A Stress Singularity Approach for the Prediction of Fatigue Crack Initiation in Adhesive Bonds. Part 1: Theory

Since crack initiation in adhesive bonds tends to occur near the interface corners where the stress fields are singular, we define a fatigue initiation criterion using stress singularity parameter, Q (a generalized stress intensity factor) and the singular eigenvalue, λ.

Hattori et al., successfully used a generalized stress intensity factor to characterize the static strength of bimaterial interfaces. We show that this criterion is only appropriate for situations in which the adhesive contact angle is no larger than 90° and the modulus ratio (adhesive to adherend) is smaller than 0.1. Fortunately, these conditions are often met in real joints, permitting the use of a single eigenvalue approach. We then extend this criterion to the case of fatigue arising from mechanical, thermal, or hygroscopic cycling.

In preparation for Part 2 (experimental), the special case of an epoxy wedge on a flat aluminum substrate is considered. The singularity is analyzed both analytically and numerically. The scale of the region dominated by the singularity is found to be of the order of 100 μm. The size of the plastically yielded zone near the apex is found to decrease extremely rapidly as the stress intensity factor goes down, thereby increasing the applicability of the method at the low stress levels often encountered in fatigue.     

The Stress Intensity Factor in Bonded Quarter Planes after a Change in Temperature

High stresses can occur in bonded dissimilar materials after a change in temperature in the vicinity of the intersection of the interface and the free edge. These stresses depend on the thermal expansion and on the elastic constants of the two materials. In bonded quarter planes the stresses near the intersection of the interface and the free edge can be described by the sum of one singular term and one regular term which is independent of the distance to the singular point. With the exception of the stress intensity factor of the singular term, all parameters can be calculated analytically. The stress intensity factor was evaluated numerically using the finite element method. Joints with different ratios of height to length and various material combinations were investigated. An empirical relationship between the stress intensity factor, the elastic constants and the ratios of height to length of the joint is given by exponential and polynomial equations.     

Development of a Failure Model for the Adhesively Bonded Tubular Single Lap Joint

The accurate calculation of the stresses and torque capacities of adhesively bonded joints is not possible without understanding the failure phenomena of the adhesive joints and the nonlinear behavior of the adhesive.

In this paper, an adhesive failure model of the adhesively bonded tubular single lap joint with steel-steel adherends was proposed to predict the torque capacity accurately.

The model incorporated the nonlinear behavior of the adhesive and the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermally-induced stresses from fabrication.     

Optimal Design of the Adhesively-Bonded Tubular Single Lap Joint

In this paper, a method for the optimal design of the adhesively-bonded tubular single lap joint was proposed based on the failure model of the adhesively-bonded tubular single lap joint. The failure model incorporated the nonlinear mechanical behavior of the adhesive as well as the different failure modes in which the adhesive failure mode changed from bulk shear failure, via transient failure, to interfacial failure between the adhesive and the adherend, according to the magnitudes of the residual thermal stresses induced by fabrication.

The effects of the design parameters for the adhesively-bonded tubular single lap joint, such as the thicknesses of adhesive layer and adherends, the bonding length, and the scarfs of adherends, on the torque transmission capability and the efficiency of the adhesive joint were investigated.     

Factors Affecting the Durability of Ti-6Al-4V/Epoxy Bonds

Factors influencing the durability of Ti-6Al-4V/epoxy interphases were studied by determining chemical and physical properties of Ti-6Al-4V adherend surfaces and by characterizing the strength and durability of Ti-6Al-4V/epoxy bonds.

Ti-6Al-4V adherend surfaces were oxidized either by chemical etch or anodization. Four principal pretreatments were studied: chromic acid anodization (CAA), sodium hydroxide anodization (SHA), phosphate fluoride acid etch (P/F) and TURCO basic etch (TURCO). The oxides were characterized by SEM, STEM, profilometry, contact angles and XPS.

All adhesive bonding was carried out using a structural epoxy, FM-300U. Both lap shear and wedge test samples were tested in hot, wet environments. The results lead to the conclusion that the interfacial area between the adhesive and adherend is the primary factor affecting bond durability.     

Influence of Fabrication Residual Thermal Stresses on Rubber-toughened Adhesive Tubular Single Lap Steel-Steel Joints under Tensile Load

The tensile load bearing capability of adhesively-bonded tubular single lap joints which is calculated under the assumption of linear mechanical adhesive properties is usually much less than the experimentally-determined because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of rubber-toughened epoxy adhesives. Also, as the adhesive thickness increases, the calculated tensile load bearing capability with the linear mechanical adhesive properties increases, while, on the contrary, the experimentally-determined tensile load bearing capability decreases.

