Mar 29, 2006 - and the bearing strength of bolted woven composite joints. The main ... Many papers deal with the failure analysis of bolted composite joints.
A NUMERICAL AND EXPERIMENTAL STUDY OF WOVEN COMPOSITE PIN-JOINTS F. PIERRON∗ , F. CERISIER∗ and M. GREDIAC∗∗ ∗
Department of Mechanical and Materials Engineering Ecole des Mines de Saint-Etienne 158, cours Fauriel 42023 Saint-Etienne Cedex 02, France ∗∗
LERMES
Universit´e Blaise Pascal Clermont II 24, avenue des Landais, BP 206 63174 Aubi`ere Cedex, France
Submitted to Journal of Composite Materials Revised version March 29, 2006
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Abstract A numerical and experimental study was carried out to determine the stiffness and the bearing strength of bolted woven composite joints. The main objective was to investigate the possibility of predicting the properties of the joint from the properties of the material measured with standard tests. A refined finite element model was developed in which the nonlinearities due to both the material and the contact angle between the pin and the hole were taken into account. Particular attention was paid to account for the influence of the clearance which has been shown to be very significant. In conclusion, good agreement beetween experimental results and numerical predictions has been obtained.
1
INTRODUCTION
Many papers deal with the failure analysis of bolted composite joints. This is mainly due to the fact that joining composite structural components often requires mechanical fasteners which ultimate mechanical response is difficult to predict. Contrary to many metallic structural parts, for which the strength of the joints is mainly governed by the shear and the tensile strengths of the pins, composite joints present specific failure modes due to their heterogeneity and anisotropy. Three main basic failure modes are often described in the literature: bearing, net-tension and shear-out ([1, 2] for instance). In the present work, the specimen geometry is adjusted so that the bearing mode is enhanced. The main reason is that net-tension and shear-out can be avoided by increasing the width and the end-distance of the structural part for a given thickness. On the contrary, the bearing strength involves local effects which are mainly influenced by the material properties and the contact area between the pin and the hole. As a result, this type of failure cannot be avoided by any modification of the geometry of the structural part for a given thickness and pin diameter and can be considered an intrinsic property of the joint for given constitutive material, stacking sequence, diameter and clearance. The final objective of the present study is to develop a model for failure prediction
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of the joints. However, many such models already exist in the literature [3, 4, 5, 1], for instance, though generally the materials under study are carbon/epoxy laminated composites. Nevertheless, it has appeared to the present authors that a common weakness of the above papers is the lack of thorough experimental validation of the numerical finite element models used to calculate the stress and strain fields around the hole. Indeed, Hamada et al. [3] use a linear elastic finite element model with a rather crude contact model for the pin/composite interface and by using a YamadaSun failure criterion together with a caracteristic length approach [6], the strengths of the pin-joints are predicted. Nevertheless, no experimental validation of the model is given and their good agreement between predicted and measured failure loads does seem rather fortuitious. A more rigorous approach is presented by Hung et al. [5] who use a cumulative damage model to predict the response of the pinned and clamped joints. An experimental validation of the finite element model is given in the form of comparisons between strain gauge measurements and numerical results. These seem rather satisfactory. However, the difference between measured and calculated strains increase when the gauges get closer to the hole though the closest gauge remains one hole radius away from the hole edge, which is too far away since failure occurs much closer to the hole edge. Moreover, clearance between the pin and the composite is not considered and the behaviour of the joint seems linear up to failure because of the particular quasi-isotropic lay-up. Therefore, the validation presented in this paper does not seem to be particularly conclusive. The objective of the present paper is to study the behaviour of woven glass fibre epoxy pin-joints both numerically and experimentally, with particular attention given to the sensitivity of the model to different parameters (clearance, friction, non-linear material behaviour). This work is aimed at a thorough experimental validation of the numerical results so that the model can subsequently be used for the development of a relevant predictive failure model.
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2
TESTING
2.1
Joint testing configuration
The test specimen is shown in Figure 1. The width w and the end length e have been chosen so that bearing failure occurs. The value of the length l has been chosen high enough so that Saint-Venant’s effect due the grip is avoided. The diameter of the pin is 16 mm. The diameter of the hole is between 16.1 and 18 mm, so as to observe the influence of the clearance. This range of clearances corresponds to classical values from the mechanical construction standards [7]. The specimens were cut from the panels using a diamond coated blade. The hole is drilled in the composite plate with a silicon carbide mill. Care was taken during the drilling process to avoid damage on the back surface of the specimens by using wasted wedges. The material is a woven glass fibre cloth embedded in an epoxy resin. The panels have been autoclaved from a 7781/XE85AI Hexcel prepreg. The resin is a 120◦ C curing system. The final fibre volume fraction lies around 45%. The panels were 6.5 mm [±45]12s . The reason for this is that the present study is related to a wider project involving the design of a composite structural component for the railway industry [8, 9] for which the fibres orientations are ±45 ◦ . A double lap fixture shown in Figure 2 was used to perform the tests. All parts of the fixture are made of high strength steel. The influence of the clamping pressure was not studied in the present work for the sake of simplicity, therefore, the bolt was not tightened. The lower edge of the specimen was clamped with hydraulic grips to control the pressure fixed at 4 MPa according to the manufacturer recommendations. The magnitude of the applied load is measured by a load cell mounted on the testing machine. The displacement of the bottom grip is also recorded during the tests. The cross-head rate was 1 mm.mn−1 . Preliminary testing has been performed on specimens with clearances of 0.1 mm, 0.5 mm, 1 mm, 1.5 mm and 2 mm. The idea was to check the influence of the clearance on the joint behaviour as well as to have a first set of data to start the modelling. The results are given in Figure 3 as load-displacement curves. As can
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be seen on this figure, the behaviour of the joint is very dependent on the clearance between the pin and the hole, particularly the failure load that is reduced by about 30% when the clearance varies from 0.1 mm to 2 mm. On the contrary, the joint global stiffness does not vary very much (slopes of the curves in Figure 3), suggesting that the influence of the clearance is concentrated locally near the hole. This result is not surprising but implies that the prediction of the joint strength as a function of the clearance will necessitate the development of a model able to describe local effects of load distribution on the stress and strain fields near the hole. Many such models have been proposed over the years, both analytical and numerical [10], but the present authors have noticed that there was a lack of experimental validation of these models. Nevertheless, such validations are essential to demonstrate the validity of the failure prediction models that use as input values the computed stresses and strains near the hole. The rest of the present paper is dedicated to the development and validation of finite element calculations aimed at modelling the behaviour of the pin-joints described above.
