Fatigue behaviour of a box-welded joint under biaxial cyclic loading: effects of biaxial load range ratio and cyclic compressive loads in the lateral direction

ABSTRACT The biaxial fatigue of a steel plate (JIS SM400B) having a box‐welded (wrap‐around) joint was experimentally studied. Special concerns were focused on the effects of the biaxial load range ratio and compressive cyclic loading in the lateral direction. The direction of fatigue crack propagation under biaxial cyclic tensile loading, which has a phase difference of π, changed according to the biaxial load range ratio, R_xy = ΔP_x/ΔP_y. When R_xy was less than 0.56, fatigue cracks propagated along the toe of the weld in the x‐direction because the principal tensile stress range Δσ_y at that location exceeded the orthogonal value Δσ_x at the box‐weld toe. The fatigue lives in biaxial tests related well to the data from uniaxial tests when invoking the Δσ₅ criterion. However, the location and direction of Δσ₅ should be chosen according to the R_xy value and the failure crack direction. An increase in Δσ₅, as induced by the Poisson's ratio effect from either the out‐of‐phase tensile loading or the in‐phase compressive loading in the y‐direction, leads to an increase in fatigue damage (decrease in fatigue resistance or specifically a faster crack propagation rate), and this effect can be successfully estimated from uniaxial fatigue test data.     

Effect of rotationally restrained and Pasternak foundation on buckling of an orthotropic rectangular Mindlin plate

This article, based on first-order shear deformation theory, presents the buckling analysis of a rotationally restrained orthotropic rectangular Mindlin plate resting on a Pasternak elastic foundation. Thus, the Mindlin–Reissner plate theory is employed for which the governing equations are solved by the Rayleigh–Ritz method. Uniformly distributed in-plane loads are applied to two simply supported opposite edges of the plate and the other two edges have rotationally restrained conditions without loading. Finally, the effects of plate parameters, such as foundation stiffness coefficients, aspect ratios, and ratio of elastic modulus in the x to y direction on the buckling loads are presented. The results show that the buckling load would increase when the ratio of the elastic modulus in the x to y direction increases and the plate is close to isotropic. The variation of buckling load versus changing ratio of elastic modulus in the x to y direction in the state of without elastic foundation and with clamp support is more than the rest of the state.     

Primary aberration changes produced by arbitrary movements of paraxial rays

A general algorithm is proposed for evaluating variations of primary monochromatic and chromatic aberrations of single surface or thin-lens components when the paraxial marginal and chief rays are arbitrarily moved. Compared to the earlier algorithm, optical invariants of the original and the new optical configurations could be different, which is common when the object distances are changed or for zoom lenses with different f-numbers on zooming. According to the positions of object and pupil, four special cases arise which lead to the need for four separate sets of coefficients, and a new parameter which is always determinate is used to indicate which set is to be chosen.     

Hollow Gaussian beams with the power-exponent-phase vortex

A kind of hollow Gaussian beams with the power-exponent-phase vortex is introduced. Based on the Collins integral, an analytical expression of a hollow Gaussian beam with the power-exponent-phase vortex passing through a paraxial optical system described by the ABCD matrix approach is derived. The analytical expressions for the beam propagation factors and the orbital angular momentum density of such hollow vortex Gaussian beam passing through a paraxial optical system described by the ABCD matrix approach are also derived, respectively. As a numerical example, the propagation properties of a hollow Gaussian beam with the power-exponent-phase vortex are demonstrated in free space. The evolutions of the normalized intensity, the phase and the orbital angular momentum density distributions are investigated, respectively. The influences of the power order and the topological charge on the beam propagation factors in the x- and y-directions are analysed. The introduced hollow Gaussian beam has potential applications in the atom manipulation and the optical trapping.     

Identification of Specimen Position and Orientation Using Standard Deviation of Intensity in Phase‐Shifting Digital Holography1

Abstract: Phase‐shifting digital holography is a useful method to measure the displacement distribution and the strain distribution of an object surface. The complex amplitude distribution of an object surface is obtained as the complex amplitude distribution at a reconstruction distance. It is, however, difficult to measure the reconstruction distance by actual measurement. We discovered that the standard deviation of the intensity on the reconstructed image becomes the maximum value when the reconstruction distance is the same as the actual optical path length. The displacement distributions are obtained for the x‐, y‐ and z‐directions. When the normal direction of an object surface inclines from the z‐direction, the displacements defined on the xyz‐coordinate system should be transformed into the object coordinate system. It is, therefore, required to develop a measurement method of the orientation of the object to obtain the parameters for transforming from the xyz‐coordinate system into the object coordinate system. In this paper, the method to identify the position and the orientation of a specimen using the standard deviation of the intensity distribution is proposed.     

