REPORT. Customer Ref: AH 9/3. File No: 29570/601. Document Series: PREDICTING THE LIFETIME OF ADHESIVE JOINTS IN HOSTILE ENVIRONMENTS.

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1 MTS Adhesives Project 3: Environmental Durability of Adhesive Bonds Report No 5 Predicting the Lifetime of Adhesive Joints in Hostile Environments AJ Kinloch* August 1994 * Imperial College

2 AEA Technology 424 Harwell Didcot Oxfordshire OX 11 ORA United Kingdom Customer Ref: AH 9/3 Telephone Facsimile Document Ref: AEA-ESD-0082 File No: 29570/601 Document Series: REPORT Title: PREDICTING THE LIFETIME OF ADHESIVE JOINTS IN HOSTILE ENVIRONMENTS ISSUE RECORD Issue Date Author Checked by Approved by 1 22/8/94 AJ Kinloch

3 Foreword Many UK manufacturers are aware of the merits of adhesives in certain critical roles. However, the range of applications of adhesives is still limited largely due to the lack of consistent test methods and validated test data which the engineer needs in order to specify adhesives for a given application. In a recent survey the Centre for Adhesive Technology was commissioned by the DTI to establish specific areas where validated test methods could improve confidence in predicting joint life. The survey identified measurement methods for use in design, environmental durability and process control as priority areas and five projects were finally selected by the DTI for support through the Measurement Technology and Standards (MTS) budget. The projects started in December 1992 and are 100% funded by the DTI at the level of 5.4M over three years. A key area that was identified in the survey was the need to provide a means for the quantification and prediction of the lifetime of bonded joints when exposed to a hostile environment, and this forms the basis of Project 3 of the Adhesives programme. The project is being carried out through a collaboration of AEA Technology and Oxford Brookes University, together with important contributions from Imperial College, DRA (Holton Heath) and Loughborough University. The basis of the project is that there still remains considerable uncertainty in predicting joint lifetime under typical operating conditions, despite the enormous prior investment in durability studies. This difficulty represents perhaps the single most significant impediment to the wider use of adhesive technology. The programme combines a fresh look at testing procedures and predictive methods with a rigorous examination of previous work. Together the two strands of the approach produce a work plan which has a strong industrial focus. In addition to tasks on test methods and design, a series of forensic studies will be undertaken on examples of bonded structures which have seen extensive service life, in order to evaluate the reasons for their success. This will provide practical feedback into the other aspects of the programme as well as indicating to designers tangible evidence of the potential of bonding technology which they will be able to relate to their own particular application. This project is divided into seven tasks: Appraisal of Test Methods and Durability Data Development of an Experimental Database Characterisation of the Moisture Absorption Process Forensic Studies Assessment of Microstructural Failure Mechanisms Development of Methodologies for Life Prediction Technology Transfer

4 SUMMARY The quantitative prediction of the lifetime of an adhesive joint when subjected to a hostile environment is still very much in its infancy. Typically the main problem is when the adhesive joint is subjected to an aqueous environment, possibly accompanied by elevated temperatures and by constant or cyclically applied loads. The main problem when attempting to formulate any predictive model is that the attack by the environment typically occurs in the regions at, or very close to, the adhesive/substrate interface. Modelling the rate of such attack and assigning failure criteria to the interracial failure event are not trivial tasks. Several different approaches to the quantitative prediction of the lifetime of an adhesive joint when subjected to a hostile environment may be identified from considering the existing literature: (i) A mechanistic app roach - from a knowledge of the detailed kinetics and mechanisms of environmental attack the rate of attack is modelled, and then this information is combined with a stress analysis or fracture mechanics approach to predict the loss of joint strength as a function of time. The effect, if any, of a constantly-applied, or cyclically-applied, load to the joint should be accounted for when considering both (a) the detailed kinetics and mechanisms of environmental attack and (b) the stress analysis or fracture mechanics approach. (ii) A fracture mechanics approach - as commented above, fracture mechanics may be used in the mechanistic approach, but at the heart of the mechanistic approach is the knowledge and modelling of the kinetics and mechanisms of the environmental attack process. In the more general fracture mechanics approach, tests are conducted measuring the rate of crack growth through the joint versus the applied strain-energy release rate, or stress-intensity factor. A test geometry being selected which may be analysed readily using a fracture mechanics approach, and the environment being one which is of direct interest. The lifetime of any other type of joint design in such an environment is then predicted using a standard fracture mechanics analysis. This may involve needing to deduce the inherent flaw size and final crack length in the joint, or it may be simply based upon the knowledge of the threshold value of the fracture energy (or fracture toughness). In any event, the geometry factor for the design of the adhesive joint of interest (or the compliance function of the joint) does have to be ascertained. (iii) A stress analysis approach - here, again, the detailed mechanisms are not really considered. A stress analysis is conducted on the adhesive joint of interest and a suitable failure criterion is assumed. The relevant properties of the adhesive and substrate are experimentally measured as a function of time in the environment of interest. This approach appears to work reasonably well when failure is via cohesive fracture through the adhesive layer or substrate, but it is far more difficult to employ when the failure is at, or close to, the interface. (iv) An approach based upon a correlation to the water uptake in the adhesive layer - here the mass uptake of water in the adhesive layer in the joint is either directly measured, or calculated via measuring the water absorption properties of the bulk adhesive, and correlated to the measured loss of joint strength. Predictions of joint strength are simply based upon extending the correlations established from the shorter time scales over which the

