Stress distributions and stress intensity factors in ceramic roller bearing rings

A method is presented which allows to compute the stress intensity factors (SIFs) of a ceramic roller bearing ring with a surface flaw. First, the stresses due to mechanical loads applied to the surfaces of the undamaged ring are computed, using Michell's expression for Airy's stress function in polar coordinates ([l]). Second, the stress intensity factors of the flaw are obtained using Tada's additivity principle ([2]), namely by integration of the point force solution for the SIF of a surface crack with the aforementioned stresses as input parameter. To illustrate the procedure, the special case of a ring with a surface flaw which is loaded by six equidistantly spaced cylindrical rollers will be studied numerically.     

Inclined semi-elliptical crack for predicting crack growth direction based on apparent stress intensity factors

Linear elastic criterion of the inclined semi-elliptical crack growth direction is elaborated on the basis of the strain energy density theory. Stress and displacement fields are presented for higher order terms asymptotic expansion. Solutions for elastic stress intensity factors are accounting for the function describing of the crack tip fields near the free surface of plate. The mixed mode behavior of crack growth direction angle along the semi-elliptical crack front for different combination of biaxial loading, inclination crack angle and surface flaw geometry is determined.     

A critical evaluation of numerical solutions to the ‘Benchmark’ surface-flaw problem

Recent precise, elastic numerical solutions to a surface flaw in a plate under remote tension and bending have been compared to arrive at a ‘best estimate’ of the stress-intensity-factor variation along the flaw border. The geometry of the semielliptical surface flaw examined had a depth to length ratio of 0.25 (a/2c=0.25) and 25- and 75-percent relative crack depths (a/t=0.25, 0.75). The analysis methods used to determine the solutions included: Schwarz alternating technique, finite-element method and boundary-integral-equation method. The derived best-estimate curve for the stress-intensity factor is believed within 3 percent of the actual value along the crack front. The best-estimate curve compared well with scarce experimental data (±10 percent). The difference between the best-estimate curve and experiment is thought largely due to differences in geometry and Poisson's ratio.     

Stress-intensity distributions for corner cracks emanating from open holes in plates of finite width

A series of frozen stress photoelastic tests is carried out in the present investigation. Linear Elastic Fracture Mechanics is used to analyze the problem of a part-through corner crack at an open hole in a plate of finite width loaded in tension. The photoelastic modeling capability of three-dimensional subcritical crack growth problems is assessed. This is achieved by comparing monotonically grown flaw shapes in epoxy models with crack profiles relative to fatigue crack propagation tests in a different material. Photoelastic stress-intensity factor distributions are checked against numerical results obtained for quarter elliptical geometries. The dependence of stress intensity factors on flaw shape is also discussed.     

Weight functions for a surface semi-elliptical crack in a finite thickness plate

Weight functions for the surface and the deepest point of a semi-elliptical crack in a finite thickness plate were derived from a general weight function and two references stress intensity factors. The weight functions were validated against finite element data by comparison of stress intensity factors calculated for several linear and non-linear stress fields. Differences were less than 2% for the surface point and 5% for the deepest point. The final weight functions are given in closed forms suitable for computer numerical integration. The weight functions appear to be particularly suitable for fatigue crack growth prediction of semi-elliptical cracks and fracture analysis of such cracks in complex stress fields.     

Noise processing of flaw reconstruction by wavelet transform in ultrasonic guided SH waves

The ultrasonic guided wave technique is a potential and useful tool for nondestructive testing. The scattered or reflected wave from a flaw can give its qualitative or even quantitative information such as location, size and severity. However, in experiments and in situ tests, the noises always exist together with signals. In this paper, we propose a wavelet-transform based noise processing approach for reflected wave signals to the quantitative reconstruction of surface flaws on a plate using guided SH waves. We suggest two different denoising methods based on wavelet transform (WT) in time and wavenumber domains respectively. Numerical results show that wavenumber-domain WT operation gives a better denoising effect than direct time-domain WT denoising. Using the former, one can successfully perform the inverse reconstruction of flaw by reflected signals with signal noise ratio as high as ?5 dB. This research can act as a theoretical reference for practical applications of ultrasonic guided SH waves in quantitative nondestructive evaluation.     

爆炸复合板边界效应研究

认为引起边界效应的主要因素不仅有炸药和基、复板边界稀疏的影响，而且尚受复板反弹拉伸的作用。设计了不等面积复合板爆炸焊接工艺，超声探伤结果表明，复合板的边界效应极小，满足工程需要。     

Stress-strain state of an anisotropic plate with curved cracks and thin rigid inclusions

We solve the bending problem for an anisotropic plate with flaws like smooth curved nonoverlapping through cracks and rigid inclusions. The problem is solved by the method of Lekhnitskii complex potentials specified as Cauchy type integrals over the flaw contours with an unknown integrand density function. We use the Sokhotskii—Plemelj formulas to reduce the boundary-value problem to a system of singular integral equations with the additional conditions that the displacements in the plate are single-valued when going around the cut contours and the equilibrium conditions for stress-free rigid inclusions. After the singular integrals are approximated by the Gauss-Chebyshev quadrature formulas, the problem is reduced to solving a system of linear algebraic equations. We study the local stress distribution near flaw tips. We analyze the mutual influence of flaws on the stress distribution character near their vertices and compare the well-known solutions for isotropic plates with the solutions obtained by passing to the limit in the anisotropy parameters (“weakly anisotropic material”) and by using the method proposed here.     