2.2
Material characterization
The first step to develop a finite element model of the joint is to characterize the material behaviour. In order to do so, several mechanical tests have been performed.
2.2.1
Tension
Tensile tests have been performed on 6 rectangular specimens with fibres aligned with the specimen long axis (0◦ ), according to the ASTM D3039-76 standard [11]. The specimens dimensions were 225 mm by 25.4 mm by 2.69 mm. Composite tabs of 2.7 mm thickness cut from the tested panel have been used so that the final gauge length was 150 mm. Each specimen has been instrumented by a 0/90 rosette (HBM 6/120XY13) fixed in the centre of both faces of the specimen so that the effect of parasitic bending could be eliminated. The grips used are MTS servohydraulic grips. The clamping pressure has been selected to 4 MPa according to the manufacturer recommendations. The cross-head speed was fixed at 0.5 mm.mn−1 .
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The stress strain curves are nearly linear up to failure. A limited non-linearity appears towards the end of the life of the specimen, which is well known for fabric reinforced composites because of the fibres alignment. Longitudinal modulus and Poisson’s ratio have been calculated from the linear part of the curve. The results are as reported in Table 1. It can be seen that no significant differences have been noticed between the warp and weft directions.
2.2.2
Shear
The in-plane shear response of the material has been measured using the 45◦ offaxis tensile test, following the ASTM D3518 standard [11]. The dimensions of the specimens were equal to that of the tension tests. The shear specimens were equiped as the tension ones. A typical shear response is represented in Figure 4. As can be seen, the response is highly non-linear. The implications of this will be discussed later in the modelling section. In terms of modulus and failure stress, the results are reported in Table 1. It is to be noted that the in-plane shear failure stress is only an approximation of the shear strength [12].
2.2.3
Compression
Compression tests have been performed using a slightly modified version of the ASTM D3410-87 standard [13]. The specimens were 112 by 12 by 2.69 mm. They were equipped with 50 mm long and 2 mm thick tapered tabs from the same material as the tested one. The values found for the compressive failure stress was 365 MPa in the warp direction and 355 MPa in the weft direction. These values were much lower than that reported in the manufacturer technical data sheet (values reported in Table 1). It is to be noted however that the behaviour of a compression specimen is basically a structural one because of the instability driven failure mode [14, 15]. Therefore, a first approximation of the compressive strength will be taken as equal to the tensile strength which is consistent with the values measured by Hexcel (Table 1). Now that the material properties have been evaluated, the modelling of the joint can be performed. This is the object of the next section.
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3
FINITE ELEMENT MODELLING
In order to calculate the stress distribution around the hole of the composite joint, a finite element model has been developed. The package used for this analysis is ABAQUS 5.5. In order to reduce the number of parameters, only the two extreme clearance values have been considered, that is 0.1 mm and 2 mm. The specimen dimensions are that of Figure 1. The mesh used for the present study is represented in Figure 5. The elements used for this study are eight-noded biquadratic plane stress CPS8 elements. In order to assess the influence of certain parameters on the joint response, several levels of modelling have been considered. First, a linear elastic model has been developed. The boundary conditions are as follow. The right hand side of the model of Figure 5 is clamped and a pressure with a sine profile is applied on the left hand side of the hole, simulating the pressure of the bolt on the composite hole. These are classical boundary conditions used in the literature [16]. The second model considered is that taking the contact between the bolt and the composite into account. In order to simulate this contact, a rigid surface has been modelled to represent the bolt. ABAQUS uses an iterative surface interaction technique to solve this problem. It is not the scope of the present paper to describe this numerical approach. All details can be found in [17]. The local meshes used for the two clearance values are represented in Figure 6. Within this model, the influence of the friction coefficient has also been investigated. Finally, because of the strongly non-linear in-plane shear behaviour of the material, the contact model previously described has been refined by introducing this material nonlinearity. In order to do so, the shear response in Figure 4 has been modelled by a fifth order polynomial, assuming that the response is the same when the shear stress changes sign. This is implemented by an ABAQUS UMAT procedure programmed with the specific ABAQUS language, with the following stress-strain
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relationship (for εs ¿0): σs = 9.081014 ε5s − 1.411014 ∗ ε4s + 8.881012 ∗ ε3s (1) −2.9010
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∗
ε2s
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+ 5.4910 ∗ εs
However, because of the debonding of the strain gauges after a 6% shear strain (see Figure 4), the following part of the stress strain curve has been modelled by a straight line in the continuity of the measured stress-strain curve: σs = 4.14108 ∗ εs + 4.67107
(2)
The next step is now to validate the above models experimentally and to find out which level of modelling is necessary to represent the pin-joint response correctly. This is the objective of the next section.