5 measurements were made. The extensions may involve the extrapolation of a plot of loss of joint strength versus water uptake in the adhesive, or by determining a mathematical description of this relation and deducing the effect of longer time periods using the mathematical model. (v) Extrapolations from accelerated ageing tests - in this approach an acceleration factor is assigned from undertaking a set of accelerated ageing tests, and this factor is then used to estimate the lifetime of joints subjected to less demanding, but more natural, ageing conditions. In this report these various approaches are considered together with recommendations for possible future work areas.

6 TABLE OF CONTENTS SUMMARY INTRODUCTION MECHANISTIC APPROACH Introduction Gledhill et al Approach Extending the Gledhill et al Model Possible Future Work Areas FRACTURE MECHANICS APPROACH Introduction Basic Approach Possible Future Work Areas STRESS ANALYSIS APPROACH Introduction Previous Work Possible Future Work Areas CORRELATIONS TO WATER UPTAKE IN THE ADHESIVE Introduction Typical Results Possible Future Work Areas EXTRAPOLATIONS FROM ACCELERATED AGEING TESTS Introduction Basic Approach OTHER RELEVANT ASPECTS Introduction Role of Water Diffusion Role of Applied Stress Possible Future Work Areas REFERENCES

7 1 INTRODUCTION This report was compiled as part of the activities of Task 6 Development of Methodologies for Life Prediction. The report is intended as a review of methods for predicting the lifetime of adhesive joints in hostile environments. Design approaches which are considered include: Mechanistic Fracture mechanics Stress analysis Correlations to water uptake in the adhesive Extrapolation from accelerated ongoing tests The objective of any design method must be to enable the engineer to predict within known confidence limits the performance of a joint of the required geometry under specified conditions of environment and load. Ideally, the data needed for implementation of the method should be generic in nature as opposed to being derived from complex tests over extended periods. In this review each of the approaches cited above are considered in this context together with recommendations for possible future work areas. 2 MECHANISTIC APPROACH 2.1 Introduction Modelling the lifetime of adhesive joints upon a detailed knowledge of the kinetics and mechanisms of the environmental failure process must obviously be the preferred method. A successful modelling attempt was reported by Gledhill et. al. [1], and this was used to predict the lifetime of bonded structures aged in natural outdoor weathering trials [2]. Their work is first discussed below. However, their work was concerned with relatively simple adhesive joint systems, and several major problems arise when this approach is attempted for more complex adhesive systems, as outlined in later sections. 2.2 Gledhill et al Approach The modelling work of Gledhill et. al. was based on the idea that one could identify three stages in the environmental attack of water on an adhesive joint. This idea followed from experimental studies on the effect of water on adhesive joints which consisted of a simple, hot-cured epoxy bonding mild-steel substrates, which had been grit-blasted and solvent degreased prior to bonding. The first stage is the accumulation of a critical concentration of water in the interracial regions which must be exceeded for environmental attack to occur. The requirement of a critical concentration appears to be a general one from the many experimental observations [3-8] of attack by moisture upon many different types of adhesives joints, although its value is dependent upon the particular adhesive system. Also, it is not clear why such a critical concentration should exist, as discussed below. For the simple adhesive joints which were studied, the rate of attaining this critical concentration appeared to be governed by the rate of diffusion of water through the adhesive to the interracial regions. This observation, which was deduced from comparing activation energies for interracial debonding in the adhesive joints and the rate of water diffusion through the bulk adhesive, is a crucial aspect of the 1

