功能梯度压电/压磁双材料的周期界面裂纹问题

研究反平面载荷作用下压电/压磁双材料的周期界面裂纹问题,压电/压磁双材料由有限厚度的功能梯度压电层和功能梯度压磁层粘结而成.为便于分析,假设压电层和压磁层的材料性质沿着裂纹的法线方向呈指数变化,基于分离变量和Hilbert核奇异积分方程方法,获得应力强度因子的数值解.数值算例讨论层厚、周期带长度、梯度参数以及材料参数变动等对应力强度因子的影响.结果发现层厚以及裂纹间距的增大会降低裂纹尖端应力强度因子,梯度参数的改变对应力强度因子也有显著的影响.材料参数变动的讨论发现弹性参数的变动对应力强度因子影响最大,其次为电参数,磁参数的变动对应力强度因子影响最小.     

应用半权函数法计算界面裂纹的应力强度因子

应用半权函数法求解双材料界面裂纹的应力强度因子，得到以半权函数对参考位移与应力加权积分的形式表示的应力强度因子。针对特征值为复数λ的双材料界面裂纹裂尖应力和位移场，设置与之对应特征值为-λ的位移函数，即半权函数。半权函数的应力函数满足平衡方程，应力应变关系，界面的连续条件以及在裂纹面上面力为0；半权函数与裂纹体的几何尺寸无关，对边界条件没有要求。由功的互等定理得到应力强度因子KⅠ和KⅡ的积分形式表达式。本文计算了多种情况下界面裂纹应力强度因子的算例，与文献结果符合得很好。由于裂尖应力的振荡奇异性已经在积分中避免，只需考虑绕裂尖远场的任意路径上位移和应力，即使采用该路径上较粗糙的参考解也可以得到较精确的结果。     

圆柱形界面相裂纹在扭转载荷作用下的动态断裂

本文研究了位于界面相中的圆柱形界面裂纹的扭转冲击问题.采用Laplace、Fourier变换和位错密度函数将混合边值问题转化为求解Cauchy核奇异积分方程,利用Laplace数值反演技术计算了动态应力强度因子.讨论了材料特性和结构的几何尺寸对动态应力强度因子的影响.结果表明,随着界面相厚度的增加,无量纲化的动态应力强度因子减小.当裂纹靠近剪切弹性模量大的材料时,无量纲化的动态应力强度因子增大,反之减小.界面相两侧不同的材料组合对裂尖动态应力强度因子的影响是随着剪切弹性模量和质量密度的比值的增加而减小.界面相中裂纹长度对裂尖动态应力强度因子的影响比其他因素的影响大.     

功能梯度板条断裂分析

现存文献关于功能梯度材料断裂问题的研究大都假设材料性质为坐标的指数函数或幂函数，而对其它函数形式较少采用。本文假设功能梯度材料剪切模量为坐标的双曲函数，而泊松比为常量，研究功能梯度板条的混合型裂纹问题。利用Fourier积分变换技术将混合边值问题转化为一对奇异积分方程，通过数值求解奇异积分方程获得含裂纹功能梯度板条分别在剪切和法向载荷作用下的I型和Ⅱ型应力强度因子，并讨论了材料的非均匀性和裂纹相对尺寸对裂纹尖端应力强度因子的影响。     

功能梯度板条Ⅲ型运动裂纹问题研究

现存文献关于梯度材料断裂问题的研究大都是假设材料参数为坐标的指数函数或幂函数,而其它函数形式较少采用.本文假设功能梯度材料剪切模量和密度的倒数均为坐标的线性函数,而泊松比为常量,研究功能梯度板条的反平面运动裂纹问题.利用Fourier积分变换技术和传递矩阵法将混合边值问题化为一对奇异积分方程,通过数值求解奇异积分方程获得板条运动裂纹在反平面载荷作用下的动态应力强度因子,并讨论了裂纹运动速度、裂纹相对尺寸、以及材料非均匀性对动态应力强度因子的影响,结果证明梯度参数、裂纹速度和几何尺寸对材料动态断裂行为有显著影响.     