4 4.1
EXPERIMENTAL VALIDATION Global stiffness
The first validation that can easily be performed concerns the global stiffness of the structure, that is, the load measured by the load cell divided by the displacement of the pin. For a clearance of 0.1 mm, Figure 7 compares the global stiffness of the joint obtained from the linear elastic model, the contact model (no friction) and the contact plus the shear nonlinear material behaviour model. As can be seen from these results, the material nonlinearity is essential to describe the response of the joint. Moreover, the implementation of the contact elements does not seem to change the joint stiffness significantly. This is consistent with the fact that the influence of the pin contact pressure should be limited to the local stress and strain fields. However, even for this 0.1 mm clearance, the classically assumed sinusoidal pressure distribution is not representative of the action of the bolt on the composite. Indeed, Figure 8 shows the pressure distribution calculated from the finite element contact model compared to the sinusoidal distribution and it can be seen that the calculated pressure is significantly different from a sine function. This will lead to local differences in the stress and strain fields that will affect the strength prediction model, as already mentionned by Murthy et al. [16], for instance. Another interesting
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feature is the variation of the contact angle as a function of the load for the two clearance values. This is reported in Figure 9 obtained by recording the contact angle at each step of the iterative solving process. As can be seen, an increase in the clearance results in a smaller contact area, which explains the lower failure stress for the 2 mm configuration, as expected. Finally, when considering Figure 7, it can be seen that there is still a difference between the model and the experimental response of the joint. This is certainly due to the fact that the displacement measured experimentally is that of the machine cross-head and the displacement calculated from the finite element model is the relative displacement of the pin with respect to the clamped end of the composite plate. Since the fixture is not infinitely stiff, some deformation of the fixture is expected. This has been checked and measured using a dial gauge fixed on the pin. Since on the test machine used for this study, it is the bottom part of the fixture that moves (see Figure 2), i.e the one with the grip, the displacement of the pin relatively to the machine should be zero. Any non-zero displacement of the pin will indicate deformation of the upper part of the fixture, including the pin itself which can deform. The experimental curve from Figure 7 has therefore been corrected to take this fixture deformation into account. This was done by substracting the pin displacement to the bottom grip displacement. This is represented in Figure 10. It can be seen that the model fits the bold line very well at the beginning of the curve but that there is still a significant difference towards the end. Since any extra deformation of the upper part of the fixture is now accounted for by the use of the dial gauge, the explanation has been sought on the lower part of the fixture. Using a second dial gauge measuring the relative displacement of the top of the grip and the specimen, it was found that some sliding in the grips was present. It was sufficient to account for the few tenths of millimeters difference between the model and the corrected experimental results of Figure 10. In order to fully check the model, it would be necessary to use a device that would measure the relative displacement between the pin and a fixed reference
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on the specimen near the grips. However, the validation performed here was thought sufficient to give some initial confidence in the finite element modelling. Since what is of interest to predict the failure load is the local stress and strain distributions around the hole, it was decided to carry on the validation by using local strain measurements.
4.2
Local validation
The local validation of the finite element model has been performed by two different means.
4.2.1
Strain gauges
First, two specimens - one for each clearance value - have been equipped with two back-to-back Vishay Micromeasurement WA-13-060WR-120 rosettes each and tested. The center of the rosettes was positioned 2.5 mm away from the hole edge and the gauge length was 1.5 mm. Again, it should be noted that the gauges are here much closer to the hole edge than in [18] where they are positioned at least one hole diameter away from the hole edge, that is, away from the failure initiation zone. The specimen with the 0.1 mm clearance has first been tested twice up to 9 kN while being taken out of the rig, turned around and fitted back into the fixture between the two tests. This was performed to check whether significant and reproduceable differences existed between the strains on the two specimen faces. The results are reported in Figure 11 for the longitudinal strain. It can be seen that more than 100% strain differences are recorded between the two faces. Moreover, it is the same specimen face that exhibits the lower strain. This is consistent with other observations on Iosipescu shear specimens where it was shown that the cause of this phenomenon is in-plane Saint-Venant effects due to the local load heterogeneity that results from uneven pin/composite contact [19, 20], as sketched in Figure 12. Therefore, proper interpretation of the results must be ensured by averaging out the strains over the two faces, as demonstrated in [19]. This is the procedure adopted to produce to following results. It should be noted that such a procedure is rarely applied in practice in other published studies ([18], where only one specimen face is strain gauged) and
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discrepancies between model and experiment could well arise from this point. To the present authors opinion, this is one of the significant contributions of the present paper. In order to compare the computed results to the experimental ones, the finite element strains have been calculated over a certain number of elements to simulate the strain gauge. Also, in order to check whether friction had any effect on the local strain distributions, models with different friction coefficients have been developed for both pin-joint configurations. The nominal friction coefficient input in the model has been evaluated by sliding a metallique bar on a composite plate and by measuring the sliding angle. This experiment gave a friction coefficient of about 0.3. The results are reported in Figures 13 and 14. The first observation that arises from these results is that the influence of friction is very dependent on the clearance value. Indeed, for the 0.1 mm clearance specimen, the difference between a 0 and 0.3 friction coefficient is very important (nearly a 100% strain difference for a 15 kN load). On the other hand, when the clearance value increases, this influence decreases and for a 2 mm clearance value, there is only a very small difference between the responses obtained with and without friction. This result is important since although the influence of friction has been numerically pointed out by several authors [21, 22, 23], the mixed experimental and numerical studies very often neglect the influence of friction, even for clearance-fit configurations [3, 2, 5]. In the case of the work by Hung and Chang [5], a validation using strain gauges has also been performed and good agreement between model and experiment was found but the closest gauge was positioned one hole radius away from the hole edge (details in [18]). It is interesting to note (Figure 17 of reference [5]) that the strains from the first two gauges, positioned 3 and 5 radius away from the hole edge were exactly predicted by the model but that for the last gauge, positioned one radius away from the hole edge, the experimental strains were lower than that given by the model, exactly as in Figure 13 when friction is not taken into account. Though this difference remained small in [5] (about 20%), it seems that if the strain measurement location was moved up further towards the hole edge, where the failure
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is actually initiated, results such as that of Figure 13 would have been found (in the present work, the strain gauge is positioned
1 8 th
of the radius away from the hole
edge). In the other reference cited above ([3]), no experimental validation of the local strain distribution obtained from the finite element model is provided. Finally, it can be said that the results of Figures 13 and 14 are very satisfactory, even more so since the strain gauges have been positioned very close to the hole edge where high strain gradients are present. It is important to note that if only one gauge had been used or if friction had been neglected, such a thorough validation would have been impossible.
