Interfacial Fracture Mechanics Research Articles

Effects of the presence of compression in transverse cyclic loading on fibre–matrix debonding in unidirectional composite plies

Fatigue of composite materials is of great concern in load-carrying structures. The first type of damage to appear is generally transverse cracks in off-axis plies. These cracks form when fibre-matrix debonds coalesce. The underlying mechanism is hence fatigue growth of debonds at the fibre-matrix interfaces. In the present study, debond growth has been characterized under tensile and compressive cyclic loading of single glass fibres embedded in polymer matrix. The debond length was deter-mined by in situ microscopy with transmitted polarized light showing the more damaging effect of tension-compression cyclic loading than tension-tension cyclic loading. A boundary element model has been developed and interfacial fracture mechanics concepts applied over the numerical results aiming to give an explanation of this experimental fact. These results may be used to formulate a fatigue growth law at a local microscopic level, at a stage prior to the formation of any visible damage, i.e. transverse cracks. Ideas of how to develop this methodology further are also discussed.

Measurement of Mechanical Properties and Residual Stresses of Bridged Gold Films and Circular Gold Membranes

In order to measure the mechanical properties of gold films on silicon substrate, two types of specimens, i.e., bridged films and circular membranes, are manufactured. Using a wedge tip, the bridged gold films are indented so that the films are pushed off, which is called as V-peel test. The load-deflection curves obtained by the V-peel test are analyzed with the concept of geometrically nonlinear beam by using the minimum potential energy theory together with Ritz method. Thus, Young’s modulus and residual stress of the bridged gold films are obtained. Blister test is also conducted to measure the Young’s modulus and residual stress of a circular gold membrane, of which deformation is measured by Twyman-Green interferometer. By gradually increasing the external pressure applied on the membrane, the interfacial fracture toughness between the gold membrane and silicon substrate is measured based on the concepts of interfacial fracture mechanics.

Delamination in patterned films

When the dielectric constant of an insulator in an interconnect is reduced, mechanical properties are often compromised, giving rise to significant challenges in interconnect integration and reliability. Due to low adhesion of the dielectric an interfacial crack may occur during fabrication and testing. To understand the effect of interconnect structure, an interfacial fracture mechanics model has been analyzed for patterned films undergoing a typical thermal excursion during the integration process. It is found that the underlayer pattern generates a driving force for delamination and changes the mode mixity of the delamination. The implications of our findings to interconnect processes and reliability testing have been discussed.

Contributions to the interfacial adhesion in co-sintered bilayers

The adhesive strength of co-sintered bilayers is influenced by several factors, including the nature of bonding along the joined interface, residual stresses evolved during processing, and the sintered properties of the individual layers. Here these separate contributions are isolated through careful control of the co-sintering process for W/Al2O3 bilayers, and in particular through control of the W-layer properties by using the process of activated sintering. Four-point bending delamination tests are used to evaluate adhesion and strength of the bilayers, and the interfacial fracture mechanics of the system is numerically studied using finite element simulations. Improvements in sintered density are found to increase the adhesive strength of the system only up to a point, beyond which shrinkage mismatch compromises the intrinsic toughness of the interface.

Growth analysis of interfacial delamination in a plastic ball grid array package during solder reflow using the global–local finite element model

This work first investigated the initial location of the possible delamination in a plastic ball grid array (PBGA) package under moisture preconditioning and subsequent solder reflow by applying the modified Tsai-Hill failure criteria. The fracture parameters, such as the stress intensity factor (SIF), the strain energy release rate, and the phase angle at the delamination tip, were calculated to study delamination growth. A two-dimensional PBGA finite element model was considered and the hygrothermal stress at the interfaces was calculated to examine the initiation of delamination. A three-dimensional PBGA finite element model was applied in the study of three-dimensional delamination growth. A global-local finite element analysis and two-dimensional linear interfacial fracture mechanics were used to calculate fracture parameters at the delamination tip for different delamination lengths. The effect of vaporized moisture inside the PBGA package on the growing delamination was examined. A series of popcorn experiments on PBGA packages was carried out to verify the simulation results. The agreement between the predicted and experimental results was good.