8 success of the modelling studies reported by Gledhill et. al. The second stage involves a loss of integrity of the interracial regions. In the particular case of the epoxy/mild steel joints studied by Gledhill et. al. this arises from the rupture of interracial secondary bonds by the ingressing water molecules - and this can be predicted and understood from basic thermodynamic arguments [3, 15]. More generally, the mechanisms could be envisaged such as: (i) (ii) (iii) (iv) (v) the rupture of interracial secondary bonds; the rupture of interracial primary bonds; the hydration and weakening of the oxide layer on metallic substrates; the hydrolytic attack on a boundary layer of adhesive, adjacent to the interface - this boundary layer may have a different chemical/physical structure to that of the bulk adhesive due to the presence of the adjacent substrate surface; the hydrolysis of the primary bonds of any primer present - leading to a cohesive failure through the primer layer. However, it should be appreciated that if the rate of environmental attack is not governed by the rate of diffusion of water through the adhesive to the interracial regions, then the rate determining step and kinetics need to be elucidated before any mechanistic predictive modelling can be undertaken. (Note: the above mechanisms are often accompanied by plasticisation of the adhesive, and possibly the substrates, if permeable to water. However, this does not usually lead to a major loss of joint strength, and may even lead to an increase in joint strength! In any event, such changes can be readily measured and predicted.) The third stage concerns the ultimate failure of the adhesive joint. However, for the joint to fracture or lose an appreciable amount of its original strength upon subsequent testing it is usually not necessary for the weakening of the interracial regions to have proceeded completely through the joint. From basic fracture mechanics considerations only a relatively small environmental crack is required to have developed before a substantially decreased failure time, under a constant load test, or a diminished joint fracture stress is observed. Indeed, with many joint geometries subjected to an imposed load and moisture, catastrophic failure will occur when the environmental crack, which is growing by the mechanisms outlined above, attains a relatively small critical length. Gledhill et. al. therefore modelled the water diffusion into the adhesive layer assuming Fickian diffusion [9], and the critical concentration of water needed was ascertained from experimental measurements of the level needed to cause any observed loss of joint strength. Hence, the length of the environmental crack (i.e. the length of the now-debonded interface) could be deduced, see Figure 1. Then, from (i) independent measurements of the modulus and adhesive fracture energy of the bulk adhesive and (ii) calculation of the joint geometry factor for the joints whose lifetime is to be predicted, the residual strength of the joint could be predicted using basic fracture mechanics. The resulting predictions, compared to the experimental measurements, are shown in Figure 2. As may be seen, the agreement between theory and experiment is good, and this method was also successfully used for estimating the residual strength of actual bonded structures exposed to outdoor ageing over a five year period. 2

9 However, extending the above concepts to other, more complex, adhesive systems does present several problems. 2.3 Extending the Gledhill et al Model The critical water concentration The first problem with extending the above model is the concept and definition of a critical water concentration. This was introduced into the model to describe the commonly observed situation where adhesive joints may survive for many, many years in low water concentration environments (e.g. 23 C and 55% r.h.) with no significant loss of strength, but show significant losses of strength due to environmental attack occurring in a relatively short time scale at somewhat higher water concentrations. More recent work by Brewis et. al. [10] also found that a critical water concentration existed for the decay of epoxy/steel joints when exposed to various concentrations of water. They studied the absorption isotherm of water in the epoxy (bulk) adhesive and found no discontinuities which would account for a critical water concentration in terms of the clustering of water molecules in the bulk adhesive, as had previously been suggested by Comyn et. al. [11, 12]. Therefore, they suggested that a mechanism that would account for both the loss of joint strength above a critical water concentration, and the lack of any discontinuity in the water absorption isotherm, was the possible hydration of salts trapped at the adhesive/substrate interface. The basic idea arises from the fact that salt hydrates form at specific levels of water concentration [13]; salts (e.g. sodium salts) are the by-products of the formation of the epoxy adhesive and are also present from the cleaning of the substrates prior to bonding. A mechanistic route could be, for example: consider that the joints are in air at a low relative humidity/vapour pressure, which is lower than one of the definite vapour pressures of the hydrated salt compounds trapped at the interface. As the relative humidity of the air rises more water enters the adhesive and, when it reaches the interface at the required concentration, the salt will form the next higher hydrate and the water molecules will be converted to the salt hydrate. This process will be repeated as each hydrate level is filled. But once the highest hydrate has been formed, water molecules can no longer be absorbed by the trapped salts and they will be free to attack and weaken the interface. Lefebvre et. al. [8] also have reported the existence of a critical water concentration for the decay of epoxy/glass joints when exposed to various concentrations of water. However, their studies revealed a clear discontinuity in the water absorption behaviour for the three slightly different amine-cured epoxies which they studied. Further, the discontinuities occurred at the same relative humidity as the observations of the onset of the loss of strength of the epoxy/glass joints when exposed to the different relative humidities. To examine the causes for these observations they undertook several elegant experiments. Firstly, they added COCl2. 6H2O to the epoxy adhesive and showed that the discontinuities in the absorption isotherm and the loss of strength of the epoxy/glass joints both occurred at the same relative humidity, and this was as expected from the relative humidity at which the COCl2. 6H20 salt acted as a osmotic centre. Further, optical microscopy revealed the presence of fine cracks in the adhesive around each salt crystal, caused by the local osmotic pressure exceeding the fracture stress of the adhesive. Thus, this idea of the condensation of water around phase-separated, water-soluble impurities is very similar to that advanced above by Brewis et. al. [10]. 3

