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Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads
Accepted Manuscript Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads
Alireza Gorjipoor, Suong Van Hoa, Rajamohan Ganesan
PII: DOI: Reference:
S1270-9638(16)30848-3 http://dx.doi.org/10.1016/j.ast.2016.10.008 AESCTE 3794
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
7 July 2016 6 September 2016 10 October 2016
Please cite this article in press as: A. Gorjipoor et al., Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads, Aerosp. Sci. Technol. (2016), http://dx.doi.org/10.1016/j.ast.2016.10.008
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Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads Alireza Gorjipoor a, Suong Van Hoa b, Rajamohan Ganesan c
Department of Mechanical Engineering, Concordia Center for Composites, Concordia University, Montreal, Canada, H3G1M8.
a
Corresponding Author: Alireza Gorjipoor, [email protected] b
[email protected], c [email protected]
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Abstract In this study, strain distributions in a thick composite plate subjected to bolt loads have been investigated both numerically and experimentally. Recently, major industries such as aerospace, automobile and marine are interested in development of thick composites applications. One of these applications is the yoke of the helicopter, which connects main blades to the rotor hub using bolt joints. In the present work, a three dimensional finite element model of a thick composite plate subjected to bolt loads is created using ANSYS 14.5. Strains at the surface (around the washer) and along the laminate thickness have been measured using strain gages and Digital Image Correlation method, in order to verify simulation results. The model is used to investigate the effect of thickness on distributions of interlaminar stresses. Keywords: Thick composite laminate; Finite element analysis (FEA); Bolt loads; Digital Image Correlation.
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1. Introduction High specific strength and high specific stiffness of composite materials make them an appropriate choice for many industrial applications. Designers and manufacturers are able to replace parts made of common materials like steel and aluminum with composite materials. The specific benefit of composite materials is their ability to be designed in a way to achieve specific material properties in a desired direction. So far, thin composite plates have been widely used in different industries. Therefore, design and analysis methods for thin composites have been widely developed [1,2] and several techniques have been invented by manufacturers to produce more complicated parts [3]. One of major applications of composite materials is in aerospace structures where weight reduction has been always the most challenging endeavor. Aerospace structures are always made up of several components which should be assembled using methods. Joint design has its own significance and complexity especially when composite materials are engaged in the structure. The most common method for composite parts assembly is mechanical fasteners. Bolt joint, which is considered as a type of mechanical fasteners, is more popular and practical since it is inspectable, repairable and undoable. Some of the applications of bolt joints in aerospace industry are such as wing to fuselage joint in Boeing/MDD Harrier, Boeing/Bell V-22 Osprey, Boeing 777 and Grumman X-29 (NASA) [4]. This study is motivated based on the application of thick composite laminates as the yoke of helicopter. Yoke is the part which connects main rotor blades to the hub. It is made of thick tapered composite laminate which is connected to the other parts of the system using bolt joints. Bolts are considered as the most vulnerable parts of the assembly. The failure of the yoke may cause the helicopter to stall. This paper focuses on introducing an effective model for the stress analysis of a thick composite plate subjected to bolt loads. The proposed model is a part of a holistic model which includes all major concepts in design process of the yoke such as bending loads and centrifugal forces. The holistic model will be utilized for failure prediction and fatigue analysis in design process to reduce the number of iterative costly experimental tests. The significant amount of transverse normal and shear stresses along thickness make stress analysis in thick laminates more complicated in comparison with thin laminates, where plane stress assumption is applicable in most study cases [5–7]. Two dimensional methods which have been developed so far are not suitable for prediction of structural behavior in thicker laminates, hence more advanced experimental and analytical methods have been utilized in the literature for stress