功能梯度材料涂层平面裂纹分析

研究粘接于均质基底材料上功能梯度涂层平面裂纹问题. 假设功能梯度材料剪切模量的倒数为坐标的线性函数，而泊松比为常数. 采用Fourier变换和传递矩阵法将该混合边值问题化为奇异积分方程组，通过数值求解获得 应力强度因子. 考察了材料梯度变化形式、结构几何尺寸和材料梯度参数对裂纹应力强度因子的影响，发现 功能梯度材料涂层尺寸、裂纹长度以及材料梯度参数均对应力强度因子有显著影响.     

垂直磁压电材料界面三维裂纹的超奇异积分法

应用有限部积分概念和广义位移基本解，垂直于磁压电双材料界面三维复合型裂纹问题被转 化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而，通过主部 分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后，通过将裂纹表面 位移间断未知函数表达为位移间断基本密度函数与多项式之积，使用有限部积分法对超奇异 积分方程组建立了数值方法. 最后，通过典型算例计算，讨论了广义应力强度因子的变化规 律.     

功能梯度夹层多个环形界面裂纹扭转冲击

研究位于功能梯度层和外部均匀材料之间多个环形界面裂纹的扭转冲击问题,功能梯度材料 (FGM)粘结在两种不同的弹性材料之间，功能梯度层和外部材料之间环形界面裂纹的数目是任意的．引进积分变换和位错密度函数将问题化为求解Laplace域里标准的Cauchy奇异积分方程，进而化为求解代数方程；应用Laplace数值反演技术，计算时域里的动应力强度因子(DSIF)．考查了结构几何尺度和材料特性对裂尖动态断裂特性的影响．数值结果表明，DSIF存在一个主峰，到达主峰后，在其相应的静态值附近波动并最终趋于稳定；增加FGM的梯度能减小DSIF的峰值．     

粘弹性双材料界面裂缝的缝端位移场及动态断裂分析

本文研究的是经常在实际工程中遇到的粘弹性双材料界面裂缝的动断裂问题.由于粘弹性自身的复杂性,使得粘弹性双材料界面裂缝缝端应力的奇异性较弹性呈现出更为复杂的形式,从而使动断裂问题的分析变得更为困难.根据此情况,本文采用复阻尼理论反映粘弹性体的运动规律,用复势理论和平面问题复变函数解答的科洛索夫公式推导了粘弹性双材料界面裂缝缝端位移场及动态应力强度因子的求解公式,利用特解边界元进行了粘弹性双域耦合动力响应计算,按求得的公式用位移外推法计算了单边裂纹板在动荷载作用下的动态应力强度因子.分析了粘性,弹模比和缝长对动态应力强度因子的影响,得出了一些有益的结论.     

功能梯度材料涂层平面运动裂纹分析

研究粘结于均匀材料基底上功能梯度材料涂层平面运动裂纹问题,假设功能梯度材料剪切模量和密度为坐标的指数函数,而泊松比为常数.采用Fourier变换和传递矩阵法将该混合边值问题转化为一对奇异积分方程,通过数值求解奇异积分方程组获得功能梯度材料涂层平面运动裂纹的应力强度因子.考察了结构几何尺寸、裂纹运动速度以及材料梯度参数对运动裂纹的应力强度因子的影响,发现材料梯度参数、结构几何尺寸、裂纹长度以及运动速度均对功能梯度材料动态断裂行为有显著影响.     

