Applied Strain Energy Release Rate Research Articles

An experimental setup for characterizing subcritical debonding of materials interface under mixed mode fatigue loading

A mixed mode bending experimental setup was developed for quantifying the subcritical debonding growth behavior for materials interfaces under a full spectrum of loading mode mixity. In the experimental system, the control program calculates and adjusts the cyclic bending forces to maintain a constant phase angle at the prescribed value. The relationship between the subcritical crack growth rate and the applied strain energy release rate range is obtained by post-processing the experimental results with analytical formulas. As a preliminary application example, a phase-angle dependent power-law model was constructed for the subcritical debonding growth rate of the Al-epoxy interface. It was observed that both the logarithm of the scaling constant and the power-law exponents of the subcritical debonding growth model exhibit linear relationships with the phase angle.

Corrosion of Si-O based porous low-k dielectrics

The corrosion behavior of low-k dielectric films used in today's microelectronic interconnects is reported. We study the dielectric constant, k, range 2.7 to 2.05, with all materials based on a Si-O-Si network. A corrosion mechanism based upon the reaction of water molecules with strained crack-tip bonds is used to model crack velocity vs. applied strain energy release rate curves and to extract key atomistic parameters for each dielectric. It is found that bond strength is invariant and bond density varies linearly with k. The data indicate that no new mechanism plays a part in the corrosion of these Si-O-Si based films with dielectric constants down to ∼2.

Numerical simulations of the cathodic delamination of adhesive bonded rubber/steel joints

Abstract Cathodic delamination of mechanically loaded rubber/steel adhesive bonds occurs due to bondline degradation (weakening) followed by crack growth under mechanical (here, mostly cleavage) load. In this paper, a mechano-chemical failure criterion is proposed, which couples fracture mechanics principles with the weakening mode of debonding due to environmental effects. The latter is mainly described by electrolyte type, cathodic potential, and temperature and may be analytically described according to the recently introduced [1] analytical model based on liquid-solid reactions and is capable of simulating the weakening mode of bond degradation. This paper extends the model advanced in [1] to where we now account for externally applied mechanical loading (mostly peel mode). Such loads cause already weakened bonds to delaminate thus resulting in physical separation of the rubber from the steel substrate. For the rubber/metal, variable- G , strip blister specimen (SBS) used in this work, progressive delamination proceeds as the applied strain energy release rate, G , decreases from an initial maximum value, G T0 (of about 2.24 kJ/m 2 for the most utilized specimen configuration). As the applied G decreases, delamination correspondingly proceeds at progressively slower rates. The fact that delamination rates decrease with increasing delaminated bond lengths has already been established experimentally and simulated using empirical [2] and semi-empirical models [3] but will be simulated numerically in this paper. The model is validated using such experimental data of bond delamination under a variety of cathodic conditions. The validated methodology provides numerical simulations of joint delamination of the SBS under the combined action of mechanical peel loads and cathodic environment.

The effects of test temperature and humidity on the mixed-mode fatigue behavior of a toughened adhesive aluminum joint

The effects of test environment humidity and temperature on the fatigue threshold and crack growth behavior of P2-etched and commercial coil-coated (CC) aluminum adhesive joints were studied under mixed-mode loading using aluminum asymmetric double cantilever beam (ADCB) specimens. Under dry conditions, increasing the temperature to 80 °C had an insignificant effect on the fatigue threshold, but caused an increase in the crack growth rates. At 40 °C, the fatigue behavior was insensitive to moisture at higher crack growth rates, but became sensitive to moisture level in the test environment as crack growth rates slowed to the threshold. The effect of moisture and temperature were explained by the observed changes in the crack path, which in general moved progressively closer to the more highly-strained adherend as the applied strain energy release rate, and consequently the crack growth rate, decreased. Furthermore, the residual adhesive thickness on the more highly-strained adherend, t r , increased with increasing temperature, and the crack path shifted to the hydrated aluminum oxide interface when the test environment was saturated with moisture. The degrading effect of a hot-wet environment was similar for both P2-etch and CC pretreatments. At higher crack growth rates, the joint fatigue performance was degraded solely due to the effect of the increased temperature, whereas at low crack growth rates, the fatigue performance was degraded predominantly because of elevated moisture.