analysis of thick composite plates [8]. In analytical approach finite element simulation was performed by using either brick elements provided by commercial software or the new elements introduced and developed by researchers [5,6,8–12]. For experimental investigation Digital Image Correlation method and strain gages were utilized to verify finite element simulation results [8]. For thick composites bolt joint is the most frequent assembly method [13]. Several researches have been performed in order to study the effect of bolt joints in composite structures [14]. Some researchers used two dimensional analysis [15]. However, it is shown by Ireman [16] that in the vicinity of the bolt hole, the field of stress is three dimensional and significant interlaminar stresses exist at the free edges. It was shown by 3
Ireman that the distribution of bolt-hole contact pressure is not uniform along the thickness of the composite plate. Therefore, three dimensional finite element analysis is critical when through the thickness effect of composite bolt joint is the study subject. More recently, finite element simulation and experimental tests were implemented in order to investigate the effect of different parameters such as washer size, clamping torque, bolt stiffness, friction coefficient, bolt-hole clearance, plate geometry and layers sequences on the stress and strain distribution in a composite bolt joint [17–20]. Progressive damage model was utilized to predict the failure initiation point and propagation pattern in composite bolt joint with different joint configurations and layer orientations [21–23]. However, the previous studies did not take into account composite laminates with higher thicknesses (more than 15 mm). Recently some studies focused on effect of bolt joints on thick composite structural behavior. In a study by Cloud et al. [24], strains beneath the washer were detected using Digital Speckle Pattern Interferometry (DSPI) method. In this work, to investigate strains beneath the washer, a transparent washer was manufactured from polycarbonate sheet. The polycarbonate washer was made with a thickness of about 4.3 times of a steel washer with the same inner and outer diameters, in order to provide the same stiffness. In another study by Isaicu et al. [25], embedded fiber optic strain gages and finite element simulation were utilized to find strain distributions in a thick composite bolt joint. A very rough estimation was utilized in this research, to convert the clamping torque to bolt preload. A study was done by G. Restivo et al. [26], in order to find through thickness stress distribution in a composite laminate connected to aluminum plate using single-lap bolt joint. In this study the preload was measured using a load cell transducer. In all three above studies a single-lap bolt joint was considered and joint is subjected to axial tension. However, studies on the effect of the bolt joint itself on a thick composite laminate are still lacking. What is studied in this paper is the first step in introducing a numerical model to predict failure behavior and fatigue life in the yoke of the helicopter considering all including aspects such as centrifugal forces, bending moments and clamping loads. The model was developed fully parametric to provide adequate design flexibility. In this first step, the principle goal is to introduce an effective three dimensional finite element model which is able to simulate the structural behavior of a thick composite plate subjected to bolt loads. In addition, two experimental approaches are implemented to validate the finite element simulation results.
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2. Finite element simulation The dimensions of the modeled plate are illustrated in Figure 1. It is made of 80 layers of glass epoxy. Each layer has a thickness of 0.009 inch (0.23 mm), therefore total thickness of the plate is 0.72 inch (18.3mm). All layers are made of unidirectional prepregs provided by Cytec Engineered Materials company (product number: FX E773/S-2). Four holes were drilled at each side of the plate using diamond twist drills. The inner surface of holes was inspected visually to make sure that drilling process did not cause any damage at this area. The dimensions of the plate and the configuration of the holes are selected regarding the application of the structure as the yoke of helicopter. In order to study the effect of the bolt, a full three dimensional finite element model is created using finite element software ANSYS 14.5. The model is created fully parametric to make it suitable for sensitivity analysis which is the point of interest for future studies. Figure 1
