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Statistical aspects of the mechanical behaviour a paste adhesive
International Journal of Adhesion & Adhesives 40 (2013) 70–79
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International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Statistical aspects of the mechanical behaviour a paste adhesive Gregory Bresson a,b,c,d, Julien Jumel a,b,c, Martin E.R. Shanahan a,b,c,n, Pierre Serin d a
University Bordeaux, I2M, UMR 5295, F-33400 Talence, France CNRS, I2M, UMR 5295, F-33400 Talence, France Arts et Metiers ParisTech, I2M, UMR 5295, F-33400 Talence, France d Centre National d’Etudes Spatiales, Direction des Lanceurs, Rond Point de l’Espace, 91023 Evry Cedex, France b c
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 7 June 2012 Available online 26 June 2012
We present experimental results describing the mechanical behaviour of an epoxy-based structural paste adhesive with aluminium powder filler under proportional loading. The main aim of the present study is to relate the dispersion on joint strength (variability) to void and particle sizes and distributions, also taking into account effects of the curing cycle. Tensile tests with dogbone specimens were done at different strain rates. The statistical nature of results is related to the heterogeneous material microstructure, containing voids as well as mineral particles for reinforcement. A Weibull-type statistical analysis is suggested for use when the stress distribution is heterogeneous. Mechanical dynamical analyses were done with evaluation of polymerisation steps. Multiple dynamical testing was done with temperature scanning on samples having undergone various cure cycles. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Adhesive strength Curing conditions DMA Statistics Weibull analysis
1. Introduction Joining parts with adhesives offers many advantages compared to traditional techniques making use of mechanical fasteners [1,2]. The aerospace industry shows an interest in this technique which enables the joining of dissimilar materials and generally leads to important mass and stress reduction [3,4]. Nevertheless, a lack of confidence limits the use of this technology [5], due to a high level of dispersion (variability, or variance) on the mechanical strength of bonded joints, especially in ageing conditions. Moreover, this statistical behaviour can be attributed to many causes such as, ageing [6], adhesive or surface preparation defects, and dimensional precision of the bondline [7]. The overall aim of this work is to make a preliminary investigation of the influence of the adhesive per se, in the behaviour and strength of adhesive bonds. Such effects as different crosslinking cycles and the presence of particle fillers and voids (bubbles) have an intrinsic rˆole to play. To obtain better understanding of the damage of adhesively bonded joints, we use a standard tensile test with dogbone specimens to measure the load displacement curve of the cured adhesive paste. The adhesive studied (Hysol EA 9394) [8] presents a highly heterogeneous microstructure made of both reinforcement particles and voids produced during the manual mixing prior to application. Our aim is to relate this dispersion on the joint strength to the void and particle sizes and distributions. This work constitutes a logical extension to Ref. [9], in which we presented a heterogeneous
n Corresponding author at: University Bordeaux, I2M, UMR 5295, F-33400 Talence, France. Tel.: þ33 5 40 00 62 22; fax: þ 33 5 40 00 69 64. E-mail address: [email protected] (M.E.R. Shanahan).
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijadhadh.2012.06.006
distribution of porosities in the adhesive layer due to the assembly process and degassing effect during the cure. This study is mainly focused on the description of protocols and tests required to supply engineers with the data required for correct polymerisation. Besides this, Dynamic Mechanical Analysis (DMA) is performed to monitor the curing kinetics of the adhesive paste for different curing conditions using an annular shear pumping configuration technique. Following this, a specific tension fixture is used on small rectangular specimens in order to characterise the glass transition temperature and to follow mechanical stiffness as a function of the temperature. These experimental methodology basic analyses are performed with an eye to quality control of the manufactured adhesive. The study shows the limitations of using oversimplified mechanical testing and the real need for detailed characterisation.
2. Experimental 2.1. Materials The adhesive, Hysol EA 9394, is a two-part structural paste adhesive, which cures at room temperature and possesses excellent strength up to ca. 180 1C and even higher temperatures. It is an amine-cured epoxy adhesive paste with an aluminum powder filler. Its thixotropic nature prior to cure and excellent high temperature compressive strength also make it ideal for potting, filling and liquid shim applications. The weight part ratio of resin and hardening agent is 100:17. In this study, the two part adhesive was hand mixed using spatulae. Various cure cycles were employed, with an aim to study
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their effects on mechanical properties, in particular complex modulus (viscoelastic modulus) and fracture strength. The conditions ranged from 1 day at ambient temperature up to 45 min at 75 1C, the effects being discussed below.
2.2. Dynamic mechanical analysis (DMA) Dynamic mechanical analysis, or DMA, is commonly used to characterise the intrinsic mechanical behaviour of materials as a function of temperature. It consists of dynamic mechanical loading of
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the sample in oscillatory strain, while measuring viscoelastic properties in situ. The system can be applied to several types of dynamic displacement or loading while controlling temperature during the test. Its use in mechanical characterisation to study structural changes in epoxy systems [10] is widely spread. As discussed by Tamulevitch and Moore [11], the cure time and temperature can have a dramatic effect upon the glass transition temperature, Tg, of any given epoxy resin system, the glass transition temperature being the reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle state into a molten or rubber-like state.
Fig. 1. Viscoelastic data during cure: tan d (in shear) and shear modulus, G, vs. cure time for temperatures of (a) 66 1C and (b) ambient (25 1C)—frequency 50 Hz. At the origin, the adhesive is still a paste and these graphs effectively monitor cure behaviour.
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To obtain optimal characterisation and curing protocol of the adhesive paste studied, several dynamic mechanical tests were done. Technical data indicate two main curing temperatures to obtain complete cure of the adhesive paste, with room temperature during 8 day and 66 1C in an oven for 80 min. Monitoring of mechanical properties, under controlled static temperature, was done for both curing cycles, using an annular shear pumping configuration technique. Shear modulus, G, and tan d were monitored as a function of testing time. Tan d corresponds to the loss factor of the adhesive paste where d, is the dephasing angle between applied load and measured deformation. Apart from the above test performed during cure, a second test with a specific tension fixture was used on small rectangular specimens (already cured) in order to characterise the glass transition temperature, Tg, and mechanical properties of the hardened adhesive as a function of temperature. Specimens were cured in an oven for 80 min at 66 1C. For the ambient curing temperature, mechanical testing was effected after various periods of polymerisation to see the evolution of mechanical properties as a function of time. Finally, with an aim to decrease curing time, another cycle was used, with crosslinking at 75 1C for 45 min. Young’s modulus and tan d were monitored as a function of the temperature, for a temperature rise gradient of 1 1C/min from ambient temperature to 250 1C. It should be pointed out that the curing cycles were chosen in accordance with those used for adhesive joints (see below) but that, due to the exothermic properties of crosslinking and different geometries of bulk and adhesion test pieces, in particular surface/volume ratio, strictly identical thermal conditions are virtually impossible to reproduce. 2.3. Tensile tests The characterisation of the adhesive paste with standard tests was a first step in a study of mechanical behaviour and its temperature sensitivity. Mechanical testing with standard tensile tests was also used to observe the macroscopic behaviour of the cured EA9394 adhesive. The statistical technique of Weibull was
then applied to study the dispersion of fracture strength as a function of strain rate. The standard ISO tensile test specimen format was used to characterise mechanical behaviour. ISO 527-2 (‘‘Determination of tensile properties—Part 2: Test conditions for moulding and extrusion plastics’’) dogbone samples were cast in specific moulds with thickness, applying a load of ca. 200 N, with weights, to limit void occurrence. As mentioned above, samples were polymerised in an oven for 1 h at 66 1C, according to standard manufacturer protocol. The effective length and sample thickness were 33 mm and 2 mm, respectively. Stress/strain curves were obtained with a tensile machine (Zwicks Z010) with a 10 kN load cell and strain extensometer. A range of strain rates was used (0.01 min 1 to 1 min 1) and Young’s modulus measured in the linear elastic zone. The main objective here was to study the effect of strain rate on fracture stress and Young’s modulus (corresponding to elastic behaviour).
