A Robust <Emphasis Type="Italic">in situ</Emphasis> TEM Experiment for Characterizing the Fracture Toughness of the Interface in Nanoscale Multilayers

A novel in situ transmission electron microscopy (TEM) bending method using a nano-cantilever specimen that includes a naturally sharp pre-crack at the interface between a 500 nm-thick SiN layer and a 200 nm-thick Cu layer on a Si substrate is developed in order to precisely characterize the fracture toughness of the interface in nanoscale multilayers. By fabricating a perpendicular nanoscale notch in the SiN layer close to the horizontal Cu/SiN interface, a sharp pre-crack is successfully introduced at the Cu/SiN interface. In addition, by changing the relative position of the notch with respect to the fixed end of the specimen, both the instant and continuous interface crack propagation behaviors could be in situ observed using TEM. Finite element analysis shows that the crack propagation from the sharp pre-crack is dominated by a singular stress field within a region 100 nm from the crack tip under a mixed-mode state in all specimens. On the other hand, the fracture toughness represented by the critical energy release rate for the start of crack propagation along the Cu/SiN interface in all specimens is determined through a compliance method and shows good agreement with an average value of 7.1 J/m². This indicates the robust reliability and high precision for characterizing the fracture toughness of the interface in nanoscale multilayers.     

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.     

纳米悬臂梁Si/Cu界面破坏的弹塑性内聚力模拟

实验测试表明[Thin Solid Films 516: 1925-1930],纳米悬臂梁Si/Cu/SiN/Pt/C在弯曲载荷作用下发生沿Si/Cu界面的分层破坏,其载荷—位移曲线表现出明显的非线性行为。本文基于连续介质力学模型,对该实验观察到的界面裂纹萌生和沿界面扩展过程进行了数值模拟计算与分析。模拟计算中,采用指数型内聚力来表征Si/Cu界面本构关系,对Cu薄层分别按照线弹性和遵守Ramberg-Osgood型弹塑性本构关系来处理。通过与实验结果校准的方法,确定了该纳米悬臂梁中Si/Cu界面的结合强度诸参数。研究发现,内聚强度和内聚能是该内聚力模型的主导性参数;Cu薄膜层遵从线弹性本构关系更为适合于描述Si/Cu界面的分层破坏;与块体材料相比,纳米尺寸的Cu材料表现出很高的屈服应力和硬化指数,因此在整个过程中产生的塑性变形很小,这与前述的实验结果是一致的。     

Stress intensity factors for interface crack in finite size specimen using a generalized variational approach

A generalized variational approach together with eigenfunction expansion is applied to determine the stress intensity factors for interface crack in finite size specimen. Application is also made of the complex potentials such that a complex stress intensity factor with components corresponding to the Mode I and II stress intensity factors can be identified with one of the leading coefficients in the eigenfunction expansion. Obtained are the numerical values of the stress intensity factors for an interface edge crack in a bimaterial rectangular specimen. The outside boundary is subjected to uniform stress normal and parallel to the crack. Solutions are also obtained for the same crack aand specimen geoinetry is subjected to a pair of equal and opposite concentrated forces along the open end away from the edge crack. The third example pertains to the case of three-point bending where the centre concentrated load is directed along the interface dividing the two materials. Numerical results are obtained for four different combinations of the bimaterial specimen with an interface edge crack.     

Stress intensity factors and crack initiation directions for ceramic/metal joint

Four points bending tests for Si₃N₄/Cu/S45C joint specimen showed that the bending strengths depend on the residual stresses that originated from joining process. The residual thermal stresses caused an edge sub-interface crack to initiate in the ceramic. The stress intensity factors (SIFs) of the edge sub-interface crack located at distance h from the interface with or without interlayer metal were calculated by the Green's function obtained from a finite element analysis. The crack path at the joint specimen under four points bending loading with the influence of residual stresses was also evaluated by the maximum tensile stress criterion. Finally the effect of residual stress on the crack path was found numerically; the interlayer metal decreases the deflection angle of crack from interface by reducing the residual stress.     

