A unified approach to problems of stress concentration near V-shaped notches with sharp and rounded tip

The paper proposes a unified approach to problems of stress concentration near notches with sharp and rounded tip based on the method of singular integral equations. A solution for an elastic region having a V-shaped notch with rounded tip of large curvature is first found. Then, the stress intensity factor at the tip of a sharp-tipped notch is calculated by passing to the limit. Numerical results are obtained for a slit and a square hole in an elastic plane and an edge notch in a half-plane __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 70–87, February 2007. For the centenary of the birth of G. N. Savin.     

A singular element for calculating the stress intensity factor

This paper proposes a new type of special element (sectorial singular element) for calculating the linear elastic stress intensity factor. The shape of element not only accords with the demands of finite element analysis, but also coincides with the theory of linear elastic fracture mechanics. The accuracy and economy of the result in this paper are satisfactory.     

Interface crack-tip generalized stress field and stress intensity factors in transversely isotropic piezoelectric bimaterials

Transversely isotropic piezoelectric (TIP) bimaterials with an impermeable interface crack have been classified [Int. J. Frac. 119 (2003) L41] into two classes corresponding to the vanishing of the two singularity parameters or κ. It is shown in the present paper that the related eigenvalue problems for either =0 or κ=0 are not degenerate. The crack-tip generalized stress fields are obtained subsequently. A new definition of crack-tip intensity factors is presented for interface cracks in practical TIP bimaterial of practical interest. Such defined intensity factors are real numbers, which dominate the maximum crack-tip stress singularity and do not generate any phase angle change under any dimension system transformation for physical quantities.     

应力强度因子分析的三角形Williams单元

弹性断裂分析的Williams广义参数单元计算模型中忽略了紧邻裂尖的微区域,为了进一步完善该计算模型,本文提出并建立了三角形Williams单元。首先围绕裂尖将奇异区均匀分割为有限个三角形单元,利用改进的Williams级数建立该单元的整体位移场计算模型;其次沿径向将该三角形单元进一步离散为多个相似四边形微单元和裂尖三角形微单元,并利用经典有限元理论建立微单元的局部位移场计算模型;然后利用整体位移场控制各微单元结点位移,并在此基础上研究建立裂尖奇异区三角形Williams单元及其控制方程。该单元模型中含有与裂尖应力强度因子相关的参数,能够直接计算裂尖处的应力强度因子。最后结合算例详细分析了三角形Williams单元计算模型中径向离散因子、离散数、Williams级数项对计算结果的影响。算例分析表明,三角形Williams单元所得的应力强度因子具有对奇异区尺寸不敏感的优点,且收敛快,计算精度高。     

Application of the holographic interferometry method to determine the stress intensity factor

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 155–158, January–February, 1990.     

A domain integral for the calculation of generalized stress intensity factors in sliding complete contacts

In this study, a procedure for calculating the generalized stress intensity factor (GSIF) for 2D sliding complete contacts is presented. The method is based on a domain integral equivalent to a path-independent integral. The domain character of the approach makes it very suitable for the post-processing of finite element solutions. The robustness and accuracy of the method are assessed through numerical examples, comparing the obtained results with other techniques, such as stress extrapolation and the path-independent contour integral. In addition, the multiplier constants for other terms in the expansion series are also computed.     

A brief history of the crack tip stress intensity factor and its application

The primary objective of this work is to discuss the origins, background and development of the elastic crack tip stress intensity factor, K, as they occurred. The further development of the three modes and the compilations of related formulas in the literature are discussed. The origins of applications to static crack growth stability, and sub-critical growth due to fatigue and environmental effects are included. Significant events such as the formation of the ASTM committee on Fracture Mechanics, the adoption of Damage Tolerance Analysis by the aircraft industry using Fracture Mechanics as a basis, and the further extension of the methods to large-scale plasticity conditions are presented. Finally a discussion of early predictions of crack paths is discussed.     

Determination of stress intensity factor with direct stress approach using finite element analysis

In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy.     

Algorithms and restrictions in the application of optical methods to stress intensity factor determination

By applying the method to several problems of technological interest, this paper illustrates the features and expected accuracy of a hybrid frozen stress-moiré interferometric method for estimating stress intensity distributions in three dimensional cracked body problems associated with complex subcritical flaw growth, the precursor to most service fractures.     

The dynamic stress intensity factor for a crack due to arbitrary rectilinear screw dislocation motion

The dynamic stress intensity factor for a stationary semi-infinite crack in an elastic plane due to the rectilinear motion of a screw dislocation is obtained analytically. The intensity factor is studied for its dependence on the (initial) dislocation position, orientation and speed. The speed is subsonic and possibly non-uniform. The position and orientation are arbitrary, so that crack-dislocation intersection is considered. It is assumed that a dislocation traveling toward the crack surface arrests upon arrival. It is found that, in general, dislocation motion initiation and arrest cause discontinuities in the intensity factor. In the latter instance, the factor takes on a constant value and, in the case of arrest on the crack surface, this value depends only on the initial dislocation position.     

