Cohesive zone criterion for cracking along the Cu/Si interface in nanoscale components

Crack initiation and propagation along the Cu/Si interface in multilayered films (Si/Cu/SiN) with different thicknesses of the Cu layer (20 and 200 nm) are experimentally investigated using a nano-cantilever and millimeter-sized four-point bending specimens. To examine the cohesive zone model (CZM) criterion for interfacial delamination along the Cu/Si interface in nanoscale stress concentration, an exponential type of CZM is utilized to simulate the observed delamination processes using the finite element method. After the CZM parameters for the Cu/Si interface are calibrated by experiment, interface cracking in other experiments is predicted. This indicates that the CZM criterion is universally applicable for describing cracking along the interface regardless of specimen dimensions and film thickness which include the differences in plastic behavior and residual stress. The CZM criterion can also predict interfacial cracking along Cu/Si interfaces with different stress singularities.     

Numerical simulation of interface crack in thin films

The de-adhesion of a thin film from a rigid substrate is studied. It is assumed, that a periodic array of micro-cracks exists along the film/substrate interface. During formation, the film expands, while being constrained by the substrate. This phenomenon leads to development of compressive stresses. Then buckling may occur and cause crack growth either along the interface or in the film towards the free surface. A finite element model has been developed, which simulates film buckling and subsequent interfacial crack growth, based on film/substrate adhesive constitutive relations. These relations have been motivated by atomistic calculations on bimaterial failure. The model does not require any facture criterion. Interfacial work of separation has a significant effect on damage growth ahead of the crack tip, along the interface. Also, a critical remote compressive stress exists, at which damage progresses without further loading of the film. The relation between the critical compressive stress for extensive damage and the interfacial work of separation can be used in combination with experiments for the quantitative characterization of the film/substrate interface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Single-fibre Broutman test: fibre–matrix interface transverse debonding

The single-fibre Broutman test was used to study the fibre–matrix interface debonding behaviour when subjected to a transverse tensile stress. During testing, damage was detected using both visual observation under polarized light and acoustic emission (AE) monitoring. Separation of failure mechanisms, based on AE events, was performed using time domain parameters (amplitude and event width) and fast Fourier transform (FFT) frequency spectra of the AE waveforms. The latter can be considered as a fingerprint allowing to discriminate fibre failure, matrix cracking, fibre–matrix interface debonding, friction and ‘parasite noise’. Stresses in the specimens were evaluated using a two-dimensional finite element model (FEM) and monochromatic photoelasticity was used to verify the simulated stress distribution.Two failure mechanisms appeared to be in competition in the Broutman test: fibre failure under compressive stresses and fibre–matrix interface debonding under transverse tensile stresses. For systems in which the interfacial adhesion is not so ‘good’, like glass fibre–polyester systems for instance, fibre–matrix debonding was observed, and the progression of the debonding front with the interfacial transverse stress was recorded. Thermal stresses are also discussed, and a FEM simulation shows that they encourage fibre failure under compressive stresses.     

Enhanced adhesion of atomic layer deposited titania on polycarbonate substrates

Interfacial adhesion of atomic layer deposited titania films on polycarbonate substrates with and without a water-plasma treatment has been studied using in situ observation during microtensile testing. Specific attention is paid to multiple tension-generated transverse cracks in the titania films when subjected to externally applied uniaxial tensile stresses. The strength, fracture toughness and interfacial adhesion of the titania film on polycarbonate were deduced from theoretical models based on experimentally determined parameters. The tensile tests were conducted in a micromechanical tester positioned under an optical microscope allowing in situ viewing of cracking damage. The strain to initiate first cracking and the crack density as a function of strain were obtained. The in situ observations indicated different interfacial behaviour between water-plasma-treated and non-treated samples. It is shown that the water plasma treatment drastically improves the adhesion of the titania film to polycarbonate. Calculations show that the fracture energy required for film debonding in the plasma-treated polycarbonate is 5.9 J/m² compared to 2.5 J/m² for the untreated sample. A simple chemical structure model was used to explain the observed differences.     

