Critical Plane Orientation Influence on Multiaxial High-Cycle Fatigue Assessment

In the present paper, the multiaxial fatigue lifetime of structural components failing in the high-cycle fatigue regime is evaluated by employing the modified Carpinteri-Spagnoli (C-S) multiaxial fatigue criterion based on the critical plane approach. In the above criterion, the critical plane position is linked to averaged principal stress directions through an off-angle 8. Then, the fatigue damage parameter used is determined by a nonlinear combination of an equivalent normal stress amplitude and the shear stress amplitude acting on the critical plane. In the present paper, some modifications of the original expression for the off-angle 8 are implemented in the modified Carpinteri-Spagnoli criterion. In particular, modified expressions recently proposed by Lagoda et al. are in accordance with the assumption originally developed by Carpinteri and co-workers, that is, the off-angle is a function of the ratio between the fatigue limit under fully reversed shear stress and that under fully reversed normal stress. Such expressions can be employed for metals ranging from mild to very hard fatigue behaviour. Some experimental data available in the literature are compared with the theoretical estimations and, only for materials with hard and very hard fatigue behaviour, the modified 8 relationships are shown to yield fatigue lifetime results slightly better than those determined through the original 8 expression.     

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.     

Finite-element analysis of the mechanical behavior of Au/Cu and Cu/Au multilayers on silicon substrate under nanoindentation

Finite-element analysis of the nanoindentation into Au/Cu and Cu/Au multilayers was performed to deduce their mechanical characteristics from nanoindentation response. Different bilayer thicknesses, numbers, and sequences were studied using the load–displacement curve, hardness, indentation, and the residual surface profile as well as the von Mises equivalent stress. The characteristics of the multilayers were found to be dispersed between the Au and Cu. Nevertheless, if the indentation depth is smaller than the uppermost individual layer thickness of the multilayers, the intrinsic properties can be obtained. Using the von Mises equivalent stress as a failure criterion, the results showed that thinner multilayers would induce a greater potential of shear banding deformation. PACS 61.43.Bn; 62.20.-x; 68.03.Hj; 68.05.Cf; 68.08.De     

径向阵列非傍轴椭圆高斯光束的相干和非相干合成

 从瑞利-索末菲衍射积分公式出发,推导出径向阵列非傍轴离轴椭圆高斯光束相干合成和非相干合成在自由空间中的解析传输公式,给出其远场分布和傍轴表示式。研究表明:合成光束的光强分布与f参数、径向阵列半径、光束数、传输距离和合成方式有关;N束光相干合成和非相干合成在远场的光强最大值分别为单光束在远场最大值的N₂和N倍。     

Simple approach to approximate predictions of the vapor–liquid equilibrium curve near the critical point and its application to Lennard-Jones fluids

We propose a simple analytical form of the vapor–liquid equilibrium curve near the critical point for Lennard-Jones fluids. Coexistence densities curves and vapor pressure have been determined using the Van der Waals and Dieterici equation of state. In described method the Bernoulli differential equations, critical exponent theory and some type of Maxwell?s criterion have been used. Presented approach has not yet been used to determine analytical form of phase curves as done in this Letter. Lennard-Jones fluids have been considered for analysis. Comparison with experimental data is done. The accuracy of the method is described.     

A general solution to the Schrödinger–Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation.     

铝-银合金在疲劳过程中所表现的一些特点

本工作进行了淬火Al-7.27％Ag合金的扭转疲劳试验,测定了各种扭应变下的△E-N曲线,并且观察了经过各种循环数以后试样的表面金相变化。实验结果指出,当扭应变较小时,△E随着循环数N的增加而逐渐下降,△E-N曲线的变化类似Al-Cu和Al-Mg合金在较低扭应变下的情况。但当扭应变较大时,△E开始略有下降,随后上升到某一较高值后再下降,直至试样断裂。△E-N曲线的形状与Al-Cu和Al-Mg合金完全不同。试样表面的金相变化分为两个明显不同的阶段。在疲劳的起始阶段,滑移痕迹细而均匀,但经过一定循环数后,少数滑移痕迹变得集中而深化。随着循环数的增加,新的滑移带在原有滑移带之间不断地出现,没有纯Al和Al-Mg合金中滑移带变宽的情况。还看到了裂纹沿晶界的形成和发展。根据溶质银原子与位错的电交互作用和位错切割银原子簇的观点,对所得到的结果进行了讨论。 关键词：     

Line-integral solution for the stress and displacement fields of an arbitrary dislocation segment in isotropic bi-materials in 3D space

