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Development of a finite element model for analysis of pultruded structures using thermoelastic data
Composites: Part A 39 (2008) 1311–1321
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Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Development of a finite element model for analysis of pultruded structures using thermoelastic data S.W. Boyd a,*, J.M. Dulieu-Barton a, O.T. Thomsen b, A. Gherardi a a b
Fluid Structure Interactions Research Group, School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK Department of Mechanical Engineering, Aalborg University, Denmark
a r t i c l e
i n f o
Article history: Received 27 April 2007 Received in revised form 22 January 2008 Accepted 29 March 2008
Keywords: A. Adhesion C. Finite element analysis E. Pultrusion Thermoelastic stress analysis (TSA)
a b s t r a c t Thermoelastic stress analysis (TSA) is used to determine the stress field in the through thickness direction of an orthotropic pultruded material. An economical means of experimentally obtaining the thermoelastic constant and some mechanical properties of each of the constituent layers in the pultruded structure is devised. The stresses in a bonded joint are obtained using thermoelastic stress analysis. The calibrated thermoelastic data is used to validate a finite element model of the joint. It is shown that to accurately interpret thermoelastic data from layered structure, such as that of the pultrusion, calibration is an essential step. It is also demonstrated that the thermoelastic approach provides an excellent means of validation of finite element models. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction There is an increased interest in the use of composite materials as non-primary structure in commercial and military vessels. Such applications include superstructure in commercial vessels and hangars and communication masts in military vessels. One of the important design aspects associated with the use of composite materials is reduced weight. This can be exploited either by increased payload or increased speed depending on the operation requirements of the vessel. In addition, the reduction in weight can be designed to reduce the vertical centre of gravity and hence increase the stability of the vessel. This has been the subject of a number of studies involving military vessels [1]. Pultrusion is a method of continuous composite manufacture whereby fibre reinforcement rovings and fabrics, wetted by resin, either by being pulled through a resin bath, or through injection of resin into a closed die, are pulled through forming dies and finally through a heated die that exerts pressure for the consolidation of the composite profile. The resulting profiles can be cut to the desired length using an in-line saw. Due to the expected length of composite superstructures and limitations on feasible transportation lengths, joints will be required. Pultrusions are commonly found in the civil engineering industry as a replacement to traditional steel sections. There are a number of studies on the use of bolted connections in pultrusions, however as with all continuously reinforced composites, drilled holes result in fibre disconti* Corresponding author. E-mail address: [email protected] (S.W. Boyd). 1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2008.03.017
nuity and stress concentrations. Adhesive bonding provides an alternative to this which offers significant advantages, including reduced weight and parts count, as well as maintaining fibre continuity. In addition, adhesive bonding facilitates load transfer between components through a larger area reducing stress concentrations. However, it is known that adhesively bonded lap joints result in peel stresses in the vicinity of the joint due to either external bending of the joint (single lap joints) or internal bending moments (double lap joints). This imparts peel stresses in the adhesive connection in the through thickness direction of the laminate. Although peel stresses are an issue for all laminated composite materials where the fibres tend to lie in the plane of each lamina, resulting in reduced interlaminar strength compared to in-plane strength, they are exacerbated in pultrusions due to material non-homogeneity. Fig. 1 is a micrograph of a pultruded section that shows the extent of this non-homogeneity; the unidirectional fibre bundles and the surface fibre mats are encapsulated by extensive resin rich areas. Boyd et al. [2] conducted an experimental evaluation of adhesively bonded pultruded joints involving a number of pultrusions and adhesive types and found that the joint efficiency was not related to the adhesive but the interlaminar strength of the pultrusion, similar findings were observed by Keller and Vallée [3]. In an effort to avoid imparting a through thickness stress in the pultruded laminate, the feasibility of using finger joints was addressed by Boyd et al. [2]. In further work [4] the applicability of thermoelastic stress analysis (TSA) in studies of finger joints in composite structure was assessed. TSA is a well-established technique that has been used in a wide range of engineering applications, e.g. [5]. TSA uses a highly
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Fig. 1. Micrograph of pultruded section.
sensitive infra-red detector to measure the temperature changes induced in a material as a result of the thermoelastic effect. The temperature change (DT) is directly related to the stress change. The working equation for orthotropic materials, such as that obtained from pultrusion, is
DT ¼
T
qC p
ða11 r11 þ a22 r22 Þ
ð1Þ
where T is the absolute temperature of the specimen surface, q is the density, Cp is the specific heat at constant pressure, a11 and a22 are the coefficients of thermal expansion in the principal material directions and r11 and r22 are the direct stresses in the principal material directions. TSA has been used extensively for the analysis of composite materials and structures examples of early work are that of Rowlands and his co-workers, e.g. [6,7] and Bakis and Reifsnider [8]. Recently, [9] a general means of calibrating the thermoelastic signal from a laminated composite has been devised; this work also provides a review of the theory associated with the application of TSA to orthotropic composites. Previously, TSA has been carried out on pultruded composite laminates, e.g. [10]. However, in [10] the focus of the investigation was to assess the in-plane stress field, where the resin rich layer acts as a ‘strain witness’, which means that in this case the thermoelastic response results from the isotropic surface resin rather than the orthotropic composite. In the present paper the through thickness plane is studied where the resin rich layer is absent. To quantitatively apply TSA in this situation, where the response is that of an orthotropic material, knowledge of the material properties of the constituent layers of the pultrusion is required. As the relevant properties vary between even nominally identical laminates the approach is to group the material properties, so that a ‘calibration constant’ can be derived experimentally at the test temperature. In Ref. [4] the TSA successfully identified not only the position and magnitude of the stress concentration with changing finger
tip angle, but also manufacturing defects and the development of fatigue damage. The TSA also provided a validation for a simple finite element (FE) model of the finger joint. However, it was recognised that to apply the technique generally to pultruded structures much more detailed thermoelastic and mechanical analysis of the constituent layers would be necessary. This premise is supported by the work of Keller and Vallée [3,11] who investigated the prediction of the strength of pultruded composite lap joints using 2D finite element analysis (FEA) [3], and devised a failure load prediction model [11]. Some of the pultrusion material properties were provided by the manufacturer, but the through thickness elastic modulus was determined experimentally [11] using readings from a strain gauge bonded in the through thickness direction. In [3] the FEA showed that the strength of the adherend–adhesive interface is greater than the interlaminar strength of the adherend, and indicated that failure would occur in the pultrusion. This is confirmed by the experimental results obtained by both Boyd et al. [2] and Keller and Vallée [3]. The failure model [11] located the point of failure but under-predicted the actual failure by about 60%, so correction factors were introduced to account for the localised peak stresses in the joints that brought the experimental and predicted failure loads into good agreement. However, the use of global elastic moduli [3,11] to represent the whole of the pultrusion neglects its inhomogeneous nature through the cross-section as observed in the micrograph shown in Fig. 1. The motivation for the present work is therefore to obtain the stress distribution in the joints experimentally using TSA. The approach accounts for the different constituent layers in the pultrusion, allows the determination of the resulting non-uniform stress field in the through thickness direction, and provides further insight concerning the failure of pultruded joints. It would be inefficient to use TSA to examine each joint design. Therefore, the ultimate goal of this work is to develop a FE model that is capable of predicting the stresses in each layer through the thickness of the inhomogeneous pultruded material and applying this procedure to double lap joints (Fig. 2) in pultruded material. The work described in this paper addresses the following points to achieve this goal: 1. Experimental evaluation of the material properties of each of the constituent layers in the pultruded material as an input to the FE model. 2. Development of a manufacturing process that models the pultrusion process so that test specimens can be manufactured from each of the pultrusion constituent layers. 3. Thermoelastic calibration of the pultrusion constituent layers. 4. TSA of the bonded joint specimens. 5. Production of an FE model of the bonded joint that adequately models the layered construction of the pultrusion and includes the adhesive layer and spew fillet (see Fig. 2). 6. Validation of the FE model using the calibrated TSA and assessment of the effects of the inhomogeniety in by comparing the FE with the TSA.
Fig. 2. Schematic of a double butt strap joint.