Effect of adhesive thickness on fatigue and fracture of toughened epoxy joints – Part II: Analysis and finite element modeling

The effect of bondline thickness on the fatigue and fracture of aluminum adhesive joints bonded using a rubber-toughened epoxy adhesive was studied using finite element analysis. The fatigue data of Part I examined the dependence of the fatigue threshold and cyclic crack growth rate on the adhesive thickness under both mode-I and mixed-mode loading. The fracture data of Part I illustrated the relation between the adhesive thickness and the quasi-static crack initiation and steady-state critical strain energy release rates. These experimental trends are explained in terms of the effects of the adhesive thickness and the applied strain energy release rate on the stress distribution in the bondline, the stress triaxiality at the crack tip, and the plastic zone size in the adhesive layer.

Effect of Surface Roughness on the Performance of Adhesive Joints Under Static and Cyclic Loading

The role of surface roughness on the fatigue and fracture behavior of a toughened epoxy adhesive system was investigated experimentally. Fatigue studies covered both the fatigue threshold strain energy release rate, G th , and fatigue crack growth rates, while the strain energy release rate for crack initiation, , and the steady-state value, , were measured under quasi-static loading. Mixed-mode fatigue results showed a significant dependency on surface roughness. G th increased with roughness, reached a plateau, and then decreased for very rough surfaces. This increase in G th was explained in terms of the increase in bonding and fracture surface area, crack growth retardation due to the microtopography of the substrate, and crack path deviation from the interface. The decrease in G th for very rough substrates was attributed to void formation and stress concentration at the tip of asperities. The effect of roughness on fatigue diminished as the applied strain energy release rate increased. This was a result of the crack path becoming more cohesive, moving away from the interface. Similarly, no effect of surface roughness was observed in the mode-I fatigue results and the mixed-mode fracture results, since the crack path in these cases was far enough from the interface.

The effect of mode ratio and bond interface on the fatigue behavior of a highly-toughened epoxy

The fatigue threshold and the cyclic crack growth of a highly-toughened epoxy adhesive were studied under mode I and several mixed-mode loading cases and compared with the quasi-static critical fracture energies. Four different adhesive systems were examined using steel and aluminum substrates having different surface roughness, and surface treatment. The effect of increasing the amount of mode II (increasing the phase angle) on the fatigue threshold strain energy release rate and the cyclic crack growth rate was found to be insignificant at low phase angles. However, a significant increase in the fatigue threshold and decrease in the cyclic crack growth rate was observed at higher phase angles. These trends were similar to that seen in adhesive joint fracture. Adherend surface roughness and surface preparation affected the fatigue behavior significantly, particularly at low crack speeds and high phase angles. The fatigue properties were essentially the same for both steel and aluminum adherends provided that the crack paths were cohesive. A general observation was that the fatigue crack path moved progressively closer to the more highly strained adherend under mixed-mode loading as the applied strain energy release rate and hence the crack speed, decreased. This caused mixed-mode cracks to be nearly interfacial in the threshold region.

Studies on the Prediction of Elastomer-to-Steel Adhesive Bond Life in Cathodic Environments