3. Results and discussion 3.1. Effects on mechanical properties of curing conditions Our preliminary investigation consisted of monitoring mechanical properties during cure at fixed temperature. Both shear modulus, G, and tan d were followed during cure with the annular pumping fixture, both at 25 1C and 66 1C. Shear modulus, G, and tan d are plotted as a function of time in Fig. 1 in order to observe structural changes during adhesive paste hardening. For crosslinking at 66 1C, the adhesive paste was apparently completely crosslinked after ca. 80 min, with a final shear modulus of 0.23 GPa (Fig. 1a). At 25 1C, EA9394 can be considered completely cured after 9 h with a final shear modulus of 0.2 GPa. Thus, the final shear modulus is little affected by crosslinking temperature (Fig. 1b). The conditions of crosslinking can be very important in adhesive preparation in order to optimise final behaviour. After
Fig. 2. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive cured at 66 1C for 1 h 20 min (adhesive already cured).
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fixing the polymerisation procedure, it is of interest to observe adhesive behaviour for both crosslinking temperatures. Small rectangular, tensile test specimens were cut in order to analyse mechanical behaviour under dynamic loading as a function of temperature, with a standard tension fixture. Both tan d and Young’s modulus, E, were followed as a function of temperature from ambient to 250 1C. The temperature increase rate imposed was 1 1C/min. Results are presented in Fig. 2, for the sample cured
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for 80 min at 66 1C. However, it should be noted that during the test, some further crosslinking may occur, particularly at the higher temperatures of the DMA test. The evolution of tan d and Young’s modulus, E, versus temperature has been plotted for various frequencies. Mechanical properties are affected by the strain rate. The glass transition temperature, as defined by the peak of tan d, varies from 185 1C to 210 1C for, respectively, 0.1 Hz and 100 Hz frequencies. Glass
Fig. 3. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive cured at ambient temperature for 8 day (adhesive already cured).
Fig. 4. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive already cured at ambient temperature but for only 4 day.
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transition temperatures correspond to tan d peaks, and a drop of Young’s modulus. At ambient temperature, a Young’s modulus of ca. 2.5 GPa was obtained and 0.14 GPa at 250 1C. Young’s moduli are comparable to those obtained with tensile tests (ca. 2.5 GPa to 2.8 GPa), as will be seen below. A specimen of EA9394 polymerised 8 day at ambient temperature was studied in the same manner between 30 1C and 250 1C, with a 1 1C/min rate of temperature increase. Results are presented in Fig. 3.
It is immediately obvious that very different behaviour results. Indeed, a first drop of Young’s modulus can be observed at ca. 80 1C. (This phenomenon was present, but barely visible, in the previous figure, with polymerisation at 80 min at 66 1C: the effect on Young’s modulus is much less marked.) This could possibly be attributed to incomplete crosslinking of the adhesive paste at this temperature after 8 day. The chemical reaction seems not to be totally finished at ambient temperature, revealing a secondary transition temperature, Tb, at 80 1C. In order to investigate this
Fig. 5. Evolution of (a) Young’s modulus, E, and (b) tan d vs. temperature for already (at least partially) cured adhesive—comparison of curing processes.
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aspect, a higher crosslinking temperature could be applied or a longer crosslinking time considered. Glass transition temperatures vary from ca. 175 1C to 200 1C, respectively, for 0.1 Hz and 100 Hz frequencies. At ambient temperature, Young’s moduli of 3.4 GPa and 3.9 GPa for, respectively, 0.1 Hz and 100 Hz frequencies are observed. Young’s modulus is influenced by loading speed, with a higher value for the higher strain rate. At 250 1C, a Young’s modulus of 0.14 GPa can be noted, as with the other crosslinking conditions (80 min at 66 1C). Incomplete crosslinking is expected be present for intermediate polymerisation times. In order to investigate this behaviour, a sample cured for 4 day at ambient temperature was tested. DMA results are presented in Fig. 4. Glass transition temperatures were only slightly modified (ca.180 1C at 0.1 Hz, up to ca. 205 1C at 100 Hz, but in the direction opposite from that expected), but changes in mechanical characteristics, dependent on loading frequency and crosslinking process, were more marked. A large drop in Young’s modulus can be observed at a temperature of ca. 60 1C. In this case, the secondary transition temperature, Tb, with a tan d peak at 58 1C, indicates a lower viscosity and thus a higher mobility of some molecular chains in the polymer. Both Young’s modulus and tan d are seen to be sensitive to crosslinking conditions. In order to compare the evolution of these mechanical characteristics, both are represented on separated graphs for a unique frequency of 10 Hz in Fig. 5. The following curing cycles were compared to that of 80 min at 66 1C, already tested:
1, 2, 4 and 10 day at ambient temperature 45 min at 75 1C in an oven. These different curing cycles are compared in Fig. 5, with separate representations of the evolution of Young’s modulus and tan d with temperature. The evolution of Young’s modulus is readily associated with a higher value resulting from oven polymerisation. At ambient
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temperature, Young’s modulus increases slowly with crosslinking time. Nevertheless, even after 10 day of curing at ambient temperature, the adhesive rigidity is less than that obtained at higher temperatures, and reveals a secondary transition generating a Young’s modulus drop and tan d peak at ca. 70 1C. In industrial conditions, the completion of crosslinking of adhesives (or other polymers) is often judged from hardness tests alone. Therefore consideration of the relationship between the degree of crosslinking and hardness could be of the utmost importance. As a consequence, we have given consideration to this aspect. After monitoring crosslinking at ambient temperature (Fig. 1b), we noted an almost final value of rigidity after only 9 h (ca. 30,000 s). However, when looking at the adhesive’s properties after one day of curing (Fig. 5), a secondary transition temperature, Tb, was observed at ca. 65 1C. This disappeared almost totally for more complete crosslinking cycles (80 min at 66 1C or 45 min at 75 1C). Comparison of curing at ambient temperature for 10 day with that obtained in an oven shows a non-negligible difference in behaviour. Indeed, Young’s modulus of the adhesive at 30 1C is similar for both curing cycles (ca. 2.6 GPa). At higher temperature, the Young’s moduli of the adhesive present different behaviour. The evolution of tan d in Fig. 5 shows equivalent behaviour. It shows a decrease of the secondary b transition as a function of crosslinking time and temperature. When the adhesive is completely cured, this transition disappears and a unique transition remains (in the temperature range considered), corresponding to the glass transition temperature, Tg. Once again, in the case of ambient temperature curing cycles, the b transition (observed between 60 1C and 75 1C) does not disappear even after 10 day of curing. Thus we infer that curing is still incomplete. The glass transition is readily associated with large-scale molecular movement in the polymer network. The secondary, low temperature, b transition in glassy polymers is often a result of segmental chain mobility triggered by the system’s thermal characteristics. This transition has been identified in several epoxy systems [10]. The secondary transition is generally accepted to be
Fig. 6. Evolution of Young’s modulus, E, and tan d vs. temperature for 2 samples of adhesive already cured at 75 1C for 45 min.
