Elastic analysis for a radial crack in a circular ring

The plane elastic problem corresponding to a radial crack emanating from the internal boundary of a circular ring is considered. Uniform external tension on the outer boundary is chosen as the applied load. The stress intensity factors at the crack tip are found by using the recently derived ‘modified mappingcollocation’ technique. Accurate data are found for varying crack depths over a representative range of wall ratios for fracture mechanics applications to pressurized hollow circular cylinders.     

Solutions of torsion crack problems of a rectangular bar by harmonic function continuation technique

A torsion problem of a rectangular bar with a crack perpendicular to the section contour is discussed (see Figs. 1–3). When solving the Dirichlet problem of the Laplace equation, we divide the original section into several rectangular regions, and using the Duhem theorem [1] (a theorem of continuation of harmonic function), the solution on original section can be found. The calculation of torsional rigidity is in a usual way. Using the compliance method, the K₃ is obtained. All numerical results are shown in Tables 1–6.     

Analysis of a radial crack in a circular ring segment

The problem considered is a segment of a circular ring with a radial crack emanating frorn the surface with the smaller radius. Pure bending and three-point loading are chosen for solution. The problem is solved usiag the ‘modified mapping-collocation’ technique and partitioning. Numerical data is presented for varying crack lengths and thicknesses.     

Longitudinal vibration of a bar with a breathing crack

The dynamics of a cracked fixed-free bar with a breathing crack in longitudinal vibration is investigated. The Hu–Washizu–Barr variational formulation was used to develop the equation of motion and the boundary conditions of the cracked bar as a one-dimensional continuum. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods. The eigenfrequency changes due to a single open-edge breathing crack, are shown to depend on the bilinear character of the system. The associated linear problems are solved over their respective domain of definition and then the solutions are matched through the initial conditions. These changes are smaller than the ones caused by open cracks. The method has been tested for different bar configurations corresponding to crack location, crack depths, cross-section dimensions, and Poisson’s ratio. The natural frequencies obtained from this model agree well with experimental results.     

Elastic analysis of a mode II fatigue crack test specimen

A mode II specimen for fatigue crack growth measurements was described by Buzzard, Gross and Srawley [1]. Subsequently Buzzard [2] published results of displacement measurements at the crack mouth and at a selected point on the crackline for this specimen. A preliminary analysis of crack mouth displacements and stress intensity factors using boundary value collocation was also given [1]. The analysis while giving qualitatively useful results could not accurately represent all boundary conditions. The present paper presents a finite element analysis of the mode II specimen which gives more accurate stress intensity factors and displacement results than previously presented. In addition, load point displacements were measured in order to allow an experimental determination of the stress intensity factors.

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Résumé Buzzard, Gross et Srawley [1] ont décrit une éprouvette pour la mesure de la croissance d'une fissure de fatigue sous un Mode II. Dans la suite [2], Buzzard a publié pour cette éprouvette des résultats de mesures de déplacement à l'ouverture de la fissure et en divers points sélectionnés sur l'axe de la fissure. On a également fourni une analyse préliminaire des déplacements de l'ouverture de la fissure et des facteurs d'intensité d'entaille, en recourant à une collocation des valeurs aux limites. L'étude présente ici une analyse par éléments finis de l'éprouvette de Mode II qui fournit des facteurs d'intensité de contraintes et des résultats de déplacement plus précis que ceux obtenus précédemment.En outre, on a mesuré les déplacements aux points d'application des charges, de manière à permettre une détermination expérimentale des facteurs d'intensité de contrainte.

     

转炉用扭力杆系统振动理论研究

扭力杆系统的动态特性对转炉设备工作的可靠性有着重要影响,研究其振动频率和阵型是设备自主创新的关键技术之一。综合考虑扭力杆系统实际结构组成,提出了均质杆和集中质量杆一端铰支另一端简支反对称弯曲振动梁、均质杆和集中质量杆一端固支另一端简支反对称弯曲振动梁等四种振动模型。以某厂150 t氧气顶吹转炉扭力杆系统为例进行了理论计算。结果表明,扭力杆系统振动模型采用集中质量杆一端固支和一端简支反对称弯曲振动梁模型更合理。并用有限元法对其正确性进行了验证,两种方法的计算结果吻合,都可以对扭力杆系统进行研究,但是理论解更为简单方便,便于工程技术人员直接引用,为指导工程实际设计和生产提供了理论基础。     

双横臂双扭杆悬架中上下扭杆的刚度匹配和等强度设计

 通过对双横臂双扭杆悬架中上下扭杆的刚度匹配和等强度设计问题的研究,提出了扭杆的设计方法.分析了双横臂双扭杆悬架的导向机构模型简图,得到了导向机构的运动关系和进行悬架刚度计算的方程;以满足悬架载荷要求和悬架刚度要求为前提,分析了上下扭杆的刚度匹配条件;在上下扭杆在悬架运动时的强度始终相等的前提下,分析了上下扭杆的等强度条件.通过对扭杆直径和有效长度的实例计算,证明所提出的上下扭杆的刚度匹配和等强度设计的方法是可行的.     

