A non-contact, thermally-driven buckling delamination test to measure interfacial fracture toughness of thin film systems

Interfacial fracture toughness measurements of thin film-substrate systems are of importance in many applications. In the microelectronics industry, the interfacial adhesion between the dielectric-barrier-metal layers on a semiconductor chip is critical for chip reliability. In this paper, we propose a thermally-driven patterned buckling delamination test that does not use a pre-existing weak interface. The test relies on causing a patterned film to debond from its substrate by inducing a compressive stress due to heating of the film on a thick silicon substrate. The compressive stress causes the film to buckle and debond from the substrate. A model for the propagation of the buckling-induced debond is then developed to estimate interfacial fracture toughness. The efficacy of the thermally-driven buckling test is demonstrated on a model Al/SU8/Si film-substrate system wherein the Al film debonds along its interface to SU8. The interfacial toughness of the Al/SU8 interface is estimated using the proposed test and is compared to the toughness for the same system obtained using an alternative test with a weakened interface to validate the developed elastic-plastic model for buckling-induced debond propagation.     

Numerical simulation of fatigue‐driven delamination using interface elements

This paper presents a computational technique for the prediction of fatigue‐driven delamination growth in composite materials. The interface element, which has been extensively applied to predict delamination growth due to static loading, has been modified to incorporate the effects of cyclic loading. Using a damage mechanics formulation, the constitutive law for the interface element has been extended by incorporating a modified version of a continuum fatigue damage model. The paper presents details of the fatigue degradation strategy and examples of the predicted fatigue delamination growth in mode I, mode II and mixed mode I/II are presented to demonstrate that the numerical model mimics the Paris law behaviour usually observed in experimental testing. Copyright © 2005 John Wiley & Sons, Ltd.     

Measurement of fracture toughness of anode used in Solid Oxide Fuel Cell

Reliability prediction and design of multi-layered structure necessitates the knowledge of the mechanical properties of the individual layers, in particular fracture toughness. To measure fracture toughness of typical anode, composed of 60 wt.% NiO and 40 wt.% 3YSZ (60:40 Ni-YSZ) used in Solid Oxide Fuel Cell (SOFC), controlled buckling test was used. A simple set-up was made where a compressive strain was applied on a thin substrate supporting the anode. Both curvature and film strength are calculated from the applied strain, elastic modulus and geometric dimension of the sample. The fracture toughness is calculated to be .     

Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues

The finite element analysis of delamination in laminated composites is addressed using interface elements and an interface damage law. The principles of linear elastic fracture mechanics are indirectly used by equating, in the case of single‐mode delamination, the area underneath the traction/relative displacement curve to the critical energy release rate of the mode under examination. For mixed‐mode delamination an interaction model is used which can fulfil various fracture criteria proposed in the literature. It is then shown that the model can be recast in the framework of a more general damage mechanics theory. Numerical results are presented for the analyses of a double cantilever beam specimen and for a problem involving multiple delamination for which comparisons are made with experimental results. Issues related with the numerical solution of the non‐linear problem of the delamination are discussed, such as the influence of the interface strength on the convergence properties and the final results, the optimal choice of the iterative matrix in the predictor and the number of integration points in the interface elements. Copyright © 2001 John Wiley & Sons, Ltd.     

A three-dimensional finite element analysis of interface delamination in a ductile film/hard substrate system induced by wedge indentation

Interface delamination and arching of a ductile thin film on a hard substrate subject to microwedge indentation were investigated systematically using a three-dimensional finite element method. A traction-separation law was introduced to simulate the cohesion and failure behavior of the interface between the film and the substrate. The effects of the interface strength and the length of the microwedge indenter on the onset and growth of interface delamination and film arching were analyzed. It was shown that a two-dimensional to three-dimensional transition of stress state occurs during indentation, depending on the indenter length and indentation depth. Conditions for using two-dimensional and three-dimensional models were suggested.     

锌漆薄膜/钢基底系统界面断裂韧性的试验与模拟

以锌漆薄膜与304不锈钢基底之间的界面裂纹为研究对象,采用声发射与显微镜实时检测技术与三点弯曲试验相结合的方法,测量了锌漆涂层的界面断裂韧性。同时将界面裂纹长度的有限元模拟结果和实验结果相比较,结果较为吻合。通过ABAQUS有限元模拟发现,界面断裂韧性与多种影响因素有关,界面裂纹扩展长度随薄膜厚度和外荷载的增加而增加,随界面断裂韧性和薄膜弹性模量的增大而减小,而泊松比对其影响不大。     

Influence of substrate compliance on buckling delamination of thin films

A thin film subject to in-plane compressive stress is susceptible to buckling-driven delamination. This paper analyzes a straight-sided delamination buckle with a focus on the effects of substrate compliance, following earlier work by B. Cotterell and Z. Chen. The critical buckling condition, the energy release rate and the mode mix of the interface delamination crack are calculated as a function of the elastic mismatch between the film and substrate. The average energy release rate at the curved end of a tunneling straight-sided blister is also determined. The more compliant the substrate, the easier for the film to buckle and the higher the energy release rates. The effect becomes significant when the modulus of the substrate is appreciably less than that of the film. When the substrate modulus is comparable to that of the film, or higher, the usual assumption is justified to the effect that the film is clamped along its edges. When the substrate is very compliant the energy release rate at the curved front exceeds that along the straight sides.     

