求解受钉传载荷正交各向异性板双边缺口边缘裂纹应力强度因子的复变－广义变分解法

本文以单边边缘裂纹二维应力场与位移场展开式为基础，采用广义变分方法研究受钉传载菏各向异性板双边缺口边缘裂纹应力强度因子。首先建立精确满足正文各向异性板基本微分方程、裂纹表面边界条件、钉载孔处位移单值条件与合力平衡条件的应力场和位移场的级数表达式。然后应用广义变分方法满足边界条件从而确定应力强度因子，在变分方程中只存在沿板边界的线积分、计算程序简单，输入数据很少，结果收敛迅速，并与已知结果相当吻合而且所需机时较少。     

求解受钉传载荷正交各向异性板双边缺口边缘裂纹应力强度因子的复变——广义变分解法

本文以单边边缘裂纹二维应力场与位移场展开式为基础,采用广义变分方法研究受钉传载菏各向异性板双边缺口边缘裂纹应力强度因子。首先建立精确满足正文各向异性板基本微分方程、裂纹表面边界条件、钉载孔处位移单值条件与合力平衡条件的应力场和位移场的级数表达式。然后应用广义变分方法满足边界条件从而确定应力强度因子,在变分方程中只存在沿板边界的线积分、计算程序简单,输入数据很少,结果收敛迅速,并与已知结果相当吻合而且所需机时较少。      

对称斜交铺层复合材料层板在平面变形情况下分层问题的解析-广义变解法

本文采用弹性力学的位移解法研究对称斜交铺层复合材升层板在平面变形情况下的分层问题,得到了满足所有基本方程,层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式.然后利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定裂纹尖端附近奇异应力场的控制量--广义应力强度因子.由于所有基本方程预先得以满足,在变分方程中只有线积分而无面积分.计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速.     

对称角铺层复合材料层板在反平面变形情况下分层问题的解析—广义变分解法

本文采用弹性力学的位移解法研究对称角铺层复合材料层板在反平面变形情况下的分层问题,得到了满足所有基本方程、层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。再利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定应力强度因子。由于所有基本方程预先得以满足,变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。     

对称斜交铺层复合材料层板在平面变形情况下分层问题的解析—广义变解法

本文采用弹性力学的位移解法研究对称斜交铺层复合材升层板在平面变形情况下的分层问题,得到了满足所有基本方程,层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。然后利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定裂纹尖端附近奇异应力场的控制量——广义应力强度因子。由于所有基本方程预先得以满足,在变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。     

对称角铺层复合材料层板在反平面变形情况下分层问题的解析—广义变分解法

本文采用弹性力学的位移解法研究对称角铺层复合材料层板在反平面变形情况下的分层问题,得到了满足所有基本方程、层间连续条件与裂纹表面静力边界条件的位移场与应力场的本征展开式。再利用分区广义变分原理代替裂纹表面以外的边界条件,确定位移场与应力场表达式中的待定系数,进而确定应力强度因子。由于所有基本方程预先得以满足,变分方程中只有线积分而无面积分。计算表明,本文方法前期准备工作简便,计算节省机时,结果收敛迅速。     

均匀热流作用下含裂纹板I 型温度应力强度因子的解析解

研究一种新的温度边值问题。含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角。当裂纹面上维持一恒定温差时,采用复变函数理论,得出了温度场、温度应力场与位移场的解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12 材料进行了相应数值计算,分析了热流密度大小与方向对温度分布与温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅰ 型温度应力强度因子,不产生Ⅱ 型温度应力强度因子。温度应力场取决于热流密度沿裂纹方向的分量,垂直于裂纹方向的分量对温度应力场没有影响。     

均匀热流下导热裂纹Ⅱ型温度应力强度因子的解析解

研究含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角的情况。当垂直于裂纹面方向有定量热流穿过裂纹时,采用复变函数理论,得出了温度、应力与位移场解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12材料进行了数值计算,研究了裂纹导热情况与热流方向对温度场及温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅱ型温度应力强度因子,不产生Ⅰ型温度应力强度因子。热荷载可等效为一个远场均匀作用的剪应力。Ⅱ型温度应力场取决于热流密度沿垂直裂纹面方向的分量,平行于裂纹方向的热流分量对温度应力场没有影响。     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

复合材料层合梁在横向载荷作用下分层问题的解析—广义变分解法

对于复合材料层合梁在横向载荷作用下的分层问题,本文根据Muskhe Lishvili的求解各向同性平面问题与Lkhnisikii的求解各向异性平面问题的复变函数方法,得到了满足所有基本方程、裂纹表面边界条件与层间连续条件的应力场、位移场的本征展开式。进而利用分区广义变分原理代替裂纹表面以外的边界条件,确定应力强度因子。由于所有基本方程预先得以满足,在变分方程中只有线积分而无面积分。计算表明,本方法前期准备工作很少,计算节省机时,结果收敛迅速。     

Hybrid stress finite element analysis of bending of a plate with a through flaw

A hybrid stress finite element procedure for the solution of bending stress intensity factors of a plate with a through-the-thickness crack is presented. Reissner's sixth-order plate theory including the effects of transverse shear deformation is used. The dominant singular crack tip stress field is embedded in the crack tip singular elements and only regular polynomial functions are assumed in the far field elements. The stress intensity factors can be calculated directly from the crack tip singular stress solution functions. The effects of the plate thickness, the ratio between the crack size and the inplane dimension of the plate, and the singular element size on the stress intensity factor solution are investigated. The effects of the explicit enforcement of traction-free conditions along crack surfaces, which are the natural boundary conditions in the present hybrid stress finite element model, are also investigated. The numerical results of bending of a plate with a straight central crack compare favourably with analytical solutions. It is also found that the explicit enforcement of traction-free conditions along crack surfaces is mandatory to obtain meaningful results for the Mode I type of bending stress intensity factor.     