All parts of the model were meshed using a specific solid element (Solid185) from the software element library. This element can be used to model both structural and layered solid parts. It has 8 nodes and three translation degrees of freedom at each node and can use both reduced and full integration methods. In order to define the layers thicknesses and orientations, a shell section was associated with the solid element. Since in this study the laminate is made of 80 unidirectional layers, a section consisting of 4 unidirectional layers was defined and 20 elements were created along the thickness. Material properties of glass epoxy, washer and bolt are defined according to the material library of the finite element software (ANSYS) and summarized in Table 1. Table 1: Material properties (extracted from ANSYS workbench 14.5 material library) Glass/Epoxy Plate
E1
E2 = E3
7.25 (Msi)
1.16 (Msi)
50 (GPa)
8 (GPa)
Technical
7-9 (Msi)
1-2 (Msi)
Data Sheet*
48-62 (GPa)
7-14 (GPa)
ANSYS
Washer Bolt Nut
v23
v12 = v13
0.4
0.3
-
-
G23
G12 = G13
0.56 (Msi)
0.73 (Msi)
3.8 (GPa)
5 (GPa)
-
-
Steel E
v
29 (Msi)
0.30
200 (GPa)
* www.cytec.com-CYCOM E773 Epoxy Prepreg Data Sheet (Page 4)
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Figure 2 shows the mesh pattern created for each part. Similar mesh pattern and sizing were implemented in contact areas between washer, bolt and plate. The created mesh improves the accuracy of contact simulation between these parts and facilitates the convergence of nonlinear contact analysis. Elements TARGE170 and CONTA174 were created at the mentioned areas to model three dimensional contact. Figure 3 demonstrates contact definition at corresponding areas. Contact behavior between bolt head-washer, washer-plate and bolt stud-hole inner area were all defined as flexible surface-to-surface contact. Figure 2
Figure 3
Mesh sensitivity analysis was done in order to find the optimum mesh sizing. In this analysis, number of elements along the thickness remained constant and the meshing pattern on the surface of the plate was changed. The contact force between washer and plate was calculated and considered to perform mesh sensitivity analysis. A very simple static analysis of the bolt and washer shows that the contact force between washer and plate should be theoretically equal to the pretension force applied in the stud of the bolt. Table 2 summarizes the results obtained from three different meshing patterns (different number of elements). In all three cases of Table 2, the same preload (8700 lbs. or 38.7 KN) was applied to the bolt. As it is illustrated in Table 2 mesh pattern 2 improved the accuracy by about 60%, considering that the time of solving increased by 40%. Comparing patterns 2 and 3 shows that the running time increased about 5 times and the accuracy improved up to 47%. In addition by using mesh pattern 3, software did not show any warning or error about the aspect ratio of elements. Therefore it was decided to use mesh pattern 3. In this pattern elements sizes vary between 0.18 to 24.25 mm3 for the plate. Table 2: Mesh sensitivity analysis results Mesh
Total
Number of contact
Solving
Calculated
Difference between contact
pattern
elements
elements washer-plate
time
contact force
force and bolt preload
1
22880
80
5 min
8624
0.90%
2
41118
160
7 min
8670
0.35%
3
128084
320
40 min
8684
0.18%
The dimensions of the bolt and washer used in the simulation and experiments are shown in Figure 4. To reduce the complexity of the finite element model, the hexagonal shape of the bolt head and nut was replaced with a circle with the same area. The thickness of the nut and bolt head are both 0.35 inch and bolt and nut were glued to each other. The thickness of the washer was selected as the average of the range introduced by
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the manufacturer. To model the tension force propagated in the stud of the bolt due to clamping torque, a pretension section was created at the axial middle section of the shaft of the bolt. The nodes of the pretension elements (PRETS179) are able to collapse into each other. Since the bolt is constrained at each side by the contact with washers, collapsing of pretension nodes into each other produces tension in whole length of the shaft of the bolt. Figure 4
To calculate the bolt preload due to clamping torque, a simple approximation introduced by Speck [27] was used. Based on the mentioned method, the load can be obtained using Equation 1, where T is clamping torque, D is thread pitch diameter and K is friction coefficient. During experimental tests, the bolt tension was measured by a load transducer installed in the shaft of the bolt. Also a calibrated torque meter was utilized to apply different clamping torques. The experiments results were utilized with Equation 1, to find the relation between the force and the torque for this type of joint. ܶ ൌ ܭൈ ܦൈ ܨ
Equation 1
