基于Kirchhoff板中裂纹尖端辛本征解的有限元应力恢复方法

对于含穿透裂纹的板结构,裂纹尖端应力场及应力强度因子的计算精度对评估板的安全性具有非常重要的影响。基于含裂纹Kirchhoff板弯曲问题中裂纹尖端场的辛本征解析解,该文提出了一个提高裂纹尖端应力场计算精度的有限元应力恢复方法。首先利用常规有限元程序对含裂纹板弯曲问题进行分析,得到裂纹尖端附近的单元节点位移;然后根据节点位移确定辛本征解中的待定系数,得到裂纹尖端附近应力场的显式表达式。数值结果表明,该方法给出的应力分析精度得到较大提高,并具有良好的数值稳定性。     

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...     

新的估算表面裂纹应力强度因子经验公式

该文给出了新的估算拉伸和纯弯曲载荷下表面裂纹应力强度因子的经验公式。根据疲劳裂纹扩展的数值模拟结果确定强度因子分布函数;利用按已知应力强度因子分布函数求裂纹形状及相应应力强度因子的方法计算给定尺寸的表面裂纹的应力强度因子;通过对数值结果的曲线回归得到估算表面裂纹应力强度因子经验公式。利用该公式对有限厚度和宽度平板内表面裂纹的应力强度因子进行了估算,并与已知的半椭圆形表面裂纹的应力强度因子解进行了比较。该文结果为估算表面裂纹应力强度因子提供了一种新的途径。     

裂纹板贴补应力分析

本文采用含裂纹无限大板特殊基本解和合力边界条件,用体积力法对含裂纹金属薄板的胶贴补强问题进行应力分析。使用一满足胶贴层位移连续条件的剪切单元,把问题转化为对裂纹板和贴片的分析。由于使用的特殊基本解精确满足裂纹面自由力边界条件,避免了对裂纹尖端附近的奇异场进行离散处理,因而可以比较精确地求出裂纹尖端附近的应力分布,同时由于单位集中力引起的裂纹尖端应力强度因子可以解析得到,因而可以较准确地反映出用应力强度因子的降低来表征的贴补效果。作为贴补计算的例子,文中计算了受拉力和剪力作用时,含中心裂纹的金属裂纹板在贴补前后裂纹尖端应力强度因子的降低,给出了贴片的厚度、弹性模量和尺寸及肢贴层厚度等对贴补效果的影响。     

红外热像技术测量Ⅰ型裂纹应力强度因子的研究

目前工程中出现的裂纹形态主要是I型,大多数工程构件中裂纹的应力强度因子难以直接接触测量,建模计算也因受力条件复杂而耗时和困难。红外热像技术以非接触式测量方法为研究材料和结构的断裂问题提供新的实验手段。通过研究在不同频率循环拉伸条件下304不锈钢试件的热-力响应,得到材料体积应变与温度变化的定量关系,进而对紧凑拉伸试件进行循环加载,同步测量裂纹尖端的温度场,获得I型材料裂尖附近应力强度因子。实验结果表明:在近绝热条件下,材料热弹性区的温度变化与体积应变成定量线性关系;不同荷载条件下实测裂纹尖端附近应力强度因子与理论值对比,误差均在2%以内,说明利用红外热像实验方法测量工程实际中循环荷载情况下的应力强度因子是可行并且可靠的。     

热冲击下带裂纹功能梯度厚壁圆筒的分析

针对功能梯度材料热冲击下的断裂问题,对功能梯度材料的材料参数分类进行加权处理,建立带裂纹功能梯度厚壁圆筒的模型;给出热量平衡方程与边界条件,建立相关问题的有限元分析格式;改进Calahan算法以适用于带状稀疏矩阵的一阶非齐次常微分方程组,完善温度场的求解过程,计算了裂纹尖端的温度应力强度因子,并且分析功能梯度材料组分构成对温度应力强度因子的影响。以上研究为带裂纹功能梯度厚壁圆筒的可靠性分析及结构优化设计提供了参考。     

含周期性裂纹正交各向异性板平面问题的应力场分析

通过引入适当的Westergaard应力函数,采用复变函数方法和待定系数法对含周期性裂纹正交各向异性纤维增强复合材料板的Ⅰ 型、Ⅱ型问题中裂纹尖端附近的应力场进行了力学分析。在远处对称载荷与斜对称载荷作用下,先给出Ⅰ型、Ⅱ型问题在裂纹尖端处的应力强度因子,然后导出用应力强度因子表示的Ⅰ型、Ⅱ型裂纹问题应力场的解析表达式。此外,应力场大小与材料常数有关,这是正交各向异性材料不同于各向同性材料的特征。由于裂纹的周期分布,应力强度因子的大小取决于形状因子。结果表明,形状因子随着裂纹长度的增加而增大,随着裂纹间距的增大而逐渐下降,当裂纹间距趋于无穷大时,退化为含单个中心裂纹正交各向异性纤维增强复合材料板的结果。      

非均匀复合材料中反平面裂纹的动态断裂力学研究

对于非均匀复合材料中多个裂纹的动态断裂力学问题, 提出了一种分析方法, 假设复合材料为正交各向异性并含有多个垂直于厚度方向的裂纹, 材料参数沿厚度方向为变化的, 沿该方向将复合材料划分为许多单层, 假设单层材料参数为常数, 应用柔度矩阵/刚度矩阵方法及Fourier变换法, 在L aplace 域内推导出了控制问题的奇异积分方程组, 并用虚位移原理求解, 给出了应力强度因子及能量释放率的表达式, 然后利用Laplace 数值反演, 得出了裂纹尖端的动态应力强度因子和能量释放率。作为算例, 研究了带有两个裂纹的功能梯度结构, 分析了材料参数的优化对降低应力强度因子的意义。      

压电介质夹杂功能梯度压电带界面双裂纹反平面问题

利用积分方程方法,本文研究了夹在两个均匀压电半空间的功能梯度压电带界面共线双裂纹的反平面问题。在电渗透型边界条件下,通过Fourier余弦变换将所考虑的问题化为一对偶积分方程,再用Copson方法将该对偶积分方程转化为Fredholm方程进行数值求解,从而给出了裂纹尖端的应力强度因子,电位移强度因子的表达式。分析了裂纹长度,功能梯度非均匀参数以及材料的几何尺寸等对应力强度因子的影响。     

非均匀材料界面裂纹的Cell-Based光滑有限元法

为提高非均匀材料界面裂纹尖端断裂参数的求解精度,基于非均匀材料界面断裂力学、Cell-Based光滑有限元(Cell-SFEM)和非均匀材料的互交作用积分法,提出了求解非均匀材料界面裂纹尖端断裂参数的CellBased光滑有限元法,推导了基于Cell-Based光滑有限元法的非均匀材料的互交作用积分法,对非均匀材料间的界面裂纹尖端处正则应力强度因子进行了求解,并与参考解进行了比较,讨论了互交积分区域大小和光滑子元个数与正则应力强度因子的关系。数值算例结果表明:本方法具有很高的计算精度,对积分区域大小不敏感,可为设计、制造抗破坏非均匀材料提供依据。     

Stress intensity factors of two diametrically opposed edge cracks in a thick-walled functionally graded material cylinder

A method is developed to evaluate stress intensity factors for two diametrically-opposed edge cracks emanating from the inner surface of a thick-walled functionally graded material (FGM) cylinder. The crack and the cylinder inner surfaces are subjected to an internal pressure. The thermal eigenstrain induced in the cylinder material due to nonuniform coefficient of thermal expansion after cooling from the sintering temperature is taken into account. First, the FGM cylinder is homogenized by simulating its nonhomogeneous material properties by an equivalent eigenstrain, whereby the problem is reduced to the solution of a cracked homogenized cylinder with an induced thermal and an equivalent eigenstrains and under an internal pressure. Then, representing the cracks by a continuous distribution of edge dislocations and using their complex potential functions, generalized formulations are developed to calculate stress intensity factors for the cracks in the homogenized cylinder. The stress intensity factors calculated for the cracks in homogenized cylinder represents the stress intensity factors for the same cracks in the FGM cylinder. The application of the formulations are demonstrated for a thick-walled TiC/Al₂O₃ FGM cylinder and some numerical results of stress intensity factors are presented for different profiles of material distribution in the FGM cylinder.     

Dynamic stress intensity factor of a functionally graded material under antiplane shear loading

Summary The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.     

A model for interface cracks in layered orthotropic solids: Convergence of modal decomposition using the interaction integral method

The mode‐partitioning problem for bimaterial interfaces is still not resolved by the classical fracture mechanics approach in a satisfactory manner. Stress oscillations and overlapping crack faces are a direct consequence of the rigorous solution of the elastic boundary value problem, if the constitutive law changes discontinuously across the interface. Conversely, continuously varying material properties, also referred to as functionally graded materials (FGM), avoid these physically not admissible drawbacks. In this case the crack tip fields are of the same nature as those known from homogeneous materials. Therefore, the well‐established stress intensity factor concept can be used without any changes. Following this motivation an FGM‐interface model for delaminated composite beam structures was developed and its characteristics with respect to the modal decomposition of the crack tip fields were investigated. The considered beam structures consisted of two orthotropic layers, each of a different material. The spatial variation of the material properties in the interface region was modeled by a tanh ‐function introducing one transition parameter that controlled the FGM‐gradient. Four load cases were analyzed for each structural configuration: either a unit normal force or a unit bending moment was imposed on each end of the split beam. Thus, any load case can be simply reconstructed from the presented results by means of superposition. The stress intensity factors for modes I and II were then evaluated using an interaction integral method along with the finite element method. The corresponding results are given depending on the mesh density of the interface region, the integration domain and the transition parameter. In this manner, the influence of the transition parameter on the mode ratio and on the convergence behavior of the modal decomposition scheme with respect to its integration domain was identified. Finally, the ability of the FGM‐interface model to represent bimaterial interfaces while still maintaining the advantages of crack analysis in homogeneous materials was highlighted. Copyright © 2008 John Wiley & Sons, Ltd.     

Longitudinal shear of a crack in a multi-material circular cylinder

This is an article dealing with the longitudinal shear of a crack contained in a circular cylinder, which is embedded in and fixed by perfect bonding to a composed hollow circular cylinder, consisting of a number of hollow sub-cylinders of different materials. A rigorous solution to the problem is developed. With the material and geometric constants of the composed hollow circular cylinder as parameters, numerical values of stress intensity factors for the crack are worked out. The delicate behavior in the variation of the stress intensity factors, when the number of the hollow sub-cylinders becomes large, is analyzed and discussed. The solution is developed by utilizing a simplified and improved technique using complex variables.     

Crack Spacing Effect on the Brittle Fracture Characteristics of Semi-infinite Functionally Graded Materials with Periodic Edge Cracks

The effect of crack spacing on the brittle fracture characteristics of a semi-infinite functionally graded material (FGM) with periodic edge cracks is discussed. The incompatible eigenstrain induced in the material due to mismatch in the coefficients of thermal expansion is considered in the analysis. The nonhomogeneity of the material is simulated by an equivalent eigenstrain, whereby the problem is reduced to that of a cracked homogeneous material with incompatible and equivalent eigenstrains. A method is then formulated to calculate the stress intensity factor of periodic edge cracks in such a semi-infinite homogeneous medium and applied to calculate apparent fracture toughness of a semi-infinite FGM from its prescribed composition profile. Inverse calculation is also carried out to compute composition profile from prescribed apparent fracture toughness of the semi-infinite FGM. Numerical calculations are carried out for semi-infinite TiC/Al₂O₃ FGM and the results are shown in the figures.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce 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, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

含半椭圆表面裂纹圆柱壳体的三维热弹性动态断裂

研究了含轴向半椭圆表面裂纹的圆柱壳体在热应力与冲击载荷作用下的动态断裂情况,并应用所研制的三维动态断裂有限元程序进行了大规模的数值计算,确定了圆柱壳体的三维温度分布及热-力耦合下的动态应力强度因子,所得结果在一定程度上揭示了热-力作用下圆柱壳体的边界表面、裂纹面、物质惯性和弹性波的相互作用在结构动态断裂中的重要性。     

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.     

Inverse problem of material distribution for desired fracture characteristics in a thick-walled functionally graded material cylinder with two diametrically-opposed edge cracks

This study concerns the inverse problem of evaluating the optimum material distribution for desired fracture characteristics in a thick-walled functionally graded material (FGM) cylinder containing two diametrically-opposed edge cracks emanating from the inner surface of the cylinder. The thermal eigenstrain developed in the cylinder material due to nonuniform coefficient of thermal expansion as a result of cooling from sintering temperature is taken into account. Based on a generalized method of evaluating stress intensity factors developed in a previous study, an inverse method is developed to optimize material distribution intending to realize prescribed apparent fracture toughness in the FGM cylinder. To present some numerical results, a TiC/Al₂O₃ FGM cylinder is considered and the inverse problems are solved to evaluate material distributions for two examples of prescribed apparent fracture toughness. The effect of cylinder wall thickness on the material distribution and comparison of material distributions corresponding to a single and two cracks are also discussed. The numerical results reveal that the apparent fracture toughness of FGM cylinders can be controlled by choosing the material distributions properly.     

Three dimensional fracture analysis of FGM coatings under thermomechanical loading

The main objective of this study is to examine the three dimensional surface crack problems in functionally graded coatings subjected to mode I mechanical or transient thermal loading. The surface cracks are assumed to have a semi-elliptical crack front profile of arbitrary aspect ratio. The cracks are embedded in the functionally graded material (FGM) coating which is perfectly bonded to a homogeneous substrate. A three dimensional finite element method is used to solve the thermal and structural problems. Collapsed 20-node isoparametric elements are utilized to simulate the strain singularity around the crack front. The stress intensity factors are computed by using the displacement correlation technique. Four different coating types are considered in the analyses which have homogeneous, ceramic-rich (CR), metal-rich (MR) and linear variation (LN) material composition profiles. In the mechanical loading problems, the composite medium is assumed to be subjected to fixed-grip tension or three point bending. In the thermal analysis, a transient residual stress problem is considered. The stress intensity factors calculated for FGM plates are in good agreement with the previously published results on three dimensional surface cracks. The new results provided show that maximum stress intensity factors computed during transient thermal loading period for the FGM coatings are lower than those of the homogeneous ceramic ones.