有限元模拟TIN 膜/碳钢基材体系的摩擦磨损试验

对TiN膜/碳钢基材体系摩擦磨损过程的有限元模拟表明:磨痕边缘的多种应力集中、磨痕内外的张应力、膜/基界面切应力,都将影响体系的摩擦学行为.用销/盘试验验证了有限元模拟结果,根据对膜层中裂纹的萌生、扩展和体系的损伤、破坏情况分析,摩擦磨损过程分为磨合、稳定磨损、膜层失稳、体系失效阶段.提出了小载荷摩擦磨损下过软基材的膜/基体系失效机制,即膜层在集中应力和张应力作用下发生裂纹萌生和扩展的脆性破坏,其中,由于体系变形引起的磨痕边缘应力集中对膜层早期损伤进而导致体系磨损失效具有最重要作用.     

Application of bimaterial interface corner failure mechanics to silicon/glass anodic bonds

Motivated by the existence of a universal singular stress field at bimaterial interface corners, a fair amount of work has been performed to support the use of the corresponding critical stress intensities to correlate fracture initiation. The approach is in the spirit of interface fracture mechanics but applicable to a different class of problems, specifically, when a crack does not previously exist (or cannot be detected, at least economically), and when subsequent crack propagation does not necessarily occur along the interface. Here we further progress toward the development, understanding, and application of the approach, both experimentally and theoretically, for a series of silicon/glass anodically bonded structures. To this end we designed and fabricated two series of silicon/glass anodically bonded bimaterial specimens with different interface corner geometries that commonly arise from different silicon etching technologies. Offset three-point flexure tests were performed that resulted in brittle fracture that initiated at the interface corner. From a rigorous stress analysis at the interface corner, we determined the order of the stress singularities and the angular variation of the stress fields. We computed the corresponding stress intensities via full-field finite element analyses of the silicon/glass specimens loaded in offset three-point flexure. Measured fracture data show that although the failure stress varies significantly with bond size, the corresponding critical stress intensity of the dominant mode is constant, thus providing support for its use as a fracture initiation criterion. In the light of both the stress analysis and the measured fracture data, we discuss the effect of mode mixity (loosely shearing versus opening) and show that it has little influence on the results for the specimens and loading considered in this study. Via an idealized model of a small crack, either interfacial or extending into one of the adherends, we study the effects of geometrical perturbations at the interface corner on the stress state, and discuss implications for fracture analysis and interpretation of fracture data. We also explore the prediction of the crack initiation angle and achieve reasonable success with a simple criterion based on the maximum circumferential stress near the uncracked interface corner.     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

High-order asymptotics and perturbation problems for 3D interfacial cracks

We present an asymptotic algorithm for analysis of a singularly perturbed problem in a domain containing an interfacial crack. The crack is assumed to be flat and its front, initially straight, is perturbed in the plane containing the crack. The aim of the work is to determine the asymptotic representation of the stress-intensity factors near the edge of the crack. Mathematically, the limit problem is reduced to the analysis of a matrix, 3×3, Wiener-Hopf problem, and its solution generates the “weight matrix-function” characterised by a special singular solution near the crack edge. The two-term asymptotic representation for the weight function components is required by the asymptotic algorithm, together with two-term asymptotics for stress components associated with the physical fields near the edge of the crack. The particular feature of the solution is the coupling between the normal opening mode (Mode-I), and the shear modes (Mode-II and Mode-III), and the oscillatory behaviour of certain stress components near the crack edge. Explicit asymptotic formulae for the stress-intensity factors are obtained at the edge of a “wavy crack” at an interface.     

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.     