In this paper, we present a summary of the research done to date on modeling the debonding of elastomer-to-steel adhesive bonds under cathodic conditions. In the Introduction Section, we address some of the peculiarities of the two documented debonding modes: weakening and delamination. In the following sections, we first discuss the accelerated durability data collected (some under highly accelerated conditions) using a primer/adhesive system specially formulated for bonding elastomers to metals. For enhanced durability, this control system was also modified by incorporating γ-aminopropyltriethoxysilane (γ-APS). This modification resulted in improved resistance to the alkali as evidenced by decreased mass uptake of free-standing, neat primer films. Also, cathodic durability results of adhesively bonded joints show a decrease in delamination rates for the silane-modified bonds as compared to the control system. Having collected a significant amount of cathodic durability data (for both loaded and unloaded adhesive bonds), we set on developing mathematical models that are capable of predicting the life of these bonds under cathodic conditions. A semi-empirical model that simulates the weakening (unloaded) mode of bond debonding (both weakening rates and the characteristic delay time) under various cathodic conditions is first reviewed. Then and for simulating the delamination (loaded) mode of cathodic debonding, we address two models: one empirical and one semi-empirical. The latter model utilizes some of the physical principles underlying the delamination phenomenon. Both of these models offer mathematical equations which relate cathodic debonding rates of elastomer-to-steel bonds to environmental parameters as well as G, the applied strain energy release rate. These models may serve as predictors of service life for similar elastomer-to-steel adhesive bonds in cathodic environments.

Subcritical Delamination in Epoxy Bonds to Silicon and Glass Adherends: Effect of Temperature and Preconditioning

The effects of temperature and preconditioning in deionized (DI) water and a cyan ink vehicle used in inkjet printer cartridges on the durability of glass/epoxy and silicon/epoxy systems have been investigated. A test matrix consisting of test temperatures, preconditioning temperatures, preconditioning times, and nature of adherends and adhesives was developed and a series of experiments was conducted using wedge test specimens (glass or silicon coupons bonded with epoxy) to investigate the subcritical adhesion performance of the glass/epoxy and silicon/epoxy interfaces. The glass/epoxy and silicon/epoxy interfaces were found to be relatively insensitive to temperature over a range of 22–60°, but significant temperature effects, more complex than suggested by time-temperature superposition (TTSP), were observed above 60°C, depending on the environmental chemistry and nature of the adhesive used. Specimens made of silicon coupons bonded with epoxy were subjected to preconditioning in DI water and the cyan ink vehicle prior to wedge insertion to study the effect of prior environmental exposure. The wedge test data from preconditioned specimens were compared with standard wedge test results and the Si/epoxy interface was found to be insensitive to preconditioning in DI water but was affected significantly by preconditioning in the cyan ink vehicle. Plots of crack velocity versus applied strain energy release rate for particular sets of environmental conditions are presented and a comparison is made for different environmental conditions to quantify the subcritical debonding behavior of systems studied.

Hygrothermal Delaminations in Lead-Free Solder Reflow of Electronic Packages

The use of environmentally friendly lead-free solder in electronic assembly requires a higher process temperatures that double the saturated steam pressure inside the electronic package. We studied the interfacial delamination fractures created by the trapped steam inside the defect voids in packages by computationally modeling the steam diffusion and evaporation processes and the hygrothermal fracture behaviors. These results were compared with results from the conventional saturated steam pressure approach. The comparisons revealed that the saturated steam approach is appropriate for small defects, while the evaporative-diffusion approach is suited for delamination analyses of small and large defects. Our results showed that the strain energy release rate increased with initial defect growth, but reached a defect-size independent plateau when the defect had grown larger than the temperature-dependent critical defect size. To control delamination in packages undergoing lead-free solder reflow, the interfacial fracture energy release rate should be engineered to be above this plateau by controlling the interfacial adhesion, and the applied strain energy release rate should be reduced by reducing the diffusion and evaporation rate of water in the materials.