Color coding of the two-dimensional coordinates of events in position-sensitive radiation detectors

A new approach to determining the coordinates of events is proposed, which allows the point coordinates on a plane to be determined on line using a virtually single-channel readout system. According to the proposed method of color coding, each element of the area of a detecting target is assigned its color defined as a ratio of the component radiation wavelengths. Defined in this way, the color of the ith point on the mapping plane is in one to one correspondence with the (x _i , y _i ) coordinates of this point on the target.     

Partially coherent J 0-correlated Schell-model beams beyond the paraxial approximation

The concept of partially coherent J ₀-correlated Schell-Model (JSM) beams is extended to the nonparaxial regime. By using the generalized Rayleigh-Sommerfeld diffraction integral, analytical propagation equations of nonparaxial JSM beams in free space are derived. Under the paraxial approximation our results reduce to the corresponding paraxial ones. The free-space propagation properties of nonparaxial JSM beams are illustrated with numerical examples. A comparison with paraxial JSM beams shows that the nonparaxial approach should be used if the parameters f and σ are not small.     

Langzeit- und Dauerschwingfestigkeit des Vergütungsstahls 25CrMo4 bei mehrachsiger Beanspruchung durch drei schwingende Lastspannungen

High-Cycle and Long-Life Fatigue of 25CrMo4 under Multiaxial Load Conditions by three Alternating Stresses Statistically verified experimental results from high-cycle and long-life fatigue tests (HCF and LLF) with altogether 537 unnotched solid cylindrical and thin-walled hollow specimen are demonstrating the fatigue behaviour (S-N-characteristics, scatterband) of 25CrMo4 under uniaxial loading with superimposed static stresses (consideration of the mean stress effect) and under biaxial loadings in variation of phase differences between the three combined normal and torsional stresses σ_x, σ_y, τ_xy The fatigue strength is commonly decreasing with life time in the high-cycle regime until reaching the fatigue endurance limit in the transition range to infinite life. The “ductility level” τ_w/σ_w and the “mean stress sensibility” p = p (σ_w, σ_zSch, R_m) are relatively independent of the intensity by stress amplitudes and fatigue life to failure. In comparision with the specific case of biaxial combined loading with synchroneous amplitudes, the fatigue resistance characteristics are detrimentally influenced by out-of-phase normal stresses σ_x, σ_y; a phase difference of 180° between the normal stress amplitudes is the most critical state of combination, especially in the lower cycle regime caused by a greater slope coefficient (probability of survival P_s = 50%). On the contrary is there in the high-cycle regime as well as in the long-life range no significant influence to the fatigue strength by biaxial load conditions of simultaneously normal stresses with out-of-phase torsional stress τ_xy     

A 3D cylindrical finite element model for thick curved beam stress analysis

A finite element model is proposed to perform stress analysis for thick curved beams and panels subjected to various types of loadings. The model has 18 nodes in a three‐dimensional cylindrical co‐ordinates system. Three stress components on radial surface (σ_rr, τ_rθ, and τ_rz) and three displacement components (u_r, u_θ, and u_z) are used as nodal degrees of freedom. Therefore, the continuity condition for both stresses and displacements is achieved in the radial direction. Formulation of nodal shape functions and equilibrium equations are based on three‐dimensional elasticity theory and a minimum potential energy method. The accuracy of the method is verified with the standard test problems and exact solutions from the theory of elasticity. The model shows no locking phenomena. Convergence is investigated and the application to layered composite panel is illustrated. Copyright © 2003 John Wiley & Sons, Ltd.     

Nonlinear oscillations of laminated plates using an accurate four-node rectangular shear flexible material finite element

The objective of the present paper is to investigate the large amplitude vibratory behaviour of unsymmetrically laminated plates. For this purpose, an efficient and accurate four-node shear flexible rectangular material finite element (MFE) with six degrees of freedom per node (three displacements (u, v, w) along thex, y andz axes, two rotations (θ _x and θ _y ) abouty andx axes and twist (θ _xy )) is developed. The element assumes bi-cubic polynomial distribution with sixteen generalized undetermined coefficients for the transverse displacement. The fields for section rotations θ _x and θ _y , and in-plane displacementsu andv are derived using moment-shear equilibrium and in-plane equilibrium equations of composite strips along thex- andy-axes. The displacement field so derived not only depends on the element coordinates but is a function of extensional, bending-extensional coupling, bending and transverse shear stiffness as well. The element stiffness and mass matrices are computed numerically by employing 3×3 Gauss-Legendre product rules. The element is found to be free ofshear locking and does not exhibit any spurious modes. In order to compute the nonlinear frequencies, linear mode shape corresponding to the fundamental frequency is assumed as the spatial distribution and nonlinear finite element equations are reduced to a single nonlinear second-order differential equation. This equation is solved by employing thedirect numerical integration method. A series of numerical examples are solved to demonstrate the efficacy of the proposed element.     