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2. Characterisation of the pultrusion
Table 2 Volume fractions of the pseudo-pultruded laminates
2.1. Global material properties
Process parameters
Fibre fraction
Resin fraction
Void fraction
1 bar vacuum, 90 °C 3 bar pressure, 90 °C 3 bar pressure, 115 °C
0.18 0.25 0.39
0.71 0.72 0.56
0.11 0.03 0.05
The pultruded composite material used for this study was a 140 10 mm strip profile of polyester resin and E-glass reinforcement. The profile was supplied by Fiberline Composites A/S in Denmark. The polyester resin is isophthalic and contains an inorganic fire retardant. Within the pultruded profile a number of E-glass reinforcement types were used: unidirectional rovings that make up the majority of the reinforcement content and a complex mat containing a layer of woven roving stitched to a layer of chopped strand mat, similar to the needle mat used in Ref. [2]. Three tensile test specimens with dimensions of 250 25 10 mm were cut from the pultruded strip profile using a table mounted water cooled diamond impregnated circular saw. These specimens were subjected to a tensile load using a 50 kN electromechanical Instron test machine and a 50 mm gauge length extensometer. The average Young’s modulus was determined as 29.4 GPa with a coefficient of variation of 3.8%. This is 27.8% greater than the value provided by the supplier. The fibre volume fraction of the pultrusion was determined using a burn off test and was found to be 46%. This is 15% higher than that quoted by the manufacturer and goes some way to explaining the larger Young’s modulus. The aim of the material characterisation is to determine the material properties of each of the constituent layers in the pultrusion. Therefore, it is important obtain a measure of the quantity of each of the constituent layers in the pultruded product. Fig. 1 shows a micrograph of the pultruded material and clearly shows the various materials present; i.e. the outer ‘‘combination” mats, the resin rich areas and the central unidirectional core. Although from a different manufacturer this is essentially a similar lay-up as that observed by Boyd et al. [2]. Of particular importance here is the resin rich pockets trapped between the unidirectional core and the fabric layers of ‘‘combination” mat that lead to the reduced interlaminar strength [2,3,11]. In Fig. 1 there are essentially three ‘layers’ in the pultruded material: the central unidirectional rovings and the outer ‘‘combination” mat. Although these layers are not uniform throughout the pultrusion, to simplify matters the average thickness of each layer was determined from micrographs measurements. The average dimensions of the layers contained in the nominally 10 mm thick profile are provided in Table 1; there is a 7% variation in the measurements which is insignificant in the context of this work. 2.2. Constituent layer mechanical properties To accurately model the entire pultrusion, elastic properties of each constituent layer within the pultrusion must be obtained. It was not practical to obtain pultrusions of each of the constituent layers due to the prohibitive costs associated with the manufacture of the dies for such small production runs. Therefore, to obtain specimens representative of each of the pultrusion constituent layers it was decided to simulate the pultrusion process using the application of heat and pressure in an autoclave to produce a vacuum consolidated laminate. Samples of the individual reinforce-
Table 1 Thicknesses of layers in pultrusion Measurement
Value (mm)
CoV (%)
Upper outer layer Lower outer layer Core
2.22 2.48 5.12
7.2 6.6 7.0
ments as well as samples of the pultrusion resin were provided by Fiberline Composites A/S. Three processes were investigated using the combination mat in an attempt to determine the correct combination of temperature and pressure to obtain the properties of the pultruded product. The fibre volume fraction was chosen as the metric to determine if the pseudo-pultruded product was representative of the actual pultruded product. The first process involved basic vacuum consolidation of the laminate at 90 °C for 150 min. This resulted in a laminate thickness of 2.88 mm. The fibre, resin and void content are given in Table 2. The void content was obtained from a burn off test that provided the weight of fibre and resin in the laminate. With knowledge of the densities of the resin and fibre the volume of each was determined. The difference between the measured volume of the laminate and the sum of the determined resin and fibre volumes provides an approximation of void volume fraction. It can be seen in Table 2 that the void content was found to be quite high at 11%. The second process used the same lay-up of reinforcement. However, the laminate was cured under a pressure of 3 bar at 90 °C and gave a laminate thickness of 1.85 mm. The results in Table 2 show that the resin content was similar. However, there was an increase in fibre volume fraction and a corresponding drop in void volume fraction. In the process for the final panel the curing temperature was increased to 115 °C and further increased the fibre volume fraction through the use of less resin. It was concluded that the final panel was the closest representation of the pultruded product as it had a similar fibre volume fraction and therefore the process to produce pseudo-pultruded materials was established. The volume of fibres used in each of the processes is the same, therefore this study has shown that it is the resin that controls the quality of the final product. The increased temperature and elevated curing pressure ensure good wetting of the reinforcement through reduced resin viscosity at elevated temperature. This minimises the possibility of entrapped air (reduced void content in the final laminate) and increases the ability of the pressure to consolidate the laminate resulting in increased fibre volume fraction. Panels of the unidirectional material, ‘‘combination” mat and the resin were manufactured using the defined process so that specimens from each could be used to determine Young’s modulus. The unidirectional laminate was manufactured using a jig to align the E-glass rovings which were then consolidated in the autoclave as described above. The density of the material was determined experimentally, and burn off tests were conducted to determine the fibre volume fraction. The fibre, resin and void volume fractions were found to be 55%, 38% and 7%, respectively. The high fibre volume fraction of the unidirectional material was expected as the fibres can be packed densely into the laminate. Tensile specimens were cut from the panel and tested in an electro-mechanical Instron test machine using a 50 kN load cell and a 50 mm gauge length extensometer. The results are presented in Table 3 and show a relatively high unidirectional laminate material stiffness. The final panel used to formalise the pseudo-pultrusion manufacturing technique was used to determine the Young’s modulus of the combination mat layer and the results can be seen in Table 3. In addition Table 3 shows the results from bulk mouldings of the resin that were cast using the same process parameters.
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Table 3 Properties of the individual layers in the pultrusion Layer
Young’s modulus (CoV)
Fibre vol fraction (CoV)
K1 (MPa1)
Unidirectional Combination Resin
35.0 GPa (4.1%) 13.2 GPa (5.2%) 2486 MPa (12%)
0.55 (1.4%) 0.39 (3.1%) –
3.81 106 9.58 106 –
2.3. Constituent layer thermoelastic characterisation In TSA the temperature change, DT, is related to the stress changes (see Eq. (1)). In the present research a Cedip Silver infrared thermography system is used. This system is radiometrically calibrated and allows the direct determination of DT. In linear elastic isotropic, homogeneous materials, such as the resin, the working relationship is [12]:
Dðr1 þ r2 Þ ¼ ADT
ð2Þ
where D(r1 + r2) is the sum of the principal surface stress change and A is a calibration constant. The calibration constant, A, can be found experimentally [13] as
A¼
1 KT
ð3Þ
where T is the absolute temperature of the specimen surface and K is the thermoelastic constant:
K¼
a qC p
ð4Þ 2.4. Validation of thermoelastic calibration approach
It should be noted that A is different to that defined in the previous work on TSA, e.g. [5] and [9] and here is only a function of the thermoelastic constant and the absolute temperature of the specimen surface. Substituting two orthotropic thermoelastic constants, K1 = a11/ qCp and K2 = a22/qCp, into Eq. (1) results in the following expression for orthotropic materials:
DT ¼ ðK 1 T Dr11 þ K 2 T Dr22 Þ
ð5Þ
Rearranging Eq. (5) provides an expression in terms of stress rather than temperature change as follows:
DT K2 ¼ Dr11 þ Dr22 K1T K1
ð6Þ
The thermoelastic constant K1 of each of the constituent layers can be determined experimentally from a uniaxial tensile test. In a tensile test the second term on the right hand side of Eq. (6) is eliminated as Dr22 = 0, so that the calibration constant, A* = DT/ Dr11 = K1T, for each material can be obtained. This is then used to calibrate DT in to stress terms as follows:
DT K2 ¼ Dr11 þ Dr22 A K1
valid, as the transverse fibres would not provide any traction that results in a finite transverse stress. DT was obtained from the unidirectional specimen at 7 cyclic stress ranges (Dr11) from 25 to 102 MPa and from the combination mat specimen at 8 cyclic stress ranges (Dr11) from 9 to 41 MPa. In both cases DT was plotted against stress and a linear relationship was established from which the calibration constants for both the unidirectional and combination layers in the longitudinal direction were obtained as 874 MPa K1 and 348 MPa K1 respectively. The thermoelastic constant values K1 are given in Table 3. Experimentally obtaining the transverse calibration constants has been set aside, as the type of specimen necessary to obtain these would be difficult to manufacture and therefore it was decided to use approximations of K2 in the FEA to assess the influence of this quantity. During the calibration exercises described above a detailed study was carried out to establish if the response was adiabatic [8]. The specimens were loaded over a frequency range of 2– 25 Hz. This showed that at frequencies of above 10 Hz the response was uniform indicating adiabatic behaviour, hence the loading frequency used in the tests to obtain the calibration constants reported above and in the TSA reported in the following sections of the paper was in all cases 20 Hz. For the acquisition of the TSA data the collection times were around 15 s. This provided sufficient data for averaging as the sampling frequency was 83 Hz. During acquisition no heating of the specimen was observed, and hence it was not necessary to correct the changes in surface temperature.
