Determination of stresses in slightly orthotropic plates using off-axis horizontally polarized ultrasonic shear waves

Many structural materials display a slight orthotropy when they are rolled into plate form. A theory is developed for propagation of horizontally polarized ultrasonic shear waves in the planes of (orthotropic) material symmetry of these plates. The waves propagate at an angle θ to the plate normal. If E represents a measure of the shear stress field, then pure-mode waves can be propagated if both cos² θ and sin² θ E; the polarization directions are the material symmetry axes.

The theory can be applied to ultrasonic stress measurements. The (normalized) velocity difference (acoustic birefringence) between two pure-mode SH-waves propagating in orthogonal material symmetry planes is related to stresses in the plate, and to the (initial) birefringence in the unstressed state. By making measurements of birefringence at two or more values of θ, the dependence upon the initial birefringence can be removed and information about the stresses obtained.     

声双折射法研究再结晶退火处理对45#钢微观组织的影响

本文在研究超声测试应力的过程中为了减小材料组织结构以及残余应力对应力测试结果的影响,对45#钢试样进行再结晶退火热处理,并用超声双折射法研究试样的再结晶退火组织,分析其微观组织和各向异性。实验结果表明,试样中横波声速随其偏振化方向改变而变化,存在声速快轴和慢轴且两者相互垂直;试样经650℃炉温,保温40分钟炉冷再结晶退火热处理后,声各向异性因子小,表现出材料微观组织均匀,晶粒细,各向异性小,并与金相实验结果一致。     

Residual stress determination in aluminium using electromagnetic acoustic transducers

The residual stresses in a shrink-fit specimen were measured ultrasonically, using shear-horizonal (SH) waves transmitted and received by noncontacting electromagnetic acoustic transducers. The presence of stress induces a small change in the velocity of the SH-waves. The difference in velocities of orthogonally polarized SH-waves (acoustic birefringence) was measured with a simple time-interval averaging system; this velocity difference can be related to the difference of principal stresses. The presence of material anisotropy (texture) in the specimen also causes relative velocity changes comparable to stress-induced changes. A simple method was used to remove the anisotropy-dependent component of the total relative velocity change, thereby allowing a determination of residual stress. This method consisted of measuring the birefringence in unstressed reference specimens and subtracting it from the birefringence measured at stressed locations. For the specimen used here, good agreement between theoretical and experimental values of stress was obtained.     

Numerical analysis of immersed finite cylindrical shells using a coupled BEM/FEM and spatial spectrum approach

This study numerically analyzes submerged cylindrical shells using a coupled boundary element method (BEM) with finite element method (FEM) in conjunction with the wave number theory, in which the spatial Fourier transform of surface velocity for cylinders is directly related to pressure in a far field. The acoustic loading is formulated using a symmetric complex matrix derived from a boundary integral equation where the symmetry is based on an acoustic reciprocal principle for surface acoustics. In this formulation the acoustic loading matrix is a large acoustic element whose degree of freedom is connected to the normal displacement of the vibrating structures. The coupled BEM/FEM equation is a banded, symmetric matrix, and thus its bandwidth can be minimized using a proper algorithm. This formulation significantly increases numerical efficiency. The computed normal velocity is thus transformed to wave number representation to examine acoustic radiation. A finite plane cylindrical shell, without attached stiffeners, and a shell with internal ring stiffeners are chosen to demonstrate the present analysis procedure. The far field pressure computed directly from the integral equation and predicted by wave number theory correlates closely with increasing vibrating frequency. Meanwhile, the influences of the internal ring structures on acoustic radiation are examined using the wave number theory, which helps in understanding how internal structures influence radiated noise.     

Stress distribution and birefringence measurement in double-clad fiber

Modal birefringence and stress distribution measurements in a single-mode double-clad Nd⁺³-doped fiber are reported. The contribution of different mechanisms, such as stress-induced birefringence, bending and core ellipticity, to the total birefringence is determined for a fiber wound onto a drum. A stress distribution pattern in the cross-section of the fiber is presented. The stresses are shown to be applied to a fiber core along the cladding minor axis.     