The influence of hygrothermal conditions on the damage processes in quasi-isotropic carbon/epoxy laminates

The effects of hygrothermal conditions on damage development in quasi-isotropic carbon-fiber/epoxy laminates are described. First, monotonic and loading/unloading tensile tests were conducted on dry and wet specimens at ambient and high temperatures to compare the stress/strain response and damage development. The changes in the Young's modulus and Poisson's ratio were obtained experimentally from the monotonic tensile tests. The critical stresses for transverse cracking and delamination for the above three conditions are compared. The delamination area is measured by using scanning acoustic microscopy (SAM) at various loads to discuss the effects of delamination on the nonlinear stress/strain behavior. Next, the stress distributions under tensile load including hygrothermal residual stresses are computed by a finite-element code and their effects on damage initiation are discussed. Finally, a simple model for the prediction of the Young's modulus of a delaminated specimen is proposed. It is found that moisture increases the critical stresses for transverse cracking and delamination by reducing the residual stresses while high temperature decreases the critical stresses in spite of relaxation of the residual stresses. The results of the finite-element analysis provide some explanations for the onset of transverse cracking and delamination. The Young's modulus predicted by the present model agrees with experimental results better than that predicted by conventional models.     

低速冲击下复合材料层合板损伤分析

根据低速冲击下复合材料层合板的分层损伤机理,发展了一种分层失效准则,该准则同时考虑了层间拉应力、层间剪应力和基体开裂等因素对分层损伤的影响,并在损伤分析中,区分了冲击正面由挤压应力引起的纤维挤压损伤和冲击背面由弯曲拉应力引起的纤维断裂损伤,模拟了纤维断裂、纤维挤压、基体开裂、基体挤压、分层等五种损伤的起始和扩展过程,完善了作者以前发展了低速冲击逐渐累积损伤模型.通过与实验结果进行比较,验证了模型的合理性.     

The nature of stresses in hot-filament chemical vapour deposited diamond thin films on WC substrates

The nature of film stresses in hot-filament chemical vapour deposited (HFCVD) diamond thin films on tungsten carbide substrates, is reported. Commercial WC substrates were subjected to various surface treatments. Subsequently, they were coated with a diamond film and examined for stresses using X-ray diffraction. All but one of the stress measurements indicated various levels of compressive stresses in the film and at the film–substrate interface. These stresses are compared with those obtained by other researchers. Intrinsic film stresses were also computed for diamond films and found to be tensile. WC drills, of 0.125 in. diameter, were also diamond coated and the stress levels measured along drill flanks and flutes. Significant variations were found in these stresses, and the results were analysed from a film–substrate adhesion perspective.     

Experimental analysis and finite element modelling of nano-scratch test applied on 40-120 nm SiCN thin films deposited on Cu/Si substrate

In this work, the nano-scratch test is used to characterize the interfacial adhesion of amorphous SiCN thin films deposited by plasma enhanced chemical vapour deposition on Cu/Si substrates. The experimental results show that the critical load F_c is directly related to the rupture of the SiCN/Cu interface. A strong linear dependence of F_c to the SiCN thickness independently to the adhesion is also put in evidence. A three-dimensional finite element model of the test is then built. The results show a clear relation between the stresses into the coating and the cracking and buckling of the film observed experimentally. We then discuss how the interfacial tensile stresses can explain the increase of F_c with the film thickness.     

Fe基体上Ni膜和Cu基体上Ag膜的膜内应力

直流电沉积法在Fe基体上制备Ni膜和在Cu基体上制备Ag膜,利用悬臂梁法在线测量了膜中的平均应力,并计算了膜内分布应力,且对膜内平均应力的实验结果与Thomas?Feimi?Dirac?Cheng(TFDC)电子模型理论估算结果进行了对比。结果表明,Fe基体上Ni膜的平均应力和分布应力均为拉应力,而Cu基体上Ag膜的平均应力和分布应力均为压应力。两种膜的内应力均由界面应力引起。对于相同的基体和镀膜,膜内平均内应力的理论估算值与实验值较接近。     

Crack initiation at free edge of interface between thin films in advanced LSI

Since electronic devices are made of multi-layered sub-micron films, delamination along the interface is one of the major failure mechanisms. This paper aims to develop a method for evaluating the mechanical criterion of interface cracking between thin films on a substrate. The focus is put on crack initiation from the free edge of the interface where the stress concentrates due to the mismatch of elastic deformation. In the evaluation, it is important to exclude plastic deformation and fracture of the thin metal film, because they bring about ambiguity on the measured magnitude of interface strength. In this study, an experimental method is proposed on the basis of fracture mechanics concepts, and the validity is examined by tests on Cu (conductor metal)/TaN (barrier metal) interface in a large-scale integrated circuit. The critical stress intensity at delamination crack initiation is successfully analyzed by the boundary element method.     