ð7Þ
This means the TSA data is calibrated to give a stress metric and provides data in the form of full field ‘stress’ map. It is unnecessary to obtain K2 to calibrate the thermoelastic data. However, it is necessary to obtain K2 to make comparisons or validate finite element data, i.e. the FE must be presented in the form of the right hand side of Eqs. (6) and (7). To obtain K1 for the unidirectional and combination layers, specimens were prepared using the pseudo-pultrusion method discussed in Section 2.1. Knowing the cross sectional area of the specimens and applying a known tensile (uniaxial) load, the stress in the specimen can be determined. The major assumption here is that Dr22 is eliminated from Eq. (6) by the uniaxial loading (see above). In the unidirectional specimen this is valid. In the through thickness plane of the combination mat this was also considered
A tensile specimen of the pultruded material with dimensions of 250 25 9.8 mm was loaded with load amplitudes of 4 kN and 8 kN with a mean load of 8 kN. The 16 kN load range was approximately 25% of the failure load of the specimen. Thermoelastic data was obtained from the through thickness edge of the specimen. The Cedip system is capable of automatically applying a single calibration constant to the thermoelastic signal to obtain a full field stress map. As the pultruded materials contains two materials and hence two calibration constants, i.e. for the unidirectional and combination reinforcement layers, the automatic Cedip calibration could not be applied. Therefore, the data was output to a data file that was subsequently read by a Matlab subroutine. This code distinguished between the two layers of the pultrusion and applied the appropriate calibration constant by using the known thicknesses of each layer given in Table 1. The result is that a stress map of the pultrusion through thickness can be generated. Fig. 3a shows the uncalibrated data and Fig. 3b shows the calibrated stress map of the pultrusion through thickness subjected to a load cycle of 8 ± 8 kN. Fig. 3a shows that the uncalibrated data provides a practically uniform response, whereas Fig. 3b shows that, as expected, the core unidirectional material carries the majority of the stress induced by the loading. This result demonstrates the crucial importance of obtaining quantitative data when using TSA to examine this type of composite structure. Simple qualitative comparisons based on only the thermoelastic response would result in a gross misinterpretation of the stress field. To validate the result an average plot across the specimen shows that the applied load range obtained from the thermoelastic stress data is approximately 15.57 kN, i.e. very close to the applied load. This provides good confidence that the thermoelastic constants obtained experimentally from the pseudo-pultruded materials manufactured in the laboratory closely represent the layers in the actual pultrusion. This also validates the assumption that in the through thickness plane Dr22 is zero for a tensile loading.
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Fig. 3. Thermoelastic signal (a) and calibrated stress (b) plot of loaded pultrusion through-thickness.
3. Thermoelastic stress analysis of double butt strap joints Specimen coupons were cut from the 10 mm thick pultruded plank using a table mounted water cooled diamond impregnated circular saw. Two adherend coupons with nominal dimensions of 150 50 10 mm and two strap coupons with dimensions of 100 50 10 mm made up each double butt strap joint as shown schematically in Fig. 2. The components of the joints were bonded using a two-part epoxy adhesive Araldite 2015. A light abrasion surface preparation was conducted followed by a solvent wipe prior to bonding. The joints were allowed to cure at room temperature for 24 h and were post cured at 50 °C for a further 24 h. The butt strap joints were loaded quasi-statically in tension to determine the average ultimate failure load of the joint. It was calculated that the average stress in the adherend was 93.3 MPa when the joint failed, which is equivalent to 20% of the ultimate strength
of the pultruded material. The failure mode was due to interlaminar failure of the adherend between the two combination mats and is shown in Fig. 4. For the thermoelastic stress analysis, K1 for the pultruded layers in the longitudinal direction was obtained experimentally as described above. For the adhesive the thermoelastic constant was obtained from Eq. (4) using values from Ref. [14], providing a thermoelastic constant (K) for the adhesive of 2.88 105 MPa1. Using Eq. (3) and the known test temperature (300 K), the calibration constant for the adhesive of 115.7 MPa K1 was obtained. The double lap joint was subjected to a mean load of 8 kN with a cyclic load amplitude of 5 kN. Firstly, the whole strap area was examined; Fig. 5a shows the thermoelastic signal data and Fig. 5b shows the calibrated stress data. Fig. 6a shows the thermoelastic signal from the upper half of the strap joint. This increases the resolution of the TSA data and allows detailed data to be
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Fig. 4. Failure of the specimen within the pultrusion.
obtained from the spew fillet and end of the strap. Fig. 6b provides the calibrated stress data and shows that the stress sum in the adhesive is close to zero, this is as expected as the adhesive will be predominantly in shear. However, there is a stress concentration present within the strap on the left-hand side of the joint at the location equivalent to the interface between the combination mat and the unidirectional layers. In addition, there is a stress concentration at the spew fillet. In the main adherend there appears to be an increase in stress in the region of the strap ends. Again this is concentrated at the interface between the unidirectional and combination layers. Fig. 6b indicates that the differences in the mechanical properties of the materials contained in the pultruded joint may be caused by stress concentrations within the pultruded material, which ultimately could lead to the interlaminar failure of the joint. It has been shown that the layers of material in the pultrusion have different mechanical properties, and therefore the thermoelastic constants and the stress field within adhesively bonded pultruded joint are dictated by the layered nature of the pultrusion. Thus, it would be inefficient to examine every joint or pultrusion using experimental techniques such as thermoelastic stress analysis. Therefore, the following sections of the paper concentrate on the production and validation of an FE modelling approach for the design of adhesive joints in pultruded material. 4. FE model The joint was modelled using the ANSYS FEA package using 2D, 8-noded quadrilateral elements (PLANE82). In order to reduce the error in the loading of the model, the whole joint was modelled and the load applied away from the bonded region. Initially a coarse model was produced. It was assumed that a pressure load applied to the ends of the model reproduced the stress field induced by the test machine grips in the experimental work. The boundary conditions for the coarse model were therefore such that the upper adherend was fully constrained, and the pressure load was applied to the lower adherend to generate a tensile stress. The adherends and adhesives were assumed to be perfectly connected as the previous work [2,3,10] showed that the failure of the joints occurs within the adherend material. Some of the mechanical properties of each layer of the pultrusion were calculated from the experimental tests conducted in Sec-
tion 2. The remainder were obtained either from literature or through calculation. The adopted material properties are detailed in Table 4. The joint was divided into areas of specific materials, i.e. the unidirectional core, the combination outer layers and the adhesive. The latter is defined as an isotropic material with material properties obtained form the manufacturer. The pultrusion layers were defined with anisotropic material properties. All materials were assumed linear elastic as the load applied during the testing produced less than 40% of the ultimate strength of the pultrusion. Sub modelling was employed so that a much finer mesh was constructed allowing a detailed examination of features. This allowed the introduction of the spew fillets, which were modelled as triangular sections with the triangular side being twice as long as the thickness of the adhesive as was used as the equivalent spew fillet by Frostig et al. [15]. The upper portion of the double butt strap, equivalent to that examined experimentally as shown in Fig. 6, was modelled by the sub model. The displacement boundary conditions for the sub model were interpolated from the coarse model at the appropriate locations and these were imparted on the sub model boundaries. The boundary stresses for both the coarse and sub models were compared to ensure continuity between the two models. The mesh used for the sub model is shown in Fig. 7a. The mesh density is such that the adhesive layer and the inner combination mat appear as the solid black areas in the figure. In fact the adhesive layer is half the width of the spew fillet. To directly compare the FEA results to the calibrated TSA results it is necessary to obtain the quantity K2 as an input for the FEA (see Eq. (7)). It was decided to use values for the resin (a, q and Cp) obtained from the manufacturer, giving a value of 4.8 105 MPa1, as an upper bound in the FEA. As a lower bound, isotropic behaviour was assumed by defining K2 = K1 for each material layer in the FEA. Fig. 7b shows the FEA results for the lower bound data.