4.2.2
Whole-field measurements
The previous validation has been very successful but it is only a very punctual verification. In order to spread this validation over a larger field, a whole-field displacement measurement technique has been used. The technique is based on the deformation of a unidirectional grid followed by a CCD camera [24]. The phase of the grid is measured before and after specimen loading and the difference between these two phase fields is related to the inverse displacement field, u−1 (r), which, for small displacements, is equal to −u(r). The image acquisition and processing is ensured by the Frangyne software developed in-house and based on phase-stepping [25]. The grid used in the present study is a M´ecanorma Normatex 3121 grid of 610 µm pitch. The grid is bonded on the composite using the VPAC-1 glue from Vishay Micromeasurement but before bonding, a thin layer of white paint is spread onto the composite specimen to ensure good contrast of the grid. Details of the procedure can be found in [9, 26, 27, 28]. In order to be able to see the grid above the pin-head, the fixture was modified by machining the flanges in this area. The direct results from the experiments are the longitudinal displacements for the two clearance specimens. These results are presented in Figure 15. It can be seen that there is an excellent correlation between the calculated and measured displacement fields, and also that the shapes of the contour lines are somewhat different between the 0.1 mm and the 2 mm clearances. From these displacement maps, it is possible
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to obtain the longitudinal strain by differentiating the data numerically with respect to the x2 coordinate. However, this procedure requires some spatial smoothing to obtain reasonable results. In the present case, the best least-square linear fit over 5 pixels has been used to derive the strains. The resulting strain maps are represented in Figure 16. What can be said from these results is that there is good correlation with the calculated fields, though significant noise is present on the experimental strains because of the differentiation process. The information given by these results is complementary to that from the strain gauges. Indeed, in the present case and contrariwise to the strain gauges procedure, the local strain values close to the hole edge are not precisely measured, though this would be possible by using a finer grid (this work in on-going at Ecole des Mines). Nevertheless, the present procedure enables the measurement of the whole longitudinal displacement and strain fields around the hole, which strain gauges cannot perform. Therefore, both the validation results enable to put good confidence in the finite element model and particularly in the difficult process of modelling the boundary conditions. This step towards the final goal of strength prediction appears essential to the present authors, all the more since such validation is often absent or incomplete in other studies from the literature. It is the authors opinion that there is no need in developing and implementing complex damage models if the computations are not thoroughly validated by experimental work.
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STRENGTH PREDICTION
Once the finite element model has been validated, the last step is to use the calculated strain or stress fields together with some damage/failure model to predict the failure load of the joint, since this is what is of interest to the designers. In order to reach the above objective, additional experimental work has been carried out to investigate the failure of the specimens. A classical force displacement curve is represented in Figure 17 together with the visible specimen damage associated with the first and the final load drops. The first load drop (failure 1) is
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associated with the appearance of a swollen V-shaped zone under the contact point. This phenomenon, also described by Wang et al. [18], is caused by the dramatic propagation of interlaminar cracks. After this event, the joint bears further load until the final failure (failure 2) occurs as a complete crushing of contact zone. Clearly, alhough the joint carries on bearing load after failure 1, the designer must ensure that the joint never reaches failure 1 since the joint cannot recover its properties after that point (irreversible damage). Therefore, the present study will concentrate on the part of the curve leading to failure 1. Although failure 1 is due to interlaminar cracks, it is certainly the accumulation damage due to in-plane stresses that is the cause of the interlaminar cracks, as already suggested by Wang et al. [18]. In order to investigate this point, four specimens for each clearance value have been tested up to failure. These joints have been equipped with an acoustic emission sensor (type EPA-Dunegan S9220) connected to an EPADunegan 3000 acquisition board (100 channels). The system has been calibrated according to the ASTM E1118-89 standard [29]. The results are reported in Table 2 and typical curves are given in Figures 18 and 19. The first thing that can be seen in Table 2 is that there is not much scatter on the failure forces for the four tested specimens. This justifies the fact that no additional data have been sought. Concerning Figures 18 and 19, the main observation is that the acoustic emission is much more important for the 0.1 mm clearance specimen that for the 2 mm one. Also, for the latter, the start of the events is very close to the failure point. This phenomenon may well be caused by the fact that there is much more sliding between the pin and the hole for the 0.1 mm specimen (see also the influence of friction in the previous section). Therefore, it might be misleading to consider the emitted noise as representative of damage. In any case, these acoustic emission results show an important increase of noise near the first load drop. This suggests that significant in-plane damage is to be sought near this first load drops. In order to check for significant in-plane damage before the ‘macroscopic’ failure point (first load drop), and to identify what type of damage occurs (i.e. caused by