Variation of stress intensity factor and crack opening displacement of semi-elliptical surface crack

In this paper a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3D surface crack. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Then the problem is formulated as an integral equation with a singularity of the form of r ^-3. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function; that is, the exact density distribution to make an elliptical crack in an infinite body. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and Poisson's ratio. The present method gives rapidly converging numerical results and highly satisfactory boundary conditions throughout the crack boundary.     

Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method

In this paper a singular integral equation method is applied to calculate the distribution of stress intensity factor along the crack front of a 3D rectangular crack. The stress field induced by a body force doublet in an infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r ^–3. In solving the integral equation, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function, which expresses stress singularity along the crack front in an infinite body. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary.     

Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions

This paper is concerned with the analysis of stress intensity factors of a strip with a longitudinal crack subject to tension and bending along its edges, and the tension of rectangular plates with a central crack. For both problems three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered.Analysis is based on Laurent expansions of the complex potentials satisfying the stress free relations along the crack.The expansion coefficients are determined from boundary conditions along outer edges, by using a perturbation technique in the first problem and a boundary collocation procedure based on resultant forces and mean displacements in the second problem. Numerical calculations are performed for various plate configurations, and the results are summarized in forms ready for practical use. The accuracy of numerical results are also examined, and they are regarded as correct up to four figures.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

A method to compute mixed-mode stress intensity factors for nonplanar cracks in three dimensions

Methods to compute the stress intensity factors along a three-dimensional (3D) crack front often display a tenuous rate of convergence under mesh refinement or, worse, do not converge, particularly when applied on unstructured meshes. In this work, we propose an alternative formulation of the interaction integral functional and a method to compute stress intensity factors along the crack front which can be shown to converge. The novelty of our method is the decoupling of the two discretizations: the bulk mesh for the finite element solution and the mesh along the crack front for the numerical stress intensity factors, and hence we term it the multiple mesh interaction integral (MMII) method. Through analysis of the convergence of the functional and method, we find scalings of these two mesh sizes to guarantee convergence of the computed stress intensity factors in a variety of norms, including maximum pointwise error and total variation. We demonstrate the MMII on four examples: a semiinfinite straight crack with the asymptotic displacement fields, the same geometry with a nonuniform stress intensity factor along the crack front, a spherical cap crack in a cylinder under tension, and the elliptical crack under far-field tension and shear.     

Sickle-shaped surface crack in a notched round bar under cyclic tension and bending

A sickle-shaped surface crack, also called crescent-moon (or crescent) crack, is assumed to exist at the root of a circular-arc circumferential notch in a round bar under tension and bending. For different notch sizes (i.e. different values of the stress concentration factor), the stress intensity factor along the crack front is computed through a three-dimensional finite-element analysis. The effect of the stress concentration factor on the stress intensity factor values is examined for several crack configurations. Finally, the surface crack growth under cyclic loading is analysed through a numerical procedure that employs the stress intensity factor values obtained. Some results of the present study are compared with those by other authors.     

Crack aspect development curves and fatigue life prediction for surface cracks at weld toes in the presence of residual stress

An engineering procedure is proposed for estimating the crack growth behaviour and fatigue lives of semi-elliptical surface cracks at weld toes, based on a database of stress intensity factors. Some examples of crack aspect development curves (CADC) are given for some typical cracked welded joints subjected to service loading and residual stress conditions. The significance for predicting fatigue life according to the natural crack growth path, namely along the CADC, is emphasized through examples.     

Influence of foreign object damage on fatigue crack growth of gas turbine aerofoils under complex loading conditions

Foreign object damage (FOD) has been identified as one of the main life limiting factors for aeroengine blades, with the leading edge of aerofoils particularly susceptible. In this work, a generic edge ‘aerofoil’ geometry was utilized in a study of early fatigue crack growth behaviour due to FOD under low cycle fatigue (LCF), high cycle fatigue (HCF) and combined LCF and HCF loading conditions. Residual stresses due to FOD were analyzed using the finite element method. The longitudinal residual stress component along the crack path was introduced as a nodal temperature distribution, and used in the correction of the stress intensity factor range. The crack growth was monitored using a nanodirect current potential drop (DCPD) system and crack growth rates were correlated with the corrected stress intensity factor considering the residual stresses. The results were discussed with regard to the role of residual stresses in the characterization of fatigue crack growth. Small crack growth behaviour in FODed specimens was revealed only after the residual stresses were taken into account in the calculation of the stress intensity factor, a feature common to LCF, HCF and combined LCF + HCF loading conditions.     

Coupled transient thermoelastic contact problems for axial cracks in hollow cylinders

A coupled transient thermoelastic behaviour of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.