Reliability study of underfill/chip interface under accelerated temperature cycling (ATC) loading

Interface reliability issue has become a major concern in developing flip chip assembly. The CTE mismatch between different material layers may induce severe interface delamination reliability problem. In this study, multifunctional micro-moiré interferometry (M 3I) system was utilized to study the interfacial response of flip chip assembly under accelerated thermal cycling (ATC) in the temperature range of −40 °C to 125 °C. This in-situ measurement provided good interpretation of interfacial behavior of delaminated flip chip assembly. Finite element analysis (FEA) was carried out by introducing viscoelastic properties of underfill material. The simulation results were found to be in good agreement with the experimental results. Interfacial fracture mechanics was used to quantify interfacial fracture toughness and mode mixity of the underfill/chip interface under the ATC loading. It was found that the interfacial toughness is not only relative to CTE mismatch but also a function of stiffness mismatch between chip/underfill.

Characterization of interfacial mechanical properties in carbon fiber/aluminium matrix composites by the nanoindentation technique

Interfacial mechanical properties in an AA6061 reinforced with short carbon fibers coated with different metallic films by electroless were investigated using the nanoindentation technique. Copper and nickel coatings on carbon fibers surface were applied to control the interfacial reactivity of fibers with the molten aluminium during composite manufacture, jointly with the objective of improving its wetting behaviour. Because of the coating, local microstructure of the composites can be significantly altered, creating differences between the properties of the interphase regions and the bulk composite. Nanoindentation is a suitable technique to measure hardness and elastic modulus profiles on a micrometric range. Besides, from nanoindentation tests, information on interfacial fracture mechanisms can be obtained. Three types of nanoindentation tests were carried out for the interfacial mechanical characterization: (1) nanoindentation profiles across the matrix/fiber interfaces to determine changes in hardness and elastic modulus of the modified matrix; (2) single indentations in the interface proximity to evaluate the interfacial fracture tendency; and (3) individual push-out tests on perpendicularly aligned fibers to the composite surface, to measure the interfacial shear strengths. SEM and TEM studies at the interfacial zones were applied to relate the change in mechanical properties with the interfacial formation mechanisms.

The dentin–enamel junction and the fracture of human teeth

The dentin-enamel junction (DEJ), which is the interfacial region between the dentin and outer enamel coating in teeth, is known for its unique biomechanical properties that provide a crack-arrest barrier for flaws formed in the brittle enamel1. In this work, we re-examine how cracks propagate in the proximity of the DEJ, and specifically quantify, using interfacial fracture mechanics, the fracture toughness of the DEJ region. Careful observation of crack penetration through the interface and the new estimate of the DEJ toughness ( approximately 5 to 10 times higher than enamel but approximately 75% lower than dentin) shed new light on the mechanism of crack arrest. We conclude that the critical role of this region, in preventing cracks formed in enamel from traversing the interface and causing catastrophic tooth fractures, is not associated with the crack-arrest capabilities of the interface itself; rather, cracks tend to penetrate the (optical) DEJ and arrest when they enter the tougher mantle dentin adjacent to the interface due to the development of crack-tip shielding from uncracked-ligament bridging.

界面破壊力学による建築仕上げの変形追従性能評価

In this paper, a new method to predict the critical deformation of composite materials with interface cracks under mixed mode conditions by stress intensity factors K_1 and K_2 is presented, and also fracture criterions of the interfaces between concrete and cementitious wet-finishings are evaluated. Two kinds of stress intensity factors are based on interfacial fracture mechanics. Stress distribution and singularity on the interface between dissimilar materials are obtained by two-dimensional boundary element elastostatic analyses under a plane strain state. Two kinds of stress intensity factors determine the mixed mode fracture criterions of the interfaces. Predictions about delamination initiation and extension by these factors are compared with the results of observations made by compressive tests on composite model specimens that consist of several kinds of finishings. It was clarified that critical deformation could generally be predicted by the presented method.

