Properties,applications and manufacture of wear-resistant hard material coatings for tools

Wear processes during machining with cemented carbides and the effect of coatings on wear and on toughness are described. The requirements for coatings relating to optimum tool life are reviewed. Recently developed multilayer coatings with and without ceramic layers are described and examples for improvements in the tool lifetime are given. Additionally, some examples for the application of coatings for milling and chipless forming are presented.The wear-reducing effect of coatings on steel tools is described and possibilities for applications of steel tools coated using chemical vapour deposition (CVD) are elucidated. A number of examples for coated cutting and chipless forming steel tools are described.Finally, useful processes for the coating production are considered. A comparison between physical vapour deposition and CVD processes with respect to the coating temperature, the consistency and the adhesion of the coating is presented. The CVD process for economic production is considered and a suitable coating unit is outlined.     

具有共同分量的相关数据的加权平均

对比不相关数据的加权平均法,讨论了对具有共同分量的一组相关数据的加权平均法。分析了比对数据的相关性,将相关数据的不确定度分解为共同分量与不相关分量的组合。提出了具有较好可操作性的估计比对数据溯源链共同分量不确定度的简单方法。结论为加权平均应以不相关分量的不确定度为权重因素;共同分量的不确定度是“固有”的,不随参与平均计算的数据数量的增加而减小;忽略数据相关性,不仅影响加权平均的权重,进而影响平均值,也会导致平均值不确定度计算结果偏小。以压力比对为例分析了共同分量的不确定度的评定以及不同取值结果的差异。     

Design of short fiber Bragg gratings by use of optimization

We demonstrate an optimization approach for designing fiber Bragg gratings. A layer-peeling inverse-scattering algorithm is used to produce an initial solution, which is optimized numerically with an iterative optimization method. To avoid problems with local minima, we use merit functions that are zero for wavelengths for which the predefined demands (acceptance limits) are fulfilled, making it possible to alter the local minima under the optimization process without disturbing the global minimum. Because short gratings are difficult to design with inverse scattering, and because the time consume of the optimization increases rapidly with the grating length, the method is particularly useful for designing short gratings. The method is also useful when the demands are complex and difficult to handle with inverse-scattering methods. Design examples are given, including a dispersionless bandpass filter suitable for dense wavelength-division multiplexing and a filter with linear reflectivity.     

A particle method for elastic and visco-plastic structures and fluid-structure interactions

A new particle method is proposed for elastic and visco-plastic structures based on the concept of MPS (Moving Particle Semi-implicit) method which was developed for fluid dynamics. Particle interaction models for differential operators are prepared in MPS method. The government equations of elastic structures are interpreted into interactions among particles. These interactions are equivalent to those of normal and tangential springs. Therefore the present particle method is simple and corresponding physical meaning is clear. Model for visco-plastic structure is represented to replace these elastic springs into visco-plastic ones. Elements or grids are not necessary. A tensile plate and a cantilever beam as elastic structures are analyzed by the present method. The results are in good agreement with theoretical solutions. Visco-plastic analysis for creep deformation and fracture of a cracked plate is also carried out and the result is in good agreement with an experiment. The present particle method for elastic structures is combined with MPS method for fluid-structural interaction problems. Since both methods are based on the same particle modeling in Lagrangian coordinates, large deformation of the interfaces can be easily analyzed. Water falling on a cantilever beam is analyzed by the combined method. Crash of water and resultant displacement of the beam are successfully analyzed. Structural analysis in a breakwater is carried out with wave propagation. The calculated pressure distribution on the breakwater is in good agreement with a theory. Received 21 November 2000     

Nonlinear behavior of functionally graded circular plates with various boundary supports under asymmetric thermo-mechanical loading

The equilibrium equations of the first-order nonlinear von Karman theory for FG circular plates under asymmetric transverse loading and heat conduction through the plate thickness are reformulated into those describing the interior and edge-zone problems of the plate. A two parameter perturbation technique, in conjunction with Fourier series method is used to obtain analytical solutions for nonlinear behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with known results in the literature. The load–deflection curves for different loadings, boundary conditions, and material constant in a solid circular plate are studied and discussed. It is shown that the behavior of FG plates with clamped or simply-supported boundary conditions are completely different. Under thermo-mechanical loading, snap-through buckling behavior is observed in simply-supported FG plates which are immovable in radial direction. Moreover, it is found that linear theory is inadequate for analyzing FG and also homogenous plates with immovable boundary supports in radial direction and subjected to thermal loading, even for deflections that are normally considered small.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

A fatigue model developed by modification of Gough’s theory, for random non-proportional loading conditions and three-dimensional stress fields

As a first stage, fatigue damage models proposed by some well-known references and the corresponding assumptions are discussed and some enhancements are proposed. Generally, these models are suitable for bending–torsion fatigue problems with zero mean stress and are restricted to cases where the numbers of cycles of the stress components are identical. In the present paper, a general fatigue model for the HCF regime is proposed. This model overcomes most of the shortcomings of the previous theories and is suitable for life assessment in three-dimensional stress fields. Furthermore, a different critical plane concept is introduced and a different life assessment algorithm is presented. Since results of the previous fatigue theories are generally validated by experiments done on simple components with simple loading time histories, the discrepancies exist among the various theories have not been invoked appropriately. In the current paper, validity of these theories as well as the modified versions proposed in the current paper and the new criterion is examined for more general cases with non-proportional random loadings and complicated geometries. Finally, results of the various theories are compared with the experimental results. Experimental results are prepared for both proportional and non-proportional cases. Significant enhancements are observed due to employing the proposed modifications, especially for three-dimensional stress fields and random loadings.     