In this paper, the stress analysis of adhesively-bonded tubular single lap steel-steel joints under tensile load was performed taking into account the nonlinear mechanical properties and fabrication residual thermal stresses of the adhesive. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive.

Using the results of stress analysis, the failure criterion for the adhesively-bonded tubular single lap steel-steel joints under tensile load was developed, which can be used to predict the load-bearing capability of the joint. From the failure criterion, it was found that the fracture of the adhesively-bonded joint was much influenced by the fabrication residual thermal stresses.     

Yield in Adhesive Joints and Design of Zones with Constant Elastic Shear Stresses

Yield in adhesive joints has been investigated by several scientists among whom L. J. Hart-Smith¹ especially is to be mentioned.

In the following, a method is demonstrated which is based on a simple elastic-plastic model. It shows the distribution of stresses in the adhesive and gives a total picture of the development of the length of the yield zones and their strain as a function of load.

Methods are given for the design of adhesive joints with constant elastic shear stresses at their ends or throughout their whole length. These stresses are obtained by varying the thickness of the adherends, the adhesive, or a combination of both. The constant elastic shear stress zones can be designed to take into consideration all known factors as temperature and hardening stresses, moments, etc. The characteristic yield properties as well as internal stresses after yield and unloading are determined together with the modified stress distribution for a new load.     

Peak stress intensity dictates fatigue crack propagation in UHMWPE

The majority of total joint replacements employs ultra-high molecular weight polyethylene (UHMWPE) for one of the bearing components. These bearings may fail due to the stresses generated in the joint during use, and fatigue failure of the device may occur due to extended or repeated loading of the implant. One method of analysis for fatigue failure is the application of fracture mechanics to predict the growth of cracks in the component. Traditional analyses use the linear elastic stress intensity factor K to describe the stresses near a loaded crack. For many materials, such as metals, it is the range of stress intensity, ΔK, that determines the rate of crack propagation for fatigue analysis. This work shows that crack propagation in UHMWPE correlates to the maximum stress intensity, K_max, experienced during cyclic loading. This K_max dependence is expected due to the viscoelastic nature of the material and the absence of crazing or other cyclic load dependent crack tip phenomena. Such a dependence on a non-cyclic component of the stress allows cracks to propagate under load with little or no fluctuating stresses. Consequently, traditional fatigue analyses, which depend on the range of the stress to predict failure, are not always accurate for this material. For example, significant static stresses that develop near stress concentrations in the component locking mechanisms of orthopedic implants make such locations likely candidates for premature failure due the inherent underestimate of crack growth obtained from conventional fatigue analyses.     

The fracture behaviour of a PXE/HIPS polyblend

As part of an overall examination of the fatigue crack propagation (FCP) behaviour of impact-modified polymers, a study of the fracture morphology of a PXE/HIPS polyblend polymer subjected to monotonic and cyclic loading conditions is reported. The HIPS rubbery-phase particles are found to fail by particle rupture in both fatigue and fast fracture. Another impact modifying addition, PE, is found to fail by a combination of interfacial rupture and tearing, the balance depending on the prevailing stress intensity value and the strain rate. Matrix failure is via multiple crazing at low fatigue crack growth rates, but shear yielding is believed to become a major fracture mechanism with increasing K. The degree of plastic deformation of the matrix increases with increasing strain rate. This fact is manifested by the increasing void size associated with the interfacial separation of the PE particles.     

Filler Debonding in Particulate-Filled Composites

The decrease in Young's modulus after mechanically loading particulate-filled composites serves as a measure of the fraction of debonded filler particles.

For composites based on plasticized rubber and fine ammonium perchlorate these effects have been studied for various stresses and for both varying amounts and particle sizes of the filler.

It was found that debonding filler particles during loading is strongly dependent both on the filler concentration and the particle size. Composites with small particles are characterized by higher stresses at which debonding takes place. The effects observed are supposed to be connected with different conditions of the stress distribution depending on the filler particle size and amount. Another reason is the varying fraction of the interphase zone formed at the filler-matrix boundary.     

