涂层式裂纹监测系统中基体裂纹穿越行为研究

建立了智能涂层的两相模型与三相模型,基于能量准则分别用这两种模型研究了基体裂纹达到涂层界面后的穿越/偏转行为. 用有限元法分析了相对裂纹扩展长度、弹性错配参数及界面层厚度对偏转裂纹与穿越裂纹能量释放率之比的影响,结果表明当基体裂纹到达驱动层与基体界面时,能量释放率之比不仅与基体和驱动层之间的弹性错配相关,而且当驱动层较薄时对驱动层与传感层之间的弹性错配亦有较强的依赖性. 此外,随着驱动层厚度的增加,能量释放率之比对驱动层与传感层之间的弹性错配的依赖性逐渐降低. 通过与实验结果相比,建立的模型能够较好的解释基体裂纹在界面的扩展行为,可用于智能涂层裂纹传感器的优化设计.      

Effect of crack position on stress intensity factor in particle-reinforced metal-matrix composites

In this study, a numerical model was developed to study the effects of mechanical properties of the particle and matrix materials, the crack position (in particle/in matrix) and loading conditions (mode 1 and mixed-mode) in particle-reinforced metal-matrix composites. The finite element technique was used to calculate the stress intensity factors for crack at and near-interface. The Displacement Correlation Method was used to calculate the stress intensity factors K₁ and K₂. In the present model, the particle and matrix materials were modeled in linear elastic conditions. The interface crack was considered between the particle and matrix, without the presence of the interface. For near-interface crack problem, two different crack positions (in particle/in matrix) were selected. The obtained results show the key role on the stress intensity factors played by the relative elastic properties of the particle and matrix. The results also show that loading condition has an important effect on the K₂ stress intensity factor and the crack deflection angle.     

Asymptotic solutions for buckling delamination induced crack propagation in the thin film-compliant substrate system

In a thin film-substrate system in-plane compressive stress is commonly generated in the film due to thermal mismatch in operation or fabrication process. If the stress exceeds a critical value, part of the film may buckle out of plane along the defective interface. After buckling delamination, the interface crack at the ends may propagate. In the whole process, the compliance of the substrate compared with the film plays an important role. In this work, we study a circular film subject to compressive stress on an infinitely thick substrate. We study the effects of compliance of the substrate by modeling the system as a plate on an elastic foundation. The critical buckling condition is formulated. The asymptotic solutions of post-buckling deformation and the corresponding energy release rate of the interface crack are obtained with perturbation methods. The results show that the more compliant the substrate is, the easier for the film to buckle and easier for the interface crack to propagate after buckling.     

Boundary element analysis of cracked film–substrate media

This study evaluates the stress behavior of a cracked film–substrate medium by applying the multi-region boundary element method. Four problems addressed herein are the crack tip within a film, the crack tip terminating at the interface, interface debonding, and the crack penetrating into the substrate. The multi-region boundary element method is initially developed and, then, the stress intensity factors or the energy release rates are evaluated according to the different stress singularities of the four considered problems. These results indicate that the stress intensity factors or the energy release rates of the four problems rely not only on the different elastic mismatches and crack lengths, but also on the thickness ratio of the film and the substrate.     

The role of constraint in the fields of a crack normal to the interface between elastically and plastically mismatched solids

Asymptotic solutions are presented for a stationary crack normal to the boundary between two elastically mismatched solids such that the crack tip is located at the interface. The second-order term in the elastic asymptotic expansion was determined as a function of elastic mismatch for a thin cracked film on a substrate and for a thin cracked lamina between two substrates. Elastic-plastic analysis was performed using both modified boundary layer formulations and full field analyses. Analytic and numerical solutions in small strain yielding identify elastic mismatch and the T-stress as the determinants of crack tip constraint. The effect of constraint on the competition between interface failure and penetration is discussed.     