Cathodic delamination of elastomer-to-metal adhesive joints: Experimental data and empirical modeling

In order to estimate the cathodic delamination rates of metal adhesive/steel adhesive bonds, an empirical model based on crack growth is developed. To this end, a considerable amount of delamination data was experimentally collected under several levels of cathodic environmental harshness (some highly accelerated) and applied peel stress. For a given electrolyte, cathodic delamination was found to depend on cathodic voltage (or current density), temperature, and applied strain energy release rate, G. In order to describe the progress of delamination under various cathodic environments as a function of applied G, the collected, experimental delamination-distance-versus-time data were used to develop characteristic curves of log delamination rates versus log G. For all conditions tested, these log–log plots were dominated by linear regions (commonly referred to as Region II) that follow the Paris law. In this region, it was found that bond delamination rates vary dramatically depending on the environment. Furthermore, and unlike with the critical fracture toughness ( G c), the threshold value of G ( G th) for the degraded bond varies from one set of cathodic conditions to another. To model delamination rates as function of the cathodic environment and G, a nonlinear equation capable of modeling subcritical crack growth behavior was used. The experimental delamination data was fitted to this equation in order to determine the coefficients of this equation. For each environment tested, one equation was determined and which describes the bond delamination rate versus G behavior over the entire G-range. Consequently, these coefficients were consolidated into master, easy-to-use, empirical equations that relate delamination rates to G. The resulting empirical model is applicable over a wide range of cathodic conditions of voltage and temperature.

Influence of Experimental Setup and Plastic Deformation on the Shaft-Loaded Blister Test

ABSTRACT In the shaft-loaded blister test (SLBT), plastic deformation often occurs at the contact area between the shaft tip and adhesive layer, leading to a larger displacement (blister height) than if the film was loaded elastically. As a consequence, incorporating the displacement variable into the analysis can result in misleading values of the applied strain energy-release rate, 𝒢. In this work, the influence of plastic yielding at the contact area on 𝒢 of a thin film was investigated as a function of some common SLBT experimental variables, namely, substrate hole diameter, film thickness, and shaft-tip diameter. Test specimens consisted of plies of pressure-sensitive adhesive tape adhered to a rigid glass substrate. 𝒢 was calculated from the following Equations: (1) load-based, (2) hybrid, (3) displacement-based, and (4) combination. Decreasing the film thickness, increasing the hole diameter, or decreasing the shaft-tip diameter lead to more plastic yielding at the contact area as well as to an increase in blister height. The increased blister height resulting from plastic deformation leads to disagreement among the values of 𝒢 calculated from the different Equations when the displacement variable was included in the calculation. However, the load-based equation, which does not include the displacement, was determined to be independent of plastic yielding and the “correct” equation for calculating 𝒢. In addition, the film tensile rigidity (Eh) was calculated using an experimental compliance calibration. The effects of film thickness on the mechanical behavior of the film (bending plate vs. stretching membrane) as well as methods to determine the displacement resulting from plastic deformation are also discussed.

Constituent and composite quasi-static and fatigue fracture experiments

Quasi-static and fatigue Mode I fracture experiments were performed at a variety of loading rates and temperatures using a polymer-matrix composite (PMC) (IM7/977-3) and its neat resin (977-3). Neat resin quasi-static toughness showed slight increases in toughness with increasing loading rate and no dependence on temperature until the test temperature neared the glass transition temperature, where the toughness decreased. Composite quasi-static delamination initiation toughness showed no clear trends with respect to temperature or loading rate, but toughness values were generally higher at higher temperatures. Composite fatigue delamination onset and crack propagation rates were strongly dependent on temperature, with delamination onset occurring at a lower number of cycles and crack propagation rates being higher for a given maximum applied strain energy release rate. The neat resin fracture mechanisms were a key factor in explaining the composite quasi-static and fatigue behavior, but no quantitative predictions of composite fracture behavior could be made since the crack tip mechanisms apparently changed.