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curing temperature while decreasing time improves adhesive paste crosslinking. A curing cycle of 45 min at 75 1C was used to investigate the influence on mechanical properties of a higher crosslinking temperature (Fig. 5). This improved curing cycle revealed an interesting advantage with an increase of Tg (205 1C) and a decrease of crosslinking time, while retaining the Young’s modulus at ambient temperature. Fig. 6 shows the evolution of mechanical properties with temperature of two samples cured for 45 min at 75 1C. Young’s modulus, E, and tan d are represented for 2 samples of adhesive. These correspond to a frequency of 10 Hz. The evolution of Young’s modulus presents a unique decrease starting at ca. 160 1C and corresponding to the beginning of the glass transition. The evolution of tan d shows a peak for a temperature of ca. 205 1C. Presumably due to the higher crosslinking temperature, the secondary b transition does not appear anymore, implying complete adhesive curing. A small tan d peak is nevertheless observed at ca. 100 1C, but it is not sufficiently important to refer to it as a significant secondary transition.
due to a combination of molecular rotation of main-chain side groups, motion of some segments of main-chain side groups or motion of small molecules dissolved in the polymer. The Tg can be a measurement of the degree of crosslinking of an epoxy resin system [12,13]. Fig. 5b illustrates the relationship between tan d and temperature, for different curing times and temperature, for the adhesive paste EA9394. A specimen cured 80 min at 66 1C is clearly more highly crosslinked than that at ambient temperature and attains both higher Tg and Tb. Higher temperature cycles in an oven improved crosslinking of the adhesive paste, as expected, by accelerating curing of the polymeric chains and possibly other mechanisms, such as reduced initial viscosity leading to better chemical proximity and therefore reaction. The curing cycle 80 min at 66 1C presented an (apparently) complete crosslinking of the adhesive paste resulting in a unique glass transition temperature. Increasing
3.2. Tensile test Having established the importance of crosslinking conditions on the viscoelastic properties of the adhesive, we turned our attention to tensile properties up to fracture. Cast dogbone specimens were made in order to obtain stress/strain plots at different strain rates. Strain rate has an important effect on polymer rigidity and fracture stress, as already implied in the present case from the viscoelastic data. Strain rates used were principally 0.01 min 1, 0.1 min 1 and 1 min 1 (these effective values correspond to displacement/ [effective gauge length, l0* s]). Young’s modulus, strain and stress up to fracture were studied. The adhesive behaviour was found to
Fig. 7. Stress/strain curves of dogbone samples of adhesive at a constant strain rate of 0.1 min 1—Samples are 2 mm in thickness and cured at 75 1C for 45 min.
Table 1 Failure stresses, srupt, failure strains, erupt, and values of Young’s modulus, E, of 2 mm thick samples of adhesive EA9394 strained at 0.1 min 1. Cure was effected for 45 min at 75 1C. e ¼2 mm V¼0.1 min 1
rrupt (Mpa) erupt (%) E (Gpa)
1
2
3
4
5
6
7
8
9
10
11
12
Mean
Std. dev.
32.1 1.9 3.8
31.4 1.7 4.3
30.5 1.8 4.2
30.5 1.6 4.2
32 1.7 3.6
30 1.6 4.4
31.2 1.7 4
33.4 1.8 4.3
27.8 1.7 3.7
31.4 1.8 3.8
33.4 1.7 4.8
30.5 2.2 4
31.5 1.76 4.1
1.5 0.16 0.1
Fig. 8. Weibull statistical representation of (a) fracture stress and (b) fracture strain for 2 mm thick tensile test samples loaded at a strain rate of 0.1 min 1.
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be non-linear, but leading to brittle fracture. Typical results of tensile tests on samples of 2 mm thickness are presented in Fig. 7 and summarised in Table 1. Dispersion on measured parameters was evaluated. 3.2.1. Statistics of failure It is of interest to identify a probabilistic model which could reasonably quantify the variability of the measured variables. The population of results gathered here is limited, but sufficient for such a treatment. The statistical theory of Weibull is widely used for analysing mechanical test results as a function of several parameters [14,15]. Based on the criterion of the weakest link leading to failure, Weibull statistics is applied under two main considerations. The first is that the fracture stress of each loaded volume element of the structure corresponds to a random independent variable. The second assumption is that the global fracture of the sample occurs after the fracture of one of the elements. With these hypotheses, it has been shown [16] that the scale change relation linking fracture probability of a single element, pr ðs,V 0 Þ, Table 2 Mechanical properties of EA9394 depending on strain rate (cured for 45 min at 75 1C). V (min 1)
EYoung (GPa)
srupt (MPa)
erupt (%)
0.01 0.1 1
306 7 0.4 3.9 7 0.5 4.6 7 0.5
27.2 75 31.2 71.5 42.5 74
1.5 7 0.4 1.8 7 0.2 2.1 7 05
to that of the entire ‘‘chain’’, pr ðs,V 0 Þ, is given by: Z 1 pr ðsðmÞ, ½ðV 0 ÞdV pr ðs,V 0 Þ ¼ 1exp
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ð1Þ
0
where, m, is known as the Weibull modulus, whose magnitude gives a measure of statistical scatter. The Weibull distribution is used to compute failure probabilities as a function of applied stress [17]. We therefore directed the present study towards the determination of the Weibull modulus, m, of the distribution associated with the tensile strength of dogbone specimens of the structural adhesive. The Weibull equation (for a two-parameter distribution) yields the cumulative probability of failure, Pr, as a function of the applied stress, s, and a characteristic volume, V, and is given by: m s V pr ¼ 1exp ð2Þ s0 V 0 Requisite parameters are obtained by regression analysis of the experimental data using Eq. (2) in the following form: In½In½ð1P r ,iÞ ¼ m Inðsi Þm Inðs0 Þ
ð3Þ
To have a representative sample for statistical viability, a batch of at least 10 samples was used for each strain rate. The N fracture stress results being ranked in increasing order, the fracture probability of the ith sample may be obtained using the relation of Benard and Bos-Levenbach [18], also known as the Chego– Dayev [19] formula: Pi ðsi Þ ¼
i0:3 N þ0:4
ð4Þ
Fig. 9. Weibull statistical distribution of fracture stresses for a strain rate of (a) 0.01 min 1 and (b) 1 min 1. Equivalent strains at fracture for (c) 0.01 min 1 and (d) 1 min 1.
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Thus, for each strain rate, a plot of In[ In(1 Pf)] vs. In(s), with corresponding regression line, is correlated with experimental results. The Weibull parameter, m, represents the gradient of the regression line of the experimental results [Eq. (3)]. This parameter quantifies the dispersion of test results. The higher m is, the lower is the dispersion. Weibull statistical methods have been applied to the study of the dispersion of fracture stresses and strains for an imposed strain rate of 0.1 min 1 with 12 samples (Fig. 8). We see that fracture stresses are in good agreement with Weibull statistics, as shown by the linear evolution in Fig. 8a. For these results, we obtained a Weibull modulus, m, of 21.5 for the fracture stresses, and a mean fracture stress, s0, of ca. 31 MPa. For the fracture strain results, linearity of the distribution is debateable, and a Weibull modulus of 11 is found, with a mean fracture strain, e0, of 1.76%. This is clearly less impressive, although still acceptable.