Theoretical and Experimental Analysis of the Scarf Joint Bonded Structure: Influence of the Adhesive Thickness on the Micro-mechanical Behavior

In this work, we have studied the influence of the adhesive thickness on the micro-mechanical behavior of a scarf joint bonded structure loaded in uniaxial tension. Adherends are made of mild steel containing 0.18% Carbon (French Standard XC18), the adhesive is a two-component epoxy resin with a 5800 MPa elastic modulus. The experimental method is based on strain gauge measurements and acoustic emission. It makes it possible to determine the following zones:

—the areas of the joint where the start of microcracks occurs (threshold Fd);

—the areas where crack propagation occurs (threshold Fg) up to the failure (threshold Fr). The experimental results confirm the good correlation between the different thresholds. They also show that there is an optimal adhesive thickness close to 0.1 mm, which confers to the scarf joint the greatest resistance to microcrack initiation and crack extension. We have compared our experimental measurements with the main theories in this domain to determine their limits and their fields of application, particularly in the angular singularities regions near the ends of the lap.     

Mechanical Characterization of Adhesive Layer in-situ and as Bulk Material

An extensive test series was conducted on bulk and in-situ adhesive specimens with a view to characterizing their mechanical properties under different loading modes and states of stress.

It was found that a good correlation exists between the in-situ and the bulk properties of shear yield strength and elastic modulus derived from torsion tests. The properties derived from uniaxial testing of the bulk adhesive were related to those of an in-situ adhesive layer in shear by a combined stress law which follows a modified Von Mises failure criterion. It was thus concluded that the basicelastic and strength characteristics of the in-situ adhesive under a compound state of stress may be evaluated through simple tests on the bulk material in uniaxial tension and compression.     

The Interfacial Bond Strength in Glass Fibre-Polyester Resin Composite Systems

The interfacial bond strength in glass fibre-polyester resin composites has been investigated using various experimental techniques. These included blocks of resin containing fibre (in which, depending on the geometry of the specimen, failure occurs in either a shear or tensile mode) the pullout of a fibre from a disc of resin and a short beam shear test for interlaminar shear strength determination.

Low power optical microscopy and optical retardation measurements of stress induced birefringence were used to detect the difference between intact and debonded fibre resin interfaces. The shear modulus and shear strength of the resin were obtained from torsion tests on cylindrical rods of the resin.

The single fibre shear debonding specimen and the short beam shear test are shown to be the most viable test methods but interpretation of the results is complicated by the various modes of failure possible and by the different stress states which exist in the area of the specimen where debonding starts. Stress concentration factors obtained by finite element analysis and photoelastic analysis have been applied to the results from these tests and the corrected interfacial bond strengths are in close agreement.

The real interfacial bond strengths of well bonded glass-fibre polyester resin systems is shown to be of the order of 70 MN m^-2.     

Adhesion: Comparison Between Physico-chemical Expected and Measured Adhesion of Oxygen-plasma-treated Carbon Fibers and Polycarbonate

The adhesive interaction between oxygen-plasma-treated, polyacrylonitrile-based, high-tensile-strength carbon fibers and a polycarbonate matrix has been studied. Several models have been used to predict the impact of the plasma treatment process on the strength of adhesion between both jointing partners. These approaches have been the thermodynamic work of adhesion which was calculated from the solid surface tensions, based on the results of contact angle measurements versus test liquids, the contact angle which was directly obtained via polycarbonate melt droplets on single carbon fibers and the zeta (ς)-potential data provided by streaming potential measurements. The results have been compared with the interfacial shear strength determined from the single-fiber fragmentation test. Additionally, the single-fiber tensile strength of the oxygen-plasma-treated carbon fibers was determined.

We confirmed that any physico-chemical method on its own fails to describe exactly the measured adhesion. However, for the investigated system, the conscientious interpretation of the data obtained from wetting measurements, in conjunction with the thermodynamic approach, is sufficient to predict the success of a modification technique which has been applied to one component in order to improve adhesion.     

Comparison Between Experimental and Theoretical Analysis of Stress Distribution in Adhesively-Bonded Joints: Tenon and Mortise Joints and Single-Lap Joints

We have studied the agreement between theoretical computations and experimental results of surface strains of bonded joints of two types: tenon and mortise, and single-lap joints, for different lengths of the lap. For instance, with the single-lap joint, we have tested four lengths of the overlap from 14 mm to 88 mm. Surface strains are measured by an extensometrical method with electrical gauges, when the specimen is loaded in uniaxial traction on a universal testing machine.

Experimental results and computations made by an improved method, such as the asymptotic expansions method, agree but only if the global traction load applied on the specimen is low, or if the overlap in respect with the others dimensions of the section of test specimen is long.

