The effect of biaxial load on stress and strain concentrations in a finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of a finite thickness plate containing a circular hole subjected to a biaxial load are systematically investigated using the finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different even if the plate is in elasticity state. The maximum stress and strain concentration factors do not always occur on the mid plane of the plate. The maximum stress and strain concentration factors of the notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to constant values related to the load biaxiality ratio, respectively. The stress and strain concentration factors at the notch root of free surface are the monotonic descent functions of thickness. Their values decrease rapidly and tend to lower the limit values related to the load biaxiality ratio with increasing plate thickness. The differences of stress and strain concentration factors between maximum and surface value increase rapidly and tend to constant values related to the load biaxiality ratio with increasing plate thickness. The smaller the load biaxiality ratio, the larger these differences. Copyright © 2007 John Wiley & Sons, Ltd.     

开孔碳纤维层合板层间应力分析

针对具有典型铺设角 的开孔碳纤维层合板, 采用三维有限元数值模拟方法, 分析了在单向拉伸载荷作用下孔边附近的层间应力, 讨论了界面层参数对层间应力的影响, 详细给出了典型铺设角之间层间应力的分布规律和最大层间应力产生的位置。结果表明: 对于相同铺设角的界面层, 沿厚度方向的位置影响层间应力的大小, 但不影响分布趋势; 而铺层顺序(如 或 )对层间应力的大小和分布趋势影响则较小。最大层间正应力产生于 的界面层, 位于与拉伸方向成90°的位置, 是外加拉伸应力的51%; 最大层间剪应力产生于 的界面层, 最大层间环向剪应力位于与拉伸方向成74°的位置, 是外加拉伸应力的64%; 而最大层间径向剪应力位于与拉伸方向成66°的位置, 是外加拉伸应力的25%。      

Catalogue of photoelastic fringes for a biaxially loaded infinite plate with a hole

This paper presents a typical catalogue of "virtual" photoelastic isochromatic fringes around the hole of a biaxially loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. Use of this catalogue allows visualisation of the stress distribution around the hole, and a first approximation to the solution of the inverse problem using photoelasticity.     

孔口缝合补强对含孔层板应变集中影响的实验研究

对复合材料开口缝合补强结构进行了实验研究。测试了不同缝合参数(针距、行距、边距、单重和双重缝合) 补强的含孔复合材料层板的拉伸强度, 研究了孔边应力集中、应变集中对强度、刚度等力学性能参数的影响, 分析讨论了孔边及邻近区域应变集中及应变分布的规律, 得到不同缝合参数、孔边不同位置以及不同载荷条件下的应变集中系数。结合实验结果和分析讨论, 给出了含孔复合材料层板缝合补强的缝合设计参数。      

Interlayer stress in laminate beam of piezoelectric and elastic materials

This paper studies interfacial mechanical behavior of laminate beams, consisting of two piezoelectric facial sheets and an elastic core. The study is based on coupled multi-filed finite element formulation. The emphasis is placed on mechanical and electric behavior of interfaces between piezoelectric material and elastic material, including effect of geometrical parameters, stress distribution and stress concentration near free edge of the beam subjected to coupling electric and mechanical loads. In particular, various parametric effect of laminate beam is explored and some conclusions are presented which may be useful for designing laminate beam and minimizing stress concentration at the free edges of the beam.     

含孔复合材料层合板孔边的应力集中

针对含孔有限宽复合材料层合板的应力集中问题,提出一种计算孔边应力分布及应力集中因子的方法：先利用经典层板理论,将复合材料层合板化归为各向异性板;再将各向异性板等效转换为一偏轴拉伸的单向纤维层板;最后利用含孔偏轴单向板的孔边应力计算公式来分析一般铺层层合板孔边应力集中情况。根据所推导的计算公式,分析讨论了板宽/孔径比、铺层比例、铺层方式、材料性能参数等因素对孔边应力集中的影响。     

Photoelastic inverse problem solution for a biaxially loaded infinite plate with a hole

This paper presents an inverse problem solution for the case of photoelastic isochromatic fringes around the hole of a biaxially uniformly loaded infinite plate for two problems. Problem 1 relates to an infinite plate in which the circular hole is drilled first and then the loads are applied. Problem 2 is the residual stress problem in which the hole is drilled after the biaxial load is applied to the infinite plate. This "hole method" solution may be used for all cases of biaxial, far field uniform loading conditions.     

Piezoelectric study for a coated hole of quasi-polygonal shape in an infinite plate

This paper studies the piezoelectric problems for a coated hole of quasi-polygonal shape embedded in an infinite matrix subjected to electromechanical loadings. The electromechanical loadings considered in this work include a screw dislocation, a point force, a point charge, a far-field anti-plane shear and an in-plane electric field. Each component is assumed to be transversely isotropic medium belonging to a hexagonal crystal class 6 mm and poled in the x₃ direction. Based on the complex variable and analytical continuation method, the general expressions for the complex potentials can be derived in each medium. Numerical results are provided to show the effect of hole shape, the material combinations and the loading condition on the electro-elastic fields due to the presence of the coated film. The image force exerted on a dislocation, which can be used to probe the mobility of the screw dislocation, will be calculated by means of the generalized Peach-Koehler formula.     

深孔爆破巷道动态应力比评价安全判据

为研究爆破振动波在石英岩中的传播规律,以建德大岩山石英矿阶段运输巷道为依托,通过对采场深孔爆破时阶段运输巷道底板的速度—时间信号的采集,结合萨道夫斯基公式,以动力应力比评价为依据,判断爆破振动对巷道稳定性的影响,结果发现在钻孔孔径90 mm、单响药量30.5 kg、爆心距15.7 m的条件下,巷道围岩不会发现明显损伤。     

Electroelastic analysis of an interface anti-plane shear crack in a layered piezoelectric plate

The problem of an anti-plane interface crack in a layered piezoelectric plate composed of two bonded dissimilar piezoelectric ceramic layers subjected to applied voltage is considered. It is assumed that the crack is either impermeable or permeable. An integral transform technique is employed to reduce the problem considered to dual integral equations, then to a Fredholm integral equation by introducing an auxiliary function. Field intensity factors and energy release rate are obtained in explicit form in terms of the auxiliary function. In particular, by solving analytically a resulting singular integral equation, they are determined explicitly in terms of given electromechanical loadings for the case of two bonded layers of equal thickness. Some numerical results are presented graphically to show the influence of the geometric parameters on the field intensity factors and the energy release rate.     

Effect of calcium substitution on superconductivity and hole concentration in La1·5Ba1·5Cu3O z

The superconducting properties of single phase La_1·5−x Ca _x+y Ba_1·5−y Cu₃O _z , 0·0≤x≤0·60 (LC) and 0·0≤y≤0·70 (CB), compounds with tetragonal triple-perovskite structure are studied, using X-ray diffraction for their resistivity, a.c. susceptibility, and oxygen-content. La_1·5−x Ca _x Ba_1·5Cu₃O _z (LC) samples, 0·15≤x≤0·60, are superconducting withT _c ^R=0 between 40 and 74 K. With the increase inx, the oxygen content, hole concentration in the CuO₂ layers as well as theT _c increase. It is interesting to find that although the hole concentration and oxygen stoichiometry of the LaCa_0·5+y Ba_1·5−y Cu₃O _z (CB) compounds increase with the increase iny, theT _c ^R=0 remains nearly constant around 74 K fory=0·0−0·70. A correlation exists between theT _c and the hole concentration for LC and CB compounds.     

Nonlinear free and forced vibration behavior of functionally graded plate with piezoelectric layers in thermal environment

In the present study, finite element formulation based on higher order shear deformation plate theory is developed to analyze nonlinear natural frequencies, time and frequency responses of functionally graded plate with surface-bonded piezoelectric layers under thermal, electrical and mechanical loads. The von Karman nonlinear strain–displacement relationship is used to account for the large deflection of the plate. The material properties of functionally graded material (FGM) are assumed temperature-dependent. The temperature field has uniform distribution over the plate surface and varies in the thickness direction. The considered electric field only has non-zero-valued component E_z. Numerical results are presented to study effects of FGM volume fraction exponent, applied voltage in piezoelectric layers, thermal load and vibration amplitude on nonlinear natural frequencies and time response of FGM plate with integrated piezoelectric layers. In addition, nonlinear frequency response diagrams of the plate are presented and effects of different parameters such as FGM volume fraction exponent, temperature gradient, and piezoelectric voltage are investigated.     

Finite element analysis of defence hole systems for the reduction of stress concentration in a uniaxially-loaded plate with two coaxial holes

A comprehensive plane stress finite element study is made of the effect of three different types of defence hole systems (A, B and C) upon the stress concentration in a uniaxially-loaded plate with two coaxial holes. Throughout this project, the geometry definition, model creation aspects for meshing the plate and generating elements and nodes, model preparation for applying the appropriate loads and restraints, model checking for coincidence nodes and element distortion, and output display of the many cases investigated were all carried out interactively using SDRC (SUPERTAB-IDEAS) pre- and post-processors. The finite element analysis was carried out in the analysis section of the package, known as SUPERB. The study reveals that the introduction of defence holes on either side of the main holes helps to smooth the flow of the tensile principal stress trajectories past the original holes, and thus effect a reduction in stress concentration factor (SCF), an improvement in component strength and a reduction in its weight. Reductions in maximum SCF ranging from 7.5% to 11% have been achieved by the present technique. With such reductions in maximum stress levels, the improvement in fatigue life of a component can be significant.     

