Ag nano-catalyst, which is ascribed to the reason that bimetallic Cu-Ag has lower binding energy and is easier to transfer electrons in the catalytic reduction of 4-NP compared to monometallic catalyst. The optimal kinetic catalytic rate constants for Cu-Ag/PVA is 0.54 min−1, and the conversion of 4-NP maintained above 98% after twelve consecutive catalytic cycles. Therefore, this inexpensive, efficient, and recyclable Cu-Ag/PVA catalyst has potential application in organic wastewater treatment.

Bending vibration transfer equations of variable-section piezoelectric laminated beams

The model prediction is one of the adequate approaches to evaluate the bending vibration suppression of variable-section piezoelectric laminated beams (VPLBs). Nevertheless, the changing section and the coupling between stress and electric fields bring difficulties to the bending vibration calculation. To solve the above issues, we deduce the bending vibration transfer equations of VPLBs by the transfer matrix method and the step-reduction method. The VPLBs are approximated as a combination of several constant-section piezoelectric laminated beams (CPLBs). First, the bending vibration transfer equations of the CPLBs are derived using the Timoshenko beam theory and the constitutive properties of PZTs. Then, the transfer conditions between the two adjacent CPLBs are formulated according to the mechanical and electrical connections. Finally, the bending vibration transfer matrix of the VPLB is created by assembling transfer matrixes of inner CPLBs in sequence. To verify the feasibility of the developed bending vibration transfer equations, a piezoelectric actuator and a piezoelectric cantilever beam are designed as modeling examples. The experiment investigations and finite element simulation are carried out to validate the transfer matrix models of the two modeling examples, respectively. The multi-group comparison results show that the proposed transfer equations comprehensively describe the bending vibration characteristics of the VPLBs.

Electromechanical coupling model of variable-section piezoelectric composite beams in longitudinal vibration

The traditional step-reduction method is popular for modeling mechanical vibration of variable-section homogeneous beams (VHBs). However, this method cannot transfer electrical information and cannot depict electromechanical coupling behaviors of variable-section piezoelectric composite beams (VPCBs) in longitudinal vibration. To solve this defect, considering the structural continuity and parallel circuit factors, we propose the electromechanical step-reduction method for VPCBs. Longitudinal vibration transfer equations, linking input and output state vectors, are first created for VPCBs according to the proposed method. Then, a piezoelectric actuator excited by a VPCB is designed as a case study. Its transfer matrix model, involving mechanical and electrical properties, is developed to prove the correctness of the proposed method and the created transfer equations. Besides, an actuator prototype was manufactured for experimental verifications. The calculation results show that the longitudinal vibration frequency and velocity tend to be stable with the increase of the division number n. Their velocity vibration shapes are also consistent with each other. The calculated and experimental impedance curves have the same trend. The minimum and maximum impedance differences between the calculated and experimental are 107 ohm and 127 ohm, respectively. Finally, the modeling differences between the traditional and electromechanical step-reduction methods are compared and discussed in detail. The proposed method is more applicable to the modeling of VPCBs, which provides a theoretical tool for optimizing the excitation of the longitudinal vibration.

Nanostructured pH-responsive biocompatible chitosan coated copper oxide nanoparticles: A polymeric smart intracellular delivery system for doxorubicin in breast cancer cells

In this study, we report a novel feasible single step reduction method for the active synthesis of biocompatible chitosan coated copper oxide nanoparticles (Cs-CuO NPs), for loading and delivery of doxorubicin (DOX) into breast cancer cells. The formulated nanoparticles (NPs) were characterized by size, shape and surface charge using various sophisticated instruments. Interestingly, these formulated particles showed profound drug loading activity and also showed its versatile nature of DOX release at different pH which makes them as ideal particles for breast cancer therapy. Intracellular uptake was evaluated through fluorescence microscopy studies with the help of coumarin. Morphological and apoptotic studies with the DOX-Cs-CuO NPs on MCF-7 cells showed its ability to induce apoptosis in breast cancer cells, which was clearly substantiated by ROS generation with the loss of mitochondrial membrane potential. Our results clearly showed the therapeutic nature of novel biocompatible Cs-CuO NPs in delivering DOX with a pH-dependent manner.