In these joints, effectively, stress fields are disrupted near the butts and become very difficult to compute. Actually, near the ends of the overlap, stresses can reach high limits with only low global load applied on the test specimen. With a short length of the overlap, linear behaviour disappears almost totally because of a strong interaction of the two perturbed fields. On the contrary, with a high length of overlap, stress fields become linear on the major part of the overlap, even with a high tensile load applied on the specimen. So, the length of the overlap has a great effect on the linear behaviour of the joint.     

Relationship Between Viscoelastic and Peeling Properties of Model Adhesives. Part 2. The Interfacial Fracture Domains

The viscoelastic and peeling properties of polybutadiene/tackifying resin compatible blends have been studied in detail. Viscoelastic properties have been described through the variations of the complex shear modulus, G*(w), as a function of frequency, W, and peeling properties through the variations of peeling force (F) as a function of peeling rate (V).

The first paper of this series presented the cohesive fracture domain and the present paper explores the interfacial fracture domain: (i) rubbery interfacial (interfacial 1); (ii) stick-slip; (iii) glassy interfacial (interfacial 2). After a general survey of the properties in the three domains we present a quantitative relationship between the peeling and linear viscoelastic properties as a function of the adhesive formulation, discussing the use of time-temperature equivalence for adhesive properties. The third part of the paper presents the trumpet model of de Gennes describing the crack shape and propagation: starting from a mechanical analysis of the peeling test, it is shown how one may calculate the variations of the peeling force as a function of peeling rate in the various interfacial fracture domains: this model defines a single interfacial fracture criterion which coexists with the cohesive fracture criterion defined earlier, whatever the fracture location.

We present as a conclusion a critical discussion of the relevance and physical meaning of such a criterion and present a new outlook for the modeling and improvement of adhesive formulations.     

The Effect of Moisture Content in Epoxy Film Adhesives on their Performance. III: Bulk Properties

Humidity absorbed by epoxy film adhesives during low temperature storage or exposure to atmosphere may result in reversible changes and irreversible modifications. Vacuum treatment may partially remedy the reversible changes. The consequences of vacuum drying are manifested in enhancement of both the peel and shear properties of bonded joints (Part I and Part II of this series of papers) and the thermal, physical and mechanical properties of the bulk adhesive, characterized in the present study.

Experimental results have shown that the bulk properties of structural epoxy based adhesives are highly correlated with the aging processes caused by water absorption in the prepolymerized adhesive. Applying the vacuum process is harmful to fresh unaged adhesive due to devolatization of low molecular species of the film adhesive.

The characterization of bulk properties for the purpose of following the aging and recovery processes is advantageous, since the bulk is independent of geometrical and interfacial effects which dominate in the case of property evaluation of the adhesive in a bonded joint.     

Strength Analysis of Adhesively-Bonded Tubular Single Lap Steel-Steel Joints Under Axial Loads Considering Residual Thermal Stresses

The static tensile load bearing capability of adhesively-bonded tubular single lap joints calculated using linear mechanical adhesive properties is usually far less than the experimentally-determined one because the majority of the load transfer of adhesively-bonded joints is accomplished by the nonlinear behavior of the rubber-toughened epoxy adhesive

In this paper, both the nonlinear mechanical properties and the residual thermal stresses in the adhesive resulting from joint fabrication were included in the stress calculation of adhesively-bonded joints. The nonlinear tensile properties of the adhesive were approximated by an exponential equation which was represented by the initial tensile modulus and ultimate tensile strength of the adhesive.

From the tensile tests and the stress analyses of adhesively-bonded joints, a failure model for adhesively-bonded tubular single lap joints under axial loads was proposed.     

The Stresses in an Adhesive Layer

A simple method has been developed for calculating the stresses near the ends of a parallel-sided adhesive layer. The method can be applied to adhesive layers having aspect ratios of 10 or greater, and Poisson's ratios of 0.49 or less. For a layer subject to uniform boundary conditions of displacement at the adhering surfaces, the stress fields at distances greater than about five layer thicknesses from the free surfaces are uniform. The stress field throughout the layer is uniquely determined by the stresses in the uniform stress region. If the stress field is expressed by functions of reduced coordinates of position, obtained by dividing the cartesian coordinates by the layer thickness, these functions are for practical purposes independent of the aspect ratio or the thickness.

The method has been used to calculate shrinkage stresses, the stresses in a joint under tension perpendicular to the plane of the adhesive layer, and the stresses in a joint under shear. The features of the stress fields are described, and where necessary, shown in the form of graphs or contour plots.     

MAXIMIZING SELECTIVITY OF LIQUID-LIQUID REACTION SYSTEMS. CONTROL OF THE DISPERSION PROCESS

Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper.

The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.

The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed.