Anti-plane elastodynamic analysis of a cracked orthotropic strip

Stress analysis is carried out in an orthotropic strip containing a Volterra-type screw dislocation. The distributed dislocation technique is used to construct integral equations for an orthotropic strip weakened by multiple smooth cracks under time-harmonic anti-plane deformation. These equations are of Cauchy singular type at the location of dislocation, which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determine stress intensity factors for multiple smooth cracks under anti-plane deformation. Several examples are solved and the stress intensity factors are obtained. The effects of the geometric parameters, cracks location and orientation on the stress intensity factors of cracks are investigated.     

Anti-plane analysis of functionally graded materials weakened by several moving cracks

This paper considers several finite moving cracks in a non-homogeneous material. The shear modulus and mass density of the plane are considered for a class of functional forms for which equilibrium equation has analytical solutions. The distributed dislocation technique is used to carry out stress analysis in a non-homogeneous plane containing moving cracks under anti-plane loading. The solution of a moving screw dislocation is obtained in a non-homogeneous plane by means of Fourier transform method. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is employed to derive integral equations for a plane weakened by moving cracks. Finally several examples are solved to show the effects of the material non-homogeneity and speed of cracks on the stress intensity factors.     

Fracture analysis of composites by time independent moving-crack orthotropic XFEM

Time-independent orthotropic enrichment functions are introduced for dynamic propagation analysis of moving cracks in composites by the extended finite element method (XFEM). The proposed enrichment functions are derived from the analytical solutions for a moving/propagating crack in orthotropic media, and can be considered as a new extension to the available XFEM techniques for dynamic analysis of stationary and moving cracks in orthotropic materials. They are included within the framework of partition of unity and XFEM to enhance the accuracy of basic FEM solution near a moving crack tip in orthotropic media. The method allows for analysis of the whole crack propagation pattern on an unaltered finite element mesh, which is independently defined from the existence of any predefined crack or its propagation path. A combination of dynamic crack initiation toughness and crack orientation along the maximum circumferential stress is used to design a relatively simple and efficient formulation. Dynamic stress intensity factors (DSIFs) are evaluated by means of the domain separation integral method and the dynamic energy release rate. The time dependent XFEM equations are constructed by discretizing the standard weak formulation of the governing elastodynamics equation. They are solved by the unconditionally stable Newmark time integration scheme. A number of benchmark and test problems are simulated and the results are compared with the available reference results to illustrate the accuracy and efficiency of the proposed scheme.     

Stress analysis in a cracked strip

The stress fields in a strip containing climb and glide edge dislocations are obtained utilizing a complex Fourier transform. The dislocation solutions are then employed to perform integral equations for the analysis of a strip weakened by multiple cracks with any configuration and arrangement. The integral equations are solved numerically for the dislocation density on the cracked surfaces. The stress-intensity factors for two straight cracks compared favorably with the results rendered in literature. Three new examples are solved to demonstrate the applicability of the procedure.     

Application of modified mapping-collocation method to cracks emanating from a circular hole in an orthotropic finite plate

A modified mapping-collocation method is applied to the analysis of cracks emanating from a circular hole in an orthotropic finite plate under uniform stress. To check the effectiveness of this procedure, we present the various results for comparison with references. Then, the stress intensity factors are presented for several plate configurations of [0 _n /90 _m ] _s laminates. The results show that the modified mapping-collocation method is effectively applicable to analyzing such cracks in an orthotropic finite plate. The results also show that the stress intensity factors depend on the material orthotropy and geometry.     

Static and dynamic fracture analysis for the interface crack of isotropic-orthotropic bimaterial

In the present study, interfacial cracks between an isotropic and orthotropic material, subjected to static far field tensile loading are analyzed using the technique of photoelasticity. The fracture parameters are extracted from the full-field isochromatic data and the same are compared with that obtained using boundary collocation method. Dynamic photoelasticity combined with high-speed digital photography is employed for capturing the isochromatics in the case of propagating interfacial cracks. The normalized stress intensity factors for static cracks are greater when α=90° (fibers perpendicular to the interface) than when α=0° (fibers parallel to the interface), and those when α=90° are similar to ones of isotropic material. The dynamic stress intensity factors for interfacial propagating cracks are greater when α=0° than α=90°. For the velocity ranges (0.1<c/c _s1 <0.7) observed in this study, the complex dynamic stress intensity factor |K _D |, I increases with crack speedc, however, the rate of increase of |K _D | with crack speed is not as drastic as that reported for homogeneous materials.     