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3. Experimental investigation Verification of the finite element simulation accuracy was done using two experimental methods. First, strain gages were used to measure strain at critical points around the washer and along the thickness of the laminate. The gage measurements were compared with the results obtained from finite element model. Second, Digital Image Correlation method was used to find the strain field at the surface. For the first step, six Tee Rosettes (Vishay WK-06-030WT-120) were installed around the washer using M-Bond 200 Adhesive from MicroMeasurements Company. The gage sensitivity for this type of strain gage is 50×10-6 (50 micro) strain. The gages were positioned at the points where the maximum and minimum strains (along fibers and in transverse direction) were obtained from finite element analysis. Figure 5 shows the positions and orientations of the installed strain gages. Gages numbered 1, 3 and 5 (G1, G3 and G5) measured the strain in fiber direction and gages numbered 2, 4 and 6 (G2, G4 and G6) measured strain transverse to the fibers. Although the critical points were positioned at the edge of the washer according to analysis, during experimental investigation the gages were placed at a distance of 0.2 in (5 mm) from the edge to prevent gage damages. Hence, the radial distance of the center of G1 to G4 to the center of the hole was 0.825 in (21 mm). Center point of G5 and G6 were positioned at the middle thickness and along the central axis of the hole. To find the relation between applied torque and the tension force in the stud of the bolt, a special bolt equipped with a transducer gage installed in its shaft was utilized. The output of the transducer gage is helpful to modify the load calculation done in numerical analysis. Figure 5
Digital Image Correlation (DIC) method was utilized to find strain distribution pattern around the hole in upper surface. DIC is a practical tool for full-field in-plane strain investigation. The method is based on comparison between digital images taken before and after loading. The whole process consists of three main steps: 1) preparing the specimen and imaging setup, 2) capturing photos before and after load application and 3) image processing using computer. During the last step the computer tracks the different node displacements during loading and interpolates the displacement between these nodes to find the full displacement and strain fields [28]. To make the specimen ready for test it is required to make random black and white spots in order to provide trackable patterns for the image processing. As Figure 6 shows a speckle pattern was created on the desired surface using paint spray. Cameras with the resolution of 5 mega pixels were used to capture images. The resolution of images was 289855 dpi and the field of view was 3.1 inch ൈ 2.6 inch. Figure 6
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4. Results 4.1.Bolt preload The bolt preload versus the elapsed time is shown in Figure 7. As it was expected the tension force was zero at the beginning because there was no clamping torque. As a clamping torque of 25 lb-ft was applied in the first step the tension force increased to 3.2 Klbs. During several steps the tension force increased when higher torque was applied. At the very first few seconds of each torque increasing step, the tension jumped to a high level but in a few seconds it released until reaching a steady value. This phenomenon is highlighted for clamping torque of 90 lb-ft in Figure 7. The mentioned tension reduction varied between 5% for 25 lb-ft of torque to 15 % at the clamping torque of 90 lb-ft. This behavior reveals the viscoelastic reaction of thick composite laminates when they are subjected to bolt clamping pressure. Right after applying a higher torque, the plate resists against deformation which causes higher tension to be produced in the bolt shaft. Then the contact pressure of washer pushes the material away in radial direction, therefore the material beneath the washer moves to the sides and resistance against washer will decrease. As a consequence the tension in the bolt shaft releases. Figure 7
Although the effect of the thickness and material properties on the viscoelastic behavior of thick composites requires further investigation (which is not the subject of the present study), a simple comparison between the sample made of 80 unidirectional layers of glass/epoxy and an aluminum plate with the same dimensions has been performed. Figure 8, compares the relaxation of the bolt tension between aluminum and composite plate at the clamping torque of 90 lb-ft. As it can be seen in Figure 8, for composite laminate higher tension was produced in the bolt while in case of aluminum plate, the tension relaxation occurred with a faster rate. The reduction in the force until reaching the steady value was 12.5 % for composite plate and 5.3% for the aluminum one. Figure 8