Partial mixed 3-D element for the analysis of thick laminated composite structures

For the analysis of thick laminated composite structures this paper proposes a partial mixed 3-D element. The variational principle of this new element is obtained by modifying the Hellinger–Reissner principle. The functional of the present stationary principle is constructed by treating three displacements (u, v, w) and two transverse shear stresses (τ_xz, τ_yz) as independent of each other. Hence the nodal variables of the present mixed element contain three displacements and two transverse shear stresses. The other stresses (σ_x, σ_y, τ_xy, σ_z) are computed from the assumed displacement field and nodal displacement field and nodal displacements. The present element can satisfy the requirements of (1)transverse shear stress continuity between laminate layers and (2)boundary conditions of free transverse shear stresses on the top and bottom surfaces. These requirements are violated by conventional displacement finite elements. Since the stiffness matrix of the present element is formulated by combining a displacement model and a mixed model, it is definite, rather than indefinite as for the conventional mixed elements. Also, these two transverse shear stresses are part of the solution variables and are solved directly together with displacements. Examples are presented to demonstrate the accuracy and efficiency of this proposed partial mixed 3-D element in the analysis of thick laminated composite structures.     

Algorithm for converting 3D objects into rolls using spiral coordinate system

The article reports about the algorithm of converting objects into a flat ribbon in the process of roll powder sintering (RPS) additive manufacturing technology. The main idea of the author is to conform the transformation of spiral of Archimedes to 3D space. This algorithm is based on linear rolling effect. It is well known that any plane can be transformed into a roll and, in this way, the third dimension appears. Thus, two-dimensional space and height provide the conformity between (x, y, z) and (l, z) coordinates. This work describes how the algorithm of precise transformation of a 3D object to a flat ribbon, using the spiral coordinate system, has been designed and implemented with a varied layer thickness, a winding axle and resolution. The algorithm has been extensively tested with the help of several parts of computer aided design models based on the RPS process.     

Ray-tracing and Aberration Formulae for a General Optical System

Abstract

All aspects of the ray-tracing and of the calculation of the monochromatic and chromatic aberrations for a completely general optical system are treated. These include the specification of the system, the ray-tracing formulae for refraction, reflection and transfer, the introduction of pseudo-paraxial variables in the object and image spaces, the determination of the pupil domain and the best image plane, plus calculation of aberrations along rays. Hopkins' canonical coordinates are employed in the object and image space to facilitate the calculation of the aberration polynomial coefficients, for use in the evaluation of diffraction-based image criteria, such as the point spread function. All the formulae involved are always determinate and of good accuracy, no matter whether the object, image or either pupil, of the system is at finite distance or at infinity.     

Diffracted radiance: a fundamental quantity in nonparaxial scalar diffraction theory

Most authors include a paraxial (small-angle) limitation in their discussion of diffracted wave fields. This paraxial limitation severely limits the conditions under which diffraction behavior is adequately described. A linear systems approach to modeling nonparaxial scalar diffraction theory is developed by normalization of the spatial variables by the wavelength of light and by recognition that the reciprocal variables in Fourier transform space are the direction cosines of the propagation vectors of the resulting angular spectrum of plane waves. It is then shown that wide-angle scalar diffraction phenomena are shift invariant with respect to changes in the incident angle only in direction cosine space. Furthermore, it is the diffracted radiance (not the intensity or the irradiance) that is shift invariant in direction cosine space. This realization greatly extends the range of parameters over which simple Fourier techniques can be used to make accurate calculations concerning wide-angle diffraction phenomena. Diffraction-grating behavior and surface-scattering effects are two diffraction phenomena that are not limited to the paraxial region and benefit greatly from this new development.     

聚变堆包层第一壁缩比部件激光选区熔化成形研究

目的 研究激光选区熔化(SLM)成形第一壁缩比结构的组织性能。方法 以316L粉末为原材料,运用Inspire软件对不同成形姿势下第一壁缩比结构的应力与变形情况进行数值模拟,选择最佳成形姿势进行SLM成形,以控制整体变形,并对成形零件进行显微组织观察与力学性能测试。结果 实验结果表明,与立放和侧放2种成形姿势相比,平放时残余应力与变形最小,最大残余应力为29.68 MPa,最大变形量为0.29 mm。成形件微观组织呈现各向异性,x–y方向主要为粗大的胞状晶组织,z–x方向为细长的柱状晶组织。力学测试结果显示,x–y方向的抗拉强度为672.1 MPa,伸长率为48.2%,冲击韧性为100.6 J/cm²;z–x方向的抗拉强度为646.9 MPa,伸长率64.4%,冲击韧性为136.3 J/cm²。结论 组织的差异性主要是由扫描工艺与熔池内部复杂的温度场引起的,微观结构的各向异性会造成力学性能的差异,x–y方向的强度高于z–x方向的,z–x方向上的塑性韧性更高。     