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which stress component), two sets of three specimens per clearance value have been tested. They were loaded up to a certain fraction of the average failure load of Table 2 and then, microscopic observation was carried out to see whether in-plane damage was visible in the mid-plane of the specimens. The results are reported in Table 3. For both configurations, significant damage is visible at around 90% of the failure load and not detectable below 70%. The aspect of the visible damage is representative of in-plane shear damage (whitening of the fibre tows), as can be seen in Figure 20. Similar observation had been made on the 45◦ off-axis tensile specimens, confirming that in-plane shear seems responsible for the specimen failure. It is important to note that the photograph of Figure 20 was taken from a failed specimen. The extend of the damage observed at 90% of the failure load is much lower. As a summary of the above experimental study, it can be said that the damage leading to the failure of the joint is suspected to be caused by in-plane shear and that significant damage has been found only around 90% of the failure load. The next step is now to compare these results to the finite element calculations. The full finite element model (including friction contact and material nonlinearity) was used to interpret the above results. The stress fields around the hole for the two clearance values are given in Figures 21 and 22 in the orthotropy axes, respectively for 25 and 17 kN, which corresponds to the values of Table 3 (i.e. 90% of the failure load). The main result from these stress maps is that only the in-plane shear stress in close to its critical value over a significant area (see Table 1). This confirms the fact that the failure of the joint is caused by in-plane shear. Looking more closely at the in-plane shear maps (Figures 23 and 24), it can be seen that for the 2 mm clearance, the negative shear (under the contact zone) is significantly higher than the positive one as for the 0.1 mm clearance, they are of the same order of magnitude. Clearly, two phenomena are in competition here, compression load at the contact point due to the local pressure of the pin but also tension at 90◦ from the contact point due to the ovalization of the hole, both causing shear in the material axes because of the ±45◦ fibre orientation. In the case of the 2 mm clearance specimen, the fact
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that the contact load is more concentrated than for the 0.1 mm one results in higher shear stress under the contact point, but for the 0.1 mm specimen, the positive and negative shear stress values are similar. This is surprising since no trace of damage has been found in the positive shear zone in the failed specimens, indicating that only the negative shear zone is important for failure. There are two possible explanations the present authors can think of. First, the finite element model does not well represent what happens at 90◦ from the contact point. Since no precise validation using strain gauges has been performed in this area, it is possible that the finite element modelling is not accurate in that area, though the full field measurements were quite reassuring. The second possible cause is related to the local Saint-Venant effects described in the previous section. Indeed, it was shown that important strain differences existed between the two specimen faces because of local contact defects, particularly for the 0.1 mm configuration. However, such differences are not to be expected on the shear strain in the positive shear zone since this area is far from the contact point. Therefore, it is probable that the damage is prematurely initiated on the higher strain side of the specimen, at higher stress values than that of the 2D map in Figure 23. This should be confirmed by localized microscopic observation. Nevertheless, this feature is an important obstacle to the correct prediction of the failure load of such joints. Finally, the previous results have been used to predict the failure load of the two types of joints. As a first approach, a very simple procedure is used. The maximum stress criterion [30] is selected as the failure model. So, the maximum shear stresses from the finite element results are compared to the in-plane shear strength, estimated from the 45◦ off-axis tensile test (Table 1). When these values meet, the computed force is recorded and compared to the experimental measurements. The results are reported in Table 4. The predicted failure loads are slightly overestimated. This again may be due to the Saint-Venant effect, as explained above. A 10% difference is compatible with the recorded strain differences at failure, as can be seen in Figure 25. Also, using the maximum stress value from the finite element maps does not take the
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influence of the gradient into account (see [6]). Nevertheless, considering the very basic failure model used here, the results are very satisfactory. This may be a hint that instead of developing complex advanced failure models that industrial design departments may not be able to use (cumulative damage etc. . . , see [5, 3]), it may be worthwhile to put more effort into the correct mechanical modelling (boundary conditions etc.) and the experimental validation and use basic failure criteria such as that largely spread among the industrial designers (maximum stress, maximum strain or Tsai-Wu, for instance).
6
CONCLUSION
The following conclusions can be drawn from the present study: • The clearance between the pin and the hole has an important influence on the failure load of pin-joints. Minimum clearance should be ensured according to the assembly requirements. • Local Saint-Venant effects due to pin-hole contact defects cause significant strain differences between the two specimen faces. Strain gauges should be fixed on the two specimen faces and the strains averaged to correctly validate the finite element local strain calculations. • The minimum level of finite element modelling required to describe the behaviour of the pin-joint considered here requires the use of friction contact and shear nonlinearity. • Thorough experimental validation of the finite element model is required to see the influence of certain parameters of the model (friction, in particular). • The failure of the present ±45◦ joints is caused by in-plane shear. • Using the maximum stress criterion applied to the maximum stress value from the finite element computations, the failure loads of the two types of joints (clearances of 0.1 and 2 mm) has been predicted within 10% of the experimental values.
