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...     

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。     

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。      

铝合金板厚度对硼纤维/环氧复合材料单面修复效果的影响

采用单向硼纤维/环氧复合材料补片真空袋压工艺单面修复不同厚度含中心裂纹铝合金板,测试了修复试件的热学及准静态力学性能,并采用三维有限元模型分析了修复试件的残余热应变和应力强度因子。结果表明：修复试件的弯曲挠度随铝合金板厚度增大而减小;修复试件铝合金板下表面裂纹尖端附近的残余热应变随铝合金板厚度增大而增大,补片上表面的残余热应变则随铝合金板厚度增大而减小,这与有限元分析结果吻合较好。含中心裂纹铝合金板的应力强度因子随铝合金板厚度增大而减小,而单面修复试件的应力强度因子随铝合金板厚度增大而增大。采用相同长度和宽度的单向硼纤维/环氧复合材料补片单面修复后,铝合金板厚度为1. 76 mm修复试件的承载能力保留率为 93. 85 %,而厚度为 10. 20 mm修复试件的只有 84. 01 %;修复试件的刚度得到了完全恢复,等效刚度均大于完好试件的刚度。     

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。      

求解含裂纹各向异性板与单向复合材料板应力强度因子的变分解法

本文推导了含边缘裂纹各向异性板与单向复合材料板的应力与位移的函数项级数表达式。该级数每一项均满足平衡方程、协调方程与裂纹表面静力边界条件。通过最小势能原理的变分方程来满足其余静力边界条件以确定级数中的待定系数,从而求得应力强度因子。最后,本文给出了长条板拉伸试件、紧凑拉伸试件与三点弯曲试件的计算结果。收敛是迅速的,几乎所有算例都能满足两位收敛。     

基于裂纹尖端应力比值的含裂纹功能梯度材料圆筒应力强度因子计算方法

由于功能梯度材料(FGM)性质的特殊性,现有含裂纹FGM结构应力强度因子计算方法难以避免复杂的矩阵运算以及数值积分。该文针对含外表面环向裂纹FGM圆筒,利用FGM圆筒与均匀材料圆筒裂纹尖端应力之间的比例关系,将复杂的FGM圆筒应力强度因子求解问题转化为简单的应力值提取问题以及经验公式计算问题,仅由均匀材料圆筒应力强度因子经验公式、均匀材料圆筒和FGM圆筒裂纹尖端应力比值即可得到任意含裂纹FGM圆筒应力强度因子。该方法仅需建立2D轴对称模型即可满足计算要求,在保证精度的基础上成功回避了传统方法中的复杂矩阵运算以及数值积分,且适用于不同FGM、筒体尺寸、裂纹深度等情况下的应力强度因子计算。通过多组算例对比分析,证明该方法计算精度高、计算过程简便,便于工程应用。     

Fracture Analysis of Double-Side Adhesively Bonded Composite Repairs to Cracked Aluminium Plate Using Line Spring Model

A line spring model is developed for analyzing the fracture problem of cracked metallic plate repaired with the double-sided adhesively bonded composite patch. The restraining action of the bonded patch is modeled as continuous distributed linear springs bridging the crack faces provided that the cracked plate is subjected to extensional load. The effective spring constant is determined from 1-D bonded joint theory. The hyper-singular integral equation (HSIE), which can be solved using the second kind Chebyshev polynomial expansion method, is applied to determine the crack opening displacements (COD) and the crack tip stress intensity factors (SIF) of the repaired cracked plate. The numerical result of SIF for the crack-tip correlates very well with the finite element (FE) computations based on the virtual crack closure technique (VCCT). The present analysis approaches and mathematical techniques are critical to the successful design, analysis and implementation of crack patching.     

Analysis of cracked plates with a bonded patch

The problem of a cracked plate repaired by an adhesively bonded patch is studied. A shear spring model is adopted to reduce the problem to the analysis of a cracked plate and a patch subjected to external loads and interacting adhesive shear. While the patch is treated by the finite element method, the cracked plate is analyzed by the boundary element method, in which a special fundamental solution satisfying the boundary condition on the crack surface is introduced. The present formulation provides comparable results on the stress intensity factor of the patched crack with less computational effort.     