Dynamic stress intensity factor of the weak/micro-discontinuous interface crack of a FGM coating

The concepts and classification are brought forth for the strong-discontinuous interface, the weak-discontinuous interface, the micro-discontinuous interface and the all-continuous interface. The mechanical model is established for the dynamic fracture problem of the weak-discontinuous interface between a FGM coating and a FGM substrate. The Cauchy singular integral equation for the crack is derived by integral transform, and the allocation method is used to get the numerical solution. Analysis of the numerical solution indicates that the weak discontinuity is an important factor affecting the SIFs of the interfacial crack. To reduce the weak discontinuity is beneficial to the decrease of the SIFs. Contrast between the solution of the weak-discontinuous interface and that of the micro-discontinuous one shows that the micro-discontinuity is a kind of connection relation of mechanical property better than the weak discontinuity for the coating–substrate structure. To make the interface be micro-discontinuous is helpful to enhance the capacity of the functionally gradient coating–substrate interface to resist dynamic fracture. The first rank micro-discontinuity is enough to reduce the SIFs notably, however, the higher-rank micro-discontinuous terms, which is equal to or higher than the second rank, have less effect on the SIFs. In addition, the thickness of the coating and the substrate and the applied peel stress are also important factors affecting the dynamic SIFs.     

Mechanical modeling and transient anti-plane fracture analysis for the graded inter-diffusion regions in a bonded structure

An inter-diffusion interface model (IDIM) is put forward for a bonded structure. Laplace and Fourier integral transforms are applied to reduce the transient anti-plane fracture problem of the structure as a Cauchy singular integral equation. Lobatto-Chebyshev collocation method and Laplace numerical inversion transform are employed to evaluate transient stress intensity factors (TSIFs). The effects of geometrical and physical parameters on TSIFs are studied. Specially discussed are the influences of the weak/micro-discontinuity of the interfaces. Comparison between IDIM and the graded interlayer model indicates that if the inter-diffusion between the two original materials is prominent, the former should be applied instead of the latter in fracture analyses of bonded structures.     

Dynamic stress intensity factors of two collinear mode-III cracks perpendicular to and on the two sides of a bi-FGM weak-discontinuous interface

The mechanical model was established for the anti-plane dynamic fracture problem for two collinear cracks on the two sides of and perpendicular to a weak-discontinuous interface between two materials with smoothly graded elastic properties, as opposed to a sharp interface with discontinuously changing elastic properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. The integral equations were solved by Erdogan's collocation method and the dynamic stress intensity factors in the time domain were obtained through Laplace numerical inversion proposed by Miller and Guy. The influences of geometrical and physical parameters on the dynamic stress intensity factors were illustrated and discussed, based on which some conclusions were drawn: (a) to increase the thickness of the FGM strip on either side of the interface will be beneficial to reducing the DSIF of a crack perpendicular to a bi-FGM interface and embedded at the center of one of the FGM strips; (b) To increase the rigidity of the FGM strip where the crack is located will increase the DSIF. However, when the material in one side of the interface is more rigid, the DSIF of the interface-perpendicular embedded crack in the other side will be reduced; (c) To decrease the weak-discontinuity of a bi-FGM interface will not necessarily reduce the stress intensity factor of a crack perpendicular to it, which is different from the case of interfacial crack; (d) For two collinear cracks with equal half-length, when the distance between the two inner tips is less than about three times of the half-length, the interaction of them is intensified, however, when the distance is greater than this the interaction becomes weak.     

Effects of the weak/micro-discontinuity of interface on the fracture behavior of a functionally graded coating with an inclined crack

The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed, the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed. It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous combination than “stiffer coating and softer substrate”.     

Dynamic stress intensity factor of a crack perpendicular to the weak-discontinuous interface in a nonhomogeneous coating–substrate structure

A mechanical model was established for the antiplane dynamic fracture problem of a functionally graded coating–substrate structure with a coating crack perpendicular to the weak-discontinuous interface. The problem was reduced to a Cauchy singular integral equation by the methods of Laplace and Fourier integral transforms. Erdogan’s collocation method and the Laplace numerical inversion proposed by Miller and Guy were used to calculate the dynamic stress intensity factors. Three conclusions were drawn through parametric studies: (a) unlike the conclusion drawn for an interfacial crack, reducing the weak discontinuity of the interface will not necessarily decrease the dynamic stress intensity factor (DSIF) of the coating crack perpendicular to the interface; (b) increasing the stiffness of the substrate when that of the coating is fixed, or decreasing the stiffness of coating when that of the substrate is fixed, will be beneficial for the reduction of the DSIF of a coating crack perpendicular to the interface; and (c) the free surface has a greater influence on the DSIF than the interface does, and the effect of the interface on the DSIF is greater than that of the material stiffness in the crack-tip region.     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