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• The present approach has been limited to a certain type of material and layups and should be extended to other configurations for additional validation. Also, the influence of the tightening of the bolt has been discarded. However, the procedure is compatible with design departments requirements where more complex failure models cannot be implemented because of the very costly identification procedures, particularly in industrial sectors where the added value is much lower than that of the aerospace industry. The present study is a step towards simplified design procedures for composite bolted joints.
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References [1] K. Hollmann. Failure analysis of bolted composite joints exhibiting in-plane failure modes. Journal of Composite Materials, 30(3):358–387, 1996. [2] C. L. Hung and F. K. Chang. Strength envelope of bolted composite joints under bypass loads. Journal of Composite Materials, 30(13):1402–1435, 1996. [3] H. Hamada, Z.-I. Maekawa, and K. Haruna. Strength prediction of mechanically fastened quasi-isotropic carbon/epoxy joints. Journal of Composite Materials, 30:1596–1612, 1996. [4] F. K. Chang, R. A. Scott, and G. S. Springer. Strength of mechanically fastened composite joints. Journal of Composite Materials, 16:470, 1982. [5] C. L. Hung and F. K. Chang. Bearing failure of bolted composite joints. Part II: model and verification. Journal of Composite Materials, 30(12):1359–1399, 1996. [6] J. M. Whitney and R. J. Nuismer. Stress fracture criteria for laminated composite containing stress concentrations. Journal of Composite Materials, 8:253, 1974. [7] R. Quatremer and J.P. Trottignon. Construction m´ecanique. Nathan, 1986. in French. [8] F. Cerisier, M. Gr´ediac, F. Pierron, and A. Vautrin. Design of a locomotive transmission in composite materials. In Proceedings of European Symposium on Design and Analysis, July 1996 in Montpellier, France, 1996. [9] F. Cerisier. Conception d’une structure travaillante en composite et ´etude de ses liaisons. PhD thesis, Universit´e Jean Monnet de Saint-Etienne, France, 1998. 7th May 1998, in French. [10] P.P. Camanho and F.L. Matthews. Stress analysis and strength prediction of mechanically fastened joints in frp: a review. Composites Part A, 28A:529–547, 1997. [11] ASTM D3039-76. Test method for tensile properties of fiber-resin composites, 1976. American Society for the Testing of Materials.
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[12] F. Pierron and A. Vautrin. New ideas on the measurement of the in-plane shear strength of unidirectional composites. Journal of Composite Materials, 31(9):889–895, 1997. [13] ASTM D3410-87. Test method for compressive properties of unidirectional or cross-ply fiber-resin composites, 1987. American Society for the Testing of Materials. [14] J.C. Grandidier, G. Ferron, and M. Potier-Ferry. Microbuckling and strength in long fiber composite: theory and experiments. International Journal of Solids and Structures, 29:1753–1761, 1992. [15] S. Drapier, J.C. Grandidier, and M. Potier-Ferry. Non linear numerical approach of microbuckling. Composites Science and Technology, 1998. to appear. [16] A.V. Murthy, B. Dattaguru, H.L.V. Narayana, and A.K. Rao.
Stress and
strength analysis of pin-joints in laminated anisotropic plates. Composites Structures, 19:299–312, 1991. [17] ABAQUS 5.5 user manual. [18] H. S. Wang, C. L. Hung, and F. K. Chang. Bearing failure of bolted composite joints. Part I: experimental characterisation. Journal of Composite Materials, 30(12):1285–1313, 1996. [19] F. Pierron. Saint-Venant effects in the Iosipescu specimen. Journal of Composite Materials, 32(22):1986–2015, 1998. [20] F. Pierron. Experimental evidence of Saint-Venant effects in composite testing. In European Conference on Composite Materials -Composite Testing and Standardisation 4, pages 47–56, 1998. 31 August to 2 September in Lisbon, Portugal. [21] M.H. Hyer, E.C. Klang, and D.E. Cooper. The effect of pin elasticity, clearance and friction on the stresses in a pin-loaded orthotropic plate. Journal of Composite Materials, 21:190–206, 1987.
20
[22] L.J. Eriksonn. Contact stresses in bolted joints of composite materials. Composite structures, 6:57–75, 1986. [23] R.A. Naik and J.H. Crews. Stress analysis method for a clearance-fit bolt under bearing loads. AIAA Journal, 24(8):1348–1353, 1985. [24] Y. Surrel and B. Zhao. Moir´e and grid methods: a ’signal processing’ approach. In Photomechanics, Proceedings of Interferometry ’94, vol. SPIE 2342, pages 118–127, 1994. 16-20 May 1994 in Warsaw. [25] Y. Surrel. Design of algorithms for phase measurements by the use of phasestepping. Applied Optics, 35(1):51–60, 1996. [26] F. Cerisier, L. Dufort, M. Gr´ediac, F. Pierron, and Y. Surrel. Application d’une m´ethode de grille ` a l’´etude du contact boulon-trou dans une pi`ece composite. In Photom´ecanique, pages 97–104, 1998. 14-16 April in Marne-la-Vall´ee, France. [27] F. Pierron, E. Alloba, Y. Surrel, and A. Vautrin. Whole-field assessment of the effects of boundary conditions on the strain field in off-axis tensile testing of unidirectional composites. Composites Science and Technology, 58(12):1939– 1947, 1998. [28] L. Dufort, M. Gr´ediac, Y. Surrel, and A. Vautrin. Applying the grid method to the measurement of displacement and strain fields through the thickness of a sandwich beam. In A. Vautrin, editor, Mechanics of sandwich structures, Proceedings of Euromech 360 colloquium, 13-15 May in Saint-Etienne, France. Kluwer Academic Publishers, the Netherlands, 1997. [29] ASTM E118-89. Practice for acoustic emission examination of reinforced thermosetting resin pipes. American Society for the Testing of Materials. [30] S.W. Tsai. Theory of composites design. Think Composites, Dayton, Ohio, USA, 1992.