Strain energy release rates of a pressure sensitive adhesive measured by the shaft-loaded blister test

The elastic solution to the shaft-loaded blister test (SLBT) was adopted to measure the applied strain energy release rate ( G ) of Kapton® pressure sensitive adhesive (PSA) tape bonded to a rigid substrate. The substrates used were either aluminum or Teflon®, a high-energy surface and low-energy surface, respectively. The values of G were calculated from three different equations: (1) load-based, (2) hybrid, and (3) displacement-based. An experimental compliance calibration was utilized to measure the film's effective tensile rigidity, ( Eh ) eff , the results of which are presented in an appendix. Plastic deformation at the contact area of the shaft tip and adhesive results in an overestimated displacement ( w 0 ) (relative to the elastic model), leading to disagreement among the values of G calculated. Estimation of the effective membrane stress in the film, ( N eff ), as well as the reasonable agreement between the value of ( Eh ) determined from a stress-strain experiment and the compliance calibration, suggest that, in spite of the plastic deformation, the assumption of linear elasticity in the crack growth region and hence the validity of the model, is reasonable. The compliance calibration has been shown to improvethe agreement among the values of G calculated from the three equations. Using the load-based equation, the assumed "correct" value of G may be obtained for a thin adhesive coating independent of the film's stiffness even in the presence of plastic deformation at the shaft tip. Comparing the value of G obtained by a pull-off test and the 90° peel test for a single ply indicates that the value of G obtained by the SLBT is of reasonable magnitude, being less than that obtained by the more firmly established pull-off test, and also that undesirable plastic deformation is reduced relative to the 90° peel test. An experimental configuration for studying the effects of liquids on the fracture energy has been demonstrated for the SLBT. This study indicates that the SLBT is an attractive and convenient test method for measuring the strain energy release rate of adhesive films, because of the insensitivity of the load-based equation to the coating stiffness, plus the independence of the value of G on the plastic deformation at the shaft tip, and the reduced plastic deformation at the crack front relative to the 90° peel.

Moisture-assisted subcritical debonding of a polymer/metal interface

Subcritical debonding of polymer/metal interfaces has important implications for the reliability of a range of modern device technologies containing thin layered structures, although the physics of the underlying crack-growth mechanisms are not well understood. This study investigates the effect of moisture on subcritical debonding at the interface between a silica-filled epoxy resin and a copper substrate electroplated with a nickel layer. Subcritical debond-growth rates in the range of 10−5 to 10−11 m/s were characterized as a function of the applied strain energy release rate, GA. Particular attention was given to the relationship between the debond tip strain energy release rate, Gtip, and the measured debond growth rates. The kinetics of interfacial debond growth were rationalized in terms of a stress-dependent chemical reaction and mass transport of the environmental species to the debond tip. The order of the chemical reaction with respect to water was determined and found to be surprisingly high (n∼5). In the transport-controlled region, the rate of debond growth was found to increase linearly with the partial pressure of water vapor. The effects of salient interface parameters including the peak stress in a cohesive zone used to model the fracture mechanism were explored.

Delamination growth from face sheet seams in cross-ply titanium/graphite hybrid laminates

A test program was conducted to study the fatigue delamination behavior of titanium/graphite hybrid laminates (TiGr) with seams in the titanium face sheets. Tension fatigue experiments were conducted at −18°C, 21°C (room temperature), 93°C, and at 177°C on cross-ply, [Ti/0/90/0 2] s, titanium/graphite hybrid laminates (TiGr). The delamination growth rate obeyed a power-law function of the applied strain energy release rate range. The prefactor on the power-law function showed a strong dependence on temperature. In addition, experiments were performed on laminates with ±30° plies. The primary damage mode in this lay-up was edge delamination of the interior plies. Analysis of the [Ti/0/90/± θ] s family of laminates indicated that for angles greater than 10°, edge delamination would be the dominant damage mode in coupon specimens.