Exchange mechanism for localization of phonons near the surface of a magnetically ordered crystal

It is shown that first-principles inclusion of nonuniform exchange interaction leads to the creation of a new type of generalized shear acoustic wave propagating near the mechanically free surface of a magnet. Criteria are formulated that can be used to specify conditions under which an “exchange” type of surface acoustic wave can exist at the boundary between a magnetic and a nonmagnetic medium once the spectrum of magnetoelastic oscillations of the unbounded magnetic crystal is known. Fiz. Tverd. Tela (St. Petersburg) 40, 299–304 (February 1998)     

Effects of boundary inclination and boundary type on shear-driven grain boundary migration

A series of molecular dynamics simulations was performed on a bicrystal to which a fixed shear rate was applied parallel to the boundary plane. Under some conditions, grain boundary motion is coupled to the relative tangential motion of the two grains. In order to investigate the generality of this type of coupled shear/boundary motion, simulations were performed for both special (low Σ) and general (non-Σ) [010] tilt boundaries over a wide range of grain boundary inclinations. The data point to the existence of two critical stresses: one for coupled shear/boundary motion and the other for grain boundary sliding. For the non-Σ boundaries, the critical stress for coupled shear/boundary motion is typically smaller than that for sliding; coupled shear/boundary motion occurs for all inclinations. For Σ5 boundaries, for which the critical stress is smaller and depends on boundary inclination, coupled shear/boundary motion occurs for some, but not all inclinations.     

Use of off-axis SH-waves to map out three-dimensional stresses in orthotropic plates

An acoustical birefringence method is proposed to measure thickness-varying stresses in slightly orthotropic plates. In this method, off-axis SH-waves at various angles of incidence are propagated in the body's planes of material symmetry, and pass through a common point. The weighted sum of times-of-flight of waves propagating in one plane is subtracted from the corresponding sum in the orthogonal plane. To a first approximation, this difference is the local birefringence at the common point and as such can be related to components of the stress tensor there.The ability of the method to map out simple stress concentrations was tested analytically. Reasonably good spatial resolution was obtained, but the method underestimated the magnitudes.     

Which stresses affect the glide of screw dislocations in bcc metals?

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2?111? screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2?111? screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.     

超声双折射法测试铝合金的内部应力

声各向同性的金属材料在应力作用下表现出声各向异性,这是用声弹性法分析材料内部应力的基础。本文用偏振方向平行或垂直于应力方向的超声纯横波对LY11型铝合金进行测试。实验结果表明:材料在拉、压单轴应力作用下,偏振方向平行和垂直于应力方向的超声纯横波的声速都发生了变化。实验在分析材料声各向异性的基础上计算材料声弹性双折射系数,得到测试LY11型铝合金内部应力的理论公式,并对其内部的残余应力进行评估。实验中利用双换能器回振法测量声速,时间测试精确度可达10^-11s,可精确测量声速的微小变化量。     

Acousto-elastic measurement of stress and stress intensity factors around crack tips

Acousto-elasticity predicts that the phase velocity of sound waves in a material will be changed slightly by stress. For a slightly orthotropic plate in a state of plane stress, the shear stress σ_xy can be calculated from $\text{σ}{}_{\mathrm{xy}}\text{=}\text{(B}\text{sin}\text{2 φ)}\text{2m}$ once measurements of the acoustic birefringence B and the angle φ have been made. The birefringence is the difference in phase velocity between SH waves polarized along the ‘fast’ and ‘slow’ acoustic axes, φ is the angle between the acoustic axes in stressed and unstressed state, and m is an acousto-elastic constant for the material.For symmetrical, two-dimensional crack-opening problems, σ_xy can be expressed as a series expansion of stress functions, each of which satisfies the equilibrium equation. The coefficients in the expansion allow the appropriate boundary conditions to be satisfied. The stress intensity factor K₁ is the coefficient of the leading term in the series.Values of σ_xy and K₁ for an ASTM standard test specimen made of 2024 aluminium were acousto-elastically determined. These were compared with those obtained from a similar photoelastic specimen. Good agreement was obtained for both σ_xy and K₁.     

