Stress-free Plate Research Articles

Simulation and experiment of complex residual stress detection of metal plate based on critical refracted longitudinal wave (LCR) method

This study is based on the principles of acoustoelasticity, analyzing the variation in sound wave time-of-flight(TOF) under different conditions using the critical refracted longitudinal(LCR) wave method. A simulation model was developed using the COMSOL finite element simulation software to mimic the propagation of LCR wave in a stress-free plate. The model was then subjected to uniaxial loading, and the change in wave TOF was observed by varying the angle between the stress direction and the sound wave propagation direction under constant load. The results were compared with theoretical calculations, showing a high degree of agreement, validating the accuracy of the designed model. Subsequently, during the tensile testing, the influence of different uniaxial loads and angle variations on the TOF of LCR wave was observed. Upon comparing the experiment data with theoretical calculations, a high degree of consistency in the trend of variation is observed, this demonstrates that the detection platform established in this study is feasible for the assessment of residual stresses in practice.

Numerical study of Rayleigh wave propagation along a horizontal semi-infinite crack buried in half-space.

The present article investigates the propagation of Rayleigh waves along a horizontal semi-infinite crack, and its interaction with the crack tip. Finite element analysis was used to simulate wave propagation and study the interaction. An incident Rayleigh wave diffracts as bulk waves into the half-space upon interaction with the crack tip. It was observed that the diffracted bulk modes can interact with the half-space boundary, and mode converts into a Rayleigh wave traveling along the boundary. A qualitative analysis was performed to determine the effect of crack depth using transmission, reflection, and scattering coefficients. Moreover, the possibility of Lamb wave generation also arises since the crack face and boundary form a stress-free plate section. The source of the "turning" Lamb modes was also identified from the observations. The characteristics of the transmitted Rayleigh wave were also explored, and a certain degree of mode coupling between Rayleigh and shear waves was observed when the crack tip was farther away from the boundary.

Shear Waves in an Initially Stressed Elastic Plate with Periodic Corrugations

The influence of the combined effect of initial stress and periodic surface corrugation on ultrasonic SH wave propagation in an elastic plate is investigated. Considering weak surface corrugations, a small parameter is defined using the ratio between the corrugation amplitude and the average thickness of the plate and the perturbation method of strained parameters is used up to the second order. An equation for evaluating the wave phase velocity in the periodically corrugated plate is realized. Numerical examples are provided to graphically illustrate the variations of the phase velocity in periodic plates, with various corrugation amplitudes and wavelengths, under compressive and tensile initial stresses over a frequency spectrum. The study reveals the dispersive nature of SH waves in corrugated plates. It is found that the wave phase velocities are slightly higher (lower) in plates under initial tension (compression) than initially stress-free plates. The influence of initial stresses on SH phase speed decreases as the frequency increases. It is shown that periodic surface roughness has a stronger effect on reducing wave phase speeds than a shallow surface waviness.

Transition to geostrophic convection: the role of the boundary conditions

Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotating while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier–Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\times 10^{10}$, at constant Prandtl number $Pr=1$, and vary the Ekman number in the range $Ek=1.3\times 10^{-7}$ to $Ek=2\times 10^{-6}$, which satisfies both requirements of supercriticality and strong rotation. We focus on the differences between the application of no-slip versus stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at $Ek\approx 9\times 10^{-7}$ for $Ra=1\times 10^{10}$ and at $Ek\approx 3\times 10^{-7}$ for $Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in $Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat-transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions, the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

Circular Crested Lamb Waves in a Fluid Saturated Incompreesible Porous Plate

The propagation of circular crested waves in a fluid saturated incompressible porous plate is analyzed. The frequency equations, for symmetric and anti‐symmetric waves, connecting the phase velocity with wave number are derived. At short wave length limits the frequency equations for symmetric and antisymmetric waves in a stress free plate reduce to Rayleigh type surface wave frequency equation and the finite thickness plate appears as a semi‐infinite medium. The results at various steps are compared with the corresponding results of classical theory and finally the variations of phase velocity, attenuation coefficient with wave number and displacements amplitudes with distance from the boundary of the plate is presented graphically and discussed.

