无限弹性基底上热电薄膜的屈曲行为研究

本文研究了热电薄膜粘合到弹性基底结构的屈曲行为．将界面剪切应力和薄膜的轴向应力结合起来,建立了热电薄膜的计算模型,利用边界条件将所求问题转化为一个奇异积分方程．通过使用切比雪夫多项式展开求解奇异积分方程,得到归一化应力强度因子．确定了膜厚度和基材与膜刚度比对薄膜应力和界面应力强度因子的影响．讨论了薄膜长度和厚度比对薄膜应力和界面应力强度因子的影响．结果显示薄膜和基底之间的刚度比对薄膜的应力水平有着较明显的影响．     

双相材料空间中受剪切载荷作用的平片裂纹问题的超奇异积分方程解法

本文利用三维断裂力学的超奇异积分方程的求解方法，对双相材料空间中垂直于界面的平片裂纹在剪切载荷作用下的问题作了研究，首先使用边元界法，在有限部分积分的意义下的问题归结为一组以裂纹面位移间断（位错）为未知函数的超奇异积分方程，然后使用有限部分的理论，并给出边界元法为其建立了数值法，在此基础上，讨论了用裂纹面位移间断计算应力强度因子的方法，最后以两个典型的平片裂纹问题的应力强度因子进行了计算，其数值结     

压电拼接电磁复合材料中裂纹对SH波的散射

利用积分变换及奇异积分方程技术研究电磁复合材料底层处裂纹对SH波散射问题。假定裂纹面的边界条件为电渗透性,通过Fourier余弦变化将问题转化为对偶积分方程,并利用Copson方法将对偶积分方程转化为第二类Fredholm积分方程求解。给出标准动应力强度因子表达式;通过数值计算分析裂纹长度、裂纹到界面距离、入射波频率及入射角对标准动应力强度因子影响。     

金属裂纹板复合材料胶接修补强度的弹塑性有限元预测

金属裂纹板经复合材料补片胶接修补后,其结构强度明显提高,但裂纹板中的裂纹会导致严重的应力集中现象,并易产生塑性变形,呈现强烈的材料物理非线性特性,需要采用弹塑性力学原理,进行复合材料胶接修复结构的静强度预测。为此,考虑金属板材料的非线性特性,建立了金属裂纹板复合材料胶接修补结构的弹塑性有限元模型,并通过试验验证了模型的有效性。在此基础上,提出了基于裂纹尖端的张开位移(COD)判据的拉伸强度预测方法,分析了修复结构的塑性应变、COD以及静拉伸强度。结果表明:相对于应力强度因子K判据, COD判据能更有效地预测修复试件的静拉伸强度。      

金属裂纹板复合材料单面胶接修补结构应力分析

考虑金属裂纹板复合材料单面胶接修补结构的几何非线性和边界条件,建立了考虑弯曲变形单面修补结构力学分析模型,计算出承受面内载荷时修补结构的弯矩和挠度,将补片自由端和金属板裂纹处的弯矩作为胶层应力控制微分方程的边界条件,推导出剪应力和剥离应力的解析解,及裂纹张开位移的表达式,并与有限元数值结果进行对比。分析结果表明,胶接修补结构应力分析理论模型和相关简化假设合理、正确。利用所建立的解析模型研究了金属裂纹复合材料单面胶接修补结构的应力分布特点及胶层主导破坏模式的失效机制,为胶接修补结构的承载能力分析以及结构改进设计提供了一定的理论依据。     

具中心直裂纹复合材料圆板周期焊接问题

研究了焊接垫圈弹性平面的剪切模数相同而其它模数不同的具中心直裂纹的复合材料圆板周期焊接问题,利用复分析方法将原问题转化为周期Riemann边值问题,进而转化为具周期核奇异积分方程,最后利用Lobatto-Chebyshev求积公式得到数值解,并计算出应力强度因子的数值。     

复合材料单面修补板裂纹尖端J积分的解析预测模型

考虑附加弯矩的影响,基于单搭接接头理论建立了单面修补含中心穿透裂纹直板解析模型,求解了修补结构基板的最大最小应力,并与有限元结果进行对比验证,研究了补片长度、宽度、厚度和胶层弹性模量对有限元模型裂纹尖端J积分的影响,通过拟合基板应力与有限元模型裂纹尖端J积分的数值关系,得到了求解修补结构裂纹尖端J积分的解析公式,并验证了其在单面修补弯曲板的适用性。通过研究和分析发现,求解的解析模型适用于承受面内载荷、面外载荷以及混合载荷下的平板和弯曲板修补结构。     