5. Validation and discussion Line data was obtained from the TSA across the adhesive joint at two locations (see Fig. 6a); at the end of the butt strap overlap and 20 mm from the end of the butt strap overlap. The principal stresses were obtained from the FEA analysis in the same locations, manipulated according to Eq. (6) and the results are presented in Fig. 8 for the upper and lower bounds of K2. Fig. 8a shows the results at the end of the strap overlap and the excellent correlation between the numerical and experimentally derived results, particularly the transitions between different layers of the pultrusion. In Fig. 8a the upper and lower bound numerical results straddle the experimental results suggesting that the K2 parameter is not equal to K1, nor is it equal to the value obtained for pure resin, but somewhere in between. This implies that there is some interaction between the resin and fibres in the through thickness direction. This is particularly relevant in the combination mat of the central adherend where the FEA is greatly over predicting the stress. A lower value of K2 in this area (due to some through thickness matrix fibre interaction) will reduce the numerical model prediction. The same is true of the unidirectional core with the lower bound K2 corresponding well in some areas, which are probably resin dominated and the upper bound over predicting as K2 for the material is likely to be less than that for the resin. Clearly, a means for experimentally evaluating K2 is required to improve the accuracy of the FE results. Therefore, the correlation between the numerical and experimental results in Fig. 8a could only be defined as moderate. However, an inspection of Fig. 8b shows a much better correspondence. Here, only the lower bound FE results are shown as Dr22 in this region will be close to zero and shows a much better correspondence in all areas of the joint, apart from a small discrepancy in the correspondence in the data from the
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Fig. 5. Thermoelastic signal (a) and calibrated stress (b) plot of double strap joint.
adhesive layer. This is because the material properties from the adhesive were taken from the literature; a better correlation would be expected if the K value for the adhesive could be obtained experimentally. Overall, the correlation between the numerical and experimental results is good. However, in some areas of Fig. 8a and b the experimental are very noisy and differ greatly from the relatively smooth numerical results. This can be attributed to the inhomogeneous nature of the pultruded material. The micrograph provided in Fig. 1 shows that there are areas in the unidirectional core that contain a large amount of resin. These areas have not been included in the numerical model, because of the random nature of the resin entrapment. Likewise the
experimental TSA signals from the resin rich areas, again due to their random locations, were not calibrated using the calibration constant for the resin material. This will result in an incorrect calculation of the stress in these localised regions, and hence the variable nature of the experimental curve presented in Fig. 8a and b. However, in general the numerical and experimental results correlate well in the interface areas of the joint, e.g. in the transition from the combination layers to the epoxy adhesive. Another consideration is the difference in the spatial resolution of the TSA and the FEA. Each pixel in the TSA was 0.273 mm. Although the mesh density varied in the FEA model, the FEA data shown in Fig. 8 was derived by interpolation, so that the distance
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Fig. 6. Thermoelastic signal (a) and calibrated stress (b) plot of upper portion of double strap joint.
Table 4 Material properties of pultrusion used for numerical modelling Material
Ex (MPa)
Ey (MPa)
mxy
Gxy (MPa)
Unidirectional Combination Adhesive
35575a 15542a 2000c
3500b 3500b 2000c
0.28d 0.28d 0.36c
1367e 1367e 735e
a b c d e
Property Property Property Property Property
obtained from experiments in Section 2. obtained from Ref. [11]. obtained from manufacturers data sheet. obtained from Ref. [16] for 55% fibre volume fraction glass/epoxy. from calculation.
between the data points was 0.15 mm. This difference in the spatial resolution is important in areas where the stress gradient is
large as exhibited at the centre of the combination mat in the butt straps. Elsewhere, the difference in spatial resolution has little effect on the correspondence of the FEA and TSA data and is insignificant in comparison to the effect of localised changes in the materials. The overall correspondence between the FE and the TSA provides confidence in the numerical modelling technique as it has been validated using experimentally derived data. In addition, it further confirms the validity of the material property data obtained from the pseudo-pultruded material to represent the actual pultruded lay-up. Moreover, even better correlation between the experimental and numerical results is obtained away from the end of the overlap (Fig. 8b). In addition, the non-ideal geometry of the test specimens resulted in stress
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Fig. 7. Sub model of double lap joint; mesh (a) and sum of the principal stress solution (b).
concentrations that were not observed in the idealised numerical model.
6. Conclusions In this research a number of key conclusions can be drawn: A pseudo-pultruded material was created using a combination of vacuum consolidation, elevated temperature and increased pressure in an autoclave to create test material for the calibration of the thermoelastic data and as input to the finite element model. The resulting material was found to be a good representation of pultruded material.
The thermoelastic signal was correctly calibrated using the experimentally derived calibration constants for each of the constituent layers in the pultrusion. This allowed the examination of experimental data for stress concentrations in the through thickness direction during loading of double lap joints in pultrusions. A FE model was created using the material properties obtained from the pseudo-pultrusion and compared to the experimental data from the TSA. The correlation was very good in particular the transition between layers in the pultruded material and the magnitude of the stresses found. This gives good confidence in the modelling approach and allows for further examination of the bonded joint numerically to further understand the failure mechanisms and examine possible ways of improving the performance of adhesively bonded joints in pultruded material.
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Fig. 8. Comparison of numerical and experimental plots of stress from lines 1 (a) and 2 (b) shown in Fig. 6a.
Further work is required to experimentally obtain the K2 value for the pultruded material constituent layers, in particular in the combination mat, in order to improve the numerical modelling prediction. Acknowledgement The authors are grateful to Fiberline Composites A/S (Middelfart, Denmark) for the supply of pultruded materials and the dry reinforcements and liquid resins for the pseudo-pultruded manufacture.
References [1] Boyd SW, Blake JIR, Shenoi RA, Kapadia A. Integrity of hybrid steel-tocomposite joints for marine application. J Eng Maritime Environ, Proc Inst Mech Eng: Part M 2004;218(M4):235–45. [2] Boyd SW, Winkle IE, Day AH. Bonded butt joints in pultruded GRP panels – an experimental study. Int J Adhes Adhes 2004;24(3):263–75. [3] Keller T, Vallee T. Adhesively bonded lap joints from pultruded GFRP profiles. Part I: stress–strain analysis and failure modes. Compos Part B 2005;B36:331–40. [4] Boyd SW, Dulieu-Barton JM, Rumsey L. Stress analysis of finger joints in pultruded GRP materials. Int J Adhes Adhes 2005;26(7):498–510. [5] Dulieu-Barton JM, Stanley P. Development and applications of thermoelastic stress analysis. J Strain Anal 1998;33:93–104.
S.W. Boyd et al. / Composites: Part A 39 (2008) 1311–1321 [6] Feng Z, Zhang D, Rowlands RE, Sandor BI. Thermoelastic determination of individual stress components in loaded composites. Exp Mech 1992:89–95. [7] Lin ST, Rowlands RE. Thermoelastic stress analysis of orthotropic composites. Exp Mech 1995:257–65. [8] Bakis CE, Reifsnider KL. The adiabatic thermoelastic effect in laminated fibre composites. J Compos Mater 1991;25:809–30. [9] Emery TR, Dulieu-Barton JM, Earl JS, Cunningham PR. A generalised approach to the calibration of orthotropic materials for thermoelastic stress analysis. Compos Sci Technol 2008;68(3–4):743–52. [10] El-Hajjar R, Haj-Ali R. A quantitative thermoelastic stress analysis method for pultruded composites. Compos Sci Technol 2003;63(7):967–78. [11] Keller T, Vallee T. Adhesively bonded lap joints from pultruded GFRP profiles. Part II: joint strength prediction. Compos Part B 2005;B36:341–50.