Stress analysis of crack problems with a three-dimensional,time-dependent computer program

A three-dimensional, time-dependent computer program is used for the stress-strain analysis of elastic-plastic materials subjected to tensile loads. Several geometries are considered. The capabilities and advantages of this explicit finite difference computer program are demonstrated, and recommendations for future applications are made.

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Résumé Un programme de calcul à 3 dimensions et indépendant du temps a été utilisé pour l'analyse en tension-déformation des matériaux élasto-plastiques sujets à des contraintes et des tractions. On considère différents types de géométries. Les possibilités et les avantages que présente ce programme de calcul par différence finie explicite sont démontrés et l'on a fait des recommandations pour ses applications futures.

     

Elastic interaction of a crack with a random array of microcracks

Two issues are addressed in the paper. The first deals with a new characterization of a random array of microcracks in terms of spatial distributions of the sizes, orientations and density of microcracks. The second is a formulation of crack-microcrack array interaction in terms of the distributions. The interaction problem is posed as a system of two coupled singular integral equations with respect to a vector field of an average microcrack opening and the main crack opening displacement. The approach is illustrated by a numerical solution of the interaction problem for two particular configurations of a random array of microcracks. It is shown that the morphology of the microcrack array may strongly alter elastic fields in the vicinity of the main crack. Specifically, it is found that a variation in the microcrack length distribution (for fixed distributions of microcrack orientation and density) has a profound effect on the solution. The main crack opening displacement is evaluated to compare the theory with the experimental observations.     

Stress intensity factors of a twisted round bar with a circumferential crack

International Journal of Fracture -     

Stressed state of a cylinder with external circular crack under dynamic torsion

We have proposed a combined analytical and experimental method for the determination of dynamic stress intensity factors in impact torsion tests of cylindrical specimens with an external circular crack. We have obtained simple analytical relations for finding dynamic stress intensity factors, which contain parameters determined experimentally. The results obtained with the use of these relations are in good agreement with those based on the finite element method. We have carried out an electron-fractographic analysis of the fracture surfaces of specimens and have described the characteristic mechanisms of fracture under high-rate torsion of cylindrical specimens. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 55–64, March–April, 2007.     

Saint-Venant torsion of a circular bar with radial cracks incorporating arbitrarily varied surface elasticity

We analytically investigate the contribution of arbitrarily varied surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack. The varied surface elasticity is incorporated by using a modified version of the continuum-based surface/interface model of Gurtin and Murdoch. In our discussion, the surface shear modulus is assumed to be arbitrarily varied along the crack surfaces. Both internal and edge cracks are studied. By using Green's function method, the boundary value problem is reduced to the Cauchy singular integro-differential equation of first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials, and the collocation method. The torsion problem of a cylinder containing two symmetric collinear radial cracks of equal length with symmetrically varied surface elasticity is also solved by using a similar method. Our numerical results indicate that the variation of the surface elasticity exerts a significant influence on the strengths of the logarithmic stress singularity at the crack tips, the torsional rigidity, and the jump in warping function.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

Dual finite element analysis for plasticity–friction torsion of composite bar

The quasi-static problem of torsion of an elastic–plastic, prismatic, composite bar is considered in the paper. The phenomenon of slip on the interfaces between the components of the bar is taken into account. The elastic–plastic behaviour of the material is described by the Prandtl-Reuss constitutive relation. The slip on the interface is governed by the Coulomb friction law—it is assumed that there is no cohesion between components of the bar. The stresses normal to the interfaces are considered to be caused by shrinkage of the matrix of the bar or by external forces acting perpendicularly to its longitudinal axis. The problem is set in the dual variational forms and solved with the help of the finite element method. Two approximate kinematically and statically admissible solutions are obtained. The stress function is used for calculation of the second one. The iterative algorithms solving the problem and some numerical results are presented in the paper.     

A circumferential crack in a cylindrical shell under torsion

The fully anti-symmetric problem for a cylindrical shell with a circumferential crack is considered. The solution of the problem is reduced to that of a system of singular integral equations of the first kind. As an example the torsion of the cylinder is discussed and membrane and bending components of the stress intensity factor ratio are given.