3D in situ observations of glass fibre/matrix interfacial debonding

X-ray microtomography was used for 3D in situ observations of the evolution of fibre/matrix interfacial debonding. A specimen with a single fibre oriented perpendicular to the tensile direction was tested at a synchrotron facility using a special loading rig which allowed for applying a load transverse to the fibre. Three distinguishable damage stages were observed: (i) interfacial debond initiation at the free surface, (ii) debond propagation from the surface into the specimen and (iii) unstable debonding along the full length of the scanned volume. The high resolution microtomography provides both qualitative and quantitative 3D data of the debonding initiation and propagation. Thus, microtomography is demonstrated as a promising technique which can assist micromechanical model development.     

Acoustic emission based tensile characteristics of sandwich composites

Sandwich composite static and fatigue testing results indicated the predominant failure to be the core damage followed by interfacial debonding, resin cracking and fiber rupture. Under static testing, crack was observed to initiate in the core and ensue planar propagation near the interface with the facesheets; whereas, onset of crack initiation in the facesheets served as a precursor to the catastrophic failure. Multiple failure initiation and propagation sites in the core and intermittent interfacial debonding were consistently observed under fatigue. An acoustic emission based stiffness reduction model is presented that seems to accurately identify the extent of damage in sandwich composites subjected to fatigue loading conditions.     

Failure response of fiber-epoxy unidirectional laminate under transverse tensile/compressive loading using finite-volume micromechanics

The transverse damage initiation and extension of a unidirectional laminated composite under transverse tensile/compressive loading are evaluated by means of Representative Volume Element (RVE) presented in this paper based on an advanced homogenization model called finite-volume direct averaging micromechanics (FVDAM) theory. Fiber, fiber-matrix interface and matrix phases are considered within the RVE in determining fiber-matrix interface debonding and matrix cracking. The simulated fracture patterns are shown to be in good agreement with experimental observations.     

A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems

This paper contains a review of the most vital concepts regarding the analysis and design of film systems. Various techniques have been presented to analyse and predict the failure of films for all common types of failure: fracture, delamination, general yield, cathodic blistering, erosive and corrosive wear in both organic and inorganic films. Interfacial fracture or delamination is the loss of bonding strength of film from substrate, and is normally analysed based on the fracture mechanics concepts of bi-material systems. Therefore, keeping the focus of this review on bonding strength, the emphasis will be on the interfacial cracking of films and the corresponding stresses responsible for driving the delamination process. The bi-material characteristics of film systems make the nature of interfacial cracks as mixed mode, with cracks exhibiting various complex patterns such as telephone cord blisters. Such interfacial fracture phenomenon has been widely studied by using fracture mechanics based applicable analysis to model and predict the fracture strength of interface in film systems. The incorporation of interfacial fracture mechanics concepts with the thermodynamics/diffusion concepts further leads to the development of corrosive degradation theories of film systems such as cathodic blistering. This review presents suggestions for improvements in existing analysis techniques to overcome some of limitations in film failure modelling. This comprehensive review will help researchers, scientists, and academics to understand, develop and improve the existing models and methods of film-substrate systems.     

Fracturing behaviors of FRP-strengthened concrete structures

In this paper, we focus on the study of concrete cracking behavior and interfacial debonding fracture in fiber reinforced polymer (FRP)-strengthened concrete beams. An experimental program is systematically reviewed according to the observed failure modes, in which it is found that the interfacial debonding may propagate either within the adhesive layer or through concrete layer in the vicinity of bond interface. A finite element analysis is performed to investigate the different types of debonding propagation along FRP-concrete interface and crack distribution in concrete. For the numerical fracture models, interfacial debonding that initiates and propagates in adhesive layer is modeled by fictitious interfacial crack model. And concrete cracking, including the debonding fracture through interfacial concrete, is modeled by smeared crack model. Properties of the interfacial adhesive layer and concrete are considered to significantly influence the debonding propagation types and crack distribution. The interactions between interfacial bond strength, interfacial fracture energy of bond adhesive layer and tensile strength, fracture energy of concrete are discussed in detail through a parametric study. According to the results, the effects of these properties on different types of interfacial debonding, concrete cracking behavior and structural load-carrying capacity are clearly understood.     