To find a single value for bolt tension at each clamping torque, the test was duplicated while the load was monitored continuously during the whole test process. When the load reached a steady value, that value was selected as the preload at the specific applied torque. Figure 9 illustrates the pretention force as a function of clamping torque in three experiments with different maximum clamping torques. As it is illustrated in Figure 9, the relation between torque and bolt preload is linear with a good approximation. Based on the results, the friction coefficient (refer to Equation 1) obtained from experiments is 0.197, 0.194 and 0.195 for three different test cases. The average of these values was used with Equation 1 to calculate bolt tension load at any clamping torque desired for finite element analysis. 9
Figure 9
Figure 10 illustrates the tension force propagation in the stud of the bolt obtained from ANSYS. As it is indicated the tension force due to clamping of the bolt has a sharp drop at both stud ends while it reaches an approximately uniform distribution in the middle section. In Figure 10, the dashed lines represent the position of the thickness of the washers at each side. It is obvious that between two washers the tension force does not have significant variation comparing to the top and bottom sections. For the analysis represented in Figure 10 the defined pretension was 8700 lbs. (38.7 KN) and the average of tension force obtained after analysis was 8635 lbs. (38.4 KN) which shows only 0.75% of difference. Figure 10
4.2.Strain gages Figure 11 represents the results obtained from strain gages at different clamping torques at positions 1 to 6 (refer to Figure 5). In Figure 11 and Figure 12 the amount of strain is represented in terms of micro strain (strain × 106). Results show that under a single bolt clamping force, strain in fiber direction at top surface was higher in G1 comparing to G3. Also, it is obvious that G4 has higher lateral strains in comparison with G2. In general, it could be concluded that lateral strains at the surface are higher compared to longitudinal strains. This was expected since the plate is unidirectional and the material is stiffer along fibers rather than transverse direction. G5 and G6 measured strains at the plate thickness. Because the loading (bolt force) is along the thickness of the plate and plate is unidirectional, the strain in thickness direction (G6) was higher compared to the longitudinal strain (G5). Considering the fact that no failure was observed up to the clamping torque of 70 lb-ft, a linear relation between strains and clamping torque was obtained. Figure 11
Figure 12 compares strains obtained from gages with ANSYS results at different clamping torques. For G1, maximum difference between experimental and finite element is 9% (35 micro strain) at clamping torque of 50 lb-ft. Hence the gages sensitivity was 50 micro strain, it can be said that ANSYS and experiment values correlate very well at this position. The same investigation for G2 reveals that the maximum difference is 9% (55 micro strains) at the torque of 70 lb-ft which also represents the good correlation between results at this position. For G3 the amount of strain was not considerable comparing to the other positions. Although the maximum difference is 35%, it is only 35 micro strains which is less than the gage sensitivity. For G4 and G6 the maximum difference is less than 5% (40 micro strains) and finally for G5, the difference is 20% (35 micro strains). All the results show that the maximum difference between strain gages and finite element analysis
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was in the order of the gages sensitivity. This fact shows that the finite element model can predict the strain with good accuracy within the gage sensitivity. Figure 12
4.3.Digital image correlation (DIC) Comparing strains fields obtained from ANSYS simulation and DIC method reveals that the model is able to predict strains accurately in thick composite plates subjected to the clamping forces induced by the bolt. Results obtained from DIC showed that structure encountered a very small rigid body motion during the test, which caused discrepancies between deformations fields obtained from DIC and ANSYS. Since the strain is not affected by rigid body motion, the verification of the finite element analysis results were done based on the strain fields comparison. Here, strains obtained at clamping torque of 70 lb-ft are reviewed to show the achieved agreement between these two methods. Figure 13 represents the areas under consideration to compare ANSYS and DIC results. In this figure the dotted line represents the outer edge of the washer. Figure 14 illustrates the distribution of the strain in axial direction (along the fibers) at the top surface between holes number 1 and number 2. Distribution of the strain in transverse direction (perpendicular to the fibers) between holes number 1 and number 3 is shown in Figure 15. Comparison between strains distribution patterns obtained from ANSYS and DIC reveals that there is a good qualitative coordination between results. Figure 13 Figure 14 Figure 15