Investigation of interfacial resistance between concrete and polymer-cement mortar and development of constitutive material model for the interface

This paper aims to investigate interfacial resistance and to propose a constitutive material model of the interface between concrete and polymer-cement mortar (PCM) in tile systems. The interfacial resistance of the concrete/PCM interface is evaluated in terms of interface fracture toughness based on an interface fracture mechanics method. The experiment is conducted under pure tension and mixed mode conditions (tension and shear) by using four-point bending tests. It is found that the interface fracture toughness is low especially at high mixity of shear stress, and that the tendency of the interface fracture toughness is different from the one of the concrete I fiber reinforce concrete (FRC) interface that is used to be the representative of the concrete/cementitious material interface in this study. Moreover, two models of the interface fracture toughness are derived from a cracking criterion, a linear cracking criterion and an elliptic one respectively, by assuming linear softening behavior. The model derived from the elliptic cracking surface shows good agreement with the experimental result of the concrete/PCM interface fracture toughness.

Modeling of Interfacial Delamination in Plastic IC Packages Under Hygrothermal Loading

Ever since the discovery of the “popcorn” failure of plastic-encapsulated integrated-circuit (IC) packages in the 1980s, much effort has been devoted to understanding the failure mechanism and modeling it. It has been established that such failures are due to the combined effects of thermal stresses and hygrostresses that arise during solder reflow of plastic IC packages. In recent years interfacial fracture mechanics has been applied successfully to the analysis of delamination or crack propagation along interfaces in plastic IC packages. This paper presents some fundamental aspects of interfacial fracture mechanics and describes some of the numerical techniques available for calculating the strain energy release rate and mode mixity at the tips of cracks at interfaces in plastic-encapsulated IC packages. A method of calculating the combined effects of thermal stress and hygrostress on the energy release rate is also described. Some case studies are presented that illustrate how the techniques are applied to predicting delaminaton in IC packages. Some experimental verification of predictive methodology is also presented.

Mesure des énergies de rupture interfaciale : problématique et exemples de résultats d'essais de gonflement-décollement

ples of results of buldge-and-blister test. The mechanical strength of interfaces between two different materials is a critical point, as well on a fundamental as on a practical aspect. Indeed, interfacial debonding is a frequent failure mechanism for multimaterial parts or coatings, which are more and more in use in advanced technologies. Several general considerations are introduced about interfacial debonding phenomena and interfacial fracture mechanics, aiming at criteria to define the most relevant adhesion mechanical tests, able to provide reproducible and physically significant results. Among the available experimental techniques for mechanical adhesion measurement, those which provide reliable values of interfacial crack propagation energy are emphasized. The example of bulge and blister testing is developed in more details. Results obtained by this technique on various film/substrate systems are presented and commented on.

Interfacial fracture mechanisms in solid solution directionally solidified eutectic oxide composites

The interfacial fracture behavior of the solid solution directionally solidified eutectic oxide, Co 1 − x Ni x O/ZrO 2(CaO), is investigated via indentation testing. An abrupt transition from interfacial delamination to interfacial penetration is observed as a function of NiO fraction ( x>0.33). The use of a focused ion beam technique is introduced as a means for exploring sub-surface cracking in brittle materials. The sub-surface observations revealed a compositional transition from energy dissipative mechanisms (e.g., delamination, secondary cracking) for cracking to brittle cracking behavior, in the Co 1 − x Ni x O phase. It is proposed that the transition in interfacial fracture behavior for the directionally solidified eutectic material is the result of competing dislocation-based crack nucleation mechanisms. The observations and analyses have significant implications for fracture behavior in composites with one phase exhibiting (pseudo-) plastic behavior.

Integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of QFN package during reflow with interfacial fracture mechanics analysis

In this paper, a comprehensive and integrated package stress model is established for quad flat non-lead package with detailed considerations of effects of moisture diffusion, heat transfer, thermo-mechanical stress, hygro-mechanical stress and vapor pressure induced during reflow. The critical plastic materials, i.e., moldcompound and die attach are characterized for hygroswelling and moisture properties, which are not easily available from material suppliers. The moisture absorption during preconditioning at JEDEC Level 1, and moisture desorption at various high temperatures are characterized. The moisture diffusivity is a few orders higher at reflow temperature than moisture preconditioning temperature. Due to coefficient of moisture expansion mismatch among various materials, hygro-mechanical stress is induced. The concept is analogous to coefficient of thermal expansion mismatch which results in thermo-mechanical stress. Thermal diffusivity is much faster than the moisture diffusivity. During reflow, the internal package reaches uniform temperature within a few seconds. The vapor pressure can be calculated based on the local moisture concentration after preconditioning. Results show that the vapor pressure saturates much faster than the moisture diffusion, and a near uniform vapor pressure is reached in the package. The vapor pressure introduces additional strain of the same order as the thermal strain and hygrostrain to the package. Subsequently, the interfacial fracture mechanics model is applied to study the effect of crack length on die/mold compound and die/die attach delamination.