3.2.2. Strain rate sensitivity The mechanical properties of the adhesive, as for polymers in general, reveal a high sensitivity to strain rate. This has been found on vitreous polymers, where a significant increase of Young’s modulus, elastic limit, and fracture stress with strain rate results [20–24]. Results for strain rates of 0.01 min 1 and 1 min 1 reveal, as seen from the gradient, comparable standard deviations (Table 2). We see, as expected, an increase of fracture stress (27.2 MPa to 42.5 MPa), Young’s modulus (3.6 GPa to 4.6 GPa), and also fracture strain (1.5% to 2.1%) for the two extreme strain rates; i.e., 0.01 min 1 and 1 min 1. It is interesting to evaluate sensitivity to the parameter, m, characterising variability of mechanical properties as a function of strain rate on a Weibull plot (Fig. 9). Weibull analysis of fracture stresses reveals, for both strain rates applied, a bimodal statistical distribution, represented by two different Weibull moduli. In principle, this
tends to invalidate use of the Weibull distribution. However, in fact, this can be attributed to the presence of two families of defects in the samples, of different size ranges, with porosities corresponding to air bubbles in the sample section. Thus, for a 0.01 min 1 strain rate, Weibull moduli for fracture stresses were found to be 3.5 and 7.1, for, respectively, significantly porous and apparently intact samples. Similarly, for a 1 min 1 strain rate, the Weibull moduli found for fracture stress were 6.2 and 20.4, for, respectively, significantly porous and apparently intact samples. The same type of porosity effect with speed sensitivity is observed on fracture strain. Thus, Weibull moduli were found to vary from 2.8 to 5.6 for a strain rate of 0.01 min 1 and 4.9 to 9.0 for a strain rate of 1 min 1, for, respectively, significantly porous and apparently intact samples. This interesting result suggests a decrease in dispersion, reducing porosity effects, when the strain rate is higher. Although at this stage, we can only surmise, it is possible that this effect is related to higher stresses near voids, leading in turn to some local plasticity. In the light of these results, it may be questioned whether two distributions are present in Fig. 8. However, the evidence is insufficient to decide about this. Fracture surfaces reveal a highly heterogeneous matrix, with large and small porosities, either of which could initiate polymer fracture (Fig. 10). We observed an important variation of porosity sizes present, as shown by the fracture surfaces, thus explaining fracture stress variability. Porosities may occur from various origins, the main two being: out-gassing associated with the crosslinking reaction generating small porosities, and more probably, from bubbles trapped during mixing of resin and hardener. Moreover, defects are introduced during sample casting, and the high viscosity of the adhesive paste prevents porosities from escaping efficiently from the mould. Thus, referring to Fig. 10 as an example, sample (a) with quasi-intrinsic small porosities offers a high fracture stress, samples (b) and (c) reveal fracture stresses in the vicinity of the mean value, and sample (d) corresponds to
Fig. 10. Fracture surfaces of adhesive tensile test samples containing (a) small porosities, (b) and (c) intermediate size porosities, and (d) a sample containing a large void (bubble).
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a sample with low fracture stress containing a huge void. Two effects (at least) are present: first, as is well-known, holes induce stress concentrations, and second, their presence clearly also reduces specimen cross-section, also increasing local stresses for a given applied load. Our results tend to suggest the latter cause as being predominant for the present material.
4. Conclusion The curing of a filled, epoxy-based adhesive has been studied with an aim to elucidate the influence of curing cycle on mechanical characteristics. Monitoring crosslinking of the adhesive paste revealed the necessary hardening time (hardening time referring to the time needed to handle the sample without damaging it). This was found to be only ca. 9 h (at ambient temperature), with Young’s modulus becoming stable. In fact, by allowing further time, we observed that still only partial crosslinking had occurred after 1 day at ambient temperature, with the presence of a secondary transition temperature (b), whose effect was reduced (or became negligible) with further curing time and/or higher temperature. Dynamic mechanical analysis (DMA) was used to identify the preferable curing cycle. Indeed, we suggest an improved version. Detailed dynamic mechanical analyses are necessary to identify the best curing conditions. Curing at ambient temperature resulted in inferior mechanical properties at intermediate temperatures, which was accompanied by a persistent secondary transition temperature. Curing cycles at elevated temperatures produced apparently rapid and complete crosslinking of the adhesive paste. A study of statistical aspects in dogbone tensile tests showed a dramatic effect of strain rate and porosity, upon Young’s modulus, fracture stress and fracture strain. The protocol of experimental process of adhesive handling strongly influences fracture stress variability and introduces uncontrolled dispersion of porosity in dogbone tensile specimens. Premature failure occurs for specimens containing large defects reducing in effective section, as may be expected. More significantly, we have proposed a first step in understanding and correlating the mechanical behaviour of an adhesive with porosities en defects due to manufacture. This has been done by applying the statistical techniques of Weibull. In particular, two populations of defects are apparently present, leading to different overall mechanical response.
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References [1] Adderley CS. Adhesive bonding. Mater Des 1988;9(5):287–93. [2] Yorkgitis EM, Marhevka VC, Lamon A Bonding of aluminium structures with advanced 1 K and 2 K adhesives. 1995. no 950724. [3] McGrath G. Not sticking to tradition—a guide to adhesive bonding. Bulletin 3 (TWI). 1991;32(3):64–7. [4] Kalpakjian S. 2nd ed. Manufacturing engineering and technology, 30. New York: Addison-Wesley; 1992. [5] Barnes TA, Pashby IR. Joining techniques for aluminium spaceframes used in automobiles Part II—Adhesive bonding and mechanical fasteners. J Mater Process Technol 2000;99:72–9. [6] De Ne ve B, Shanahan MER. Physical and chemical effects in an epoxy resin exposed to water vapour. J Adhes 1995;49:165–76. [7] Davies P, Sohier L, Cognard JY, Bourmaud A, Choqueuse D, Rinnert E, Creac’hcadec R. Influence of adhesive bondline thickness on joint strength. Int J Adhes Adhes 2009;29:724–36. [8] Guess TR, Reedy ED, Stavig ME Mechanical properties of hysol EA-9394 structural adhesive. SANDIA Report. Sandia national laboratories, 1995. [9] Bresson G, Jumel J, Shanahan MER, Serin P. Strength of adhesively bonded joints under mixed axial and shear loading. Int J Adhes Adhes 2012. [10] Mikols WJ, Seferis JC, Apicella A. Evaluation of structural changes in epoxy systems by moisture sorption–desorption and dynamic mechanical studies. Polym Compos 1982;3(3):118–24. [11] Tamulevitch TW, Moore VE The significance of glass transition temperature on epoxy resins for fiber optic applications. &Epoxy Technology, Inc. 1980. [12] Tillet G, Boutevin B, Ameduri B. Chemical reactions of polymer crosslinking and post-crosslinking at room and medium temperature. Prog Polym Sci 2011;36(2):191–217. [13] Dewaele M, Asmussen E, Peutzfeldt A, Munksgaard EC, Benetti AR, Finne´ G, Leloup G, Devaux J. Influence of curing protocol on selected properties of light-curing polymers: degree of conversion, volume contraction, elastic modulus, and glass transition temperature. Dent Mater 2009;25:1576–84. [14] Jayatilaka A, Trustrum K. Statistical approach to brittle fracture. J Mater Sci 1977;12:1426–30. [15] Trustrum K, Jayatilaka A. Applicability of Weibull analysis for brittle materials. J Mater Sci 1983;18:2765–70. [16] Daniels HE. the statistical theory of strength of bundles of threads. Proc R Soc 1945;A183:405–35. [17] Weibull W. A statistical theory of the strength of materials. Ing Vetensk Akad Proc 1939;151:1–45. [18] Benard A, Bos-Levenbach EC. The plotting of observations on probability paper. Stat Neerlend 1953;7:163–73. [19] Chow VT. Handbook of applied hydrology. NY: McGraw Hill; 1964. [20] G’Sell C. Lois de comportement me´canique des polyme res solides. Introduction a la me´canique des polyme res. [ed.] Haudin 1995:141–65. [21] Xiao X. Dynamic tensile testing of plastic materials. Polym Test 2008;27(2): 164–78. [22] Bae JS, Oh CS, Nam JE, Lee JK, Lee HJ. A tensile test technique for the freestanding PMMA thin films. Curr Appl Phys 2009;9, 1(Supplement 1):s107–9. [23] Zrida M, Laurent H, Grolleau V, Rio G, Khlif M, Guines D, Masmoudi N, Bradai C. High-speed tensile tests on a polypropylene material. Polym Test 2010;29(6): 685–92. [24] Combette P, Ernoult I Physique des polyme res, II proprie´te´s me´caniques. [ed.] Hermann. 2005.