Electrochemical properties of Ti3+ doped Ag-Ti nanotube arrays coated with hydroxyapatite

Ag-Ti nanotube array was prepared by simple anodic oxidation method and uniform hydroxyapatite were electrochemically deposited on the nanotubes, and then characterized by SEM, XRD, XPS and EIS. In order to investigate the influence of Ti3+ on the electrochemical deposition of hydroxyapatite on the nanotubes, the Ag-Ti nanotube array self-doped with Ti3+ was prepared by one step reduction method. The experiment results revealed that the Ti3+ can promote the grow rate of hydroxyapatite coatings on nanotube surface. The hydroxyapatite coated Ag-Ti nanotube arrays with Ti3+ exhibit excellent stability and higher corrosion resistance. Moreover, the compact and dense hydroxyapatite coating can also prevent the Ag atom erosion from the Ag-Ti nanotube.

The synthesis of four–layer gold–silver–polymer–silver core–shell nanomushroom with inbuilt Raman molecule for surface–enhanced Raman scattering

A facial two–step reduction method was proposed to synthesize four–layer gold–silver–polymer–silver (Au@Ag@PSPAA@Ag) core–shell nanomushrooms (NMs) with inbuilt Raman molecule. The surface–enhanced Raman scattering (SERS) intensity of 4MBA adhered on the surface of Au core gradually increased with the modification of middle Ag shell and then Ag mushroom cap due to the formation of two kinds of ultra–small interior nanogap. Compared with the initial Au nanoparticles, the SERS enhancement ratio of the Au@Ag@PSPAA@Ag NMs approached to nearly 40. The novel core–shell NMs also exhibited homogeneous SERS signals for only one sample and reproducible signals for 10 different samples, certified by the low relative standard deviation values of less than 10% and 15% for the character peaks of 4–mercaptobenzoic acid, respectively. Such a novel four–layer core–shell nanostructure with reliable SERS performance has great potential application in quantitative SERS–based immunoassay.

A novel Z-scheme visible light driven Cu2O/Cu/g-C3N4 photocatalyst using metallic copper as a charge transfer mediator

The novel Cu2O/Cu/g-C3N4 composites were successfully synthesized via one step reduction method in the presence of g-C3N4. Under visible light irradiation, the Cu2O/Cu/g-C3N4 composites exhibited higher photocatalytic activity than g-C3N4 and Cu/Cu2O, and the 20at% Cu2O/Cu/g-C3N4 photocatalyst displayed the highest photocatalytic activity. The enhanced photcatalytic mechanism was investigated by radical-trapping and electron spin resonance experiments. A Z-scheme charge transfer mechanism was proposed, in which metallic Cu particles acted as charge separation center. This work could provide some insight into the design of novel Z-scheme photocatalyst with metallic Cu particles as a charge transfer mediator.

General Step Reduction Method for Knowledge-Based Process Planning of Non-Axisymmetrical Forged Products

Abstract We propose a process planning method, which is termed the General Step Reduction (GeneSteR) method, for non-axisymmetrical cold- and warm-forged products. The GeneSteR method can produce process plans for non-axisymmetrical forged products without relying on any design cases. The basic principle of the GeneSteR method is to produce reversed forging process plans by reducing the steps that are contained in a forged product by a stepwise approach until a cylindrical billet is obtained. An experimental knowledge base was implemented based on the GeneSteR method and was applied to a universal joint yoke used in automobiles. The experimental results show that the proposed method has sufficient capability to generate satisfactory process plans that include a comparable plan as designed by an experienced engineer in a shorter time.

Single step radiolytic synthesis of iridium nanoparticles onto graphene oxide

In this work a new approach to synthesize iridium nanoparticles on reduced graphene oxide is presented. The nanoparticles were directly deposited and grown on the surface of the carbon-based support using a single step reduction method through gamma irradiation. In this process, an aqueous isopropanol solution containing the iridium precursor, graphene oxide, and sodium dodecyl sulfate was initially prepared and sonicated thoroughly to obtain a homogeneous dispersion. The samples were irradiated with gamma rays with energies of 1.17 and 1.33MeV emitted from the spontaneous decay of the 60Co irradiator. The interaction of gamma rays with water in the presence of isopropanol generates highly reducing species homogeneously distributed in the solution that can reduce the Ir precursor down to a zero valence state. An absorbed dose of 60kGy was used, which according to the yield of reducing species is sufficient to reduce the total amount of precursor present in the solution. This novel approach leads to the formation of 2.3±0.5nm Ir nanoparticles distributed along the surface of the support. The oxygenated functionalities of graphene oxide served as nucleation sites for the formation of Ir nuclei and their subsequent growth. XPS results revealed that the interaction of Ir with the support occurs through IrO bonds.