21
List of Figures 1
Pin-joint testing configuration . . . . . . . . . . . . . . . . . . . . . . . 24
2
Experimental setup for pin-joint testing . . . . . . . . . . . . . . . . . 25
3
Woven glass-epoxy pin-joint response as a function of pin clearance . . 26
4
In-plane shear response of the glass fabric epoxy composite . . . . . . 27
5
ABAQUS mesh for half the model . . . . . . . . . . . . . . . . . . . . 28
6
Detailed schematic of the finite element mesh around the hole for the two clearance values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
7
Force-displacement curves obtained from finite element analysis and experiment, for a clearance value of 0.1 mm . . . . . . . . . . . . . . . 30
8
Local force distribution on the hole obtained by finite element on the 0.1 mm clearance contact model compared to the classically assumed sine distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
9
Contact angle as a function of the load for the two clearance values . . 32
10
Force-displacement curves obtained from finite element analysis and experiment, corrected to account for fixture deformation, for a clearance value of 0.1 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
11
Force against longitudinal strain for two pin-joint tests on the same specimen, clearance=0.1 mm . . . . . . . . . . . . . . . . . . . . . . . 34
12
Local contact defect causing strain differences between the specimen faces (in-plane Saint-Venant effect) . . . . . . . . . . . . . . . . . . . . 35
13
Comparison between calculated and computed strains for the 0.1 mm clearance specimen, with different friction coefficients . . . . . . . . . . 36
14
Comparison between calculated and computed strains for the 2 mm clearance specimen, with different friction coefficients . . . . . . . . . . 37
15
Comparison of the u2 displacement fields for clearance values of 0.1 and 2 mm, friction coefficient 0.3 . . . . . . . . . . . . . . . . . . . . . 38
16
Comparison of the ǫ2 strain for clearance values of 0.1 mm and 2 mm, friction coefficient 0.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
22
17
Typical force displacement curve for a 0.1 mm clearance joint with corresponding specimen damage . . . . . . . . . . . . . . . . . . . . . . 40
18
Typical force displacement curve together with acoustic emission events for the 0.1 mm clearance joint . . . . . . . . . . . . . . . . . . . . . . . 41
19
Typical force displacement curve together with acoustic emission events for the 2 mm clearance joint . . . . . . . . . . . . . . . . . . . . . . . . 42
20
Microscopic view of the in-plane damage on a failed 2 mm clearance specimen (mid-plane)
21
. . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Stress field in material axes for the 0.1 mm clearance specimen loaded at 25 kN (90% of the failure load)
22
Stress field in material axes for the 2 mm clearance specimen loaded at 17 kN (90% of the failure load)
23
. . . . . . . . . . . . . . . . . . . . 44
. . . . . . . . . . . . . . . . . . . . 45
In-plane shear stress map in material axes for the 0.1 mm clearance specimen loaded at 25 kN (90% of the failure load) . . . . . . . . . . . 46
24
In-plane shear stress map in material axes for the 2 mm clearance specimen loaded at 17 kN (90% of the failure load) . . . . . . . . . . . 47
25
Force displacement response of a 0.1 mm clearance specimen equipped with back-to-back strain gauges . . . . . . . . . . . . . . . . . . . . . . 48
23
w = 60 mm
AAAA AAAA AAAA AA AAAA AA
e = 60 mm clearance
= 16 mm
45
l = 220 mm Fibres
AAAAAAAA AAAAAAAA AAAAAAAA F Figure 1: Pin-joint testing configuration
24
support
washer
bolt nut composite specimen
grips
F Figure 2: Experimental setup for pin-joint testing
25
30
Force (kN)
25 0.5 mm
20
1 mm
0.1 mm
1.5 mm
15
2 mm
10 5 0 0
0.5
1
1.5
2
2.5
3
Displacement (mm) Figure 3: Woven glass-epoxy pin-joint response as a function of pin clearance
26
3.5
70
Shear stress (MPa)
60 50 40 30 20 10 0 0
1
2
3
4
5
6
Engineering shear strain (%) Figure 4: In-plane shear response of the glass fabric epoxy composite
27
7
Figure 5: ABAQUS mesh for half the model
28
0.1 mm clearance
2 mm clearance
Figure 6: Detailed schematic of the finite element mesh around the hole for the two clearance values
29
contact + material nonlinearity linear elastic
30
contact
Force (kN)
25 20
experimental
15 10 5 Clearance: 0.1 mm 0 0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Displacement (mm) Figure 7: Force-displacement curves obtained from finite element analysis and experiment, for a clearance value of 0.1 mm
30
350 sine distribution 300
Force (N)
250
finite element
200 150 100 50 0 0
10
20
30
40
50
60
70
80
90
Angle ( ) Figure 8: Local force distribution on the hole obtained by finite element on the 0.1 mm clearance contact model compared to the classically assumed sine distribution
31
40
0.1 mm 2 mm
35
Force (kN)
30 25 20 15 10 5 0 0
20
40
60
80 100 Angle ( )
