WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors(SIF) of internally pressurized thick- walled cylinder was used as the reference case.SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method.The weight fumction formulas were worked out and can be used for all kinds of depth of cracks,rotating speed,material,size of thick-walled cylinder to calculate the stress intensity factors.The results indicated the validity and effectiveness of these formulas.Meanwhile,the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied.The studies are valuable to engineering application.     

STUDY ON DYNAMIC STRESS INTENSITY FACTORS OF DISK WITH A RADIAL EDGE CRACK SUBJECTED TO EXTERNAL IMPULSIVE PRESSURE

A dynamic weight function method is presented for dynamic stress intensity factors of circular disk with a radial edge crack under external impulsive pressure. The dynamic stresses in a circular disk are solved under abrupt step external pressure using the eigenfunction method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions. By making use of Fourier-Bessel series expansion, the history and distribution of dynamic stresses in the circular disk are derived. Furthermore, the equation for stress intensity factors under uniform pressure is used as the reference case, the weight function equation for the circular disk containing an edge crack is worked out, and the dynamic stress intensity factor equation for the circular disk containing a radial edge crack can be given. The results indicate that the stress intensity factors under sudden step external pressure vary periodically with time, and the ratio of the maximum value of dynamic stress intensity factors to the corresponding static value is about 2.0.     

Torsion of a thick-walled cylinder with an external crack: boundary collocation method

The boundary collocation method is used to obtain the torsional rigidity and Mode III stress intensity factor of a thick-walled cylinder with an external radial crack. When the internal radius of the cylinder is very small, the results agree well with those obtained previously from other methods for an edge crack in a solid cylindrical bar. The present method is shown to be expedient when applied to obtain results for different ratios of the internal and external radii of the cracked cylinder.     

一种散体材料SHPB被动围压试验体应力修正方法

本文利用有限元仿真给出了一种修正方法，并用数值仿真和试验验证了该方法的可靠性。研究表明:散体材料SHPB被动围压试验中，试样厚度远小于厚壁圆筒长度时，端部效应会导致厚壁圆筒不均匀凸出变形，计算材料的体应力-应变关系不能将厚壁圆筒应力状态简化为平面应力问题；厚壁圆筒处于弹性状态下，通过厚壁圆筒理论计算出的径向力与真实径向力存在一定比例关系，在一定范围内，折算系数与试样实时厚度呈二次函数关系。     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

Analysis of dynamic stress intensity factors of three-point bend specimen containing crack

A new formula is obtained to calculate dynamic stress intensity factors of the three-point bending specimen containing a single edge crack in this study. Firstly, the weight function for three-point bending specimen containing a single edge crack is derived from a general weight function form and two reference stress intensity factors, the coefficients of the weight function are given. Secondly, the history and distribution of dynamic stresses in uncracked three-point bending specimen are derived based on the vibration theory. Finally, the dynamic stress intensity factors equations for three-pointing specimen with a single edge crack subjected to impact loadings are obtained by the weight function method. The obtained formula is verified by the comparison with the numerical results of the finite element method (FEM). Good agreements have been achieved. The law of dynamic stress intensity factors of the three-point bending specimen under impact loadings varing with crack depths and loading rates is studied.     

自增强厚壁圆筒疲劳裂纹扩展寿命的可靠性分析

本文提供了自增强厚壁圆筒疲劳裂纹扩展寿命的可靠性分析的方法和公式,自增强残余应力用符合厚壁筒用钢具有强化和包辛格效应实际性能推得的公式进行计算,残余应力对应的应力强度因子的计算采用了有限元法,得到了工作内压与自增强残余应力共同作用下的厚壁筒应力强度因子公式,通过实验测定了厚壁筒用钢的断裂韧度和疲劳裂纹扩展速率等性能。     

热对流作用下筒壁涂层的边裂行为

边裂(边缘开裂)是涂层热致损伤的主要模式之一. 边缘裂纹穿透涂层后,常导致界面脱粘从而驱使涂层与基体剥离,最终丧失对基体的保护作用. 本文以热应力强度因子表征边缘裂纹的扩展驱动力,研究筒壁涂层在热对流作用下的边裂行为. 首先,利用拉普拉斯变换法,得到了瞬态温度场及热应力场的封闭解. 其次,运用Fett等的三参数法确定了筒壁涂层边缘裂纹的权函数. 最后,基于叠加原理和权函数方法计算了边缘裂纹的热应力强度因子. 探讨了无量纲时间、边缘裂纹深度、基体/涂层厚度比、热对流强度等参数对热应力强度因子的影响规律. 结果表明:热应力强度因子的峰值既非发生在热载荷初始时刻,也非发生在热稳态时刻,而出现在时间历程的中间时刻;增大热对流强度不仅可提高热应力强度因子的峰值,而且使峰值提前出现;其他条件相同时,热应力强度因子随着边缘裂纹长度的增大而降低;增大涂层厚度或减小基体厚度可增强涂层抵抗瞬态热载荷的能力.      

Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings

The elastostatic axisymmetric problem for a long thick-walled cylinder containing an axisymmetric circumferential internal crack with two claddings is considered. The claddings having different elastic properties than the hollow cylinder are assumed to be bonded to inner and outer wall of the hollow cylinder. The problem is formulated in terms of a singular integral equation of a well known type, the derivative of the crack surface displacement being the density function, using the standard transform technique. By using appropriate quadrature formulas, the integral equation is reduced to a system of linear algebraic equations. This system is solved numerically and the related stress-intensity factors are calculated for the cases of hollow cylinder with two claddings bonded to inner and outer wall of the cylinder, a cladding bonded to inner wall of the cylinder, a cladding bonded to outer wall of the cylinder and no cladding under axial tensile load. The influence of the geometrical configuration, the claddings and internal crack length on the stress-intensity factors is shown graphically.     