Surface modification of antioxidated nanocopper particles’ preparation in polyol process

A simple and efficient chemical process, which is called two step reduction route in polyol process, for producing copper nanoparticles with satisfied antioxidation property, was described here. This process’s reaction mechanism was demonstrated by analysing as prepared copper particles’ XRD patterns, SEM images and size distribution plots. The analysis results shows that all the preparation subprocesses such as reduction of copper ion, nucleation of copper particles and growth of metallic copper particles can be controlled through using polyol process. This two step reduction method can not only compulsively disconnect nucleation and nucleation growth, but also weaken conventional eruptible nucleation, which made it convenient for delaying the nuclei process and for controlling copper particles size. In addition, protective mechanisms of adopted surfactant in this process also were analysed here. When a quantitative surfactant was added into the reaction solution at the end of the reduction reaction, the electrolyte polymer covered on the new generated copper particles, some of it could still adhere on the particles’ surface after lavation, which made this agent play a role not only in particles’ dispersion, but also in particles’ antioxidation.

Two types of optimization of a cylindrical shell subjected to lateral pressure

Two types of optimization of thin-walled cylindrical shells loaded by lateral pressure are analyzed in this paper, with arbitrary axisymmetric boundary conditions and the volume being constant. The first is to find the optimal thickness to minimize the maximum deflection of a cylindrical shell. Here expressions of the objective function are obtained by the stepped reduction method. The optimal designs are reduced to nonlinear programming problems with an equality constraint. In minimizing the maximum deflection, the position of the maximum deflection from a previous iteration is used as the next one. The second is to find the optimal thickness to maximize the buckling pressure of shell. A buckling criterion of a shell is derived on the basis of an energy principle. An optimization criterion is formulated as the maximum of the buckling pressure. Moreover, the space of allowable solutions is defined. This procedure converges quickly and numerical results show the effectiveness of the method. Several examples are provided to illustrate the methods.

On the Nonaxisymmetric Loading of Nonhomogeneous Annular Plates of Variable Thickness

In this paper, the stepped reduction method is used to find general solutions for the nonaxisymmetric bending of arbitrary axisymmetric nonhomogeneous annular plates of variable thickness under an arbitrary nonaxisymmetric temperature field and an arbitrary nonaxisymmetric distributed load. In spite of a large number of steps, eventually only two simultaneous algebraic linear equations with two unknowns have to be solved. As an example, the bending of a circular plate, whose solution is known, is carried out by the proposed approach, and it is shown that results obtained by the proposed method compare well with previous solutions obtained by other methods and hence prove the accuracy of the proposed method.

Analysis of High-Speed Rotating Disks With Variable Thickness and Inhomogeneity

A rotating disk with varying thickness and inhomogeneity, and subjected to a steady, inhomogeneous temperature field is analyzed. To handle the arbitrary profile, the disk is discretized into a series of uniform annular disks possessing constant material properties and then solved by the step-reduction method. Analytic expressions for thermoelastic stresses are given, and based on these results, the formulation is extended to include the calculation of shrink fit, the solving of the inverse problem for equistrength rotating disks, and the computations of plastic stresses and creep at elevated temperatures.

General analytic solution of dynamic response of beams with nonhomogeneity and variable cross-section

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only two unknowns which are independent of the numbers of elements divided. The present analysis can also be extended to the study of the vibration of such beams with viscous and hysteretic damping and other kinds of beams and other structural elements with arbitrary nonhomogeneity and arbitrary variable thickness.

An exact element method for bending of nonhomogeneous thin plates

In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

Optimal design of cylindrical shells

In this paper, two types of problems of the optimal design of cylindrical shells with arbitrary axisymmetrical boundary conditions and distributed load, under the condition of the volume being constant, are discussed. These problems involve the minimax deflection and minimal compliancy of a cylindrical shell. Expressions of the objective function can be obtained by a stepped reduction method. In minimizing the maximum deflection, the position of the maximum deflection from the previous iteration is used as the next one. This procedure converges (Avriel 1976). Several examples are provided to illustrate the method.

An exact element method for the bending of nonhomogeneous Reissner's plate

In this paper, based on the step reduction method and exact analytic method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficients. By this method, a triangle noncompatible element with 15 degrees of freedom is derived to solve the bending of nonhomogenous Reissner's plate. Because the displacement parameters at the nodal point only contain deflection and rotation angle, it is convenient to deal with arbitrary boundary conditions. In this paper, the convergence of displacement and stress resultants is proved. The element obtained by the present method can be used for thin and thick plates as well. Four numerical examples are given at the end of this paper, which indicates that we can obtain satisfactory results and have higher numerical precision.

The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting on an elastic foundation is obtained under arbitrary axial symmetrical loads and boundary conditions. The uniform convergence of the solution is proved. This general solution can also be applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.