Empirical assessment of ductile fracture initiation in steel bars with notch and three-point bend specimen with edge crack

Proposed is a parameter defined to characterize the onset of macrocrack initiation in notched steel bars and cracked three-point bend specimens. It accounts for stress triaxiality and damage by plasticity reflected via the effective plastic strain. Results are obtained for notched round bars made of 20#, A3, DE36I and DE36II steel by assuming that the stress triaxiality increases with increasing effective plastic strain; they are compared with the results by letting the stress triaxiality to be constant. Use are made of experimental data on the necking of tensile bars. The parameter corresponding to the onset of ductile fracture were found to be nearly constant. Since the local effective plastic stress can be related to the crack tip opening (COD) distance, the same procedure can be applied to evaluate fracture initiation in three-point bend specimens with an edge crack. It is found that the COD in AS1204-350 and AS1405-180 structural steels decreased with increasing stress triaxiality.     

Failure instability of a debonded interface in the presence of a main crack

The problem of fracture initiating from an edge crack in a nonhomogeneous beam made of two dissimilar linear elastic materials that are partially bonded along a common interface is studied by the strain energy density theory. The beam is subjected to three-point bending and the unbonded part of the interface is symmetrically located with regard to the applied loading. The applied load acts on the stiffer material, while the edge crack lies in the softer material. Fracture initiation from the tip of the edge crack and global instability of the composite beam are studied by considering both the local and global stationary values of the strain energy density function, dW/dV. A length parameter l defined by the relative distance between the maximum of the local and global minima of dW/dV is determined for evaluating the stability of failure initiation by fracture. Predictions on critical loads for fracture initiation from the tip of the edge crack, crack trajectories and fracture instability are made. In the analysis the load, the length of the edge crack and the length and position of the interfacial crack remained unchanged. The influence of the ratio of the moduli of elasticity of the two materials, the position of the edge crack and the width of the stiffer material on the local and global instability of the beam was examined. A general trend is that the critical load for crack initiation and fracture instability is enhanced as the width and the modulus of elasticity of the stiffer material increase. Thus, the stiffer material acts as a barrier in load transfer.     

A Peierls perspective on mechanisms of atomicfriction

Stick-slip behavior observed from nanoscale asperity friction experiments are often modeled by the one-degree-of-freedom Tomlinson model, which is unable to explain the effects of lattice structure and interface defects, or by molecular simulations which suffer temporal limitations in modeling the velocity- and temperature-dependent frictional behavior. A Peierls-type model developed in this work views the atomic frictional process as the initiation and gliding passage of dislocations with diffused cores on the interface. As a consequence of loss-of-ellipticity instability, the occurrence of stick-slip behavior relies on the interaction among interface slip field, contact stress fields, and existing defects. The friction stress for commensurate interface under large contact area can be approximated from the Rice model of screw-dislocation nucleation from a planar crack tip. The spatially inhomogeneous nature of rate-limiting processes and the coupling effects between contact size and interface incommensurability are successfully determined, which cannot otherwise be tackled in the Tomlinsonmodel.     

Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion

Dislocation mobility and stability in inclusions can affect the mechanical behaviors of the composites. In this paper, the problem of an edge dislocation located within a nanoscale cylindrical inclusion incorporating interface stress is first considered. The explicit expression for the image force acting on the edge dislocation is obtained by means of a complex variable method. The influence of the interface effects and the size of the inclusion on the image force is evaluated. The results indicate that the impact of interface stress on the image force and the equilibrium positions of the edge dislocation inside the inclusion becomes remarkable when the radius of the inclusion is reduced to nanometer scale. The force acting on the edge dislocation produced by the interface stress will increase with the decrease of the radius of the inclusion and depends on the inclusion size which differs from the classical solution. The stability of the dislocation inside a nanoscale inclusion is also analyzed. The condition of the dislocation stability and the critical radius of the inclusion are revised for considering interface stresses.     