10 However, secondly, Lefebvre et. al. purified an epoxy adhesive, removing virtually all the impurities from the bulk adhesive. On repeating the absorption isotherm and the loss of strength experiments, they found that the pure adhesive was not significantly different in its behaviour to that of the standard adhesive. Therefore, they concluded that the presence of salts was not the mechanism responsible for their observations of a critical humidity being needed for environmental attack to occur upon the joints. (However, it should be noted that they could not, of course, exclude salt electrolytes from being present on the glass substrate, and hence being at the all-important adhesive/glass interface. Thus, their conclusions are not entirely sound in this respect.) Thirdly, they studied the effect of the concentration of diol and hydroxyl groups which are present in the epoxy adhesive due to the curing reaction. From their absorption experiments, they found that these groups gave rise to a critical humidity effect. They therefore concluded that this effect is an intrinsic property of the epoxy network and that either diol or hydroxyl groups, or both, are the major contributors. Hence, the mechanism that Lefebvre et. al. [8] proposed for the observation of a critical water concentration is water trapping, or clustering, at high humidities - i.e. above the critical water concentration, water condenses on the -OH groups of the polymer, thereby breaking interchain hydrogen bonds and displacing adsorbed -OH groups from the surface of the substrate. Thus, to summarise, the presence of a critical water concentration is firmly supported by many experimental observations reported in the literature. The most likely causes appear to be: (i) (ii) the hydration of salts in the adhesive and at the interface limiting the concentration of water molecules available for attacking the interracial regions of the joint until a critical water concentration is reached in the adhesive; or trapping, or clustering, of water molecules until, when a critical water concentration is reached, water molecules then condense on the -OH groups of the polymer, thereby breaking inter-chain hydrogen bonds and displacing adsorbed -OH groups from the surface of the substrate. However, a major problem is that the critical water concentration cannot currently be readily predicted or easily measured. In some adhesive systems it may be associated with a discontinuity in the absorption isotherm for water in the bulk adhesive, but this is not always the case. Therefore, at present, a set of careful experiments is needed to identify the critical water concentration from measuring the loss of joint strength as a function of the relative humidity of the environment used The mechanism and kinetics of environmental attack In the above work of Gledhill et. al, Brewis et. al. and Lefebvre et. al. the mechanism of water attack was considered to be the displacement of adsorbed adhesive molecules, which are adhering via secondary bonding forces, on the substrate surface by water molecules. Further, the rate of environmental attack via this mechanism was taken to be governed by the rate of water diffusion through the adhesive. Thus, once the critical water concentration was established, the rate of environmental attack could be readily modelled. However, this mechanism, and its associated kinetics, represent the simplest, and most easily modelled, mechanism of environmental attack. Other mechanisms of attack [14] which have been reported are: (i) the rupture of interracial 4

11 primary bonds, (ii) the hydration and weakening of the oxide layer on metallic substrates, (iii) the hydrolytic attack on a boundary layer of adhesive, adjacent to the interface and (iv) the hydrolysis of the primer layer. However, for many adhesive systems of commercial interest the details of the mechanisms of environmental attack are not well established. Further, and more importantly, the rate of environmental attack via these more complex mechanisms is not understood, or known in any detail. For example, the mechanism of attack on a commercial epoxy -adhesive/chromic-acid etched aluminium-alloy joint is not definitively established, even allowing for the large amount of research undertaken by the aerospace and defence industries both in Europe and in the USA. On the other hand, if we consider the problem of water attack on a epoxy/silane primer/steel joint, then the mechanism of attack appears to be via hydrolysis of the polysiloxane primer layer. However, in both of these examples, the kinetics of attack are not established. Further, even empirical modelling of the kinetics of attack has failed to yield any sensible form of rate equations, which can then be employed for predictive analyses. To summarise, whilst many plausible mechanisms of water attack have been proposed, the details are not well established except for a comparatively few simple adhesive systems. Of more importance, the kinetics of attack are only well established for a comparatively few simple adhesive systems, and even attempts at empirical modelling of the rate of environmental attack upon adhesive joints have not been very successful. 2.4 Possible Future Work Areas The mechanistic approach to predicting the lifetime of adhesive joints subjected to hostile environments has the great appeal that it should be able to handle very different joint designs and exposure conditions for a given adhesive system. The details of the mechanisms of attack would, ideally, be most useful to know. However, the more important aspects are: (i) identifying the critical water concentration and (ii) establishing the kinetics of water attack. The identification of the critical water concentration for a particular adhesive system can only really be achieved experimentally by studying the loss of joint strength as a function of the relative humidity of the environment employed. Obviously, it will depend upon not only the adhesive employed, but also such factors as the substrate type, substrate pre-treatment, use of any primer, Establishing the kinetics of water attack may be attempted by: (i) (ii) Comparing the activation energy for interracial failure progressing through the joint with known values of the activation energy for other processes, such as water diffusion through the adhesive or hydrolysis of -Si-O-Si- primer bonds. This obviously requires the loss of strength experiments to be conducted as a function of water temperature. Fitting the loss of strength data to various rate equations; for example, by trying a first-order rate equation to empirically describe the loss of strength versus time data. Again, if the data have been obtained as function of water temperature, then this greatly assists the empirical fitting of the data. 5