The solutions for the stress and displacement fields due to an arbitrary dislocation segment in an isotropic bi-material medium consisting of joined three-dimensional (3D) half spaces are derived and expressed in terms of line integrals, integrands of which are given in an exact analytical form that, in turn, can also be integrated to yield analytical expressions for the stress–displacement field. The solution is constructed by employing a general solution derived by Walpole [Int. J. Eng. Sci. 34 (1996) p.629] for any elastic singularity in joined isotropic half space, and combining it with Mura's integral formula for the displacement gradient of an arbitrary dislocation segment in homogeneous medium. The resulting new solution provides a framework for deriving analytical expressions for stress and displacement fields of dislocation curves of arbitrary shapes and orientations. The benefit of the method developed, as compared with other methods found in the literature, is that the new solution presented is naturally divided into two components, a homogenous component representing the field of a dislocation in an infinitely homogenous medium, and an image component. This makes it easy and straightforward to modify existing dislocation dynamics codes that already include the homogenous part. To illustrate the accuracy of the method, the stress field expressions of an edge dislocation with Burgers vector perpendicular to the bi-material interface are derived as a degenerate case of the general result. It is shown that our solution is identical to that found in the literature for this case.     

Gravitational four-fermion interaction on the Planck scale

The four-fermion gravitational interaction is induced by torsion, and gets essential on the Planck scale. On this scale, the axial–axial contribution dominates strongly the discussed interaction. The energy–momentum tensor, generated by this contribution, is analyzed, as well as stability of the problem with respect to compression. The trace of this energy–momentum tensor can be negative.     

Critical amplitude ratios of the Baxter–Wu model

A Monte Carlo simulation study of the critical and off-critical behavior of the Baxter–Wu model, which belongs to the universality class of the 4-state Potts model, was performed. We estimate the critical temperature window using known analytical results for the specific heat and magnetization. This helps us to extract reliable values of universal combinations of critical amplitudes with reasonable accuracy. Comparisons with approximate analytical predictions and other numerical results are discussed.     

Understanding the accuracy of Nanbu’s numerical Coulomb collision operator

We investigate the accuracy of and assumptions underlying the numerical binary Monte Carlo collision operator due to Nanbu [K. Nanbu, Phys. Rev. E 55 (1997) 4642]. The numerical experiments that resulted in the parameterization of the collision kernel used in Nanbu’s operator are argued to be an approximate realization of the Coulomb–Lorentz pitch-angle scattering process, for which an analytical solution for the collision kernel is available. It is demonstrated empirically that Nanbu’s collision operator quite accurately recovers the effects of Coulomb–Lorentz pitch-angle collisions, or processes that approximate these (such interspecies Coulomb collisions with very small mass ratio) even for very large values of the collisional time step. An investigation of the analytical solution shows that Nanbu’s parameterized kernel is highly accurate for small values of the normalized collision time step, but loses some of its accuracy for larger values of the time step. Careful numerical and analytical investigations are presented, which show that the time dependence of the relaxation of a temperature anisotropy by Coulomb–Lorentz collisions has a richer structure than previously thought, and is not accurately represented by an exponential decay with a single decay rate. Finally, a practical collision algorithm is proposed that for small-mass-ratio interspecies Coulomb collisions improves on the accuracy of Nanbu’s algorithm.     

Effects of high-order surface stress on static bending behavior of nanowires

Studies on surface effects in nano-sized materials or structures are often based on the framework of linear membrane theory, in which the field jumps at the interface are characterized by the generalized Young–Laplace equation. Here a recently proposed theoretical framework of high-order surface stress is implemented in a continuum mechanics model to simulate the bending behavior of nanowires. The high-order surface stress considers not only the effect of in-plane membrane surface stresses, but also the surface moments induced from the non-uniform surface stress across the layer thickness. We investigate the extent to which the high-order surface stress will influence the bending behavior of nanowires deviated from that predicted by the generalized Young–Laplace equation. Closed-form expressions for the deflection curves are derived for nanowires with different boundary conditions. These solutions are utilized to characterize the size-dependent overall Young's moduli of NWs. We demonstrate that, in comparison to the reported experimental data, the present framework provides more accurate results than those by the conventional surface stress model. This study might be helpful to accurately characterize the behavior of bending nanowires in a wide range of applications.     