Mechanics of interface fracture with applications in electronic packaging

The purpose of this paper is to present a brief review of the mechanics of interface fracture, with a focus on applications in electronic packaging. From a structural mechanics perspective, electronic devices can be thought of as composite structures fabricated from highly dissimilar materials. Often, the interfaces between these materials are where failure is most likely to occur when the device is subjected to thermomechanical loading. The mechanics of interface fracture is a specialized subtopic within the discipline of fracture mechanics and the nonspecialist may be unaware of some of the subtle differences encountered in applying interface fracture concepts. The mechanics associated with interface fracture introduces certain mathematical concepts that may seem to be unnecessarily complicated, but are essential for its proper application. It is important that the electronic packaging reliability engineer be aware of these concepts, understanding the most important implications. This review will focus on the mechanics and computational aspects of interface fracture in electronic structures, with a particular emphasis on some details that the nonexpert could only obtain after an extensive review of the available literature. Numerical results are presented for the important problem of corner cracking between silicon and epoxy materials subjected to thermomechanical loading. These new results provide insight into the three-dimensional nature of interfacial crack propagation at bimaterial corners.

Understanding the strength of epoxy-polyimide interfaces for flip-chip packages

Polyimides are commonly used as organic passivation layers for microelectronic devices due to their unique combination of low dielectric constant, high thermal stability, and excellent mechanical properties. Polyimides are well known to have poor adhesion to epoxy resins. Many surface treatment methods have been developed to increase epoxy-polyimide adhesion. These include various ion beam, plasma treatment, or chemical treatment methods. The goal of this research is to understand the strength of epoxy-polyimide interfaces by studying the effect of polyimide chemical structure on epoxy-polyimide adhesion. The four polyimides chosen in this study are commonly used in the microelectronics industry: poly (pyromellitic dianhydride-oxydianiline [PMDA-ODA], poly (3,3/spl acute/,4,4/spl acute/-biphenyltetracarboxylic dianhydride-phenylene diamine [BPDA-PDA], poly (hexafluoroisopropylidene-diphthalic anhydride-oxydianiline) [6FDA-ODA], and 5(6) -Amino-1-(4-aminophenyl)-1,3,3, trimethylindanbenzophenonetetacarboxylic dianhydride copolymer [BTDA-DAPI]. The adhesive strengths between an epoxy resin and these four polyimides were characterized using interfacial fracture mechanics and the critical interfacial strain energy release rates ranged from 20 to 179 J/m/sup 2/ depending on the particular polyimide used. The loci of failure for these epoxy-polyimide interfaces were analyzed using scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS), and Fourier transform infrared spectroscopy (FT-IR), and found to be at the interphase region for all four interfaces. It is interesting that the strength of the interfaces appears to be related to the predicted interfacial widths from solubility parameter theory.

Investigation of interfacial delamination of a copper-epoxy interface under monotonic and cyclic loading: modeling and evaluation

Interfacial delamination is of important concern for multilayered microelectronic packages, as it is one of the most common failures observed after reliability test. Most of the work, available in open literature, focus on delamination propagation under monotonic loading rather than delamination propagation under cyclic loading. Interfacial fracture mechanics based methodologies have been proven to be efficient in handling interfacial delamination problem under monotonic loading. In this paper, the principles of interfacial mechanics have been applied in the analysis of interfacial fatigue crack propagation. Fatigue test has been conducted in studying onset of delamination and fatigue crack propagation (FCP) of an interfacial crack along a copper-epoxy interface. Models developed in this study have also been applied in the evaluation of multilayered integrated substrate test vehicles.