Mode I delamination toughness of laminated composites with through-thickness reinforcement

Through-thickness reinforcement is an effective way to suppress delamination in laminated composites. Micromechanics based models are developed to study the effect of through-thickness reinforcement (stitching) in improving the Mode I delamination crack growth resistance of laminated composites. In the development of these models, two types of stitch geometries are considered. In the first case, the stitches are assumed disconnected as in many cases the top and the bottom surfaces of the stitched laminates are ground off to remove surface in-plane waviness caused by stitching loops. The force in the stitches in this case is estimated from frictional bonding between stitches and the matrix. In the second case, interconnected stitches are considered and the force carried by the stitches is modelled as Winkler elastic foundation type of stress-separation relation. The effect of stitches is expressed in terms of a single stitching parameter Gl or Gb and closed form analytical expressions for the crack-growth resistance (K _R (a)) are obtained. The effects of the stitching parameter and various geometric and material properties are examined.On leave at the Department of Mechanical Engineering, Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong.     

A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens

A concise constitutive law for cohesive interfaces is proposed in this paper. A new state variable is introduced to track the extent of damage accumulated at the interface. The constitutive equations not only account for mixed‐mode delamination propagation in composite materials, but also satisfactorily deal with mode ratio change during the debonding process. The interface model is implemented in the LS‐DYNA explicit finite element code. The model has been applied to scaled open hole tension tests on laminated composite material. Comparison between numerical results and experiments shows good correlation for failure modes and strengths for a range of different specimen sizes. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation into the mixed-mode delamination growth in unidirectional T800/924C laminates

This study presents the results of experimental investigations and numerical simulation on mixed-mode I/II delamination growth initiated from an artificial transverse notch. Specimens made of unidirectional carbon fiber epoxy (T800/924C) composite have been tested under three-point-bend condition. A finite element procedure has been introduced to model 3-D stable delamination growth in the specimen to generate numerical growth data including loads, displacements, delamination lengths, and the growing crack front shapes. The simulation method uses strain energy release rate criterion in conjunction with a moving mesh facility. It is shown that very good compatibility exists between experimental and numerical results. A finite element-based data reduction method is then described as an application of the simulation procedure. Based on the obtained results, it is stated that this bending specimen can effectively be used in practice to study the mixed-mode crack growth and to measure interlaminar fracture toughness of unidirectional laminates.     

Correlation of material constraint with fracture toughness of interface regions in a dissimilar metal welded joint

In this work, the constraint parameter A_p based on crack‐tip equivalent plastic strain was calculated by finite element analyses for the cracks located at different locations in two interface regions in a dissimilar metal weld joint (DMWJ). The capabilities of the parameter A_p for characterizing material constraint and establishing correlation of material constraint with fracture toughness of the interface region cracks have been examined. The results show that the parameter A_p can characterize material constraint effect caused by material mismatch and initial crack positions in the interface regions. Based on the A_p, the correlation lines and formulae of material constraint with fracture toughness of the interface region cracks in the DMWJ can be established, and they may be used for obtaining material constraint‐dependent fracture toughness for the interface region cracks. The results in this work combining with those in the previous studies indicate that the parameter A_p may be a unified constraint parameter that can characterize both geometry constraint (including in‐plane and out‐of‐plane constraints) and material constraint, and it may be used in accurate fracture assessments of welded components with different geometry and material constraints.     

Fracture toughness of alumina/lanthanum titanate laminate composites with a weak interface

Layers of lanthanum titanate (La₂Ti₂O₇) and α-alumina (α-Al₂O₃) were employed to form a layered composite in order to improve the fracture toughness of monolithic alumina. The composites were produced by two different processing methods. In the first, individually presintered pellets of α-Al₂O₃ and La₂Ti₂O₇ were stacked together and hot-forged. In the second, tape cast molten salt La₂Ti₂O₇ and dense α-Al₂O₃ were stacked together and hot-forged. The forged composite samples were investigated by optical microscopy, scanning electron microscopy (SEM), Vickers indentation and three-point bending. During the hot-forging process, an interphase, aluminum titanate (Al₂TiO₅) was found to form as a result of the reaction between α-Al₂O₃ and La₂Ti₂O₇. The flexural strength and the fracture toughness of the resulting laminate composites were found to be 320 MPa and 7.1 MPa m^1 / 2, respectively. Indentation experiments showed that the newly formed Al₂TiO₅ at the interface is sufficiently weak to promote crack deflection and hence increase the fracture energy and mechanical properties of the composite.     