Contents lists available at SciVerse ScienceDirect
International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Statistical aspects of the mechanical behaviour a paste adhesive Gregory Bresson a,b,c,d, Julien Jumel a,b,c, Martin E.R. Shanahan a,b,c,n, Pierre Serin d a
University Bordeaux, I2M, UMR 5295, F-33400 Talence, France CNRS, I2M, UMR 5295, F-33400 Talence, France Arts et Metiers ParisTech, I2M, UMR 5295, F-33400 Talence, France d Centre National d’Etudes Spatiales, Direction des Lanceurs, Rond Point de l’Espace, 91023 Evry Cedex, France b c
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 7 June 2012 Available online 26 June 2012
We present experimental results describing the mechanical behaviour of an epoxy-based structural paste adhesive with aluminium powder filler under proportional loading. The main aim of the present study is to relate the dispersion on joint strength (variability) to void and particle sizes and distributions, also taking into account effects of the curing cycle. Tensile tests with dogbone specimens were done at different strain rates. The statistical nature of results is related to the heterogeneous material microstructure, containing voids as well as mineral particles for reinforcement. A Weibull-type statistical analysis is suggested for use when the stress distribution is heterogeneous. Mechanical dynamical analyses were done with evaluation of polymerisation steps. Multiple dynamical testing was done with temperature scanning on samples having undergone various cure cycles. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Adhesive strength Curing conditions DMA Statistics Weibull analysis
1. Introduction Joining parts with adhesives offers many advantages compared to traditional techniques making use of mechanical fasteners [1,2]. The aerospace industry shows an interest in this technique which enables the joining of dissimilar materials and generally leads to important mass and stress reduction [3,4]. Nevertheless, a lack of confidence limits the use of this technology [5], due to a high level of dispersion (variability, or variance) on the mechanical strength of bonded joints, especially in ageing conditions. Moreover, this statistical behaviour can be attributed to many causes such as, ageing [6], adhesive or surface preparation defects, and dimensional precision of the bondline [7]. The overall aim of this work is to make a preliminary investigation of the influence of the adhesive per se, in the behaviour and strength of adhesive bonds. Such effects as different crosslinking cycles and the presence of particle fillers and voids (bubbles) have an intrinsic rˆole to play. To obtain better understanding of the damage of adhesively bonded joints, we use a standard tensile test with dogbone specimens to measure the load displacement curve of the cured adhesive paste. The adhesive studied (Hysol EA 9394) [8] presents a highly heterogeneous microstructure made of both reinforcement particles and voids produced during the manual mixing prior to application. Our aim is to relate this dispersion on the joint strength to the void and particle sizes and distributions. This work constitutes a logical extension to Ref. [9], in which we presented a heterogeneous
n Corresponding author at: University Bordeaux, I2M, UMR 5295, F-33400 Talence, France. Tel.: þ33 5 40 00 62 22; fax: þ 33 5 40 00 69 64. E-mail address: [email protected] (M.E.R. Shanahan).
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijadhadh.2012.06.006
distribution of porosities in the adhesive layer due to the assembly process and degassing effect during the cure. This study is mainly focused on the description of protocols and tests required to supply engineers with the data required for correct polymerisation. Besides this, Dynamic Mechanical Analysis (DMA) is performed to monitor the curing kinetics of the adhesive paste for different curing conditions using an annular shear pumping configuration technique. Following this, a specific tension fixture is used on small rectangular specimens in order to characterise the glass transition temperature and to follow mechanical stiffness as a function of the temperature. These experimental methodology basic analyses are performed with an eye to quality control of the manufactured adhesive. The study shows the limitations of using oversimplified mechanical testing and the real need for detailed characterisation.
2. Experimental 2.1. Materials The adhesive, Hysol EA 9394, is a two-part structural paste adhesive, which cures at room temperature and possesses excellent strength up to ca. 180 1C and even higher temperatures. It is an amine-cured epoxy adhesive paste with an aluminum powder filler. Its thixotropic nature prior to cure and excellent high temperature compressive strength also make it ideal for potting, filling and liquid shim applications. The weight part ratio of resin and hardening agent is 100:17. In this study, the two part adhesive was hand mixed using spatulae. Various cure cycles were employed, with an aim to study
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their effects on mechanical properties, in particular complex modulus (viscoelastic modulus) and fracture strength. The conditions ranged from 1 day at ambient temperature up to 45 min at 75 1C, the effects being discussed below.
2.2. Dynamic mechanical analysis (DMA) Dynamic mechanical analysis, or DMA, is commonly used to characterise the intrinsic mechanical behaviour of materials as a function of temperature. It consists of dynamic mechanical loading of
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the sample in oscillatory strain, while measuring viscoelastic properties in situ. The system can be applied to several types of dynamic displacement or loading while controlling temperature during the test. Its use in mechanical characterisation to study structural changes in epoxy systems [10] is widely spread. As discussed by Tamulevitch and Moore [11], the cure time and temperature can have a dramatic effect upon the glass transition temperature, Tg, of any given epoxy resin system, the glass transition temperature being the reversible transition in amorphous materials (or in amorphous regions within semicrystalline materials) from a hard and relatively brittle state into a molten or rubber-like state.
Fig. 1. Viscoelastic data during cure: tan d (in shear) and shear modulus, G, vs. cure time for temperatures of (a) 66 1C and (b) ambient (25 1C)—frequency 50 Hz. At the origin, the adhesive is still a paste and these graphs effectively monitor cure behaviour.