12 3 FRACTURE MECHANICS APPROACH 3.1 Introduction As commented above, fracture mechanics maybe used in the mechanistic approach, but at the heart of the mechanistic approach is the knowledge and modelling of the kinetics and mechanisms of the environmental attack process. In the more general fracture mechanics approach, tests are conducted measuring the rate of crack growth through the joint versus the applied strain-energy release rate, or stress-intensity factor; a test geometry being selected which may be analysed readily using a fracture mechanics approach, and the environment being one which is of direct interest. The lifetime of any other type of joint design is then predicted using a standard fracture mechanics analysis; the geometry factor for the design of adhesive joint of interest (or the compliance function of the joint) needs, of course, to be ascertained. The fracture mechanics analysis may require the values of the inherent flaw size and final crack length in the joint to be deduced, or it may be simply based upon the knowledge of the threshold value of the fracture energy (or fracture toughness). 3.2 Basic Approach The basic idea [16-18] is that: (i) For static loading - the rate of crack growth (da/dt) is measured as a function of the applied strain-energy release rate (GI) or stress-intensity factor (KI) in the selected environment. This may be undertaken using a wide variety of joint designs; i.e. the bonded double torsion specimen, double cantilever beam specimen or tapered double cantilever beam specimen. The method of analysis is usually via the energy-balance approach, since this approach does not have the theoretical problems associated with analysing cracks at interfaces which arises when the stress-intensity factor method is employed [19-21]. However, a problem with this type of experiment is that the initial (sharp) crack inserted in the adhesive layer rapidly becomes blunt under the action of the applied load and the plasticizing effect of the ingressing water [22, 23]. This means that the stress field at the interface (where water attack and further crack growth is expected to occur) diminishes and the environmental failure rate is greatly decreased. Now, increasing the applied load does not help this problem, since this results in a cohesive-in-the adhesive failure mechanism, which is typically not the one of interest. One method for overcoming the problem is to gradually increase the load with time, to compensate for the decreasing stress field at the interface. However, this must never be done so rapidly as to induce the cohesive-in-the adhesive failure mechanism. Thus, this route is possible, but not easy to achieve in practice! The graph of log da/dt versus log GI is usually linear, and so may be fitted as a power-law. The basic method of analysis is then to postulate that in the bonded joint of interest that a flaw (e.g. an intrinsic crack length or some other defect of length ao) will slowly propagate under the action of the applied load and environment until it reaches the critical size, af, for rapid crack growth. The final phase of rapid crack growth will typically only last milliseconds, or so, and can therefore be ignored in any estimate of the actual joint lifetime. Hence, the measured relationship between da/dt and log GI is integrated between aoand af Another parameter which is needed is the compliance relationship, or geometry factor, for the bonded component whose lifetime is being predicted. Also, some estimate of ao is required. The effects of temperature may be included in the above model by using an 6

13 activated rate equation to allow for different test temperatures. (ii) For dynamic (cyclic fatigue) loading - the advantage with this type of loading is that the dynamic loads should, ideally, keep the crack in a relatively sharp condition; since it is growing steadily under the oscillating loads. As mentioned above, keeping the crack-tip sharp has been a major problem in undertaking the statically-loaded type of experiment. In the dynamic type of tests, the rate of crack growth, da/dn, per cycle is measured as a maximum value of the applied strain energy release rate (Gmax) Again, when log da/dn, per cycle is plotted versus Gmax the relationship may be described by a power-law - or modified power-law. The form the modified power-law takes is: (1) where Gth is the minimum, or threshold, value of the adhesive fracture energy below which no fatigue crack growth is observed to occur, GC is the value of the adhesive fracture energy from constant rate of displacement tests (i.e. the dry, static value) and D, n, n1 and n2 are material constants. Now for a single-lap joint loaded in tension, integration [18] gives: In this equation the terms are defined in detail in [18], but the main terms are the values of the fracture mechanics parameters (i.e. D, n, n1, n2, Gth and GC), which maybe deduced from the fatigue data obtained from the fracture mechanics specimens. Further, the geometry of the single lap joint, whose fatigue behaviour is to be predicted is known, so the values of the parameters e, h, ta, and c are known; where e is a function of substrate thickness, h, and substrate bending stiffness, ta is the thickness of the adhesive layer and c is the half the bonded-overlap length. Also known is the modulus, Es, of the substrate materials forming the lap joint. So, if the values of the integration limits (i.e. a0 and af) are identified from basic fracture mechanics, then the number of cycles to failure, Nf, of the single lap joint may be predicted as a function of the maximum load per unit width, Tmax, applied to the joint during a fatigue cycle. These results are shown in Figure 3, where the experimental results are also shown for comparison. As may be seen the agreement is good. It should be noted, that the above studies were conducted at 23 C and 55% r.h, using joints which consisted of an epoxy-film adhesive bonding together unidirectional carbon-fibre/epoxy composites. Using a double-cantilever beam (DCB) specimen, the rate of crack growth per 7