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[12] Stanley P, Chan WK. Quantitative stress analysis by means of the thermoelastic effect. J Strain Anal 1985;20:129–38. [13] Dulieu-Smith JM. Alternative calibration techniques for quantitative thermoelastic stress analysis. Strain 1995;31:9–16. [14] Dulieu-Smith JM, Stanley P. On the interpretation and significance of the Gruneisen parameter in thermoelastic stress analysis. J Mater Process Technol 1998;78(1–3):75–83. [15] Frostig Y, Thomsen OT, Mortensen F. Analysis of adhesive-bonded joints, square-end, and spew-fillet-high-order theory approach. J Eng Mech 1999;125(11):1298–307. [16] Daniel I, Ishai O. Engineering mechanics of composite materials. Oxford University Press; 1994.
Contents lists available at ScienceDirect
Composites: Part A journal homepage: www.elsevier.com/locate/compositesa
Development of a finite element model for analysis of pultruded structures using thermoelastic data S.W. Boyd a,*, J.M. Dulieu-Barton a, O.T. Thomsen b, A. Gherardi a a b
Fluid Structure Interactions Research Group, School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK Department of Mechanical Engineering, Aalborg University, Denmark
a r t i c l e
i n f o
Article history: Received 27 April 2007 Received in revised form 22 January 2008 Accepted 29 March 2008
Keywords: A. Adhesion C. Finite element analysis E. Pultrusion Thermoelastic stress analysis (TSA)
a b s t r a c t Thermoelastic stress analysis (TSA) is used to determine the stress field in the through thickness direction of an orthotropic pultruded material. An economical means of experimentally obtaining the thermoelastic constant and some mechanical properties of each of the constituent layers in the pultruded structure is devised. The stresses in a bonded joint are obtained using thermoelastic stress analysis. The calibrated thermoelastic data is used to validate a finite element model of the joint. It is shown that to accurately interpret thermoelastic data from layered structure, such as that of the pultrusion, calibration is an essential step. It is also demonstrated that the thermoelastic approach provides an excellent means of validation of finite element models. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction There is an increased interest in the use of composite materials as non-primary structure in commercial and military vessels. Such applications include superstructure in commercial vessels and hangars and communication masts in military vessels. One of the important design aspects associated with the use of composite materials is reduced weight. This can be exploited either by increased payload or increased speed depending on the operation requirements of the vessel. In addition, the reduction in weight can be designed to reduce the vertical centre of gravity and hence increase the stability of the vessel. This has been the subject of a number of studies involving military vessels [1]. Pultrusion is a method of continuous composite manufacture whereby fibre reinforcement rovings and fabrics, wetted by resin, either by being pulled through a resin bath, or through injection of resin into a closed die, are pulled through forming dies and finally through a heated die that exerts pressure for the consolidation of the composite profile. The resulting profiles can be cut to the desired length using an in-line saw. Due to the expected length of composite superstructures and limitations on feasible transportation lengths, joints will be required. Pultrusions are commonly found in the civil engineering industry as a replacement to traditional steel sections. There are a number of studies on the use of bolted connections in pultrusions, however as with all continuously reinforced composites, drilled holes result in fibre disconti* Corresponding author. E-mail address: [email protected] (S.W. Boyd). 1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2008.03.017
nuity and stress concentrations. Adhesive bonding provides an alternative to this which offers significant advantages, including reduced weight and parts count, as well as maintaining fibre continuity. In addition, adhesive bonding facilitates load transfer between components through a larger area reducing stress concentrations. However, it is known that adhesively bonded lap joints result in peel stresses in the vicinity of the joint due to either external bending of the joint (single lap joints) or internal bending moments (double lap joints). This imparts peel stresses in the adhesive connection in the through thickness direction of the laminate. Although peel stresses are an issue for all laminated composite materials where the fibres tend to lie in the plane of each lamina, resulting in reduced interlaminar strength compared to in-plane strength, they are exacerbated in pultrusions due to material non-homogeneity. Fig. 1 is a micrograph of a pultruded section that shows the extent of this non-homogeneity; the unidirectional fibre bundles and the surface fibre mats are encapsulated by extensive resin rich areas. Boyd et al. [2] conducted an experimental evaluation of adhesively bonded pultruded joints involving a number of pultrusions and adhesive types and found that the joint efficiency was not related to the adhesive but the interlaminar strength of the pultrusion, similar findings were observed by Keller and Vallée [3]. In an effort to avoid imparting a through thickness stress in the pultruded laminate, the feasibility of using finger joints was addressed by Boyd et al. [2]. In further work [4] the applicability of thermoelastic stress analysis (TSA) in studies of finger joints in composite structure was assessed. TSA is a well-established technique that has been used in a wide range of engineering applications, e.g. [5]. TSA uses a highly
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Fig. 1. Micrograph of pultruded section.
sensitive infra-red detector to measure the temperature changes induced in a material as a result of the thermoelastic effect. The temperature change (DT) is directly related to the stress change. The working equation for orthotropic materials, such as that obtained from pultrusion, is
DT ¼
T
qC p
ða11 r11 þ a22 r22 Þ
ð1Þ
where T is the absolute temperature of the specimen surface, q is the density, Cp is the specific heat at constant pressure, a11 and a22 are the coefficients of thermal expansion in the principal material directions and r11 and r22 are the direct stresses in the principal material directions. TSA has been used extensively for the analysis of composite materials and structures examples of early work are that of Rowlands and his co-workers, e.g. [6,7] and Bakis and Reifsnider [8]. Recently, [9] a general means of calibrating the thermoelastic signal from a laminated composite has been devised; this work also provides a review of the theory associated with the application of TSA to orthotropic composites. Previously, TSA has been carried out on pultruded composite laminates, e.g. [10]. However, in [10] the focus of the investigation was to assess the in-plane stress field, where the resin rich layer acts as a ‘strain witness’, which means that in this case the thermoelastic response results from the isotropic surface resin rather than the orthotropic composite. In the present paper the through thickness plane is studied where the resin rich layer is absent. To quantitatively apply TSA in this situation, where the response is that of an orthotropic material, knowledge of the material properties of the constituent layers of the pultrusion is required. As the relevant properties vary between even nominally identical laminates the approach is to group the material properties, so that a ‘calibration constant’ can be derived experimentally at the test temperature. In Ref. [4] the TSA successfully identified not only the position and magnitude of the stress concentration with changing finger
tip angle, but also manufacturing defects and the development of fatigue damage. The TSA also provided a validation for a simple finite element (FE) model of the finger joint. However, it was recognised that to apply the technique generally to pultruded structures much more detailed thermoelastic and mechanical analysis of the constituent layers would be necessary. This premise is supported by the work of Keller and Vallée [3,11] who investigated the prediction of the strength of pultruded composite lap joints using 2D finite element analysis (FEA) [3], and devised a failure load prediction model [11]. Some of the pultrusion material properties were provided by the manufacturer, but the through thickness elastic modulus was determined experimentally [11] using readings from a strain gauge bonded in the through thickness direction. In [3] the FEA showed that the strength of the adherend–adhesive interface is greater than the interlaminar strength of the adherend, and indicated that failure would occur in the pultrusion. This is confirmed by the experimental results obtained by both Boyd et al. [2] and Keller and Vallée [3]. The failure model [11] located the point of failure but under-predicted the actual failure by about 60%, so correction factors were introduced to account for the localised peak stresses in the joints that brought the experimental and predicted failure loads into good agreement. However, the use of global elastic moduli [3,11] to represent the whole of the pultrusion neglects its inhomogeneous nature through the cross-section as observed in the micrograph shown in Fig. 1. The motivation for the present work is therefore to obtain the stress distribution in the joints experimentally using TSA. The approach accounts for the different constituent layers in the pultrusion, allows the determination of the resulting non-uniform stress field in the through thickness direction, and provides further insight concerning the failure of pultruded joints. It would be inefficient to use TSA to examine each joint design. Therefore, the ultimate goal of this work is to develop a FE model that is capable of predicting the stresses in each layer through the thickness of the inhomogeneous pultruded material and applying this procedure to double lap joints (Fig. 2) in pultruded material. The work described in this paper addresses the following points to achieve this goal: 1. Experimental evaluation of the material properties of each of the constituent layers in the pultruded material as an input to the FE model. 2. Development of a manufacturing process that models the pultrusion process so that test specimens can be manufactured from each of the pultrusion constituent layers. 3. Thermoelastic calibration of the pultrusion constituent layers. 4. TSA of the bonded joint specimens. 5. Production of an FE model of the bonded joint that adequately models the layered construction of the pultrusion and includes the adhesive layer and spew fillet (see Fig. 2). 6. Validation of the FE model using the calibrated TSA and assessment of the effects of the inhomogeniety in by comparing the FE with the TSA.