Crack opening displacement in plate with bonded repair patch

Mathematical techniques are extended to compute crack opening displacements in a cracked plate with an adhesively bonded composite patch. The plate and the patch are considered as orthotropic materials. The problem is reduced to the solution of integral equations. A software program is written to compute shear stresses in adhesive, stress intensity factors in the plate and the crack openings at the centreline of the crack. The effects of adhesive thickness, adhesive modulus, patch thickness and plate thickness on crack openings are investigated. A test program is carried out to obtain crack opening displacements in plate with bonded patch. A good agreement with analytical predictions is obtained. The effects of patches bonded on one or both sides of a plate on stress intensity factors are evaluated.     

A finite element model for single-sided crack patchings

A finite element model is established for analyzing the behavior of cracked plates which are repaired with a single-sided patch. The formulation is based on the Reissner-Mindlin plate theory with an assumed variation of the transverse shear and normal stresses through the thickness of the cracked -plate and patch. The generalized stress-strain relations relating the transverse shear stress resultants and the adhesive stresses to the displacements of the plate and patch are established by using a variational principle. By means of the finite element model presented herein, single-sided crack patching problems can be solved with a reasonable estimate of the adhesive stresses and the stress intensity factor. Numerical examples are provided to illustrate the effects of the patch size on the stress intensity factor in the cracked plate and the stress distribution in the adhesive layer, and compared with results from the previous analysis.     

金属裂纹板复合材料修补结构的超奇异积分方程方法

根据应力强度因子在线弹性范围内具有可叠加性,将金属裂纹板复合材料修补结构进行简化,在表面裂纹线弹簧模型的基础上,建立了基于超奇异积分方程的Line-Spring模型。利用第二类Chebyshev多项式展开的方法,将超奇异积分方程转化为线性方程组,推导出以裂纹面位移表示的应力强度因子表达式,得到了裂纹尖端应力强度因子的数值解,并利用虚拟裂纹闭合法加以验证。参数分析确定了影响对称修补裂纹板应力强度因子的两个主要参数:胶层界面刚度和补片与金属板刚度比,为胶接修补结构的承载能力分析以及改进设计提供理论依据。     

Analysis of the distribution of thermal residual stresses in bonded composite repair of metallic aircraft structures

In this study, the distribution of the thermal residual stresses due to the adhesive curing in bonded composite repair is analysed using the finite element method. The computation of these stresses comprises all components of the structures: cracked plate, composite patch and adhesive layer. In addition, the influence of these residual stresses on the repair performance is highlighted by analysing their effect on the stress intensity factor at the crack tip. The obtained results show that the normal thermal stresses in the plate and the patch are important and the shear stresses are less significant. The level of the adhesive thermal stresses is relatively high. The presence of the thermal stresses increases the stress intensity factor at the crack tip, what reduce the repair performance.     

基于全试验设计方法的含裂纹铝合金板复合材料修补参数优化

建立含穿透裂纹铝合金板复合材料单面胶接修补板条的三维有限元模型,基于位移外推法对裂纹尖端的应力强度因子(SIF)进行求解。使用全试验设计的方法对不同修补参数下修补板条的单向拉伸试验进行仿真模拟,利用二次方程描述并研究了补片长度、补片厚度及胶层弹性模量共同作用时对SIF的影响,确定了以SIF为评价指标时对修补效果影响最大的修补参数,优化了修补设计,并应用优化修补参数进行单向静拉伸试验。结果表明,当三类修补参数共同作用时,补片长度对修补效果影响最大;使用优化修补参数单面修补试验件的破坏强度比未修补板的提高了12.1%,恢复到完好板的90.5%。     

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.     

Stress intensity factor for center-cracked plate with crack surface interference

This paper presents a simple and physically acceptable analysis of stress intensity factor (SIF) for the center-cracked infinite and finite-width plates. The analysis includes the effect of crack surface interference (i.e., the upper and lower crack surfaces are not allowed to overlap) that influences both the SIF at the tension-side crack tip and the crack opening displacement (COD) profile. For an infinite plate, exact solutions are obtained by superimposing the classical (overlapping) solutions. For a finite-width plate, where the SIF solutions cannot be found in closed form, the solutions are carried out numerically. The overlapping SIF solutions from the weight function method are used. An example is given for the case of a finite-width plate under bending. It was found that the overlapping solutions underestimate the stress intensity factor at the tension-side crack tip up to 15%. The analysis results are also compared with the finite element solutions for verification purpose.     

Crack growth induced delamination on steel members reinforced by prestressed composite patch

ABSTRACT Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive‐plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive‐plate interface debond.