14 cycle, da/dn, was measured as a function of the maximum strain-energy release rate, Gmax, imposed in a fatigue cycle. The results showed that there did indeed exist a threshold value, Gth, below which no significant fatigue crack growth occurred. The value of Gth was 0.28 kj/m2, and this value of Gth was about an order of magnitude lower than the adhesive fracture energy, GC, measured under static test conditions. Obviously, one could employ the value of Gth as a very conservative design parameter and estimate the maximum fatigue loads which could be imposed on a structure without causing fatigue crack growth. Such an approach is certainly worthy of further consideration. 3.3 Possible Future Work Areas The most obvious approach for the future work is: (i) (ii) (iii) Determine the rate of crack growth, da/dn, per cycle under defined environmental conditions as a function of the range of applied strain energy release rate ( GI), or as function of the maximum value of the applied strain energy release rate (Gmax). A given frequency, mean displacement and displacement ratio to be used and a tapered double cantilever beam type of specimen to be employed. Determine: (a) whether a value of the threshold, Gth, exists and (b) whether the relationship between da/dn and Gmax is unique for these test conditions, or depends upon whether the specimens are pre-aged in water prior to fatigue testing. Attempt to use the data to predict the number of cycles to failure of lap joints which are subjected to cyclic fatigue in the given test environment. Both the full integration method and the conservative Gth method should be examined. 4 STRESS ANALYSIS APPROACH 4.1 Introduction Again, here the detailed mechanisms are not really considered. A stress analysis is conducted on the adhesive joint of interest, a suitable failure criterion is assumed and the relevant properties of the adhesive and substrate are measured as a function of the time in the environment of interest. This approach appears to be a reasonable one where failure is via cohesive fracture through the adhesive layer or substrate, but is far more difficult to employ when the failure is at, or close to, the interface - as is observed in most bonded metal or glass joints after environmental attack. Where a cohesive-in-the-adhesive (or substrates) locus of failure is observed, the properties of the adhesive and substrate may be measured when dry and wet and a suitable failure criterion for joint failure may be assigned. The change in the predicted strength of the joint as a function of time in the environment may then be deduced and compared to the experimental results. The only major problems in adopting this approach are: (i) (ii) assigning a sound failure criterion; and the assumption that the locus of failure is always cohesive through the adhesive (or substrates).

15 Unfortunately, the main locus of failure after environmental attack is invariably fracture at, or close to, the interface adhesive/substrate interface. When such failures occur the assignment of the failure criterion becomes extremely difficult and the relevant properties of the interface are unknown. 4.2 Previous Work John et. al. [24] studied the strength of double lap shear joints which consisted of carbonfibre composites bonded using a room temperature cured adhesive. The joints were exposed to 90% r. h. at 40oC for up to one year. The loss of strength was measured and the diffusion and volubility of water in the composites and adhesives ascertained. Also, measured were the changes in the elastic-plastic tensile and shear properties of the materials as a function of time in the hostile environment. Even after environmental attack the locus of joint failure was by cohesive failure through the adhesive layer - the adhesive/cfrp interface is indeed predicted to be stable to water from thermodynamic considerations. The double lap joints were analysed, using finite element analysis (FEA), and failure was assumed to occur when the yield stress of the adhesive was attained over a critical distance at the ends of the bonded overlap. This idea of a critical stress acting over a critical distance has been previously successfully used by workers examining metal [25] and epoxy [26, 27] fracture problems. From the change in mechanical properties of the adhesive and composite the joint strengths as a function of time in the environment could be predicted and compared with experimental measurements. The agreement was good. Next, the amount of water in the adhesive and substrates for a given time could be estimated, assuming Fickian water diffusion, hence the mechanical properties of the materials could be estimated at this time - from a simple empirical curve fitting of mechanical properties versus water uptake. Therefore, the joint strength could be predicted over relatively long time scales using: (i) these estimated properties, (ii) the critical stress/distance criterion and (ii) the FEA method to analyse the joints. The predicted joint strength was in good agreement with the measured value after one year of exposure. A similar approach has been reported by Imanaka et. al. [28]. They used FEA to assess the maximum normal and shear stresses in butt joints consisting of bonded thin-wall cylindrical tubes. They also determined the S-N relationships for these joints by undertaking cyclic fatigue experiments, and plotted the data in the form of the maximum cyclic normal and shear stresses in the butt joints versus the number of cycles to failure. Next, they considered bonded solid-shaft joints which were to be subjected to tensile or torsional cyclic loads, and from FEA they estimated the maximum normal and shear stresses in these joints. From the previously obtained S-N curves, they therefore predicted the S-N curves for the bonded solidshaft joints subjected to tensile or torsional cyclic loads; using the maximum normal stress attained in the joint as the failure criterion for the shaft joints load in tension and the maximum shear stress attained in the joint as the failure criterion for the shaft joints load in torsion. The S-N curves for the bonded solid-shaft joints were also experimentally measured, and the agreement between the predictions and experimental values was good. However, obviously, one has to undertake a series of tests of one given design in the environment of interest before any predictions can be made. Also, the failure criteria used by Imanaka et. al. are known to be very simplistic criteria, and are of limited use in predicting the failure of real joints.