Fig. 2. Schematic of a double butt strap joint.
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2. Characterisation of the pultrusion
Table 2 Volume fractions of the pseudo-pultruded laminates
2.1. Global material properties
Process parameters
Fibre fraction
Resin fraction
Void fraction
1 bar vacuum, 90 °C 3 bar pressure, 90 °C 3 bar pressure, 115 °C
0.18 0.25 0.39
0.71 0.72 0.56
0.11 0.03 0.05
The pultruded composite material used for this study was a 140 10 mm strip profile of polyester resin and E-glass reinforcement. The profile was supplied by Fiberline Composites A/S in Denmark. The polyester resin is isophthalic and contains an inorganic fire retardant. Within the pultruded profile a number of E-glass reinforcement types were used: unidirectional rovings that make up the majority of the reinforcement content and a complex mat containing a layer of woven roving stitched to a layer of chopped strand mat, similar to the needle mat used in Ref. [2]. Three tensile test specimens with dimensions of 250 25 10 mm were cut from the pultruded strip profile using a table mounted water cooled diamond impregnated circular saw. These specimens were subjected to a tensile load using a 50 kN electromechanical Instron test machine and a 50 mm gauge length extensometer. The average Young’s modulus was determined as 29.4 GPa with a coefficient of variation of 3.8%. This is 27.8% greater than the value provided by the supplier. The fibre volume fraction of the pultrusion was determined using a burn off test and was found to be 46%. This is 15% higher than that quoted by the manufacturer and goes some way to explaining the larger Young’s modulus. The aim of the material characterisation is to determine the material properties of each of the constituent layers in the pultrusion. Therefore, it is important obtain a measure of the quantity of each of the constituent layers in the pultruded product. Fig. 1 shows a micrograph of the pultruded material and clearly shows the various materials present; i.e. the outer ‘‘combination” mats, the resin rich areas and the central unidirectional core. Although from a different manufacturer this is essentially a similar lay-up as that observed by Boyd et al. [2]. Of particular importance here is the resin rich pockets trapped between the unidirectional core and the fabric layers of ‘‘combination” mat that lead to the reduced interlaminar strength [2,3,11]. In Fig. 1 there are essentially three ‘layers’ in the pultruded material: the central unidirectional rovings and the outer ‘‘combination” mat. Although these layers are not uniform throughout the pultrusion, to simplify matters the average thickness of each layer was determined from micrographs measurements. The average dimensions of the layers contained in the nominally 10 mm thick profile are provided in Table 1; there is a 7% variation in the measurements which is insignificant in the context of this work. 2.2. Constituent layer mechanical properties To accurately model the entire pultrusion, elastic properties of each constituent layer within the pultrusion must be obtained. It was not practical to obtain pultrusions of each of the constituent layers due to the prohibitive costs associated with the manufacture of the dies for such small production runs. Therefore, to obtain specimens representative of each of the pultrusion constituent layers it was decided to simulate the pultrusion process using the application of heat and pressure in an autoclave to produce a vacuum consolidated laminate. Samples of the individual reinforce-
Table 1 Thicknesses of layers in pultrusion Measurement
Value (mm)
CoV (%)
Upper outer layer Lower outer layer Core
2.22 2.48 5.12
7.2 6.6 7.0
ments as well as samples of the pultrusion resin were provided by Fiberline Composites A/S. Three processes were investigated using the combination mat in an attempt to determine the correct combination of temperature and pressure to obtain the properties of the pultruded product. The fibre volume fraction was chosen as the metric to determine if the pseudo-pultruded product was representative of the actual pultruded product. The first process involved basic vacuum consolidation of the laminate at 90 °C for 150 min. This resulted in a laminate thickness of 2.88 mm. The fibre, resin and void content are given in Table 2. The void content was obtained from a burn off test that provided the weight of fibre and resin in the laminate. With knowledge of the densities of the resin and fibre the volume of each was determined. The difference between the measured volume of the laminate and the sum of the determined resin and fibre volumes provides an approximation of void volume fraction. It can be seen in Table 2 that the void content was found to be quite high at 11%. The second process used the same lay-up of reinforcement. However, the laminate was cured under a pressure of 3 bar at 90 °C and gave a laminate thickness of 1.85 mm. The results in Table 2 show that the resin content was similar. However, there was an increase in fibre volume fraction and a corresponding drop in void volume fraction. In the process for the final panel the curing temperature was increased to 115 °C and further increased the fibre volume fraction through the use of less resin. It was concluded that the final panel was the closest representation of the pultruded product as it had a similar fibre volume fraction and therefore the process to produce pseudo-pultruded materials was established. The volume of fibres used in each of the processes is the same, therefore this study has shown that it is the resin that controls the quality of the final product. The increased temperature and elevated curing pressure ensure good wetting of the reinforcement through reduced resin viscosity at elevated temperature. This minimises the possibility of entrapped air (reduced void content in the final laminate) and increases the ability of the pressure to consolidate the laminate resulting in increased fibre volume fraction. Panels of the unidirectional material, ‘‘combination” mat and the resin were manufactured using the defined process so that specimens from each could be used to determine Young’s modulus. The unidirectional laminate was manufactured using a jig to align the E-glass rovings which were then consolidated in the autoclave as described above. The density of the material was determined experimentally, and burn off tests were conducted to determine the fibre volume fraction. The fibre, resin and void volume fractions were found to be 55%, 38% and 7%, respectively. The high fibre volume fraction of the unidirectional material was expected as the fibres can be packed densely into the laminate. Tensile specimens were cut from the panel and tested in an electro-mechanical Instron test machine using a 50 kN load cell and a 50 mm gauge length extensometer. The results are presented in Table 3 and show a relatively high unidirectional laminate material stiffness. The final panel used to formalise the pseudo-pultrusion manufacturing technique was used to determine the Young’s modulus of the combination mat layer and the results can be seen in Table 3. In addition Table 3 shows the results from bulk mouldings of the resin that were cast using the same process parameters.
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Table 3 Properties of the individual layers in the pultrusion Layer
Young’s modulus (CoV)
Fibre vol fraction (CoV)
K1 (MPa1)
Unidirectional Combination Resin
35.0 GPa (4.1%) 13.2 GPa (5.2%) 2486 MPa (12%)
0.55 (1.4%) 0.39 (3.1%) –
3.81 106 9.58 106 –
2.3. Constituent layer thermoelastic characterisation In TSA the temperature change, DT, is related to the stress changes (see Eq. (1)). In the present research a Cedip Silver infrared thermography system is used. This system is radiometrically calibrated and allows the direct determination of DT. In linear elastic isotropic, homogeneous materials, such as the resin, the working relationship is [12]:
Dðr1 þ r2 Þ ¼ ADT
ð2Þ
where D(r1 + r2) is the sum of the principal surface stress change and A is a calibration constant. The calibration constant, A, can be found experimentally [13] as
A¼
1 KT
ð3Þ
where T is the absolute temperature of the specimen surface and K is the thermoelastic constant:
K¼
a qC p
ð4Þ 2.4. Validation of thermoelastic calibration approach
It should be noted that A is different to that defined in the previous work on TSA, e.g. [5] and [9] and here is only a function of the thermoelastic constant and the absolute temperature of the specimen surface. Substituting two orthotropic thermoelastic constants, K1 = a11/ qCp and K2 = a22/qCp, into Eq. (1) results in the following expression for orthotropic materials:
DT ¼ ðK 1 T Dr11 þ K 2 T Dr22 Þ
ð5Þ
Rearranging Eq. (5) provides an expression in terms of stress rather than temperature change as follows:
DT K2 ¼ Dr11 þ Dr22 K1T K1
ð6Þ
The thermoelastic constant K1 of each of the constituent layers can be determined experimentally from a uniaxial tensile test. In a tensile test the second term on the right hand side of Eq. (6) is eliminated as Dr22 = 0, so that the calibration constant, A* = DT/ Dr11 = K1T, for each material can be obtained. This is then used to calibrate DT in to stress terms as follows:
DT K2 ¼ Dr11 þ Dr22 A K1
valid, as the transverse fibres would not provide any traction that results in a finite transverse stress. DT was obtained from the unidirectional specimen at 7 cyclic stress ranges (Dr11) from 25 to 102 MPa and from the combination mat specimen at 8 cyclic stress ranges (Dr11) from 9 to 41 MPa. In both cases DT was plotted against stress and a linear relationship was established from which the calibration constants for both the unidirectional and combination layers in the longitudinal direction were obtained as 874 MPa K1 and 348 MPa K1 respectively. The thermoelastic constant values K1 are given in Table 3. Experimentally obtaining the transverse calibration constants has been set aside, as the type of specimen necessary to obtain these would be difficult to manufacture and therefore it was decided to use approximations of K2 in the FEA to assess the influence of this quantity. During the calibration exercises described above a detailed study was carried out to establish if the response was adiabatic [8]. The specimens were loaded over a frequency range of 2– 25 Hz. This showed that at frequencies of above 10 Hz the response was uniform indicating adiabatic behaviour, hence the loading frequency used in the tests to obtain the calibration constants reported above and in the TSA reported in the following sections of the paper was in all cases 20 Hz. For the acquisition of the TSA data the collection times were around 15 s. This provided sufficient data for averaging as the sampling frequency was 83 Hz. During acquisition no heating of the specimen was observed, and hence it was not necessary to correct the changes in surface temperature.