Stress intensity factors for an edge interface crack in a bonded semi-infinite plate for arbitrary material combination

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary crack lengths and material combinations. In this paper the stress intensity factors of an edge interface crack in a bonded strip are considered under tension with varying the crack length and material combinations systematically. Then, the limiting solutions are provided for an edge interface crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge interface crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results.     

界面端附近裂纹的应力强度因子

结合材料的断裂形式可分为从界面端产生裂纹（沿界面或向母材内部层折）然后断裂与稍稍离开界面端处产生裂纹然后断裂这两种情况，在金属／陶瓷类结合材料中，后者出现的概率更大，本文利用结合材料界面端的奇异应力场和叠加原理，给出了界面端附近裂纹的应力强度因子近似计算公式，并用边界元数值计算验证了其有效性。     

SINGLE AND DOUBLE EDGE INTERFACE CRACK SOLUTIONS FOR ARBITRARY FORMS OF MATERIAL COMBINATION

In this paper interfacial edge crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge interface crack in a bonded strip are newly obtained and compared with those of a single-edge interface crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative crack lengths. Different from the case of a cracked homogeneous strip, the results for the double edge interface cracks are found to possibly be bigger than those for a single edge interface crack under the same relative crack length.     

平面幂律塑性Ⅰ型裂纹尖端应力场全解

在航空航天、船舶、石油管道和核电等领域,服役结构或部件在长期极端条件下运行,不可避免地会产生裂纹,因此,为研究含裂纹结构的准静态断裂行为,必须了解裂纹尖端附近区域的应力应变场特点.对于幂律材料裂纹构元,研究平面应变和平面应力条件下Ⅰ型裂纹尖端应力场的解析分布.基于能量密度等效和量纲分析,推导了能量密度中值点代表性体积单元(representative volume element, RVE)的等效应力解析方程,并定义其为应力因子,进而针对有限平面应变和平面应力紧凑拉伸(compact tension, CT)试样和单边裂纹弯曲(single edge bend, SEB)试样,以应力因子作为应力特征量,并构造用于表征裂尖等效应力等值线的蝶翅轮廓式和扇贝轮廓式三角特殊函数,提出描述幂律塑性条件下平面I型裂纹尖端应力场的半解析模型.该半解析模型形式简单,对CT和SEB试样的裂尖应力场的预测结果与有限元分析的结果比较表明,两者之间均密切吻合,模型公式可直接用于预测Ⅰ型裂纹尖端应力分布,方便于断裂安全评价和理论发展.     

Stress intensity factor for an edge crack in two bonded dissimilar materials under convective cooling

The transient thermal stress crack problem for two bonded dissimilar materials subjected to a convective cooling on the surface containing an edge crack perpendicular to the interface is considered. The problem is solved using the principle of superposition and the uncoupled quasi-static thermoelasticity. The crack problem is formulated by applying the transient thermal stresses obtained from the uncracked medium with opposite sign on the crack surfaces to be the only external loads. Fourier integral transform is used to solve the perturbation problem resulting in a singular integral equation of Cauchy type in which the derivative of the crack surface displacement is the unknown function. The numerical results of the stress intensity factors are calculated for both the edge crack and the crack terminating at the interface using two different composite materials and illustrated as a function of time, crack length, coefficient of heat transfer, and the thickness ratio.     

基于神经网络的界面裂纹尖端场分析

通过构造反向传播神经网络,对裂纹尖端的应力场进行模拟,进而实现对裂纹尖端应力场甬数的逼近。得到的网络具有较高的联想、记忆能力和相当的稳定性,并且可以快速、准确地得到带裂纹构件的裂纹尖端应力场,从而确定裂纹尖端的塑性区和分析裂纹的扩展。数值计算给出了LY12-CZ材料裂纹扩展方向的计算结果,与实验结果吻合较好,还给出了两相材料含界面裂纹在复合型载荷作用下的塑性区形状的变化情况,并对两相材料含界面裂纹在复合型载荷作用下裂纹的扩展方向进行了预测。