16 Thus, both of these groups of authors have successfully: (i) (ii) (iii) (iv) Undertaken an FEA of the joints. Assigned a failure criterion to predict joint strength. Since cohesive failure in the adhesive was always observed, and there was no degradation and failure of the interface, this was relatively straightforward. But note that each group of authors used a different failure criterion! Imanaka et. al. used a critical stress criterion, whilst John et. al. found a more complex criterion of a critical stress acting over a critical distance was required. These authors both used an elastic analysis. If a more realistic elastic-plastic analysis was used, it is probable that yet another criterion would need to be invoked. Also, the role of the adhesive fillets was ignored by both sets of authors. This has been shown [29, 30] to be of considerable importance in deciding failure criteria. Measured the properties of the adhesive (and substrates) as a function of the environment or test conditions of interest. Combined (i) to (iii) above in order to predict the strength of either joints subjected to a longer periods in the same environment, or joints of a different design. 4.3 Possible Future Work Areas The main problem with the general application of this approach is that the assignment of a failure criterion for joints is still a very controversial topic. This is especially the case when interracial failure occurs. For example, what is the failure criterion for the failure of an epoxy/grit-blasted steel interface after two years immersion in water at 60oC? Thus, for future work this approach could be of use when adhesive (or substrate) failure is observed, as is likely when bonding the plastic or composite substrates. But this approach faces the above, and common, difficulty of assigning a suitable failure criterion when interracial failure is recorded. 5 CORRELATIONS TO WATER UPTAKE IN THE ADHESIVE 5.1 Introduction Here the mass uptake of water in the adhesive layer in the joint is either directly measured, or calculated via measuring the water absorption properties of the bulk adhesive, and correlated to the measured loss of joint strength. Predictions of joint strength are simply based upon extending the correlations established from the time scales over which the measurements were made. The extension to long time scales may involve the extrapolation of a plot of loss of joint strength versus water uptake in the adhesive, or involve determining a mathematical description of this relation and deducing the effect of longer time periods using the mathematical model. 5.2 Typical Results Some typical results are shown in Figure 4. Here the strength of lap joints are plotted against the corresponding fractional mass uptake (Mt/M.) of water in the adhesive layer. A linear relationship is observed, but note that the relationship does depend upon the choice of surface 10

17 treatment. The superior anodising treatment gives a higher strength, at any given time of exposure to the hot/wet environment, than the simple grit-blasting treatment. Also, the adhesive is almost saturated at the end of these experiments; if only the test data at the earlier exposure times were taken for the extrapolation, then the degree of uncertainty in extrapolating the linear relationships to longer time scales would be relatively high. Finally, whether the same relationship would hold, and hence be unique, for different types of adhesive joint designs has not been studied. A further problem is highlighted by the results shown in Figure 5. These results show that the joint is still losing strength even after the adhesive layer has become fully saturated. Obviously this result would be expected to be observed in the case of the more durable adhesive systems. However, this result clearly reveals that the amount of water in the adhesive layer has no direct relationship to the loss of joint strength which can be expected to be observed. Nakamura et. al. [31, 32] have also adopted the approach of correlating the strength of the joint and the water uptake in the adhesive layer. They, however, suggested the empirical relationship: (3) where S is the strength of the joint at time t, SO is the initial strength of the joint, C is the mass uptake of water at time t, Cs, is the mass uptake of water at saturation and P is the ratio of the absorbed water which contributes to bond breakage. Equation (3) results in a S-shaped curve of percentage retention of strength versus time, although the exact shape is determined by the value taken for P. The problems in applying this equation are: (i) P is a fitting parameter, where O> P <1- so one really needs to know the loss of strength data before Equation (3) can be used! (Its physical meaning is stated to be the degree to which the total absorbed water contributes to the interracial failure, which is assumed to be caused by the water attack - so, again, the presence of a critical water concentration is essentially being modelled.) (ii) The value of C is deduced assuming Fickian diffusion and, as discussed by the authors, the results are dependent upon the value taken for the diffusion coefficient. They found that to obtain the correct shape for the predicted results as observed for the experimental results often required the value of P to be less than unity. This in turn led to the requirement that water diffusion through the interface was greater than that through the adhesive. They obtained the diffusion coefficient for water through the interface by fitting the Equation (3) to the experimental data. Thus, in the Nakamura et. al. model there are many aspects, such as the observation of a critical water concentration for attack to occur and the fact that the rate of attack may not be simply governed by water diffusion, which are hidden by the need to determine P by prior fitting to the experimental data for the loss of joint strength - and there is no route to the direct calculation of the value of P. Hence, the predictive power of the model is rather limited. 11