三维压电介质中不同电边界条件的裂纹分析

在不可导通、可导通和半可导通等三种电边界条件下，系统研究并给出三维无限横观各向同性压电介质中平行于各向同性面的、任意形状的平片裂纹在任意载荷作用下的不连续位移和不连续电势边界积分方程方法。无论平片裂纹的形状如何，结果都表明：对不可导通裂纹，应力强度因子只与机械载荷有关，电位移强度因子只与电载荷有关；而可导通裂纹的应力强度因子和电位移强度因子只与机械载荷有关，电位移强度因子由机械载荷通过压电效应产生。半可导通裂纹所对应的边界积分方程组为非线性方程组，文中给出一种迭代解法。在均布的机械载荷和电载荷作用下。裂纹腔内的电位移为一常数，只与外加载荷有关，而与裂纹形状无关。     

Interfacial edge crack between dissimilar orthotropic thermoelastic materials under uniform heat flow

This study analyzes an interfacial edge crack in an orthotropic thermoelastic bimaterial subjected to uniform heat flux at infinity. The problem is formulated on the basis of transformed function representations of plane solutions for anisotropic thermoelastic solids. The interface stress intensity factors are obtained in terms of four proposed thermal load parameters and two dimensionless coefficient matrices. It is shown that one of the coefficient matrices depends on eight material parameters whereas the other coefficient matrix is affected by only six material parameters. The orthotropic rescaling technique is used to examine the explicit dependence of the two coefficient matrices on one orthotropic material parameter. The effects of the other material parameters on the coefficient matrices are examined numerically. The energy release rate and mode mixity for the interface crack are also obtained.     

厚壁筒双轴向表面裂纹尖端应力强度因子影响因素的研究

在现有文献对平面结构任意分布多裂纹间相互作用影响因素及厚壁筒轴向表面单裂纹尖端应力强度因子分析的基础上,提出了包含裂纹尖端应力强度因子影响因素的厚壁筒双轴向表面裂纹尖端应力强度因子公式.根据有限元方法,利用ANSYS软件对不同厚壁筒壁厚比、不同裂纹深度比及不同裂纹夹角情况下双轴向表面裂纹尖端应力强度因子进行了计算,分析...     

压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的干涉效应

运用弹性复势方法,研究纵向剪切和面内电场共同作用下无限半平面压电材料中螺型位错和偶极子与半椭圆槽表面裂纹的电弹干涉效应,得到该问题复势函数的封闭形式解答,并由此导出广义应力场、裂纹尖端的广义应力强度因子以及作用在螺型位错上的位错力.算例结果表明:增大材料压电常数会相应增大位错力、位错对裂纹尖端的屏蔽和反屏蔽效应;增大位错离裂纹尖端的距离,位错力会相应减小;变化φ(偶极子臂与x轴正半轴夹角)值会出现一个改变位错偶极子对应力强度因子作用方向的临界值.     

A numerical study of crack interactions under thermo-mechanical load using EFGM

In this work, element free Galerkin method (EFGM) has been used to obtain the solution of various edge crack problems under thermo-mechanical loads as it provides a versatile technique to model stationary as well as moving crack problems without re-meshing. Standard diffraction criterion has been modified with multiple crack weight technique to characterize the presence of various cracks in the domain of influence of a particular node. The effect of crack inclination has been studied for single as well as two edge cracks, whereas the cracks interaction has been studied for two edge cracks lying on same as well as opposite edges under plane stress conditions. The values of mode-I and mode-II stress intensity factors have been evaluated by the interaction integral approach.     

正交各向异性板Griffith裂纹弯曲应力强度因子KⅠKⅡ的简易计算

本文给出了正交各向异性板Griffith裂纹的弯曲应力强度因子K ⅠK Ⅱ,可以应用叠加原理来计算的证明;提出了关于正交各向异性板Griffith裂纹弯曲应力强度因子的对称——反对称原理;应用这两个原理计算了十多种载荷情形的正交各向异性板Griffith裂纹弯曲应力强度因子K ⅠK Ⅱ,且列表给出了便于应用的公式。     

Contact fatigue crack initiation under repeated oblique force

This study was planned and developed with the object of obtaining further information on the mechanism for the initiation of pitting cracks. An interesting feature observed during cyclic loading tests in which a onedirectional tangential force was applied under stationary line contact is that two different types of cracks are observed at both edges of the contact region. A simple dislocation dipole model is proposed for this contact fatigue crack initiation. These two types of cracks are explained in terms of two stress values; one value is the amplitude of the average shearing stress over a semicircular plane inclined to the surface and the other is the maximum of the average normal stress over the same semicircular plane.     