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.     

An adaptive scanning scheme for effective whole field stress separation in digital photoelasticity

In photoelasticity, the method of obtaining the individual values of principal stresses/normal stresses separately is referred to as stress separation. Shear difference method is one of the widely used techniques for stress separation in digital photoelasticity. Normally a simple raster scanning approach is used in shear difference method in which stress separation is carried out for all the lines within the model domain by either row-wise horizontally or column-wise vertically starting from the boundary pixels. This requires the presence of a free boundary to start the integration scheme for every row of interest, which is not always possible in most of the practical problems. In order to overcome this, in this paper, an adaptive scanning scheme is proposed so that stress separation can be carried out even if there is only one free boundary pixel available in the model. The new scanning scheme is validated using the theoretically generated data for the problem of a ring subjected to internal pressure. Later, the applicability of this scheme is demonstrated by using two other example problems.     

Manifestation of basal-plane anisotropy and mechanical boundary conditions in magnetic birefringence of sound in hematite

The angular dependence of the magnetic birefringence of sound in hematite is experimentally investigated as a function of the direction of a magnetic field applied in the basal plane of the hematite crystal. It is found that, at room temperature, the curve of magnetoacoustic oscillations in the magnetic field, i.e., the oscillatory dependence of the amplitude of an acoustic wave transmitted through the crystal on the magnetic field strength, is characterized by hexagonal and uniaxial anisotropy. It is shown that the hexagonal anisotropy is governed by the basal-plane anisotropy of higher orders. The appearance of the uniaxial magnetic anisotropy in the basal plane of the crystal is explained by the mechanical stresses arising in the sample when piezoelectric transducers are glued to the sample ends. This assumption is confirmed by the observed change in the direction of the uniaxial anisotropy axis under variations in the boundary conditions.     

Effect of Geometry,Loading and Elastic Moduli on Critical Parameters in a Nanoindentation Test in Polymeric Matrix Composites with a Nonhomogeneous Interphase

Fiber nanoindentation models are developed for polymeric matrix composites with nonhomogeneous interphases. Using design of experiments, the effects of geometry, loading and material parameters on the critical parameters of the indentation test such as the load–displacement curve, the maximum interfacial shear and normal stresses are studied. The sensitivity analysis shows that the initial load–displacement curve is dependent only on the indenter type, and not on parameters such as fiber volume fraction, interphase type, thickness of interphase, and boundary conditions. The interfacial tensile radial stresses are not sensitive to indenter type, or to type and thickness of interphase, while the interfacial compressive radial stresses are sensitive mainly to boundary conditions and thickness of interphase; however, the influence of these factors on the interfacial radial stresses can be large. In contrast, the interfacial shear stress is sensitive to all factors, but the influence of the factors is relatively small.     

透明光学材料中缺陷吸收激光能量引起的热应力与断裂

 利用热弹性理论分析了在光学材料中由于缺陷吸收激光能量引起的温度和热应力分布，并且针对一个简单的裂纹模型分析了热应力产生的应力强度因子，并且给出了一些主要参数对于应力强度因子的影响的规律。     

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.     

Periodic microbending-induced core-to-cladding mode coupling in polarization-maintaining fibers

We investigate codirectional mode coupling induced by periodic microbending in polarization-maintaining (PM) fibers by using both an acoustic flexural wave and a pair of corrugated fixtures. The measured filtering spectra are found to be strongly polarization dependent. In addition, the coupling strength depends on the angle between the birefringence axes and the bending direction. These characteristics can be utilized for a variety of applications, such as fiber polarizers, polarization-dependent-loss compensators, and on-line alignment of birefringence axes for the manufacture of PM fiber couplers.