Fracture toughness of the interface between Ni–Cr/ceramic,alumina/ceramic and zirconia/ceramic systems

Few studies have focused on the interface fracture performance of bi‐layered structures, which have an important role in dental restorations, using ceramic materials. The purpose of this study is to evaluate the fracture mechanics performance of the Ni–Cr/ceramic, alumina/ceramic and zirconia/ceramic interfaces by investigating the propagation of an interfacial crack under a wide range of mode mixities. The effect of the mechanical properties of the base materials and the interface, on the crack initiation and crack path, will also be studied. The finite element method (FEM) was used to calibrate the production of the experimental specimens, allowing to obtain the minimum dimensions and amounts of material needed to correctly characterize the fracture event. The specimens were tested until failure using a three‐point bending test machine. The interface fracture parameters were obtained using the FEM. For all specimens, the cracks propagated into the ceramic. The results suggest that, in Ni–Cr/ceramic, alumina/ceramic and zirconia/ceramic bi‐layered structures, the ceramic is weaker than the interface, which can be used to explain the clinical phenomenon that the ceramic chipping rate is larger than interface delamination rate. Consequently, a ceramic material with a larger fracture toughness is needed to decrease the failure rate of ceramic restorations.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

Interaction of interface delamination and plasticity in tensile steel members reinforced by CFRP plates

This paper presents experimental and numerical results related to double shear lap tests performed on steel specimens reinforced using CFRP plates. These tests have been simulated taking into account the elastic–plastic behavior of the steel and the delamination between steel and CFRP by means of a cohesive approach. The results obtained are discussed in terms of: (i) maximum load bearing capacity, (ii) minimum bond length in order to exploit the maximum load bearing capacity, (iii) brittle to ductile transition of the interface failure (iv) combination of interface delamination and plastic deformation of the steel. Design formulas for the definition of the minimum bond length and the load bearing capacity of the joint are validated.     

复合材料疲劳分层的界面单元模型

提出一种三维黏聚力界面损伤模型,可以描述单调和交变载荷下层合复合材料混合型的分层损伤。损伤用界面所经历过的最大位移间断来定义,交变荷载下一个周期的加、卸载过程均考虑有损伤积累,模型还考虑了单调和疲劳损伤的门槛效应和交变载荷下裂纹的闭合效应。建立了包含该界面损伤模型的初始无厚度八节点等参界面单元,并引入加速损伤的算法,用一次计算循环代替若干次实际循环,提高计算效率。用该单元模型对某复合材料动部件疲劳分层裂纹的形成和扩展进行了模拟,得到了分层裂纹前沿界面局部损伤和结构疲劳分层的发展规律,模型预测的裂纹长度-荷载循环次数对数(a-log N)曲线和结构剩余刚度与试验数据吻合。     

Debonding of the interface as 'crack arrestor'

In this paper, we studied the interface debonding when a crack perpendicularly approaches an interface between two dissimilar elastic materials. An interface toughness law was first defined according to an adhesive model governing the interface fracture. By analysing the interaction between the normally approaching crack and the interface crack and by tacking account of the adhesive forces at ends of the interfacial crack, a model for studying the interface debonding and the debonding stability was established. It is observed that the interface debonding toughness depends strongly on the mixed mode locally produced over the plastic adhesive zone of the interface. Moreover, the interface debonding may be unstable, i.e. the interface debonding length may jump from an initial value to a certain final value under critical remote loading. This jump may be surprisedly important in certain cases. These results agree with the experimental works gathered so far and can be used to explain the mechanism of 'crack arrestor' formed by an interface.     

A new approach for evaluating crack growth resistance curve of mode II delamination by doubly end-notched tension tests

Quantitative determination of interlaminar fracture toughness that governs onset and growth of delamination is essential for engineering of composite materials and structures. This study proposes a new approach to evaluate both the initial fracture toughness and the crack growth resistance property of pure mode II delamination by tensile tests of specimens having two initial cracks, which were conceived from double-lap joints. The proposed test method achieves stable growth of mode II delamination using a fundamental testing system. This study presents the specimen configuration, the theory to evaluate the energy release rate, and experiment results. The mode II initial fracture toughness measured by the present approach agreed well with the results of conventional end-notched flexure tests. Furthermore, the crack growth resistance curves were evaluated by unloading-reloading tests of the proposed doubly end-notched tension specimens.