The Foundations of Multivariate Analysis

In robust design studies, the important noise factors are varied systematically in off-line experiments and their interactions with control factors are investigated. The choice of the noise variable settings is extremely important in being able to achieve the goal of robust design studies. However, the noise distributions are rarely known, and the choices are often based on convenience. This article demonstrates some of the unintended and undesirable consequences of such choices, including identification of small dispersion effects as important, missing of large ones, and issues with parameter optimization. The main contribution of the article is to propose an alternative method of analysis for identifying important dispersion effects, one based on separate analysis for each noise factor. The method is tailored for situations with crossed-array designs. There are, however, still challenges associated with choosing the control factor settings to achieve robust performance. Further, there are difficulties with the use of combined arrays in such cases. The focus of the article is on direct modeling of the responses but implications for mean–variance analyses are also discussed.     

Response of Elliptical Composite Cylinders to Axial Compression Loading

The results from semianalytical predictions and experiments are used to study the response of composite cylinders with elliptical cross sections loaded axially to a significant percentage of their buckling load. The semianalytical approach is based on the methods of Marguerre, Rayleigh-Ritz, and Kantorovich. The radius of curvature and the displacements are approximated by expansions in harmonic series in the circumferential arc-length coordinate, and the coefficients of the displacement series are unknown functions of x which are solved for using the finite-difference method. The primary features of the predicted response are first described. Then the experiments are described and results for elliptical cylinders with varying degrees of orthotropy are compared with predictions. Where appropriate, calculations based on the analysis of circular cylinders are compared with the semianalytical calculations for the ellipse. Correlation between experiments and predictions is good, and it is demonstrated that despite the noncircular cross section, many responses of an ellipse are very similar to the axisymmetric response of circular cylinders subjected to an axial load. The similarity is independent of the degree of orthotropy of the elliptical cylinder.     

Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

Particle methods for modeling reinforced concrete are described. The reinforcements are modeled by finite elements and are coupled to the particle method by Lagrange multipliers. The method is applicable to nonlinear problems, problems with moderate to severe cracking and deformable interfaces. Applications to the static response of reinforced concrete structures where the concrete is discretized with particles and the reinforcement with elements are described. The method is also tested for several static problems where no relative displacements between the concrete and the reinforcement are allowed.     

Asymmetric quadrilateral shell elements for finite strains

Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov–Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton–Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.     

A HIGHER ORDER EXPANSION METHOD FOR OPTIMUM DESIGN OF STRUCTURES FOR SPECIFIED FUNDAMENTAL EIGENVALUE

A higher order expansion method is presented for optimum design of structures for specified fundamental eigenvalue. The design function, fundamental eigenmode and total volume are expressed in terms of the Taylor series expansion with respect to the specified fundamental eigenvalue. A solution with null design function, where all the eigenvalues degenerate to null, is chosen as a trivial initial solution, and higher order terms are incorporated. By using the proposed method, a set of optimum designs for a wide range of fundamental eigenvalues is easily found. The proposed method is applied to an Euler-Bernoulli beam and expanded forms are presented analytically for a simply supported beam. The method is then extended to a plane truss, and the results are compared with those by an optimality criteria method.     

Wave propagation in a hollow pyroelectric circular cylinder of crystal class 6

Summary Flexural and longitudinal wave propagation in a hollow pyroelectric cylinder of crystal class 6 are considered. The frequency equation has been derived for two different cases. Case (i) is for a hollow cylinder whose inner and outer surfaces are traction free, completely coated with electrode which are shorted and thermally insulated. Case (ii) is for a hollow cylinder whose inner surface is clamped, completely coated with electrode which are shorted and thermally insulated while the outer surface is same as in case (i). The frequency equation has been analyzed numerically for Barium titanate ceramic. The results are tabulated and the dispersion curves are presented.     

A direct application of higher-order parametric programming techniques to structural optimization

Computational methods based on a sequence of parametric programming problems are presented for solving constrained optimization problems (COP) without any parameter. An auxiliary parametric programming problem (APPP) is formulated in order to solve COP. The procedure is started with an arbitrary initial solution which is the trivial solution of APPP corresponding to the initial value of the parameter. Then the optimal solution for the final value of the parameter, which is the optimal solution of COP, is estimated by Taylor's expansion with respect to the parameter where higher-order terms are incorporated. It is shown that the incorporation of the higher-order terms indeed leads to a faster convergence of the solution. As an extension of the method, a general algorithm is presented for optimum design problems with state variable constraints which are implicit functions of the design variables. Logarithmic penalty functions are incorporated and the weight coefficients for the penalty terms are updated continuously. The derivatives of the state variables with respect to the parameter and their sensitivity coefficients are expressed explicitly in terms of those of the design variables. Finally, a method of simultaneous analysis and optimization is developed for trusses with geometrical non-linearity.     