To compare the results quantitatively, strain along lines “ab” and “cd” (refer to Figure 13) have been extracted from both DIC and finite element simulation results. Figure 16 shows the distribution of strain in axial (along fibers) direction from point “a” to point “b” (refer to Figure 13). The amounts of strains obtained from both ANSYS and DIC were normalized according to the maximum strain obtained in this direction which wasͳʹͲͲ ൈ ͳͲି ݄݅݊ܿȀ݄݅݊ܿ. Also Figure 17 illustrates the distribution of the strain in transverse direction (perpendicular to fibers) from point “c” to point “d” (refer to Figure 13). Similar to axial strain the transverse strain was normalized using the maximum value which wasʹͳʹͲ ൈ ͳͲି ݄݅݊ܿȀ݄݅݊ܿ. It is obvious from Figure 16 and Figure 17, not only ANSYS model correlates qualitatively with DIC results but also there is a good match between the strains quantities obtained from these two analysis. Unfortunately the test setup did not provide enough space to install the camera close enough to the thickness side to perform DIC on the thickness. Figure 16 11
Figure 17
4.4.Thickness effect In order to demonstrate the effect of thickness on stress distribution in a composite plate under bolt load, three plates with different number of layers were considered. As it is indicated in finite element simulation section, the thickness of each layer is 0.009 inch (0.23 mm). Three numbers of layers 12, 40 and 80 were considered to investigate the effect of the plate thickness. For all analyses the material of the plate, unidirectional layers sequence, bolt and washer configurations and bolt preload remained constant. Table 3 shows the characteristics of selected plates. Table 3: Characteristics of plates considered for thickness effect investigation Number of unidirectional layers
Total thickness
Plate 1
12
0.108 in (2.74 mm)
Plate 2
40
0.36 in (9.145 mm)
Plate 3
80
0.72 in (18.29 mm)
Figure 18 shows the out of plane deformation (ܷ ) at top surface and along line “cd” (refer to Figure 13). In Figure 18, the dotted line represents the position of the edge of the washer. It can be observed that for plates with higher thickness the effect of the washer contact propagated over a larger area around the washer. In addition for the same preload in the bolt, the plate with higher thickness had higher deformation in the area beneath the washer as well as in outer region. The values of out of plane deformation (ܷ ) at the distance of 0.4 in (10.16 mm) from the hole center along line “cd” (refer to Figure 13) showed that Plate 3 deformation is 4.8 times higher than Plate 1 deformation. For all three plates the deformation changed linearly in the area beneath the washer except at regions close to the washer inner and outer edges. Since the inner diameter of washer is 0.53 inch while the hole diameter is 0.5 inch, the material at the vicinity of the hole edge is not in contact with washer and it can flip up. This phenomenon causes the nonlinear behavior which can be observed at the first points of all three graphs in Figure 18. Figure 18
As can be seen from Figure 18, the effect of washer load started to vanish at the point located on the washer outer edge (at the distance of 0.53 inch from the hole center). Therefore the edge of the washer was set as one of the critical reference points. Also two other points were selected to study the distribution of interlaminar normal and shear stresses along the thickness of the plate. The position of the mentioned points were selected in way to include the interlaminar stresses distribution investigation beneath, at the edge and in outer region of the washer. A coordinate system was defined to simplify results representation. The origin of the 12
coordinate system was placed at the center of the hole at the top surface, “X” was defined in fiber direction and “Y” was in transverse to the fibers. “Z” was considered along the thickness. According to the above coordinate system, the distribution of ܵ and ܵ at X=0 and Y= 0.4, 0.53 and 0.65 (in) through the thickness of the plate were investigated. Figure 19 presents the distribution of interlaminar normal stress (ܵ ሻ along the thickness at X=0 and Y= 0.4, 0.53 and 0.65 (inch). Since plates were unidirectional, the distribution of the stresses along thickness were symmetric. Therefore the stresses are plotted from top surface up to middle plane of the thickness. Figure 19 shows that for all three selected locations the variation of the normal stress along thickness is higher for plates with higher thicknesses. For the thinnest laminate (Plate 1) the normal stress (ܵ ሻ was almost constant at Y= 0.4 inch (beneath the washer) and the compressive stress was higher than the other two plates. At the edge of the washer (Y = 0.53 inch), Plate 2 and Plate 3 still have compressive stress along 80 to 90% of their thickness, while Plate 1 encountered tensile stress at all points. Finally, for the thinnest plate the effect of the bolt load does not propagate up to the point selected in outer region (Y = 0.65 in), while there is still a significant amount of compression at the same location inside thicker laminates. Figure 19