Holographic-interferometry applications in experimental mechanics

Holographic-interferometry techniques were surveyed in several areas of application to experimental measurement. The principles of the technique were reviewed, and the theoretical basis for quantitative experimental measurement was developed and evaluated by controlled experiment on simple beam and plate structures in static loading. Subsequently, the effectiveness of the method in steady-state vibrations analyses was demonstrated by application to typical structures components. Nondestructive-testing potential was illustrated by the application to flaw detection in a bonded honeycomb, and some moiré procedures were examined. Immersion technique was employed to demonstrate the generation of surface elevation contours in opaque objects. In summary, experimental evidence is offered that holographic interferometry is a powerful and precise tool for experimental investigations.     

各向异性板的面导纳特性研究

目前在工程上各向异性结构中的振动问题和振动能量传递的问题越来越多,然而对各向异性结构导纳的研究还不充分,对各向异性板面导纳的研究也还处于萌芽状态.面导纳不仅反映结构的振动特性还能反映能量传递的特性,因此面导纳比点导纳在工程上更加贴合实际.论文根据理论公式获得了一般各向异性板面导纳的理论解,并与有限元模型的数值解对比发现...     

The concentration of stress and strain in finite thickness elastic plate containing a circular hole

The elastic stress and strain fields of finite thickness large plate containing a hole are systematically investigated using 3D 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 except at notch root of plate surface. The maximum stress and strain do not always occur on the mid plane of plate. They occur on the mid plane only in thin plate. The maximum stress and strain concentration factors are not on mid plane and the locations of maximum stress and strain concentration factors are different in thick plate. The maximum stress and strain concentration factors of notch root increase from their plane stress value to their peak values, then decrease gradually with increasing thickness and tend to each constant related to Poisson’s ratio of plate, respectively. The stress and strain concentration factors at notch root of plate surface are the same and are the monotonic descent functions of thickness. Their values decrease rapidly and tend to each constant related to Poisson’s ratio with plate thickness increasing. The difference between maximum and surface value of stress concentration factor is a monotonic ascent function of thickness. The thicker the plate is or the larger the Poisson’s ratio is, the larger the difference is. The corresponding difference of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.     

An experimental and numerical study of fracture coalescence in pre-cracked specimens under uniaxial compression

This study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC^2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.     

弯矩作用下薄板振动的仿真分析

针对工程中广泛存在的弯矩作用下板结构的振动问题,分别建立四边固定、三边固定一边自由、两对边固定两对边自由的3种不同边界条件下板的振动模型;基于有限元法计算振动板的频率响应,计算了各节点振动速度的平方和;运用部分追加法正交试验方案分别对板厚、边界条件、板的损耗因子三因素三水平、激励点位置四水平进行了正交试验。实例结果表明,以速度平方和的大小为目标,影响薄板振动的主次因素顺序为:损耗因子、板厚、边界、激励点位置;当振动板两对边固定另两对边自由支承、板厚为0.014m、在(0.5m,0.4m)点处激励且板的损耗因子为0.0008时,此组合为薄板结构振动最小的最优组合。     

焊接残余应力平板多个共面表面裂纹的应力强度因子

采用线弹簧模型求解含焊接残余应力平板多个共面任意分布表面裂纹的应力强度因子.利用边裂纹权函数给出了裂纹表面上沿厚度非线性分布的残余应力向线性分布的转化公式.基于Reissner板理论和连续分布位错思想,将含多个共面任意分布表面裂纹的无限平板问题归结为一组Cauchy型奇异积分方程,并采用Gauss-Chebyshev方法获得了奇异积分方程的数值解.以三共面表面裂纹为例,计算了表面裂纹的应力强度因子,并讨论了裂纹间距、裂纹几何形状等因素对应力强度因子的影响.     

Equations and a fast algorithm for determining the probability of failure initiated by flaws

Powerful equations and an efficient algorithm are proposed for determining the probability of failure of loaded components with complex shape, containing multiple types of flaws. The equations are based on the concept ‘conditional individual probability of initiating failure’ characterising a single flaw given that it is in the stressed component. The proposed models relate in a simple fashion the conditional individual probability of failure characterising a single flaw (estimated by a Monte Carlo simulation) to the probability of failure characterising a population of flaws. The derived equations constitutes the core of a new statistical theory of failure initiated by flaws in the material, with important applications in optimising designs by decreasing their vulnerability to failure initiated by flaws during overloading or fatigue cycling.Methods have also been developed for specifying the maximum acceptable level of the flaw number density and the maximum size of the stressed volume which guarantee that the probability of failure initiated by flaws remains below a maximum acceptable level. An important parameter referred to as ‘detrimental factor’ is also introduced. Components with identical geometry and material, with the same detrimental factors are characterised by the same probability of failure. It is argued that eliminating flaws from the material should concentrate on types of flaws characterised by large detrimental factors.The equations proposed avoid conservative predictions resulting from equating the probability of failure initiated by a flaw in a stressed region with the probability of existence of the flaw in that region.     