Fracture analysis on a piezoelectric sensor with a viscoelastic interface

Fracture analysis is performed on a layered piezoelectric sensor possessing a Kelvin-type viscoelastic interface. An electrically permeable anti-plane crack is situated in the piezoelectric layer and perpendicular to the interface. The crack problem is solved by the methods of integral transform and Cauchy singular integral equation. The variations of the dynamic stress intensity factor (DSIF) vs. physical and geometrical parameters are investigated. At the beginning of creep and relaxation, larger viscosity coefficient always induces smaller DSIF. With time elapsing, the effect of viscosity coefficient becomes weaker and weaker. When time approaches infinity, the viscous effect disappears, and the DSIF converges to a value corresponding to the case of an elastic interface. The effect of the viscoelastic interface on the fracture behavior of the piezoelectric layer also depends on the substrate thickness. To some extent, thicker substrate may intensify the effect of the interface.     

工作电压对N36锆合金表面微弧氧化涂层磨蚀性能的影响

通过微弧氧化(MAO)设备在锆(Zr)合金表面制备氧化陶瓷涂层. 研究工作电压对Zr合金表面MAO涂层形貌、硬度、粗糙度、元素分布和相结构的影响. 分析工作电压对Zr合金表面MAO涂层腐蚀和磨蚀性能的影响. 结果表明:MAO涂层表面具有典型的多孔和火山熔融特征,主要由m-ZrO₂和t-ZrO₂相组成. MAO涂层的粗糙度比基体高,且在电压为340 V时的粗糙度最高,达到1.36 μm. MAO涂层可分为内层致密层和外层多孔层,涂层厚度随着工作电压的增加而增加,厚度为5~9 μm. 电压为260 V的MAO涂层的结合强度最高,达到44.3 N. MAO涂层相比较于基体具有更好的耐腐蚀性能,电压为260 V的MAO涂层具有最高的自腐蚀电位(?0.205 V)和最低的腐蚀电流密度(6.24×10?9 A/cm2). 这是因为电压为260 V的MAO涂层具有最致密的结构,而内层致密层可以阻碍腐蚀液进入基体. MAO涂层的主要磨损机理为磨粒磨损和氧化磨损. 工作电压为260 V的MAO涂层的磨损率仅为Zr合金基体的1/4.      

Evaluation of fracture mechanics parameters for free edges in multi-layered structures with weak singularities

This study focuses on the stress intensity factors for free edges in multi-layered structural components. The effects of elastic constants of various material combinations on the weak singularity at free edges are analyzed. Using the H-integral approach, the effects of elastic mismatch parameters, the bond area and the thickness of the thin metal layer on the stress intensity factor are quantified and the results are compared with detailed finite element solutions. A good agreement between numerical predictions obtained from the H-integral and the detailed FE results is achieved, showing the applicability of this approach. Similar to a crack problem, the singular elastic field dominates in an annular region adjacent to the notch tip. The relationship between the valid range of the K-dominated field and the thin-film thickness is then demonstrated. Furthermore, the competition of crack initiation between the free edge interface (180° opening angle) and a 90° notch interface in a generic specimen is investigated, in order to find out which is the prevailing failure mode. Comparison between isotropic Si and anisotropic Si substrate is also illustrated. Anisotropy of the Si substrate has a significant influence on the stress intensity factor when combined with an Au or Al metal layer but not with a Cu layer. Additionally, standardized numerical formulae of the dimensionless stress intensity factor have been derived to guide the engineering application.     

CRACK PROPAGATING IN FUNCTIONALLY GRADED COATING WITH ARBITRARILY DISTRIBUTED MATERIAL PROPERTIES BONDED TO HOMOGENEOUS SUBSTRATE

In this paper, a finite crack with constant length （Yoffe type crack） propagating in a functionally graded coating with spatially varying elastic properties bonded to a homogeneous substrate of finite thickness under anti-plane loading was studied. A multi-layered model is employed to model arbitrary variations of material properties based on two linearly-distributed material compliance parameters. The mixed boundary problem is reduced to a system of singular integral equations that are solved numerically. Some numerical examples are given to demonstrate the accuracy, efficiency and versatility of the model. The numerical results show that the graded parameters, the thicknesses of the interfacial layer and the two homogeneous layers, the crack size and speed have significant effects on the dynamic fracture behavior.     