18 Kayaki et. al. [33] have studied the effect of moisture on the static and fatigue strength of bonded metal lap joints which consist of cold-rolled steel or galvanised steel bonded with an epoxy adhesive. They found that the fatigue behaviour was sensitive to the environmental conditions to which the joints had been exposed prior to ageing - exposure to the hot/wet conditions being the most deleterious. They observed that the mechanisms of attack were: (i) degradation of the bonded interface and (ii) plasticisation of the bulk adhesive as has been previously discussed. They then used an empirical equation proposed by Chamis and Sinclair [34] to correlate the loss of fatigue strength to the number of cycles required for failure, using a knowledge of the initial strength and glass transition temperatures of the unaged and aged adhesive. However, whilst the calculated results are in good agreement with the experimental values, firstly a fitting factor was needed. Secondly, the Chamis and Smith equation was originally applied to fibre-composites, where the loss of fatigue strength upon exposure of the composite to a hot/wet environment was due to the plasticisation of the matrix of the composite by water, accompanied by the expected decrease in the glass transition temperature of the matrix. Their equation does not take into account the degradation of the interface. Hence, it is difficult to see how the model can predict a loss of strength from this mechanism. Finally, of interest is the observation from Kayaki et. al. that when joints were exposed to different environments as a function of time that the static tensile lap-shear strength reached a lower-bound value when exposed to the hot/wet environment of 98 % r. h and 50 C. This lower-bound value was about 75% of the initial dry value. However, when the fatigue tests were undertaken no lower-bound value was recorded, and the fatigue strength was still steadily decreasing when the experiments were halted. These observations demonstrate again the more damaging nature of fatigue tests when assessing the effect of hostile environments upon bonded joints. 5.3 Possible Future Work Areas A simple correlation between the amount of water in the adhesive layer and the loss of joint strength would obviously be appealing, and of use in estimating the lifetime of adhesive joints. However, clearly from the above comments no such simple, unique, correlation can really be expected. Nevertheless, the following aspects are worthy of further consideration: (i) (ii) (iii) For a given adhesive system (e.g. adhesive type, substrate type and choice of surface pre-treatment) a relationship such as that shown in Figure 5 maybe expected. It would be of interest to determine whether this relationship is a unique one for all types of joint design. If so, then the uptake of water into the adhesive layer for a given adhesive system could be calculated for the joint design and environment (e.g. temperature and r.h.) of interest and the predicted joint strength read from the relationship shown in Figure 5; at least up to the point when complete saturation of the adhesive has occurred. To examine the above idea, the mass uptake of water may be deduced if the diffusion and volubility coefficients of water in the adhesive (and substrates, if permeable to water) are known for the environments of interest. Next, the relationship between joint strength (normalised to the initial ( dry ) joint strength) and water uptake may be ascertained for a series of different joint designs (e.g. lap joints, butt joints, etc.). Is there an unique relationship? How do the values of the calculated water uptakes in the adhesive layers in the joint compare to the measured values? This question is probably only worthy of detailed 12

19 consideration if the above method of lifetime prediction shows promise. 6 EXTRAPOLATIONS FROM ACCELERATED AGEING TESTS 6.1 Introduction In this approach an acceleration factor is assigned to a set of accelerated ageing tests, and this factor is then used to estimate the lifetime of joints subjected to less demanding, but more natural, ageing conditions. 6.2 Basic Approach Little is to be found in the published literature on this approach but this is the way that many established adhesives laboratories undertake a first-round selection of an adhesive system. Basically, for example, the lap shear strength versus time in a given environment (e.g. 100% r. h. at 40oC) will be assessed over a time period of many months. These data will then be compared to results obtained from similar tests for adhesive systems where the long-term inservice performance is also known. Hence, a judgement will be made as to whether the new adhesive system under test is worthy of further consideration. The problems with this approach are: (i) (ii) (iii) (iv) (v) It requires staff with skill and experience to make this type of judgement. Thus, for companies not experienced in adhesives technology this approach is of little use. For example, let us suppose a manufacturer of train doors wishes to use adhesives technology and he finds that after six months in water at 60oC the loss of strength of single-lap joints of chromic-acid etched aluminium-alloy bonded with a commercial hot-cured toughened epoxy is 35%. What can he then predict about the retention of joint strength of his adhesively-bonded doors when exposed to (a) a Northern European climate and (b) a typical hot/wet Far Eastern climate? Even to an expert familiar with the adhesives systems and their intended applications, it does not reveal the exact lifetime to be expected, but merely indicates the very approximate lifetime that might be expected. It does not indicate anything about other factors, such as the possible added effects of statically or dynamically applied loads. It often takes considerable time for the good and durable adhesive systems to reveal any significant loss of strength upon exposure to the test environment. Hence, it may take a long time for any judgement to be made about the relative lifetimes to be expected from such systems. This obviously delays the selection of any improved adhesive system. The last point has led to the development of many accelerated test methods which try to increase the acceleration factor. However, one has to be very careful on this aspect of testing. In particular: (a) If the temperature of the environment is increased too much, then one may observe environmental attack mechanisms which are never observed at typical natural temperature levels. One is reminded of the saying: When did boiling an egg ever accelerate the birth of a chicken? 13