Using moiré interferometry and boundary integral hybrid method to determine mixed-mode stress intensity factor

The paper describes a hybrid experimental and numerical method of Moiré Interferometry and the boundary-integral-element method. The interference patterns used for the evaluation of the displacement vector are obtained by Moiré Interferometry. The boundary displacements obtained experimentally are conveniently used for the calculation of the stress intensity factor in the body by the boundary-integral-method. Some examples bear witness to the effectiveness and accuracy of the hybrid technique. Project is supported by the Science Fundation of the State Education Commission of China.     

数值积分法求解厚壁筒的动态应力强度因子

用数值积分法求解了厚壁筒表面裂纹的动态应力强度因子，其结果与有限元的计算结果作了比较，表明该方法简单有效，对工程应用极有参考价值     

多层材料结构的界面裂纹尖端复应力强度因子

本文建立了一种多层材料复合结构的界面裂纹问题分析模型。当两种材料之间插入第三种薄层弹性材料,裂纹位于第三种材料与第一或第二种弹性材料的界面上,且插页材料3~#的厚度相对于裂纹尺寸或平面内其他尺寸很小时,可以得到该问题裂纹尖端的复应力强度因子通式。本文用有限元法对结果进行了数值验证,并进行了有关问题的讨论。     

Analysis of stress intensity factor in orthotropic bi-material mixed interface crack

Adopting the complex function approach, the paper studies the stress intensity factor in orthotropic bi-material interface cracks under mixed loads. With consideration of the boundary conditions, a new stress function is introduced to transform the problem of bi-material interface crack into a boundary value problem of partial differential equations. Two sets of non-homogeneous linear equations with 16 unknowns are constructed. By solving the equations, the expressions for the real bi-material elastic constant εt and the real stress singularity exponents λt are obtained with the bi-material engineering parameters satisfying certain conditions. By the uniqueness theorem of limit,undetermined coefficients are determined, and thus the bi-material stress intensity factor in mixed cracks is obtained. The bi-material stress intensity factor characterizes features of mixed cracks. When orthotropic bi-materials are of the same material, the degenerate solution to the stress intensity factor in mixed bi-material interface cracks is in complete agreement with the present classic conclusion. The relationship between the bi-material stress intensity factor and the ratio of bi-material shear modulus and the relationship between the bi-material stress intensity factor and the ratio of bi-material Young's modulus are given in the numerical analysis.     

焊接节点半椭圆表面裂纹应力强度因子的权函数计算

本文采用一种改进的权函数法来计算焊接节点半椭圆表面裂纹应力强度因子ＫＩ值，并给出了相应的数值处理方法，就Ｔ型板节点进行了数值验算。     

New stress intensity factor solutions of a periodic array of cracks in residual stress field

Many important applications of crack mechanics involve self-equilibrating residual or thermal stress fields. For these types of problems, the traditional fracture mechanics approach based on the superposition principle has ignored the effect of crack surface contact when the crack-tip propagates into the residual compressive region. Contact between the crack faces and the wedging action are responsible for subsequent crack-tip reopening, which often leads to a much larger mode I stress intensity factor. In this study, an analytical approach is used to study the effect of crack face contact for a period array of collinear cracks embedded in several typical residual stress fields. It is found that the nonlinear contact between crack surfaces dominates the cracking behavior in residual/thermal stress fields, which is responsible for crack coalescence.     

The stress intensity factor history due to three-dimensional transient loading on the faces of a crack

Aprocedure is described for determining dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to tractions that result in variation of the stress intensity factor along the crack edge. The procedure is based on integral transform methods and the properties of analytic functions of a complex variable. The procedure is illustrated for the case of a pair of opposed line loads suddenly applied on the crack faces along a line perpendicular to the crack edge. An exact expression is obtained for the resulting mode I stress intensity factor as a function of time for any point along the crack edge. Some features of the solution, as well as possible extensions of the procedure, are discussed.     

A unified approach to the analysis of nonlinear stress and strain fields ahead of mode III-loaded notches and cracks

This paper provides a comprehensive evaluation of nonlinear stress fields in the neighbourhood of out-of-plane loaded notches with different opening angles, with the effect of varying notch root radius being included. Taking advantage of the unified analytical frame, stress and strain distributions ahead of the notch tip are determined for different nonlinear material laws, those most commonly used by engineers engaged in nonlinear notch analyses. Some well-known solutions due to Neuber and Rice, as well as some recent developments by the present authors can be seen as particular cases of the general approach presented herein. A discussion focused on the shape and the extension of the plastic zone ahead of the notches is also included.