拉-拉循环荷载作用下的界面脱粘研究

应用弹性力学和断裂力学基本理论，基于剪滞模型，研究了纤维增强复合材料中纤维与基体界面在拉-拉循环荷载作用下的疲劳脱粘特性。建立了描述疲劳裂纹扩展的等效Paris公式，得到了界面疲劳脱粘扩展速率、脱粘应力以及脱粘界面的摩擦系数与循环加载次数的关系式。通过数值模拟计算，进一步分析了界面疲劳脱粘的力学机理。本文分析，考虑了疲劳加载引起的脱粘界面的损伤及损伤分布的不均匀性。同时还考虑了材料泊松比的影响。     

Anti-plane fracture analysis for the weak-discontinuous interface in a non-homogeneous piezoelectric bi-material structure

The concept of weak discontinuity is extended to functionally graded piezoelectric bi-material interface, and fracture analysis for the weak discontinuous interface is performed by the methods of Fourier integral transform and Cauchy singular integral equation. Numerical results of the total energy release rate (TERR) and the mechanical strain energy release rate (MSERR) are obtained to show the effects of non-homogeneity parameters, geometrical parameters and loads. Parametric studies yield three conclusions: (1) To reduce the weak-discontinuity of the interface is beneficial to resisting interfacial fracture. The effect of the weak-discontinuity of the interface on TERR and MSERR still depends on the strip width. The wider the strip, the more sensitive the TERR and MSERR will be to the weak-discontinuity of the interface. (2) To predict the effect of electric load on crack propagation, MSERR is more appropriate than TERR to be used as a fracture parameter. To predict the effect of mechanical load on crack propagation, both of them could be used as fracture parameters, and MSERR is more conservative. (3) Mechanical load and negative electric displacement load would promote crack propagation, but positive electric displacement load would retard it. For the structure applied by combined mechanical and positive electric displacement loads, crack propagation may be impeded by appropriately selecting the strip width and the ratio of non-homogeneity parameters.     

Dynamic interfacial debonding initiation induced by an incident crack

When a crack propagates towards a weak interface, interface debonding may occur before the incident crack reaches the interface. This phenomenon refers to the “Cook–Gordon mechanism”. In this investigation, an equivalent dynamic Cook–Gordon mechanism is studied both experimentally and analytically. Two strength-based criteria incorporating dynamic fracture mechanics analysis are proposed to predict the initiation location of interface debonding ahead of a dynamic incident crack. As validation, a comparison is made between the analytical predictions and experimental measurements. Results show that the strength-based criteria can effectively predict the initiation of interface debonding. Meanwhile, effects of the stress intensity factor and the T stress of the incident crack, on the interfacial debonding initiation are investigated. It is concluded that high-stress intensity factors of the incident cracks will easily induce interfacial debonding initiation, and changing the T stress is an effective way to control interfacial debonding initiation. Furthermore, high-interfacial tensile strengths rather than shear strengths, tend to suppress interfacial debonding initiation induced by a mode-I incident crack.     

各向异性双材料界面裂纹扩展裂尖场

应用界面断裂力学理论和Stroh方法,研究了广义平面变形下动态裂纹沿着各向异性双材料界面扩展时的裂尖奇异应力及动态应力强度因子.双材料界面的动态裂尖区域特性主要由两个实矩阵W和D确定,且裂尖奇异应力和动态应力强度因子可以由包含这两个矩阵的柯西奇异积分方程确定,同时给出了动态应力强度因子和能量释放率的显示表达式.算例得出当裂纹以小速度扩展时,裂尖振荡因子ε与静态时几乎相同,当界面裂纹扩展速度接近瑞利波速时,ε趋于无穷大;同时得出应力强度因子及能量释放率随裂纹扩展速度的变化关系.