ð7Þ
This means the TSA data is calibrated to give a stress metric and provides data in the form of full field ‘stress’ map. It is unnecessary to obtain K2 to calibrate the thermoelastic data. However, it is necessary to obtain K2 to make comparisons or validate finite element data, i.e. the FE must be presented in the form of the right hand side of Eqs. (6) and (7). To obtain K1 for the unidirectional and combination layers, specimens were prepared using the pseudo-pultrusion method discussed in Section 2.1. Knowing the cross sectional area of the specimens and applying a known tensile (uniaxial) load, the stress in the specimen can be determined. The major assumption here is that Dr22 is eliminated from Eq. (6) by the uniaxial loading (see above). In the unidirectional specimen this is valid. In the through thickness plane of the combination mat this was also considered
A tensile specimen of the pultruded material with dimensions of 250 25 9.8 mm was loaded with load amplitudes of 4 kN and 8 kN with a mean load of 8 kN. The 16 kN load range was approximately 25% of the failure load of the specimen. Thermoelastic data was obtained from the through thickness edge of the specimen. The Cedip system is capable of automatically applying a single calibration constant to the thermoelastic signal to obtain a full field stress map. As the pultruded materials contains two materials and hence two calibration constants, i.e. for the unidirectional and combination reinforcement layers, the automatic Cedip calibration could not be applied. Therefore, the data was output to a data file that was subsequently read by a Matlab subroutine. This code distinguished between the two layers of the pultrusion and applied the appropriate calibration constant by using the known thicknesses of each layer given in Table 1. The result is that a stress map of the pultrusion through thickness can be generated. Fig. 3a shows the uncalibrated data and Fig. 3b shows the calibrated stress map of the pultrusion through thickness subjected to a load cycle of 8 ± 8 kN. Fig. 3a shows that the uncalibrated data provides a practically uniform response, whereas Fig. 3b shows that, as expected, the core unidirectional material carries the majority of the stress induced by the loading. This result demonstrates the crucial importance of obtaining quantitative data when using TSA to examine this type of composite structure. Simple qualitative comparisons based on only the thermoelastic response would result in a gross misinterpretation of the stress field. To validate the result an average plot across the specimen shows that the applied load range obtained from the thermoelastic stress data is approximately 15.57 kN, i.e. very close to the applied load. This provides good confidence that the thermoelastic constants obtained experimentally from the pseudo-pultruded materials manufactured in the laboratory closely represent the layers in the actual pultrusion. This also validates the assumption that in the through thickness plane Dr22 is zero for a tensile loading.
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Fig. 3. Thermoelastic signal (a) and calibrated stress (b) plot of loaded pultrusion through-thickness.
3. Thermoelastic stress analysis of double butt strap joints Specimen coupons were cut from the 10 mm thick pultruded plank using a table mounted water cooled diamond impregnated circular saw. Two adherend coupons with nominal dimensions of 150 50 10 mm and two strap coupons with dimensions of 100 50 10 mm made up each double butt strap joint as shown schematically in Fig. 2. The components of the joints were bonded using a two-part epoxy adhesive Araldite 2015. A light abrasion surface preparation was conducted followed by a solvent wipe prior to bonding. The joints were allowed to cure at room temperature for 24 h and were post cured at 50 °C for a further 24 h. The butt strap joints were loaded quasi-statically in tension to determine the average ultimate failure load of the joint. It was calculated that the average stress in the adherend was 93.3 MPa when the joint failed, which is equivalent to 20% of the ultimate strength
of the pultruded material. The failure mode was due to interlaminar failure of the adherend between the two combination mats and is shown in Fig. 4. For the thermoelastic stress analysis, K1 for the pultruded layers in the longitudinal direction was obtained experimentally as described above. For the adhesive the thermoelastic constant was obtained from Eq. (4) using values from Ref. [14], providing a thermoelastic constant (K) for the adhesive of 2.88 105 MPa1. Using Eq. (3) and the known test temperature (300 K), the calibration constant for the adhesive of 115.7 MPa K1 was obtained. The double lap joint was subjected to a mean load of 8 kN with a cyclic load amplitude of 5 kN. Firstly, the whole strap area was examined; Fig. 5a shows the thermoelastic signal data and Fig. 5b shows the calibrated stress data. Fig. 6a shows the thermoelastic signal from the upper half of the strap joint. This increases the resolution of the TSA data and allows detailed data to be
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Fig. 4. Failure of the specimen within the pultrusion.
obtained from the spew fillet and end of the strap. Fig. 6b provides the calibrated stress data and shows that the stress sum in the adhesive is close to zero, this is as expected as the adhesive will be predominantly in shear. However, there is a stress concentration present within the strap on the left-hand side of the joint at the location equivalent to the interface between the combination mat and the unidirectional layers. In addition, there is a stress concentration at the spew fillet. In the main adherend there appears to be an increase in stress in the region of the strap ends. Again this is concentrated at the interface between the unidirectional and combination layers. Fig. 6b indicates that the differences in the mechanical properties of the materials contained in the pultruded joint may be caused by stress concentrations within the pultruded material, which ultimately could lead to the interlaminar failure of the joint. It has been shown that the layers of material in the pultrusion have different mechanical properties, and therefore the thermoelastic constants and the stress field within adhesively bonded pultruded joint are dictated by the layered nature of the pultrusion. Thus, it would be inefficient to examine every joint or pultrusion using experimental techniques such as thermoelastic stress analysis. Therefore, the following sections of the paper concentrate on the production and validation of an FE modelling approach for the design of adhesive joints in pultruded material. 4. FE model The joint was modelled using the ANSYS FEA package using 2D, 8-noded quadrilateral elements (PLANE82). In order to reduce the error in the loading of the model, the whole joint was modelled and the load applied away from the bonded region. Initially a coarse model was produced. It was assumed that a pressure load applied to the ends of the model reproduced the stress field induced by the test machine grips in the experimental work. The boundary conditions for the coarse model were therefore such that the upper adherend was fully constrained, and the pressure load was applied to the lower adherend to generate a tensile stress. The adherends and adhesives were assumed to be perfectly connected as the previous work [2,3,10] showed that the failure of the joints occurs within the adherend material. Some of the mechanical properties of each layer of the pultrusion were calculated from the experimental tests conducted in Sec-
tion 2. The remainder were obtained either from literature or through calculation. The adopted material properties are detailed in Table 4. The joint was divided into areas of specific materials, i.e. the unidirectional core, the combination outer layers and the adhesive. The latter is defined as an isotropic material with material properties obtained form the manufacturer. The pultrusion layers were defined with anisotropic material properties. All materials were assumed linear elastic as the load applied during the testing produced less than 40% of the ultimate strength of the pultrusion. Sub modelling was employed so that a much finer mesh was constructed allowing a detailed examination of features. This allowed the introduction of the spew fillets, which were modelled as triangular sections with the triangular side being twice as long as the thickness of the adhesive as was used as the equivalent spew fillet by Frostig et al. [15]. The upper portion of the double butt strap, equivalent to that examined experimentally as shown in Fig. 6, was modelled by the sub model. The displacement boundary conditions for the sub model were interpolated from the coarse model at the appropriate locations and these were imparted on the sub model boundaries. The boundary stresses for both the coarse and sub models were compared to ensure continuity between the two models. The mesh used for the sub model is shown in Fig. 7a. The mesh density is such that the adhesive layer and the inner combination mat appear as the solid black areas in the figure. In fact the adhesive layer is half the width of the spew fillet. To directly compare the FEA results to the calibrated TSA results it is necessary to obtain the quantity K2 as an input for the FEA (see Eq. (7)). It was decided to use values for the resin (a, q and Cp) obtained from the manufacturer, giving a value of 4.8 105 MPa1, as an upper bound in the FEA. As a lower bound, isotropic behaviour was assumed by defining K2 = K1 for each material layer in the FEA. Fig. 7b shows the FEA results for the lower bound data.