The deformation response of sol-gel-derived zirconia thin films on 316L stainless steel substrates using a substrate straining test

Thin (78 ± 4 nm), well-bonded zirconia films were formed on 316L stainless steel substrates by dip-coating in an alkoxide precursor solution followed by annealing in air to achieve film densification. X-ray diffraction showed the film to be either metastable cubic or tetragonal zirconia. A substrate-straining test was used to investigate the mechanical characteristics of the film and interface; this protocol has been used previously to estimate interfacial shear strength through a shear-lag model. At strain levels of about 1.5%, 15 times the yield strain of the substrate, through-thickness cracking of the film was observed. These cracks were driven by deformation localized at slip bands on the substrate surface and the cracking pattern reflected the slip band pattern of the underlying substrate; the propagation of long cracks transversely to the applied stress, as observed in similar experiments previously, was not seen and consequently the shear-lag model was not applicable. As a qualitative indication of good adhesion, film debonding was not observed even at high strain levels. A non-quantitative model was proposed which examined stress transfer across the film-substrate interface on a microscopic scale, and suggested how film, substrate and interface properties affect competition between transverse and slip-band-induced modes of film cracking. This model was then used to reconcile the observations of this study with the transverse cracking observed by others.     

Internal fatigue cracks are growing in vacuum

Cylindrical specimens of 2024 and 7075 Al alloy material were heat treated with a cold water quench to obtain high residual tensile stresses at the interior. Fatigue tests showed internal cracks growing in the shear mode. By drilling a hole along the centre line internal cracks were given access to air, which then produced tensile mode cracks. Prestraining of specimens eliminated residual stresses thus producing crack initiation at the outer surface with crack growth in the tensile mode. Cracking in the tensile mode was sensitive to mean stress, whereas cracking in the shear mode was not. The shear mode crack on a micro level appeared to be slip band cracking.     

Effect of residual stresses on the strength and fracture energy of the brittle film: Multiple cracking analysis

The aim of this paper was to address the effect of the residual stresses within the brittle film on the substrate on the film strength, fracture energy, and interfacial shear strength (IFSS). Special analyses were performed on the SiO_x film/polyethulene terephthalate substrate systems. The residual stresses were evaluated by using the curvature method. The film strength, fracture energy, and IFSS were estimated on the basis of the multiple cracking analyses. In the multiple cracking analyses, the system was subjected to the combination of the residual stresses and the unidirectionally applied stress. Results showed that the relationship between the crack density in the film and the applied strain can be predicted by adopting the energy criterion on the basis of the knowledge on the residual stress distributions in the film segment. The film strength and fracture energy for the initiation of film cracking were almost proportional to the compressive residual stresses in the film. With increasing the compressive residual stresses within the film, the IFSS also increased.     

Größeneinfluß und Dauerfestigkeitseigenschaften unter Besonderer Berücksichtigung optimierter Oberflächenbehandlung

Size Effect and Fatigue Properties with Respect to Optimized Surface-Treatment. A hyperbolic function describes the geometrical size effect of notched specimens made from heat treated steel. An estimation of fatigue properties of components under one level fatigue tests is possible, if there are comparable materials and surface properties. The fatigue properties of specimens are well described by standardized stress-N graphs. The slope of the stress-N graphs in the range of load cycle depends on the concentration factor and not on the size effect. The fatigue properties of components are largely increased by thermal and mechanical surface strengthening. For the determination of the improvement of fatigue properties it is important to known the initiation of cracking. The improved fatigue properties of inductive surface hardened smooth specimens can be explained by the initiation of cracking below the surface. Mechanically strengthened notched specimens start cracking on the surface. The increase of fatigue properties for these specimens is explained by compressive residual stresses. The fatigue properties of notched specimens can be improved by the optimisation of mechanical strengthening, to higher values than for smooth surface strengthened specimens. This is due to compressive residual stresses. They decrease the tensile stresses which are responsible for crack propagation. If the tensile stress is below fatigue limit for initiation of cracking the crack arrests immediately.