An eigenfunction expansion solution for three-dimensional stress field in the vicinity of the circumferential line of intersection of a bimaterial interface and a hole

An asymptotic solution pertaining to the stress field in the neighborhood of the circumferential line of intersection of an interface of a two-layer plate made of dissimilar isotropic materials and a through-hole, subjected to far-field extension/bending (mode I), inplane shear-twisting (mode II) and torsional (mode III) loadings, is presented. A local orthogonal curvilinear coordinate system (, , ), is selected to describe the local deformation behavior of the afore-mentioned plate in the vicinity of the afore-mentioned circumferential line of intersection. One of the components of the Euclidean metric tensor, namely g ₃₃, is approximated (/a1) in the derivation of the kinematic relations and the ensuing governing system of three partial differential equations. Four different combinations of boundary conditions are considered: (i) open hole (free-free), (ii) hole fully filled with an infinitely rigid plug (clamped-clamped), (iii) hole partially (i.e., in the layer 2) filled with an infinitely rigid plug (free-clamped), and (iv) hole partially (i.e., in the layer 1) filled with an infinitely rigid plug (clamped-free). The computed eigenvalues for the clamped-free boundary condition can be obtained from their free-clamped counterparts by replacing G ₂ by G ₁ and ₂ by ₁, and vice versa. These two boundary conditions are then equivalent in the complementary sense. Numerical results presented include the effect of the ratio of the shear moduli of the layer materials, and also Poisson's ratios on the computed lowest eigenvalues.     

Comparison of techniques for residual stress determination in a bead on plate titanium sample

Residual stress determination has been carried out on production welds to provide engineering data.
A parting out technique has been used in which a strain gauged through thickness slug of material is removed from the weld area.
The centre hole technique has been used with the blind hole in the weld material.
There were differences between the results from the two techniques and a fully penetrant bead on plate fatigue sample with the bead running axially was used in order to compare the two techniques in more detail.
After parting out, the layer removal technique was carried out in order to provide a relatively detailed through thickness residual stress distribution in order to explain the differences between the results from the centre hole and parting out techniques.     

Residual stress measurements in a cruciform welded joint using hole drilling and strain gauges

Residual stress measurements were made close to the toe of each fillet weld on a load carrying cruciform welded specimen by the hole drilling technique. A standard milling guide with high speed air turbine was used in conjunction with bonded resistance strain gauge rosettes. Experimental calibrations of the method were conducted under known uniform uniaxial tension loads.
A simple incremental drilling technique was used to determine the stress gradient with hole depth. Measurements were also made both at zero load and known tensile loads in order to study the interaction between residual stresses and the applied loads.     

The effects of size and stacking sequence of composite laminated patch on bonded repair for cracked hole

The performance of a bonded repair for cracked holes has been studied using the three dimensional finite element method, linear elastic fracture mechanics and strain energy density theory. Increasing the composite patch size reduces the strain energy level at the crack tip; increasing the patch length normal to the crack is a better choice. The stacking sequences of the laminated patch have little influence on the strain energy distribution in the vicinity of the crack. To repair the cracked holes of aircraft components subjected to variable direction loading during flight, the orientations of the patch ply, 90° and ±45° with respect to the crack direction, are the optimum selection in bonded repairs.     

Creep stress concentration during loading and unloading processes in a strip with semi circular notches

The stress concentration during the loading and unloading processes of transient creep is investigated for a strip with semi circular notches by means of the photo-viscoplasticity, using specimens of celluloid at 65C. The relations between the stress concentration factor, the geometries of strips, and time during the loading and unloading processes are derived from the time dependent variations of isochromatic fringe orders. Such trends cannot be analysed by the ordinary photoplasticity in which the time effect is not taken into account.     

Interaction between crack and arbitrarily shaped hole with stress and displacement boundaries

The interaction between a crack and an arbitrarily shaped hole under stress and displacement boundaries in an infinite plane subjected to a remote uniform load is studied. The Green's functions of a point dislocation for the problems are derived and are then used to analyze the interaction problem. The superposition principle is employed to reduce the original problem to two subsidiary problems. The complex stress functions of each problem are composed of two parts, in which the second parts are always holomorphic. Using analytical continuation in conjunction with rational mapping function, the stress functions are obtained in closed form. The interaction of a hole or an inclusion with a crack is solved using dislocations to model the crack and solving a system of singular integral equations. Stress intensity factors for crack tips and stress concentration factors for inclusion corner are determined and plotted for various cases. The affecting ranges of hole and inclusion are investigated.     

The elastic interaction of screw dislocations and a star crack with a central hole

The elastic interaction of screw dislocations and a star crack with a central hole was investigated. The complex potential of the present problem was obtained from that of an internal crack in an infinite medium using the conformal mapping technique. The stress field, image force and strain energy of dislocation, and stress intensity factor at the crack tip were derived. The critical stress intensity factor for dislocation emission was calculated based on the spontaneous dislocation emission criterion. The influence of the ratio of crack length to hole radius, crack number, and dislocation source on the above mechanical variables were studied. The present solution was reduced to several special cases previously reported in the literature.