A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites

An accurate laminate model developed by using multilayer shear deformable plate modeling and interface elements, based on fracture mechanics and contact mechanics, is proposed to analyze mixed mode delamination in composite laminates. Perfect adhesion along the undelaminated portion of the delamination plane is simulated by treating interface stiffnesses as penalty parameters, whereas to enforce interface displacement continuity between plate elements constituting each sub-laminate above or below the delamination plane, the Lagrange multiplier method is used. The governing differential equations are derived through a variational procedure by using a modified total potential energy functional. Results are obtained by numerical integration of the non-linear three-point boundary value problem modeling mixed-mode delamination of the laminate plate subjected to end loading, which accounts also for the frictionless contact condition. The coupling of a penalty procedure with the Lagrange multiplier method, results in an accurate and direct energy release rate evaluation. Comparisons with results available from the literature obtained with a local continuum approach, show that mode partition may be performed to the desired accuracy by refining multilayer plate models for each sub-laminate. In addition, original analytical formulas for mode partition are obtained by coupling the interface approach and fracture mechanics concepts, evidencing the effectiveness of the proposed approach and gaining a better insight into the influence of shear effects on mode decomposition. Numerical computations for practical problems, evidence both the relative simplicity and the efficiency of the proposed model to represent mixed mode interlaminar fracturing as well as crack–face interaction.

Die Cracking at Solder (In60-Pb40) Joints on Brittle (GaAs) Chips: Fracture Correlation Using Critical Bimaterial Interface Corner Stress Intensities

We study cracking from the interface of an In60-Pb40 solder joint on a brittle GaAs die when the joint is subjected to a uniform temperature change. Our primary objective is to apply and validate a fracture initiation criterion based on critical values of the stress intensities that arise from an analysis of the asymptotic elastic stress fields at the interface corner. In some regards the approach is similar to interface fracture mechanics; however, it differs in that it is based on a singular field other than that for a crack. We begin by determining the shape that the solder bump will assume after reflow when constrained by a fixed diameter wetting pad on the GaAs. To simplify the interpretation of the results, we focus on a class of solder bumps of various sizes, but with a self-similar shape. The approach, though, can be applied to different size and shape solder bumps. We then compute the asymptotic interface corner fields when the system is subjected to a uniform temperature change. The asymptotic structure (radial and angular dependence) of the elastic fields is computed analytically, and the corresponding stress intensities that describe the scaling of the elastic fields with geometry and loading are computed by axisymmetric finite element analysis. In order to assess the validity of fracture correlation using critical stress intensities, we designed and fabricated a series of test structures consisting of In60-Pb40 solder bumps on a GaAs chip. The test structures were subjected to uniform temperature drops from room temperature to induce cracking at the interface corner. From the tests we determined the relationship between the solder bump size and the temperature change at which cracking occurred. Not unexpectedly, smaller bumps required larger temperature changes to induce cracking. The observed scaling between solder bump size and temperature change is well described by the critical stress intensity failure criterion based on only a single parameter, the critical value of the mode 1 stress intensity, K1crn. Interestingly, this is because over a significant region, the mode 2 and constant terms in the asymptotic expansion cancel each other. This failure criterion provides the necessary machinery to construct failure maps in terms of geometry and thermomechanical loading. We conclude by describing how to apply the approach in more general and more practical settings that are possibly applicable to a wide range of problems in microelectronics, optoelectronics, and microelectromechanical systems packaging.

Concepts of Separated J-Integrals, Separated Energy Release Rates, and the Component Separation Method of the J-Integral for Interfacial Fracture Mechanics

First, this paper presents the concepts of separated J-integrals and separated energy release rates. The path-independent separated J-integrals have the physical significance of energy flows into an interfacial crack tip from adjacent individual material sides or, equivalently, separated energy release rates. Thus, the J-integral and the energy release rate can be evaluated by the sum of the path-independent separated J-integrals. Second, the relations between the separated J-integrals and the stress intensity factors are derived. Third, the component separation method of the J-integral is extended for interfacial crack problems to allow accurate evaluation of the stress intensity factors. Finally, pertinent numerical analyses are carried out to demonstrate the usefulness of the separated J-integrals and the component separation method.