Lake Aggregate Mesoscale Disturbances. Part I: Linear Analysis

Abstract The steady boundary-layer responses that occur over the Great Lakes region during wintertime cold air outbreaks are examined using a two-dimensional, linear, analytic model. The planetary boundary layer (PBL) is modeled as an idealized, constantly stratified, viscous, rotating Boussinesq fluid that moves uniformly between two horizontally infinite, rigid, stress-free plates. The heat from the lakes is parameterized in terms of a specified diabatic forcing function. Solution of the governing differential equation yields an integral expression for the vertical motion of the general response. Further assessment of the response is gained by examining closed-form analytic solutions to several limiting cases. Four response types are identified that depend upon the values of the Froude number Fr, the mechanical Ekman number Ex, the thermal Ekman number Ex, and the eddy Prandtl number Pr. Four different flow regimes are found. When 0 ≤ Fr < 1 and Pr ≥ 1, there is a purely exponentially damped response th...

Surface cracks in a plate of finite width under extension or bending

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

A Review of Effective Plating for Use in the Analysis of Stiffened Plating in Bending and Compression

The review is divided into three main parts. The first is very brief and covers shear lag effects associated with stiffener plate bending. Part 2 concerns the behavior of unstiffened long plate elements (a ≥ b) in compression, which is referred to as effective ‘width’ effects. The concepts considered are maximum plate strength and how this is affected by initial distortion, normal pressure, and boundary conditions; stress distribution in plate elements before failure; and the "reduced effective width" concept for defining plate element stiffness, as required for use in stiffened-plate collapse theories. Final appraisal leads to recommendations based upon the equation advanced ten years ago for mean expected stress-free plate strength: σm/σο = (2/β) — (1/β2). It is used by the British Navy and has been recommended in Europe for box-girder bridge design. Part 3 concerns welding stress effects, and a critical strain theory is advanced for describing welded plate behavior in compression. The review has of course assessed appropriate test data, including a reappraisal from three full-scale destroyer tests. Some emphasis has been placed upon the statistical characteristics of the data, in order that this may help establish structural strength distributions for probabilistic approaches to ductile structural reliability. The paper ends with a brief historical review drawn from aeronautical, civil engineering and naval architectural sources, and a listing of the more important effective width formulas.

DYNAMIC PHOTOELASTIC STUDIES OF P AND S WAVE PROPAGATION IN PRESTRESSED MEDIA

The occasional existence of very pronounced, anomalous, horizontally polarized seismic waves from underground nuclear bomb blasts has been reported by several investigators. In order to further understanding of this phenomenon and the processes of mechanical radiation from explosions, particularly in prestressed media, a model study has been undertaken. Experimental apparatus has been developed which permits the generation and propagation of body waves from explosions in transparent plate models prestressed to various two‐dimensional stress configurations. High‐speed framing camera sequences are presented showing the explosion process and the resulting plate compressional and shear wave propagation in prestressed models. These are compared to theoretical calculations of isochromatic and [Formula: see text] isoclinic fringe patterns associated with the wave propagation in stressfree plates and plates prestressed in tension and shear. The following distinctive optical phenomena were predicted theoretically and observed in the high‐speed photoelastic patterns: a [Formula: see text] discontinuity between P and S wave isoclinics for the unstressed case; a tendency for the isoclinics to broaden and envelope the isochromatics in regions where the P and S waves are superimposed; development of serrations in the dynamic isoclinics in the presence of a prestressing field (yielding a pseudo‐isochromatic appearance to isoclinics when viewed monochromatically); and finally, a general similarity between the dynamic optical effects in media under tensile and shear prestress.