Interfacial Energies for Incoherent Inclusions

We study a variational problem describing an incoherent interface between a rigid inclusion and a linearly elastic matrix. The elastic material is allowed to slip relative to the inclusion along the interface, and the resulting mismatch is penalized by an interfacial energy term that depends on the surface gradient of the relative displacement. The competition between the elastic and interfacial energies induces a threshold effect when the interfacial energy density is non-smooth: small inclusions are coherent (no mismatch); sufficiently large inclusions are incoherent. We also show that the relaxation of the energy functional can be written as the sum of the bulk elastic energy functional and the tangential quasiconvex envelope of the interfacial energy functional.     

The roles of toughness and cohesive strength on crack deflection at interfaces

In order to design composites and laminated materials, it is necessary to understand the issues that govern crack deflection and crack penetration at interfaces. Historically, models of crack deflection have been developed using either a strength-based or an energy-based fracture criterion. However, in general, crack propagation depends on both strength and toughness. Therefore, in this paper, crack deflection has been studied using a cohesive-zone model which incorporates both strength and toughness parameters simultaneously. Under appropriate limiting conditions, this model reproduces earlier results that were based on either strength or energy considerations alone. However, the general model reveals a number of interesting results. Of particular note is the apparent absence of any lower bound for the ratio of the substrate to interface toughness to guarantee crack penetration. It appears that, no matter how tough an interface is, crack deflection can always be induced if the strength of the interface is low enough compared to the strength of the substrate. This may be of significance for biological applications where brittle organic matrices can be bonded by relatively tough organic layers. Conversely, it appears that there is a lower bound for the ratio of the substrate strength to interfacial strength, below which penetration is guaranteed no matter how brittle the interface. Finally, it is noted that the effect of modulus mismatch on crack deflection is very sensitive to the mixed-mode failure criterion for the interface, particularly if the cracked layer is much stiffer than the substrate.     

Scattering of love waves by an interface crack between a piezoelectric layer and an elastic substrate

The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration. Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China.     

界面裂纹问题中的弹性T项和应力强度因子

研究两相材料有限板含单边界面裂纹的断裂力学特性，对不同的材料组合用广义变分法分析了不同尺寸试件和裂纹长度下的应力强度因子和弹性T项，讨论了材料特性对应力强度因子和弹性T项的作用．分析了试件尺寸和裂纹长度对应力强度因子和弹性T项的影响．     

复合材料层合板低速冲击损伤分析的连续介质损伤力学模型

针对复合材料层合板低速冲击损伤问题,提出了一种各向异性材料连续介质损伤力学模型,模型涵盖损伤表征、损伤起始判定和损伤演化法则3 个方面. 通过材料断裂面坐标下的损伤状态变量矩阵完成损伤表征,并考虑断裂面角度的影响,建立了主轴坐标系下的材料损伤本构关系. 损伤起始由卜克(Puck) 失效准则预测,损伤演化由断裂面上的等效应变控制,服从基于材料应变能释放的线性软化行为. 模型区分了纤维损伤和基体损伤,并根据冲击载荷下层内产生多条基体裂纹继而扩展至界面形成层间裂纹(分层) 的试验观察,引入基体裂纹饱和密度参数表征层间分层. 以[0₃/45/-45]_S 和[45/0/-45/90]_4S 两种铺层的复合材料层合板为例,预测了不同冲击能量下复合材料层合板的低速冲击损伤响应参数,试验结果证明了连续介质损伤力学模型的有效性.模型在不同网格密度下的计算结果表明单元特征长度的引入可以在一定程度上降低损伤演化阶段对网格密度的依赖性.      

黏弹性界面断裂分析的增量“加料”有限元法

提出了一种适用于黏弹性界面裂纹问题的增量“加料” 有限元方法. 利用弹性界面裂纹尖端位移场的解答,通过对应原理和拉普拉斯逆变换近似方法,得到了黏弹性界面裂纹的尖端位移场. 用该位移场构造了黏弹性界面裂纹“加料” 单元和过渡单元位移模式,推导了增量“加料” 有限元方程,求解有限元方程可获得应力强度因子和应变能释放率等断裂参量. 建立了典型黏弹性界面裂纹平面问题“加料” 有限元模型,计算结果表明,对于弹性/黏弹性界面裂纹和黏弹性/黏弹性界面裂纹,该方法都能得到相当精确地断裂参量,并能很好地反映蠕变和松弛特性,可推广应用于黏弹性界面断裂问题的计算分析.      