5. Validation and discussion Line data was obtained from the TSA across the adhesive joint at two locations (see Fig. 6a); at the end of the butt strap overlap and 20 mm from the end of the butt strap overlap. The principal stresses were obtained from the FEA analysis in the same locations, manipulated according to Eq. (6) and the results are presented in Fig. 8 for the upper and lower bounds of K2. Fig. 8a shows the results at the end of the strap overlap and the excellent correlation between the numerical and experimentally derived results, particularly the transitions between different layers of the pultrusion. In Fig. 8a the upper and lower bound numerical results straddle the experimental results suggesting that the K2 parameter is not equal to K1, nor is it equal to the value obtained for pure resin, but somewhere in between. This implies that there is some interaction between the resin and fibres in the through thickness direction. This is particularly relevant in the combination mat of the central adherend where the FEA is greatly over predicting the stress. A lower value of K2 in this area (due to some through thickness matrix fibre interaction) will reduce the numerical model prediction. The same is true of the unidirectional core with the lower bound K2 corresponding well in some areas, which are probably resin dominated and the upper bound over predicting as K2 for the material is likely to be less than that for the resin. Clearly, a means for experimentally evaluating K2 is required to improve the accuracy of the FE results. Therefore, the correlation between the numerical and experimental results in Fig. 8a could only be defined as moderate. However, an inspection of Fig. 8b shows a much better correspondence. Here, only the lower bound FE results are shown as Dr22 in this region will be close to zero and shows a much better correspondence in all areas of the joint, apart from a small discrepancy in the correspondence in the data from the
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Fig. 5. Thermoelastic signal (a) and calibrated stress (b) plot of double strap joint.
adhesive layer. This is because the material properties from the adhesive were taken from the literature; a better correlation would be expected if the K value for the adhesive could be obtained experimentally. Overall, the correlation between the numerical and experimental results is good. However, in some areas of Fig. 8a and b the experimental are very noisy and differ greatly from the relatively smooth numerical results. This can be attributed to the inhomogeneous nature of the pultruded material. The micrograph provided in Fig. 1 shows that there are areas in the unidirectional core that contain a large amount of resin. These areas have not been included in the numerical model, because of the random nature of the resin entrapment. Likewise the
experimental TSA signals from the resin rich areas, again due to their random locations, were not calibrated using the calibration constant for the resin material. This will result in an incorrect calculation of the stress in these localised regions, and hence the variable nature of the experimental curve presented in Fig. 8a and b. However, in general the numerical and experimental results correlate well in the interface areas of the joint, e.g. in the transition from the combination layers to the epoxy adhesive. Another consideration is the difference in the spatial resolution of the TSA and the FEA. Each pixel in the TSA was 0.273 mm. Although the mesh density varied in the FEA model, the FEA data shown in Fig. 8 was derived by interpolation, so that the distance
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Fig. 6. Thermoelastic signal (a) and calibrated stress (b) plot of upper portion of double strap joint.
Table 4 Material properties of pultrusion used for numerical modelling Material
Ex (MPa)
Ey (MPa)
mxy
Gxy (MPa)
Unidirectional Combination Adhesive
35575a 15542a 2000c
3500b 3500b 2000c
0.28d 0.28d 0.36c
1367e 1367e 735e
a b c d e
Property Property Property Property Property
obtained from experiments in Section 2. obtained from Ref. [11]. obtained from manufacturers data sheet. obtained from Ref. [16] for 55% fibre volume fraction glass/epoxy. from calculation.
between the data points was 0.15 mm. This difference in the spatial resolution is important in areas where the stress gradient is
large as exhibited at the centre of the combination mat in the butt straps. Elsewhere, the difference in spatial resolution has little effect on the correspondence of the FEA and TSA data and is insignificant in comparison to the effect of localised changes in the materials. The overall correspondence between the FE and the TSA provides confidence in the numerical modelling technique as it has been validated using experimentally derived data. In addition, it further confirms the validity of the material property data obtained from the pseudo-pultruded material to represent the actual pultruded lay-up. Moreover, even better correlation between the experimental and numerical results is obtained away from the end of the overlap (Fig. 8b). In addition, the non-ideal geometry of the test specimens resulted in stress
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Fig. 7. Sub model of double lap joint; mesh (a) and sum of the principal stress solution (b).
concentrations that were not observed in the idealised numerical model.
6. Conclusions In this research a number of key conclusions can be drawn: A pseudo-pultruded material was created using a combination of vacuum consolidation, elevated temperature and increased pressure in an autoclave to create test material for the calibration of the thermoelastic data and as input to the finite element model. The resulting material was found to be a good representation of pultruded material.
The thermoelastic signal was correctly calibrated using the experimentally derived calibration constants for each of the constituent layers in the pultrusion. This allowed the examination of experimental data for stress concentrations in the through thickness direction during loading of double lap joints in pultrusions. A FE model was created using the material properties obtained from the pseudo-pultrusion and compared to the experimental data from the TSA. The correlation was very good in particular the transition between layers in the pultruded material and the magnitude of the stresses found. This gives good confidence in the modelling approach and allows for further examination of the bonded joint numerically to further understand the failure mechanisms and examine possible ways of improving the performance of adhesively bonded joints in pultruded material.
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Fig. 8. Comparison of numerical and experimental plots of stress from lines 1 (a) and 2 (b) shown in Fig. 6a.
Further work is required to experimentally obtain the K2 value for the pultruded material constituent layers, in particular in the combination mat, in order to improve the numerical modelling prediction. Acknowledgement The authors are grateful to Fiberline Composites A/S (Middelfart, Denmark) for the supply of pultruded materials and the dry reinforcements and liquid resins for the pseudo-pultruded manufacture.
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S.W. Boyd et al. / Composites: Part A 39 (2008) 1311–1321 [6] Feng Z, Zhang D, Rowlands RE, Sandor BI. Thermoelastic determination of individual stress components in loaded composites. Exp Mech 1992:89–95. [7] Lin ST, Rowlands RE. Thermoelastic stress analysis of orthotropic composites. Exp Mech 1995:257–65. [8] Bakis CE, Reifsnider KL. The adiabatic thermoelastic effect in laminated fibre composites. J Compos Mater 1991;25:809–30. [9] Emery TR, Dulieu-Barton JM, Earl JS, Cunningham PR. A generalised approach to the calibration of orthotropic materials for thermoelastic stress analysis. Compos Sci Technol 2008;68(3–4):743–52. [10] El-Hajjar R, Haj-Ali R. A quantitative thermoelastic stress analysis method for pultruded composites. Compos Sci Technol 2003;63(7):967–78. [11] Keller T, Vallee T. Adhesively bonded lap joints from pultruded GFRP profiles. Part II: joint strength prediction. Compos Part B 2005;B36:341–50.
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[12] Stanley P, Chan WK. Quantitative stress analysis by means of the thermoelastic effect. J Strain Anal 1985;20:129–38. [13] Dulieu-Smith JM. Alternative calibration techniques for quantitative thermoelastic stress analysis. Strain 1995;31:9–16. [14] Dulieu-Smith JM, Stanley P. On the interpretation and significance of the Gruneisen parameter in thermoelastic stress analysis. J Mater Process Technol 1998;78(1–3):75–83. [15] Frostig Y, Thomsen OT, Mortensen F. Analysis of adhesive-bonded joints, square-end, and spew-fillet-high-order theory approach. J Eng Mech 1999;125(11):1298–307. [16] Daniel I, Ishai O. Engineering mechanics of composite materials. Oxford University Press; 1994.