Linear Contact Between Plates and Unilateral Elastic Supports*

Abstract

The problem of frictionless linear contact between elastic line supports (beam or Winkler-type) and an elastic plate that is loaded laterally is considered. Contact is called linear if there is no initial gap or no initial pre-force on the potential contact surface. The shear deformation of the plate is taken into account. The contact problem is discretized at points on the potential contact surface. Numerical results are calculated with an optimization algorithm that is based on the force method. The effects of the thickness and Poisson's ratio of the plate and the elastic constants of the line supports are considered. Two loading cases are dealt with: a point load in the middle of the plate and a uniform load over the plate. The plate is rectangular, with side ratios 1 and 2.     

用点源函数解受集中力圆板的非对称弯曲

本文将作用于板上任意位置的一个垂直于板中面的集中力看作一个点源,用δ函数表示,导出了受集中力作用的圆板非对称弯曲微分方程的封闭式特解和级数式齐次解,从而得出了适用于全板的统一的位移表达式。     

Interaction of a deformable plate with a stressed half-space

We consider the plane and axisymmetric problems about the contact interaction between an elastic plate and an elastic half-space loaded at infinity by a uniform tensile force parallel to the half-space boundary. We assume that the plate resists extension and does not resist bending. We determine the contact tangential stresses under the plate, the plate point displacements, and the strain distortion coefficient on the half-space surface.Similar problems were considered earlier by a different method in [1].     

Experimental Investigation and Finite Element Analysis of Fatigue Crack Growth in Pipes Containing a Circumferential Semi-elliptical Crack Subjected to Bending

In this paper, a circumferential external surface flaw in a metallic round pipe under cyclic bending loading is considered. Because of very rapid changes in the geometrical parameters around the crack front region, the mesh generation of this region must be done with great care. This may lead to an increase in the run time which makes it difficult to reach valid results and conclusions. Because of the advantages of the sub-modeling technique in problems which need very high mesh density, this method is used. Stress intensity factors in mode I condition are determined using three-dimensional finite element modeling with 20 node iso-parametric brick elements in the ANSYS 9.0 standard code and the singular form of these finite elements at the crack front. In order to estimate the analysis error, the structural parameter error in energy norm criterion was used. Because of the advantages of non-dimensional analysis, this method is employed, and the stress intensity factors are normalized. For the analysis of the fatigue crack growth, the Paris law is used. The propagation path of the surface flaw is obtained from the diagram of aspect ratio versus relative crack depth. The fatigue crack growth analysis (the relative crack depth against loading cycles diagram) of different initial crack aspect ratio under cyclic loading is also considered. Fatigue shape development of initially semi-elliptical external surface defects is illustrated. The effect of the Paris exponent (material constant) on fatigue crack propagation is shown as well. Moreover, the fatigue crack growth of several specimens is assessed experimentally using a manually-constructed experimental set up. Finally, the experimental results obtained by cyclic bending loading tests are compared with the numerical results. The experimental results show good conformity with the finite element results.     

304L/Q235B大面积金属板爆炸焊接物质点法模拟分析

大面积金属板材304L/Q235B的爆炸焊接过程涉及炸药爆轰、金属板材的高速碰撞和塑性变形等。采用有限元法计算模拟这个问题时,网格单元会发生扭曲畸变现象,导致计算精度下降,甚至出现单元负体积而使计算终止,并且炸药爆轰形成气体产物飞散过程也很难模拟。为了能模拟大面积金属板材的爆炸焊接整个过程并获得合理的技术工艺参数,采用物质点法进行三维数值模拟分析。物质点法作为一种无网格法,在模拟冲击动力学问题中主要采用显式积分算法。通过将拉格朗日质点单元与固定的欧拉背景网格相结合,可以实现爆炸焊接的复板与基板的高速碰撞、炸药滑移爆轰、金属板面的塑性变形过程的数值模拟,并给出爆炸复合板材的形变、有效塑性应变和复板与基板的碰撞速度的计算结果。采用物质点法模拟的复合板材变形与爆炸焊接实验结果基本一致。计算复板与基板的碰撞速度这个重要的物理参数时,物质点法与Richter理论公式的相对误差不超过13%。数值计算和实验结果表明,物质点法在数值精度和计算效率方面具有优势,物质点法是研究金属焊接爆炸问题的一种有效数值方法。