The fracture mechanics of slit-like cracks in anisotropic elastic media

U method of continuously distributed dislocations, the problem of a slit-like crack in an arbitrarily-anisotropic linear elastic medium stressed uniformly at infinity is formulated and solved. The crack faces may be either freely-slipping or loaded by arbitrary equal and opposite tractions. If there is no net dislocation content in the crack, then the tractions and stress concentrations on the plane of the crack are independent of the elastic constants and the anisotropy; the same is true of the elastic stress intensity factors. The crack extension force depends on anisotropy only through the inverse matrix elements K _mg⁻¹, where [K] is the pre-logarithmic energy factor matrix for a single dislocation parallel to the crack front. Numerical results for crack extension forces are presented for three media of cubic symmetry.     

Moving interfacial crack between piezoelectric ceramic and elastic layers

An analysis is performed for the problem of a finite Griffith crack moving with constant velocity along the interface of a two-layered strip composed of a piezoelectric ceramic and an elastic layers. The combined out-of-plane mechanical and in-plane electrical loads are applied to the strip. Fourier transforms are used to reduce the problem to a pair of dual integral equations, which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic stress intensity factor(DSIF) is determined, and numerical results show that DSIF depends on the crack length, the ratio of stiffness and thickness, and the magnitude and direction of electrical loads as well as the crack speed. In case that the crack moves along the interface of piezoelectric and elastic half planes, DSIF is independent of the crack speed.     

ELASTO-PLASTIC BRANCHED ANALYSIS FOR AN INTERFACE CRACK BASED ON CRACK ENERGY DENSITY

The elasto-plastic finite element analyses for an interface crack indissimilar material,based on the crack energy density(CED)concept,are investigatedin mode Ⅰ loading condition.It is confirmed that the values of CED almost remainstable when the notch radius ρ is sufficiently small,both in elastic and elasto-plasticcase.Numerical results for both elastic and elasto-plastic cases show that under themode Ⅰ loading condition,when the crack propagates to the more stiff material with asmall angle,the total CED will become larger than that along the interface.If thecrack heads into the more compliant material,the CED will become less than that alongthe interface.     

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation

This paper presents an analysis of a single vertical crack and periodically distributed vertical cracks in an epitaxial film on a semi-infinite substrate where the cracks penetrate into the substrate. The film and substrate materials have different anisotropic elastic constants, necessitating Stroh formalism in the analysis. The misfit strain due to the lattice mismatch between the film and the substrate serves as the driving force for crack formation. The solution for a dislocation in an anisotropic trimaterial is used as a Green function, so that the cracks are modeled as the continuous distributions of dislocations to yield the singular integral equations of Cauchy-type. The Gauss–Chebyshev quadrature formula is adopted to solve the singular integral equations numerically. Energy arguments provide the critical condition for crack formation, at which the cracks are energetically favorable configurations, in terms of the ratio of the penetration depth into the substrate to the film thickness, the ratio of the spacing of the periodic cracks to the film thickness, and the generalized Dundurs parameters between the film and substrate materials.     

Cracking in thin multi-layers with finite-width and periodic architectures

Many applications involve thin multi-layers comprised of repeating patterns of different material sections, notably interconnect–dielectric structures in microelectronics. This paper considers a variety of failure scenarios in systems with periodically arranged features within a single layer. Crack driving forces are presented for (i) debonding between alternating material sections in a thin film (i.e. channel and tunnel cracking at material junctions), and (ii) channel cracking in a thin uniform coating above a layer comprised of alternating sections of different materials. The effects of elastic mismatch, feature spacing, crack spacing and residual stress are illustrated for a wide range of parameters. The results presented here illustrate that residual stresses in intact sections can strongly promote cracking in adjacent layers, which is in contrast to analyses of blanket film multi-layers which predict that residual stress in adjacent layers has no effect. An important finding is that decreasing the relative size of low-modulus sections significantly increases the crack driving force in adjacent layers. The implications of these results are discussed in the contexts of critical feature spacing and the impact of incorporating low elastic-modulus sections (such as polymer dielectrics) on thermo-mechanical reliability.