120
140
160
180
Figure 9: Contact angle as a function of the load for the two clearance values
32
finite element model
30
experimental
25
Force (kN)
corrected experimental 20 15 10 5 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Displacement (mm) Figure 10: Force-displacement curves obtained from finite element analysis and experiment, corrected to account for fixture deformation, for a clearance value of 0.1 mm
33
Figure 11: Force against longitudinal strain for two pin-joint tests on the same specimen, clearance=0.1 mm
34
composite specimen
strain gauge (lower strain)
strain gauge (higher strain)
threaded rod
AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA AAAAA local contact defect (magnified)
F Figure 12: Local contact defect causing strain differences between the specimen faces (inplane Saint-Venant effect)
35
Longitudinal strain (%) Figure 13: Comparison between calculated and computed strains for the 0.1 mm clearance specimen, with different friction coefficients
36
Longitudinal strain (%) Figure 14: Comparison between calculated and computed strains for the 2 mm clearance specimen, with different friction coefficients
37
Displacement in micrometer
2
1
Experimental
Finite element calculation Clearance: 0.1 mm - Force: 7900 N Displacement in micrometer
2
1
Finite element calculation
Experimental
Clearance: 2 mm - Force: 8100 N Figure 15: Comparison of the u2 displacement fields for clearance values of 0.1 and 2 mm, friction coefficient 0.3
38
Strain in microstrain
2
1
Finite element calculation
Experimental
Clearance: 0.1 mm - Force: 7900 N Strain in microstrain
2
1
Finite element calculation
Experimental
Clearance: 2 mm - Force: 8100 N Figure 16: Comparison of the ǫ2 strain for clearance values of 0.1 mm and 2 mm, friction coefficient 0.3
39
40 35
Force (kN)
30 25 20 15 10 5 0 0
1
2
3
4
5
6
7
8
9
10
Displacement (mm)
Figure 17: Typical force displacement curve for a 0.1 mm clearance joint with corresponding specimen damage
40
1000
30 Clearance: 0.1 mm
Force (kN)
800
20 600 15 400 10 200
5 0
Cumulated number of events
25
0 0
1
2
3
Displacement (mm) Figure 18: Typical force displacement curve together with acoustic emission events for the 0.1 mm clearance joint
41
1000
20 16
800
12
600
8
400
4
200
0
0 0
0.5
1
Cumulated number of events
Force (kN)
Clearance: 2 mm
1.5
Displacement (mm) Figure 19: Typical force displacement curve together with acoustic emission events for the 2 mm clearance joint
42
Figure 20: Microscopic view of the in-plane damage on a failed 2 mm clearance specimen (mid-plane)
43
Stress in Pa
Stress in Pa
σx stress
σy stress Stress in Pa
σs stress Figure 21: Stress field in material axes for the 0.1 mm clearance specimen loaded at 25 kN (90% of the failure load)
44
Stress in Pa
Stress in Pa
σx stress
σy stress Stress in Pa
σs stress Figure 22: Stress field in material axes for the 2 mm clearance specimen loaded at 17 kN (90% of the failure load)
45
Stress in Pa
σs stress Figure 23: In-plane shear stress map in material axes for the 0.1 mm clearance specimen loaded at 25 kN (90% of the failure load)
46
Stress in Pa
σs stress Figure 24: In-plane shear stress map in material axes for the 2 mm clearance specimen loaded at 17 kN (90% of the failure load)
47
average
face 1
25
face 2
20
10
Force (kN)
15
5 clearance: 0.1 mm 0 -3
-2.5
-2
-1.5
-1
-0.5
0
Longitudinal strain (%) Figure 25: Force displacement response of a 0.1 mm clearance specimen equipped with back-to-back strain gauges
48
List of Tables 1
Mechanical properties of the glass fabric epoxy composite . . . . . . . 50
2
Results of the joint tests . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3
Damage investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4
Predicted and measured failure forces for the two clearance values . . 53
49
Table 1: Mechanical properties of the glass fabric epoxy composite Type
Tensile failure stress (MPa)
Poisson’s ratio
warp
Tensile modulus (GPa) 25.4
540
0.13
weft
25.4
530
0.13
In-plane shear modulus (GPa) 5.2
In-plane shear failure stress (MPa) 91
Type warp
Compressive failure stress (MPa) 570 (Hexcel - PrEN2850)
weft
506 (Hexcel - PrEN2850)
50
Table 2: Results of the joint tests Clearance(mm) number 0.1 / spec. 1
/
Specimen
Failure load (kN) 29.2
0.1 / spec. 2
28.2
0.1 / spec. 3
29.2
0.1 / spec. 4
29.4
Mean
29.0
2 / spec. 1
18.0
2 / spec. 2
19.3
2 / spec. 3
19.7
2 / spec. 4
18.3
Mean
18.8
51
Table 3: Damage investigation Clearance(mm) Maximum / Specimen load in kN number (% of failure load) 0.1 / spec. 1 15.9 (55%)
Visible damage
NO
0.1 / spec. 2
20.1 (69%)
NO
0.1 / spec. 3
25.0 (86%)
YES
2 / spec. 1
10.0 (53%)
NO
2 / spec. 2
13.5 (72%)
NO
2 / spec. 3
17.0 (90%)
YES
52
Table 4: Predicted and measured failure forces for the two clearance values Experimental failure load (kN) Predicted failure load (kN) Relative difference (%)
0.1 mm clearance 25
2 mm clearance 17
26
19
4
12
53