Stress Intensity Factors Evaluation for Rolling Contact Fatigue Cracks in Rails

The stress intensity factors (SIFs) for multiple rolling contact fatigue cracks of a network in the Iran railway under vehicle dynamic load are evaluated in this article. Stress intensity factor evaluation under dynamic loading is simulated in three dimensions using a linear elastic boundary element code. For this purpose, a UIC60 rail with accurate geometry using a boundary element method is studied. A three-dimensional model in Franc3D is provided. Finally, the influence of the friction coefficient between the wheel and rail, crack surface friction, trapped fluid, and initial crack length on SIFs are investigated in detail.     

考虑裂纹面摩擦的有限多裂纹板的应力强度因子解析与数值方法

对在双轴压缩作用下,考虑裂纹面间摩擦力的无限大板中双裂纹与单裂纹的应力强度因子解析解进行对比分析。结果表明,裂纹面间的摩擦力对多裂纹应力强度因子的修正系数是没有影响的,只对有效剪应力产生影响。以无限板周期裂纹的解为例,将该解析解作为有限板共线多裂纹应力强度因子的近似理论解,运用有限元数值计算有限板共线双裂纹的应力强度因子,并将其结果与近似理论解进行对比分析。计算结果表明,有限板共线双裂纹应力强度因子的近似理论解与通过有限元法计算得到的数值解基本吻合,验证裂纹面间摩擦力对应力强度因子的修正系数没有影响,裂纹面间无摩擦力时多裂纹相互影响引起的修正系数可以作为考虑裂纹面间摩擦力时的修正系数。     

Stress intensity factors and kink angle of a crack interacting with a circular inclusion under remote mechanical and thermal loadings

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular integral equations for edge and temperature dislocation distribution functions are constructed and solved numerically, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.     

Finite crack propagation in a micropolar elastic solid

The dynamic propagation of a finite crack under mode-1 loading in a micropolar elastic solid is investigated. By using an integral transform method, a pair of two-dimensional singular integral equations governing stress and couple stress is formulated in terms of displacement transverse to the crack, macro and micro rotations, and microinertia. These equations are solved numerically, and solutions for dynamic stress intensity and couple stress intensity factors are obtained by utilizing the values of the strengths of the square root singularities in macrorotation and the gradient of microrotation at the crack tips. The motion of the crack tips and the load on the crack surface are not prescribed in the formulation of the problem. Therefore, the method of solution is applicable to nonuniform rates of propagation of a crack under an arbitrary time-dependent load on the crack surface. As an example, the diffraction of a micropolar dilatational wave by a stationary crack is considered. The behavior of the microrotation field and the dynamic couple stress intensity factor, influenced by microinertia, in addition to the dynamic stress intensity factor, are examined. The classical elasticity solution for the corresponding problem arises as a special case when the micropolar moduli are dropped from the present solution.     

三维多裂纹应力强度因子的有限元分析

多处损伤和广泛分布疲劳损伤是影响军用老化飞机结构完整性的主要因素之一。三维裂纹前缘应力应变场很复杂 ,除个别理想情况外 ,绝大部分迄今为止无解析解。采用三维 2 0节点等参单元 ,运用ANSYS软件 ,对含半椭圆裂纹的半无限大体进行有限元分析 ,得到裂纹前缘各点的应力强度因子 ,通过对计算结果的分析 ,讨论裂纹长度、裂纹间距比、裂纹前缘位置对应力强度因子的影响以及多裂纹之间的相互影响 ,计算结果和手册的理论值比较表明 ,数值结果准确、方法可行     

Stress singularities in dissimilar orthotropic composites containing an interlaminar crack

The problem of an interlaminar crack in dissimilar orthotropic composite materials under in-plane and anti-plane loading conditions is investigated. In the analytical model, orthotropic half-spaces are assumed to be bound together by a matrix interlayer which represents the matrix-rich interlaminar region in the fiber-reinforced composite laminate. The crack is embedded within the interlayer. With the utilization of the stiffness matrix approach, a system of singular integral equations of the first kind is derived for the current mixed boundary value problem. Numerical results are obtained for the interlaminar crack in a [0°/90°] fibrous composite laminate subjected to three basic loadings in fracture mechanics. Under each applied loading, variations of major and coupling stress intensity factors with respect to relative crack size, crack location, and fiber volume fraction are illustrated.     

带内表面裂纹的组合厚壁筒装配应力强度因子研究

由于过盈配合组合厚壁筒内会产生装配应力。文中用权函数方法导出组合厚壁筒带半椭圆形表面裂纹的内壁在装配应力下的应力强度因子公式。这些公式可用于计算组合厚壁筒在不同裂纹深度、形状和不同材料、过盈量、尺寸情况下的应力强度因子。研究装配应力强度因子随表面裂纹深度和形状的变化规律。