Effects of loading condition on very-high-cycle fatigue behaviour and dominant variable analysis

The specimens of a high carbon chromium steel were quenched and tempered at 150°C,180°C and 300°C.Such specimens were tested via rotating bending and a push-pull type of axial loading to investigate the influences of loading condition on the behaviour of very-high-cycle fatigue(VHCF).Experimental results show the different influences of inclusion size on the fatigue life for the two loading conditions.Predominant factors and mechanism for the fine-granular-area(FGA)of crack origin were discussed.In addition,a reliability analysis based on a modified Tanaka-Mura model was carried out to evaluate the sensitivity of inclusion size,stress,and KFGA to the life of VHCF crack initiation.     

Studies on dissociation energies of diatomic molecules using vibrational spectroscopic constants

New analytical expression and numerical approach are suggested to calculate dissociation energies De of diatomic molecular states using an extreme value method (EVM). Studies on some electronic states of OH, BH, N2, Br2, ClF and CO molecules show that the accuracy of the EVM dissociation energies depends on the number of correct vibrational constants used in the calculations. The convergence qualities of De are suggested to be an alternative physical criterion to measure the qualities of the various sets of vibrational constants from different literature for the same diatomic state.     

A nonlinear magneto-thermo-elastic coupled hysteretic constitutive model for magnetostrictive alloys

This paper presents a general hysteretic constitutive law of nonlinear magneto-thermo-elastic coupling for magnetostrictive alloys. The model considered here is thermodynamically motivated and based on the Gibbs free energy function. A nonlinear part of the elastic strain arising from magnetic domain rotation induced by the pre-stress is taken into account. Furthermore, the movement of the domain walls is incorporated to describe hysteresis based on Jiles–Atherton's model. Then a set of closed and analytical expressions of the constitutive law for the magnetostrictive rods and films are obtained, and the parameters appearing in the model can be determined by those measurable experiments in mechanics and physics. Comparing this model with other existing models in this field, the quantitative results show that the relationships obtained here are more effective to describe the effects of the pre-stress or in-plane residual stress and ambient temperature on the magnetization or the magnetostriction hysteresis loops.     

Analysis of crack propagation data for a strain ageing and a stabilized mild steel tested under R=0 and R=−1 loading conditions

Comparative studies of crack propagation in a strain ageing and a stabilized mild steel were carried out under axial loadings of the R = 0 and R = ?1 types. The results show the rate of fatigue crack propagation is dependent on both the tensile and the compressive stresses in the fatigue cycles, the compression stresses being less effective than the equivalent tensile stresses in causing crack growth. An equation is presented relating the rate of fatigue crack growth to a stress intensity range which is factored to allow for the variations in fatigue damage associated with the tensile and compressive parts of the stress cycle.     

A novel methodology for online detection of bearing health status for naturally progressing defect

A methodology is proposed for the online detection of health status of rolling element bearing into various damage stages for naturally progressing defect. Various damage identification parameters are derived from processing vibration data in time domain, frequency domain and time–frequency domain. The parameters are fused into a single parameter, Mahalanobis distance, by application of Gram–Schmidt Orthogonalization process. Chebyshev?s inequality is applied to the Mahalanobis distance for online monitoring and damage stage detection. A simulation study is first carried out to show working of the proposed methodology in presence of varying trends of damage identification parameters. The proposed methodology is then validated on experimental data. The first validation is on the vibration data acquired from a bearing having seeded defect. Later, two accelerated life tests are conducted on a specially designed test rig at different load and speed combinations on the bearings for ensuring naturally induced and progressed defects. The methodology is successfully verified on the vibration data acquired from the naturally induced and progressed defect experiments.     

A 2D equivalent circuit of piezoelectric ceramic ring for transducer design

In this paper a 2D equivalent circuit of longitudinally polarized piezoelectric ceramic rings is established, which is obtained as an approximated analytical solution of 3D constitutive equations in the hypothesis of axial symmetry when the shearing stress and torsion are ignored. The mechanical part of the equivalent circuit can be divided into two branches; one branch characterizes the longitudinal extensional vibration, the other represents the radial vibration. The two branches, which are coupled to an electrical port by two transformers separately, mechanically couple to each other by some mechanical impedance at the same time. Similar circuit is also presented when piezoelectric disk is concerned. Based on this model it is able to compute all the relations between the input applied voltage and the output forces and velocities on every external surface analytically. Compared with the 1D equivalent circuits, the 2D equivalent circuit gives a more comprehensive predicts of the thickness and radial modes with sufficient accuracy when the ring or disk is thin. When the ring or disk is so thick that the 1D theory is not validated, an effective predict of the coupled vibration can also be presented. Comparisons with the experimental results show this model is rather accuracy in frequency calculation.