Adhesion of benzocyclobutene-passivated silicon in epoxy layered structures

Adhesion and subcritical debonding at interfaces between a silica-filled epoxy underfill and a silicon die passivated by silicon nitride and benzocyclobutene (BCB) layers were investigated. Adhesion was measured in terms of a critical value of the applied strain energy release rate, G (J/m2). Subcritical debond-growth rates in the range of 10−9to 10−3m/s were characterized as a function of applied G. Adhesion and subcritical debonding were affected by changes in interfacial chemistry and environment. The surprisingly large effect of adjacent layer elastic properties on interfacial adhesion was demonstrated with simulations of interfacial fracture using a mechanics of materials approach. Interfacial chemistry was modified by using different adhesion promoters, by varying the BCB cure state, and by using different epoxy underfill resins. The effects of environmental variables were studied with temperature- and humidity-controlled environments in order to determine the separate roles of moisture activity and temperature.

The Effect of Fatigue on the Adhesion and Subcritical Debonding of Benzocyclobutene/Silicon Dioxide Interfaces

AbstractThe effect of fatigue loading on microelectronic thin film interfaces has until now been difficult to quantify. Most industrial fatigue testing uses HAST (Highly Accelerated Stress Testing) protocols, which inherently convolutes the effects of mechanical fatigue and the test environment. Our work focuses on isolating the deleterious effects of mechanical fatigue on interfaces, which we have found to be substantial. In this study, the integrity of a low-k polymer interface involving benzocyclobutene (BCB) and silica was examined under a variety of loading conditions. Critical (fast fracture) adhesion values were measured using standard interface fracture-mechanics geometries. Experiments were then conducted to measure the debond growth rate as a function of the applied strain energy release rate under both static and cyclic loading conditions. Our results show that even under room temperature conditions, debond growth rates measured under cyclic fatigue are considerably faster than those observed under static loading. Results are presented detailing the effects of interface chemistry (adhesion promoters), environmental moisture, and test temperature on the resistance of the interfaces to subcritical debonding. Strategies for increasing resistance of dielectric interfaces to fatigue debonding are outlined.

Adhesion and Reliability of Polymer/Inorganic Interfaces

The reliability of microelectronic components is profoundly influenced by the interfacial fracture resistance (adhesion) and associated progressive debonding behavior. In this study we examine the interfacial fracture properties of representative polymer interfaces commonly found in microelectronic applications. Specifically, interface fracture mechanics techniques are described to characterize adhesion and progressive bebonding behavior of a polymer/metal interface under monotonic and cyclic fatigue loading conditions. Cyclic fatigue debond-growth rates were measured from ~10−11 to 10−6 m/cycle and found to display a power–law dependence on the applied strain energy release rate range, ΔG. Fracture toughness test results show that the interfaces typically exhibit resistance-curve behavior, with a plateau interface fracture resistance, Gss, strongly dependent on the interface morphology and the thickness of the polymer layer. The effect of a chemical adhesion promoter on the fracture energy of a polymer/silicon interface was also characterized. Micromechanisms controlling interfacial adhesion and progressive debonding are discussed in terms of the prevailing deformation mechanisms and related to interface structure and morphology.

Residual Stress Development in Adhesive Joints Subjected to Thermal Cycling

The effect of thermal cycling on the state of residual stress in thermoviscoelastic polymeric materials bonded to stiff elastic substrates was investigated using numerical techniques, including finite element methods. The work explored the relationship between a cyclic temperature environment, temperature-dependent viscoelastic behavior of polymers, and thermal stresses induced in a bimaterial system. Due to the complexity of developing a closed-form solution for a system with time- and temperature-dependent material properties, and time-varying temperature and coupled boundary conditions, numerical techniques were used to acquire approximate solutions. The results indicate that residual stresses in an elastic-viscoelastic bimaterial system incrementally shift over time when subjected to thermal cycling. Potentially damaging tensile axial and peel stresses develop over time as a result of viscoelastic response to thermal stresses induced in the polymeric layer. The applied strain energy release rate at the ends of layered or sandwich specimens is shown to increase as axial stress develops. The rate of these changes is dependent upon the thermal cycling profile and the adhesive's thermo-mechancial response. Discussion of the results focuses on the possiblility that the increasing tensile residual stresses induced in an adhesive bond subjected by thermal cycling may lead to damage and debonding, thus reducing bond durability.