Geodesic Gaussian Processes for the Parametric Reconstruction of a Free-Form Surface

Reconstructing a free-form surface from 3-dimensional (3D) noisy measurements is a central problem in inspection, statistical quality control, and reverse engineering. We present a new method for the statistical reconstruction of a free-form surface patch based on 3D point cloud data. The surface is represented parametrically, with each of the three Cartesian coordinates (x, y, z) a function of surface coordinates (u, v), a model form compatible with computer-aided-design (CAD) models. This model form also avoids having to choose one Euclidean coordinate (say, z) as a “response” function of the other two coordinate “locations” (say, x and y), as commonly used in previous Euclidean kriging models of manufacturing data. The (u, v) surface coordinates are computed using parameterization algorithms from the manifold learning and computer graphics literature. These are then used as locations in a spatial Gaussian process model that considers correlations between two points on the surface a function of their geodesic distance on the surface, rather than a function of their Euclidean distances over the xy plane. We show how the proposed geodesic Gaussian process (GGP) approach better reconstructs the true surface, filtering the measurement noise, than when using a standard Euclidean kriging model of the “heights”, that is, z(x, y). The methodology is applied to simulated surface data and to a real dataset obtained with a noncontact laser scanner. Supplementary materials are available online.     

Analytical Solution of Functionally Graded Beam Having Longitudinal Stiffness Variation

Abstract

The aim of the present paper is to developed analytical elasticity solution for a beam having longitudinal stiffness variation using recently developed multiterm extended Kantorovich (EKM) method. By applying the EKM method, the system of 4n first order ordinary differential equations (ODEs) and 1n algebraic equation are obtained along the in-plane (x) and thickness (z) directions. The system of the equations along the thickness direction (z) having constant coefficient but the set of equations along the x-direction have variable coefficients. In the thickness direction (z), exact closed-form solutions are obtained. And along the x-direction, the system of ODEs with variable coefficients are solved by employing the modified power series. In this paper, specific predefined variations are assumed in material property and their influence on the bending response of beam, subjected to mechanical loading, is investigated. Benchmark numerical results are presented for a different combination of boundary conditions. These numerical results can be used to validate approximate one-dimensional solutions and 2D numerical results.     

Mechanical Analysis of the Coupled Gas-Solid-Thermal Model during Rock Damage

Gas fracturing technology is the key to the exploration for unconventional petroleum resources and other engineering industries, so the research on the coupled gas-solid-thermal model during rock damage has the important significance to the development of gas fracturing technology. By introducing rock damage variable, the coupled gas-solid-thermal model during rock damage is established in this paper, besides, the rock damage constitutive is written with MATLAB software, which is embedded in the multi-physics coupling software COMSOL in the process of numerical computation. Based on this, the damage rule of rock mass around drilling under high pressure gas is analyzed. The results show when the ratio between x direction local stress σ_x and y direction local stress σ_y is 1, the rock failure is dominated by shear damage due to the effect of gas; when the ratio between x direction local stress σ_x and y direction local stress σ_y is 1/10, pull damage appears on both sides of drilling in the direction of Y because of the effect of gas; with the passage of time, the pore pressure in the rock mass increases gradually, while the pressure gradient decreases gradually; the primary temperature of rock mass has little influence on the pore pressure.     

Three-dimensional Computer Reconstruction of Random Rough Surface

Abstract

The two-dimensional function f(x y) with slow variation in the y direction and describing a random rough surface in the x direction is expanded in a Fourier series i.e. considered as a sum of sinusoidal harmonic grating in the x direction. The scattered optical field by each line of this surface in the x direction is considered as a sum of the diffracted optical fields from the sinusoidal gratings. The diffracted fields are registered by consecutive scanning of the surface in the y direction, and the surface profile of each line is reconstructed using the theory developed in [1,2]. The studied surface is visualized by the reconstructed profiles in ten lines using a program visualizing a function depending on two variables. The calculated mean roughness Ra is averaged along all lines and is found to be in satisfactory agreement with that averaged by the Hobson type profilometer within the laser spot.     

An accurate low order plate bending element with thickness change and enhanced strains

A three-dimensional variational formulation is used to obtain a plate bending element which includes the thickness change of the plate. The nodal degrees of freedom for the four-node element are the deflection w, the rotations θ _x and θ _y , and the thickness change H. Bilinear functions of the in-plane coordinates ξ and η are used for the approximation of the deflection, the rotations and the thickness change. Integration in thickness direction is performed analytically. One key feature of the element is that the three-dimensional constitutive equations for the six stresses have not to be modified. Using eight enhanced strain terms, a well performing plate bending element is obtained. Received 14 September 2000