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To obtain optimal characterisation and curing protocol of the adhesive paste studied, several dynamic mechanical tests were done. Technical data indicate two main curing temperatures to obtain complete cure of the adhesive paste, with room temperature during 8 day and 66 1C in an oven for 80 min. Monitoring of mechanical properties, under controlled static temperature, was done for both curing cycles, using an annular shear pumping configuration technique. Shear modulus, G, and tan d were monitored as a function of testing time. Tan d corresponds to the loss factor of the adhesive paste where d, is the dephasing angle between applied load and measured deformation. Apart from the above test performed during cure, a second test with a specific tension fixture was used on small rectangular specimens (already cured) in order to characterise the glass transition temperature, Tg, and mechanical properties of the hardened adhesive as a function of temperature. Specimens were cured in an oven for 80 min at 66 1C. For the ambient curing temperature, mechanical testing was effected after various periods of polymerisation to see the evolution of mechanical properties as a function of time. Finally, with an aim to decrease curing time, another cycle was used, with crosslinking at 75 1C for 45 min. Young’s modulus and tan d were monitored as a function of the temperature, for a temperature rise gradient of 1 1C/min from ambient temperature to 250 1C. It should be pointed out that the curing cycles were chosen in accordance with those used for adhesive joints (see below) but that, due to the exothermic properties of crosslinking and different geometries of bulk and adhesion test pieces, in particular surface/volume ratio, strictly identical thermal conditions are virtually impossible to reproduce. 2.3. Tensile tests The characterisation of the adhesive paste with standard tests was a first step in a study of mechanical behaviour and its temperature sensitivity. Mechanical testing with standard tensile tests was also used to observe the macroscopic behaviour of the cured EA9394 adhesive. The statistical technique of Weibull was
then applied to study the dispersion of fracture strength as a function of strain rate. The standard ISO tensile test specimen format was used to characterise mechanical behaviour. ISO 527-2 (‘‘Determination of tensile properties—Part 2: Test conditions for moulding and extrusion plastics’’) dogbone samples were cast in specific moulds with thickness, applying a load of ca. 200 N, with weights, to limit void occurrence. As mentioned above, samples were polymerised in an oven for 1 h at 66 1C, according to standard manufacturer protocol. The effective length and sample thickness were 33 mm and 2 mm, respectively. Stress/strain curves were obtained with a tensile machine (Zwicks Z010) with a 10 kN load cell and strain extensometer. A range of strain rates was used (0.01 min 1 to 1 min 1) and Young’s modulus measured in the linear elastic zone. The main objective here was to study the effect of strain rate on fracture stress and Young’s modulus (corresponding to elastic behaviour).
3. Results and discussion 3.1. Effects on mechanical properties of curing conditions Our preliminary investigation consisted of monitoring mechanical properties during cure at fixed temperature. Both shear modulus, G, and tan d were followed during cure with the annular pumping fixture, both at 25 1C and 66 1C. Shear modulus, G, and tan d are plotted as a function of time in Fig. 1 in order to observe structural changes during adhesive paste hardening. For crosslinking at 66 1C, the adhesive paste was apparently completely crosslinked after ca. 80 min, with a final shear modulus of 0.23 GPa (Fig. 1a). At 25 1C, EA9394 can be considered completely cured after 9 h with a final shear modulus of 0.2 GPa. Thus, the final shear modulus is little affected by crosslinking temperature (Fig. 1b). The conditions of crosslinking can be very important in adhesive preparation in order to optimise final behaviour. After
Fig. 2. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive cured at 66 1C for 1 h 20 min (adhesive already cured).
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fixing the polymerisation procedure, it is of interest to observe adhesive behaviour for both crosslinking temperatures. Small rectangular, tensile test specimens were cut in order to analyse mechanical behaviour under dynamic loading as a function of temperature, with a standard tension fixture. Both tan d and Young’s modulus, E, were followed as a function of temperature from ambient to 250 1C. The temperature increase rate imposed was 1 1C/min. Results are presented in Fig. 2, for the sample cured
73
for 80 min at 66 1C. However, it should be noted that during the test, some further crosslinking may occur, particularly at the higher temperatures of the DMA test. The evolution of tan d and Young’s modulus, E, versus temperature has been plotted for various frequencies. Mechanical properties are affected by the strain rate. The glass transition temperature, as defined by the peak of tan d, varies from 185 1C to 210 1C for, respectively, 0.1 Hz and 100 Hz frequencies. Glass
Fig. 3. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive cured at ambient temperature for 8 day (adhesive already cured).
Fig. 4. Tan d (tensile) and Young’s modulus, E, vs. temperature for adhesive already cured at ambient temperature but for only 4 day.
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transition temperatures correspond to tan d peaks, and a drop of Young’s modulus. At ambient temperature, a Young’s modulus of ca. 2.5 GPa was obtained and 0.14 GPa at 250 1C. Young’s moduli are comparable to those obtained with tensile tests (ca. 2.5 GPa to 2.8 GPa), as will be seen below. A specimen of EA9394 polymerised 8 day at ambient temperature was studied in the same manner between 30 1C and 250 1C, with a 1 1C/min rate of temperature increase. Results are presented in Fig. 3.
It is immediately obvious that very different behaviour results. Indeed, a first drop of Young’s modulus can be observed at ca. 80 1C. (This phenomenon was present, but barely visible, in the previous figure, with polymerisation at 80 min at 66 1C: the effect on Young’s modulus is much less marked.) This could possibly be attributed to incomplete crosslinking of the adhesive paste at this temperature after 8 day. The chemical reaction seems not to be totally finished at ambient temperature, revealing a secondary transition temperature, Tb, at 80 1C. In order to investigate this
Fig. 5. Evolution of (a) Young’s modulus, E, and (b) tan d vs. temperature for already (at least partially) cured adhesive—comparison of curing processes.
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aspect, a higher crosslinking temperature could be applied or a longer crosslinking time considered. Glass transition temperatures vary from ca. 175 1C to 200 1C, respectively, for 0.1 Hz and 100 Hz frequencies. At ambient temperature, Young’s moduli of 3.4 GPa and 3.9 GPa for, respectively, 0.1 Hz and 100 Hz frequencies are observed. Young’s modulus is influenced by loading speed, with a higher value for the higher strain rate. At 250 1C, a Young’s modulus of 0.14 GPa can be noted, as with the other crosslinking conditions (80 min at 66 1C). Incomplete crosslinking is expected be present for intermediate polymerisation times. In order to investigate this behaviour, a sample cured for 4 day at ambient temperature was tested. DMA results are presented in Fig. 4. Glass transition temperatures were only slightly modified (ca.180 1C at 0.1 Hz, up to ca. 205 1C at 100 Hz, but in the direction opposite from that expected), but changes in mechanical characteristics, dependent on loading frequency and crosslinking process, were more marked. A large drop in Young’s modulus can be observed at a temperature of ca. 60 1C. In this case, the secondary transition temperature, Tb, with a tan d peak at 58 1C, indicates a lower viscosity and thus a higher mobility of some molecular chains in the polymer. Both Young’s modulus and tan d are seen to be sensitive to crosslinking conditions. In order to compare the evolution of these mechanical characteristics, both are represented on separated graphs for a unique frequency of 10 Hz in Fig. 5. The following curing cycles were compared to that of 80 min at 66 1C, already tested:
1, 2, 4 and 10 day at ambient temperature 45 min at 75 1C in an oven. These different curing cycles are compared in Fig. 5, with separate representations of the evolution of Young’s modulus and tan d with temperature. The evolution of Young’s modulus is readily associated with a higher value resulting from oven polymerisation. At ambient
75
temperature, Young’s modulus increases slowly with crosslinking time. Nevertheless, even after 10 day of curing at ambient temperature, the adhesive rigidity is less than that obtained at higher temperatures, and reveals a secondary transition generating a Young’s modulus drop and tan d peak at ca. 70 1C. In industrial conditions, the completion of crosslinking of adhesives (or other polymers) is often judged from hardness tests alone. Therefore consideration of the relationship between the degree of crosslinking and hardness could be of the utmost importance. As a consequence, we have given consideration to this aspect. After monitoring crosslinking at ambient temperature (Fig. 1b), we noted an almost final value of rigidity after only 9 h (ca. 30,000 s). However, when looking at the adhesive’s properties after one day of curing (Fig. 5), a secondary transition temperature, Tb, was observed at ca. 65 1C. This disappeared almost totally for more complete crosslinking cycles (80 min at 66 1C or 45 min at 75 1C). Comparison of curing at ambient temperature for 10 day with that obtained in an oven shows a non-negligible difference in behaviour. Indeed, Young’s modulus of the adhesive at 30 1C is similar for both curing cycles (ca. 2.6 GPa). At higher temperature, the Young’s moduli of the adhesive present different behaviour. The evolution of tan d in Fig. 5 shows equivalent behaviour. It shows a decrease of the secondary b transition as a function of crosslinking time and temperature. When the adhesive is completely cured, this transition disappears and a unique transition remains (in the temperature range considered), corresponding to the glass transition temperature, Tg. Once again, in the case of ambient temperature curing cycles, the b transition (observed between 60 1C and 75 1C) does not disappear even after 10 day of curing. Thus we infer that curing is still incomplete. The glass transition is readily associated with large-scale molecular movement in the polymer network. The secondary, low temperature, b transition in glassy polymers is often a result of segmental chain mobility triggered by the system’s thermal characteristics. This transition has been identified in several epoxy systems [10]. The secondary transition is generally accepted to be
Fig. 6. Evolution of Young’s modulus, E, and tan d vs. temperature for 2 samples of adhesive already cured at 75 1C for 45 min.
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curing temperature while decreasing time improves adhesive paste crosslinking. A curing cycle of 45 min at 75 1C was used to investigate the influence on mechanical properties of a higher crosslinking temperature (Fig. 5). This improved curing cycle revealed an interesting advantage with an increase of Tg (205 1C) and a decrease of crosslinking time, while retaining the Young’s modulus at ambient temperature. Fig. 6 shows the evolution of mechanical properties with temperature of two samples cured for 45 min at 75 1C. Young’s modulus, E, and tan d are represented for 2 samples of adhesive. These correspond to a frequency of 10 Hz. The evolution of Young’s modulus presents a unique decrease starting at ca. 160 1C and corresponding to the beginning of the glass transition. The evolution of tan d shows a peak for a temperature of ca. 205 1C. Presumably due to the higher crosslinking temperature, the secondary b transition does not appear anymore, implying complete adhesive curing. A small tan d peak is nevertheless observed at ca. 100 1C, but it is not sufficiently important to refer to it as a significant secondary transition.
due to a combination of molecular rotation of main-chain side groups, motion of some segments of main-chain side groups or motion of small molecules dissolved in the polymer. The Tg can be a measurement of the degree of crosslinking of an epoxy resin system [12,13]. Fig. 5b illustrates the relationship between tan d and temperature, for different curing times and temperature, for the adhesive paste EA9394. A specimen cured 80 min at 66 1C is clearly more highly crosslinked than that at ambient temperature and attains both higher Tg and Tb. Higher temperature cycles in an oven improved crosslinking of the adhesive paste, as expected, by accelerating curing of the polymeric chains and possibly other mechanisms, such as reduced initial viscosity leading to better chemical proximity and therefore reaction. The curing cycle 80 min at 66 1C presented an (apparently) complete crosslinking of the adhesive paste resulting in a unique glass transition temperature. Increasing
3.2. Tensile test Having established the importance of crosslinking conditions on the viscoelastic properties of the adhesive, we turned our attention to tensile properties up to fracture. Cast dogbone specimens were made in order to obtain stress/strain plots at different strain rates. Strain rate has an important effect on polymer rigidity and fracture stress, as already implied in the present case from the viscoelastic data. Strain rates used were principally 0.01 min 1, 0.1 min 1 and 1 min 1 (these effective values correspond to displacement/ [effective gauge length, l0* s]). Young’s modulus, strain and stress up to fracture were studied. The adhesive behaviour was found to
Fig. 7. Stress/strain curves of dogbone samples of adhesive at a constant strain rate of 0.1 min 1—Samples are 2 mm in thickness and cured at 75 1C for 45 min.
Table 1 Failure stresses, srupt, failure strains, erupt, and values of Young’s modulus, E, of 2 mm thick samples of adhesive EA9394 strained at 0.1 min 1. Cure was effected for 45 min at 75 1C. e ¼2 mm V¼0.1 min 1
rrupt (Mpa) erupt (%) E (Gpa)
1
2
3
4
5
6
7
8
9
10
11
12
Mean
Std. dev.
32.1 1.9 3.8
31.4 1.7 4.3
30.5 1.8 4.2
30.5 1.6 4.2
32 1.7 3.6
30 1.6 4.4
31.2 1.7 4
33.4 1.8 4.3
27.8 1.7 3.7
31.4 1.8 3.8
33.4 1.7 4.8
30.5 2.2 4
31.5 1.76 4.1
1.5 0.16 0.1
Fig. 8. Weibull statistical representation of (a) fracture stress and (b) fracture strain for 2 mm thick tensile test samples loaded at a strain rate of 0.1 min 1.
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be non-linear, but leading to brittle fracture. Typical results of tensile tests on samples of 2 mm thickness are presented in Fig. 7 and summarised in Table 1. Dispersion on measured parameters was evaluated. 3.2.1. Statistics of failure It is of interest to identify a probabilistic model which could reasonably quantify the variability of the measured variables. The population of results gathered here is limited, but sufficient for such a treatment. The statistical theory of Weibull is widely used for analysing mechanical test results as a function of several parameters [14,15]. Based on the criterion of the weakest link leading to failure, Weibull statistics is applied under two main considerations. The first is that the fracture stress of each loaded volume element of the structure corresponds to a random independent variable. The second assumption is that the global fracture of the sample occurs after the fracture of one of the elements. With these hypotheses, it has been shown [16] that the scale change relation linking fracture probability of a single element, pr ðs,V 0 Þ, Table 2 Mechanical properties of EA9394 depending on strain rate (cured for 45 min at 75 1C). V (min 1)
EYoung (GPa)
srupt (MPa)
erupt (%)
0.01 0.1 1
306 7 0.4 3.9 7 0.5 4.6 7 0.5
27.2 75 31.2 71.5 42.5 74
1.5 7 0.4 1.8 7 0.2 2.1 7 05
to that of the entire ‘‘chain’’, pr ðs,V 0 Þ, is given by: Z 1 pr ðsðmÞ, ½ðV 0 ÞdV pr ðs,V 0 Þ ¼ 1exp
77
ð1Þ
0
where, m, is known as the Weibull modulus, whose magnitude gives a measure of statistical scatter. The Weibull distribution is used to compute failure probabilities as a function of applied stress [17]. We therefore directed the present study towards the determination of the Weibull modulus, m, of the distribution associated with the tensile strength of dogbone specimens of the structural adhesive. The Weibull equation (for a two-parameter distribution) yields the cumulative probability of failure, Pr, as a function of the applied stress, s, and a characteristic volume, V, and is given by: m s V pr ¼ 1exp ð2Þ s0 V 0 Requisite parameters are obtained by regression analysis of the experimental data using Eq. (2) in the following form: In½In½ð1P r ,iÞ ¼ m Inðsi Þm Inðs0 Þ
ð3Þ
To have a representative sample for statistical viability, a batch of at least 10 samples was used for each strain rate. The N fracture stress results being ranked in increasing order, the fracture probability of the ith sample may be obtained using the relation of Benard and Bos-Levenbach [18], also known as the Chego– Dayev [19] formula: Pi ðsi Þ ¼
i0:3 N þ0:4
ð4Þ
Fig. 9. Weibull statistical distribution of fracture stresses for a strain rate of (a) 0.01 min 1 and (b) 1 min 1. Equivalent strains at fracture for (c) 0.01 min 1 and (d) 1 min 1.
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Thus, for each strain rate, a plot of In[ In(1 Pf)] vs. In(s), with corresponding regression line, is correlated with experimental results. The Weibull parameter, m, represents the gradient of the regression line of the experimental results [Eq. (3)]. This parameter quantifies the dispersion of test results. The higher m is, the lower is the dispersion. Weibull statistical methods have been applied to the study of the dispersion of fracture stresses and strains for an imposed strain rate of 0.1 min 1 with 12 samples (Fig. 8). We see that fracture stresses are in good agreement with Weibull statistics, as shown by the linear evolution in Fig. 8a. For these results, we obtained a Weibull modulus, m, of 21.5 for the fracture stresses, and a mean fracture stress, s0, of ca. 31 MPa. For the fracture strain results, linearity of the distribution is debateable, and a Weibull modulus of 11 is found, with a mean fracture strain, e0, of 1.76%. This is clearly less impressive, although still acceptable.
3.2.2. Strain rate sensitivity The mechanical properties of the adhesive, as for polymers in general, reveal a high sensitivity to strain rate. This has been found on vitreous polymers, where a significant increase of Young’s modulus, elastic limit, and fracture stress with strain rate results [20–24]. Results for strain rates of 0.01 min 1 and 1 min 1 reveal, as seen from the gradient, comparable standard deviations (Table 2). We see, as expected, an increase of fracture stress (27.2 MPa to 42.5 MPa), Young’s modulus (3.6 GPa to 4.6 GPa), and also fracture strain (1.5% to 2.1%) for the two extreme strain rates; i.e., 0.01 min 1 and 1 min 1. It is interesting to evaluate sensitivity to the parameter, m, characterising variability of mechanical properties as a function of strain rate on a Weibull plot (Fig. 9). Weibull analysis of fracture stresses reveals, for both strain rates applied, a bimodal statistical distribution, represented by two different Weibull moduli. In principle, this
tends to invalidate use of the Weibull distribution. However, in fact, this can be attributed to the presence of two families of defects in the samples, of different size ranges, with porosities corresponding to air bubbles in the sample section. Thus, for a 0.01 min 1 strain rate, Weibull moduli for fracture stresses were found to be 3.5 and 7.1, for, respectively, significantly porous and apparently intact samples. Similarly, for a 1 min 1 strain rate, the Weibull moduli found for fracture stress were 6.2 and 20.4, for, respectively, significantly porous and apparently intact samples. The same type of porosity effect with speed sensitivity is observed on fracture strain. Thus, Weibull moduli were found to vary from 2.8 to 5.6 for a strain rate of 0.01 min 1 and 4.9 to 9.0 for a strain rate of 1 min 1, for, respectively, significantly porous and apparently intact samples. This interesting result suggests a decrease in dispersion, reducing porosity effects, when the strain rate is higher. Although at this stage, we can only surmise, it is possible that this effect is related to higher stresses near voids, leading in turn to some local plasticity. In the light of these results, it may be questioned whether two distributions are present in Fig. 8. However, the evidence is insufficient to decide about this. Fracture surfaces reveal a highly heterogeneous matrix, with large and small porosities, either of which could initiate polymer fracture (Fig. 10). We observed an important variation of porosity sizes present, as shown by the fracture surfaces, thus explaining fracture stress variability. Porosities may occur from various origins, the main two being: out-gassing associated with the crosslinking reaction generating small porosities, and more probably, from bubbles trapped during mixing of resin and hardener. Moreover, defects are introduced during sample casting, and the high viscosity of the adhesive paste prevents porosities from escaping efficiently from the mould. Thus, referring to Fig. 10 as an example, sample (a) with quasi-intrinsic small porosities offers a high fracture stress, samples (b) and (c) reveal fracture stresses in the vicinity of the mean value, and sample (d) corresponds to
Fig. 10. Fracture surfaces of adhesive tensile test samples containing (a) small porosities, (b) and (c) intermediate size porosities, and (d) a sample containing a large void (bubble).
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a sample with low fracture stress containing a huge void. Two effects (at least) are present: first, as is well-known, holes induce stress concentrations, and second, their presence clearly also reduces specimen cross-section, also increasing local stresses for a given applied load. Our results tend to suggest the latter cause as being predominant for the present material.
4. Conclusion The curing of a filled, epoxy-based adhesive has been studied with an aim to elucidate the influence of curing cycle on mechanical characteristics. Monitoring crosslinking of the adhesive paste revealed the necessary hardening time (hardening time referring to the time needed to handle the sample without damaging it). This was found to be only ca. 9 h (at ambient temperature), with Young’s modulus becoming stable. In fact, by allowing further time, we observed that still only partial crosslinking had occurred after 1 day at ambient temperature, with the presence of a secondary transition temperature (b), whose effect was reduced (or became negligible) with further curing time and/or higher temperature. Dynamic mechanical analysis (DMA) was used to identify the preferable curing cycle. Indeed, we suggest an improved version. Detailed dynamic mechanical analyses are necessary to identify the best curing conditions. Curing at ambient temperature resulted in inferior mechanical properties at intermediate temperatures, which was accompanied by a persistent secondary transition temperature. Curing cycles at elevated temperatures produced apparently rapid and complete crosslinking of the adhesive paste. A study of statistical aspects in dogbone tensile tests showed a dramatic effect of strain rate and porosity, upon Young’s modulus, fracture stress and fracture strain. The protocol of experimental process of adhesive handling strongly influences fracture stress variability and introduces uncontrolled dispersion of porosity in dogbone tensile specimens. Premature failure occurs for specimens containing large defects reducing in effective section, as may be expected. More significantly, we have proposed a first step in understanding and correlating the mechanical behaviour of an adhesive with porosities en defects due to manufacture. This has been done by applying the statistical techniques of Weibull. In particular, two populations of defects are apparently present, leading to different overall mechanical response.
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