压电-压磁板条中反平面裂纹的电-磁-弹性分析

基于线性电磁弹性理论,获得了压电-压磁板条中反平面裂纹尖端附近的奇异应力、电场和磁场。假设裂纹位于和板条边界平行的中心位置,并且裂纹是电磁渗透型的。利用Fourier变换,将裂纹面的混合边值问题化为对偶积分方程,即而归结为第二类Fredholm积分方程。通过渐近分析,得到了裂纹尖端附近应力、应变、电位移、电场、磁场和磁感的封闭表达式。结果表明,对于电磁渗透裂纹,电场强度因子和磁场强度因子总为0;板条的宽度对应力强度因子有显著的影响;能量释放率总为正值。     

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。     

正交各向异性复合柱圆弧型循环对称界面裂纹

讨论反平面载荷作用下空心复合柱的循环对称圆弧型裂纹问题。复合柱由两极正交各向异性功能梯度弹性层粘接而成。采用分离变量将这个混合边值问题转化为Cauchy核奇异积分方程,并用Lobatto-Chebyshev求积法对积分方程进行数值求解,得到了应力强度因子的数值解。分析了梯度非均匀参数,几何与材料参数变动等对应力强度因子的影响。     

Interfacial fracture analysis of a piezoelectric–polythene composite cylindrical shell patch under axial shear

The present work studies the interfacial fracture in a piezoelectric cylindrical shell patch. The problem is solved by the methods of infinite trigonometric series and Cauchy singular integral equation, and the numerical results of the stress intensity factor (SIF) are obtained. The effects of the interfacial radius and crack’s location on the SIF are explained through the effects of the free surface, interfacial curvature, crack length, and interface end, respectively. An optimal stiffness matching relationship between the piezoelectric layer and dielectric substrate is suggested. The effects of the piezoelectric and dielectric coefficients are explained through the mechanism of piezoelectric stiffening.     

Stress intensity factor solution for a semi-elliptical crack in an arbitrarily distributed stress field

An equation for the stress intensity factor (SIF) for semi-elliptical crack has been developed. It is based on the Newman-Raju's solution for the crack in a plate under bending or tension. The equation can be applied when a stress distribution is described by a power function. Using the approach outlined, the SIF for a surface crack in a T-butt welded connection has been estimated. The results obtained can be used in a fracture-mechanics-based fatigue analysis.     

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading*

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.     

半刚性基层沥青路面反射裂缝扩展过程分析的Williams单元

该文对半刚性基层沥青路面结构采用弹性层状体系平面应变分析模型,利用改进的Williams级数,结合广义参数有限元法和常规等参元,建立了反射裂缝裂尖应力强度因子分析的广义参数Williams单元,并推导了Williams单元的刚度方程,据此研究了正对称荷载和偏载分别作用时,反射裂缝扩展过程中应力强度因子的变化规律;重点分析了偏载作用下路面结构层参数与应力强度因子之间的关系。Williams单元中含有与应力强度因子相关的参数,可以直接获得裂尖应力强度因子。算例分析表明:Williams单元与传统方法的计算结果吻合较好,且格式简单,计算精度高,适用于沥青路面反射裂缝扩展过程分析。     

Numerical modeling of 2-D smooth crack growth

Numerical algorithm to simulate 2-D smooth crack is presented. The stepwise method based on local criteria of propagation is used. Two crack propagation criteria are employed. At the first stage of propagation, the maximum tensile stress criterion is used to take into account the abrupt change in tangent direction. At subsequent stages, the assumption that the stress intensity factor (SIF) K_{_2=} 0 at the current crack tip is exploited. The analytical formulae for calculating SIFs are given. The displacement discontinuities (DD) involved in these formulae are found from the numerical solution of a complex hypersingular integral equation (CHSIE) for a piecewise homogeneous plane with curvilinear cracks. The new mechanism of smooth approximation of the crack path by circular arcs at each propagation stage is suggested. Numerical results are given. They confirm the efficiency of the algorithm suggested. This revised version was published online in August 2006 with corrections to the Cover Date.     

Antiplane crack analysis of a functionally graded material by a BIEM

Elastostatic analysis of an antiplane crack in a functionally graded material (FGM) is performed by using a hypersingular boundary integral equation method (BIEM). An exponential law is applied to describe the spatial variation of the shear modulus of the FGM. A Galerkin method is applied for the numerical solution of the hypersingular traction BIE. Both unidirectional and bidirectional material gradations are investigated. Stress intensity factors for an infinite and linear elastic FGM containing a finite crack subjected to an antiplane crack-face loading are presented and discussed. The influences of the material gradients and the crack orientation on the stress intensity factors are analyzed.     

Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

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.     

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.