Diffuse ultrasonic backscatter in a two-dimensional domain

The scattering of elastic waves in polycrystalline materials is relevant for ultrasonic materials characterization and nondestructive evaluation (NDE). Diffuse ultrasonic backscatter measurements are used widely to extract the microstructural parameters such as grain size and also to detect flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Line transducers are often used for ultrasonic experiments such that an appropriate model for these two-dimensional problems is needed. Here, a theoretical expression for the temporal diffuse backscatter is derived for such domains under a single-scattering assumption. The result is given in terms of transducer and microstructural parameters. In addition, the problem is examined in terms of numerical simulations using Voronoi polycrystals that are discretized using finite elements in a plane-strain formulation. The material properties of the individual Voronoi cells are chosen according to appropriate material distributions. Such numerical models also allow scattering theories, including the one discussed here, to be examined for well-controlled microstructures. Example numerical results for materials with varying degrees of scattering that are of common interest are presented. The numerical results are compared with the theory developed with good agreement. These results are anticipated to impact ultrasonic NDE of polycrystalline media.     

曲面立体完整画隐线图的标记

提出了三面顶点“流形”曲面立体完整画隐线图的标记理论和方法。在三面顶点曲面立体完整画隐线图中合法的节点型式共有69种,其中Y型节点有8种,W型节点有16种,S型节点有11种,V型节点有34种。对曲面立体完整画隐线图进行标记,能够判断其是否可能为“流形”曲面立体的投影,区分正确与不正确画隐线图。提出的完整画隐线图标记方法也适用于平面立体画隐线图。算例证明曲面立体完整画隐线图标记方法是正确、可行和有效的。     

Oscillators with symmetric and asymmetric quadratic nonlinearity

In this paper, oscillators with asymmetric and symmetric quadratic nonlinearity are compared. Both oscillators are modeled as ordinary second-order differential equations with strong quadratic nonlinearities: one with positive quadratic term and the second with a quadratic term which changes the sign. Solutions for both equations are obtained in the form of Jacobi elliptic functions. For the asymmetric oscillator, conditions for the periodic motion are determined, while for the symmetric oscillator a new approximate solution procedure based on averaging is developed. Obtained results are tested on an optomechanical system where the motion of a cantilever in the intracavity field is oscillatory. Two types of quadratic nonlinearities in the system are investigated: symmetric and asymmetric. The advantage and disadvantage of both models is discussed. The analytical procedure suggested in the paper is applied. The obtained solution agrees well with a numerical one.     

Bit error ratio performance of a receiver diversity scheme with channel estimation

The performance of diversity combining techniques with channel estimation for the case of unequal power branches is discussed. The performance of binary phase shift keying (BPSK), pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) formats is investigated and their performance with nonideal channel estimation is explored. The case of combining multiple branches with unequal power levels is considered and optimal weighting factors for a log likelihood ratio test (LLRT) detector for the BPSK case are presented. These weights are shown to operate in a similar manner to those obtained by the linear minimum mean squared error (LMMSE) criterion and are compared with the well known maximal ratio combining (MRC) technique. The probability of error of this receiver is derived and simplifications for high signal-to-noise ratios are presented. Finally, numerical results are presented to compare the performance of the LLRT, LMMSE and MRC based receivers     

Exact corotational shell for finite strains and fracture

The corotational method for frame-invariant elements is generalized to obtain a consistent large-strain shell element incorporating thickness extensibility. The resulting element allows arbitrary in-plane deformations and is distinct from the traditional corotational methods (either quadrature-based or element-based) in the sense that the corotational frame is exact. The polar decomposition operation is performed in two parts, greatly simplifying the linearization calculations. Expressions for the strain-degrees-of-freedom matrices are given for the first time. The symbolic calculations are performed with a well-known algebraic system with a code generation package. Classical linear benchmarks are shown with excellent results. Applications with hyperelasticity and finite strain plasticity are presented, with asymptotically quadratic convergence and very good benchmark results. An example of finite strain plasticity with fracture is solved successfully, showing remarkable robustness without the need of enrichment techniques.     

Asymptotic analysis and finite element calculation of a rubber notch contacting with a rigid wedge

Summary In this paper, the strain energy function given by Knowles-Sternberg in 1973 is used, and the contact problem of a rubber notch with a rigid wedge is analyzed. The basic equations of the deformation field near the notch corner are derived and solved. An analytical solution is obtained for the expanding sector while the numerical solution is given for two shrinking sectors. A special interesting case is that a half rubber-like plane contacts with a rigid wedge, for which the completely analytical solutions are obtained for both expanding sector and shrinking sectors. The analysis of this paper is also valid for the contact problem of a rubber wedge with a rigid wedge. To verify the analytical results, a finite element program of nonlinear elasticity is made with which the same problem is calculated, and the results are consistent with the analytical results very well.