Oblique edge crack in an anisotropic material under antiplane shear

An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions.     

Axisymmetric solid-of-revolution elements based on the assumed stress hybrid model

A series of axisymmetric solid-of-revolution elements with 8-node and quadrilateral cross section have been developed based on the assumed stress hybrid model. A quadratic boundary displacement assumption is employed for each element and a variety of interior stress assumptions have been made. Two different kinds of procedure used for developing stress field have been studied. Example problems of a thick-walled cylinder under internal pressure and a thick-walled sphere under internal pressure are utilized to evaluate the various elements and a desirable stress assumption has been identified. Comparisons of present results with those obtained by the use of 8-node element based on the assumed displacement model indicate that this hybrid stress element is far superior in predicting the stress distribution.     

Boundary element weight function analysis of a strip yield crack in a rotating disk

The boundary element method combined with subtration of Bueckner singular fields are used to obtain weight functions for an internal edge crack in a rotating annular disk. A previously developed, general representation of the weight function is used which leads to integrals that can be evaluated analytically to obtain the stress intensity factor and surface displacements of the crack. The determination of crack tip opening displacements for the strip yield crack is reduced to a non-singular integral which can be evaluated in closed form. The strip yield zone length and crack tip opening displacement are determined for an internal radial crack in a rotating annular disk for a range of crack lengths and rotational speeds.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

Torsion of a long circular cylinder having a spherical cavity with a peripheral edge crack

The singular stress problem of a peripheral edge crack around a spherical cavity in a long circular cylinder under torsion is investigated. The problem is solved by using integral transforms and is reduced to the solution of two integral equations. The solution of these equations is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors, and crack opening displacements are displayed graphically.     

Cracking of an orthotropic substrate reinforced by an orthotropic plate

A solution method is derived to determine the stress intensity factors for both an internal crack and an edge crack in an orthotropic substrate that is reinforced on its boundary by a finite-length orthotropic plate. The method utilizes the Green’s functions for a pair of dislocations and a concentrated force on the boundary while invoking the concept of superposition. Enforcing the traction-free boundary condition along the crack surfaces and the continuity of displacement gradients along the plate/substrate interface results in a coupled system of singular integral equations. An asymptotic analysis of the kernels in these equations for the region of the junction point between the plate corner and the substrate boundary reveals the strength of the singularity in the case of an edge crack. The numerical solution of the integral equations provides results for the stress intensity factors for both an internal crack and an edge crack perpendicular to the substrate boundary and aligned with one of the corners of the plate. The present results have been validated against previously published stress intensity factors for an internal crack and an edge crack in an isotropic substrate.     

柱状装药爆炸条件下厚壁圆筒爆室内 流场及结构动力响应分析

借助非线性动力有限元程序ANSYS/LS-DYNA,采用基于罚函数的流固耦合算法,对厚壁圆筒爆 室在柱状装药爆炸作用下的动态响应过程进行了数值模拟研究。分析了厚壁圆筒爆室内柱状装药爆炸非定 常流场的演化过程以及筒体的动力响应特征。给出了爆炸流场的压力云图、筒壁受到的爆炸压力峰值及冲量 的分布规律、筒体的等效应力云图以及等效应力的分布规律等。流场压力及筒体应变的计算结果与实测结果 吻合较好,并将动力响应的有限元计算结果与理论解进行了比较,证明轴对称平面应变假设下的理论解可以 给出问题的保守估算。分析表明,该厚壁圆筒爆室在柱状装药爆炸作用下在弹性范围内工作,爆室的强度设 计是安全的。     

自紧身管临界裂纹尺寸的概率断裂力学研究

基于概率断裂力学理论和Mome Caflo模拟方法，本文进行了自紧身管临界裂纹尺寸的可靠性研究。自紧身管内表面的疲劳裂纹考虑为半椭圆形式。裂纹尖端处的应力强度因子由内压和自紧残余应力共同产生。自紧残余应力采用了符合身管材料具有强化和包辛格效应性能推导的公式计算，它产生的应力强度因子通过权函数方法得到。根据断裂准则，可计算出自紧身管的临界裂纹尺寸。实例分析表明，对数正态分布为临界裂纹尺寸的最佳分布，同时给出了在各种置信度和可靠度下自紧身管的临界裂纹尺寸。     

Tension of a long circular cylinder having a spherical cavity with a peripheral edge crack

The singular stress problem of a peripheral edge crack around a spherical cavity in a long circular cylinder under tension is investigated. The problem is solved by using integral transforms and is reduced to the solution of three integral equations. The solution of these equations is obtained numerically by the method due to Erdogan, Gupta, and Cook, and the stress intensity factors are displayed graphically.     

Stress intensity factors for an edge interface crack in a bonded semi-infinite plate for arbitrary material combination

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary crack lengths and material combinations. In this paper the stress intensity factors of an edge interface crack in a bonded strip are considered under tension with varying the crack length and material combinations systematically. Then, the limiting solutions are provided for an edge interface crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge interface crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results.