Figure 20 shows interlaminar shear stress ሺܵ ሻ distribution through the thickness. Comparison between plates revealed that higher interlaminar shear stress produced in plates with higher thicknesses. Similar to the normal stress, the variation of shear stress ሺܵ ሻ along thickness was much higher for the Plate 3 compared to Plate 1. This phenomenon was observed at all selected three different Y positions. Figure 20 indicates that at the outer region (Y=0.65 inch), the amount of interlaminar shear stress ሺܵ ሻ is relatively higher in thicker plates across the whole thickness (i.e. for plate with 80 layers at 20% of thickness the shear stress is 1 ksi). At this point (Y=0.65 inch) Plate 1 showed very small interlaminar shear stress (22 psi) which remained constant through the thickness. As it can be seen in Figure 20, the position through the thickness where maximum shear stress ሺܵ ሻ is occurred, varies with the plate thickness. Figure 20
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5. Conclusion and discussion This paper proposes a full three dimensional finite element model to predict the strain in a thick unidirectional composite laminate subjected to a single bolt load. Two experimental approaches including strain gages and digital image correlation have been utilized to validate the model accuracy both qualitatively and quantitatively. It has been found that in case of unidirectional thick composite laminate subjected to clamping bolt forces, since the material is stiffer in axial direction (fiber direction), the axial deflection is less than transverse deflection. As a consequence the axial strain is less than transverse strain too. This behavior was observed in results obtained from both experimental and numerical studies. Results obtained from ANSYS and strain gages were in a close agreement at critical positions in axial and transverse directions. For the top surface the strain values and distributions obtained from DIC correlate well with both ANSYS simulation and strain gages. Experimental test results demonstrates that the developed finite element model is able to predict the structural behavior of a thick composite subjected to bolt loads, both in the magnitudes of strains and also the strain distribution pattern. The effect of number of layers was studied comparing plates with 12, 40 and 80 layers. Results showed that interlaminar stresses values and their variation along thickness for thick composites are more significant compared to thin laminates. In addition, for thicker plates the effect of bolt load propagates in a larger zone around the washer. Results showed that thickness has a significant influence on interlaminar stresses values and distributions. The holistic investigation of the thickness effect requires more detailed analysis which is the subject of the future studies.
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Acknowledgement This research is conducted by financial supports of Natural Sciences and Engineering Research Council of Canada (NSERC), Ministère du Développement économique de l'Innovation et de l'Exportation (MDEIE), Le Consortium de recherche et d'innovation en aérospatiale au Québec (CRIAQ) and Bell Helicopter Textron Inc.
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C.T. McCarthy, M.A. McCarthy, W.F. Stanley, V.P. Lawlor, Experiences with Modeling Friction in
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U.A. Khashaba, H.E.M. Sallam, A.E. Al-Shorbagy, M.A. Seif, Effect of washer size and tightening
torque on the performance of bolted joints in composite structures, Compost. Struct. 73 (2006) 310–317. doi:10.1016/j.compstruct.2005.02.004. [20]
P.A. Sharos, B. Egan, C.T. McCarthy, An analytical model for strength prediction in multi-bolt
composite joints at various loading rates, Compos. Struct. 116 (2014) 300–310. doi:10.1016/j.compstruct.2014.05.021. [21]
K.I. Tserpes, P. Papanikos, T.H. Kermanidis, A three-dimensional progressive damage model for
bolted joints in composite laminates subjected to tensile loading, Fatigue Fract. Eng. Mater. Struct. 24 (2001) 663–675. [22]
S. Hsien-Tang, C. Fu-Kuo, Q. Xilin, The response of composite joints with bolt-clamping loads Part
I: Model Development, J. Compos. Mater. 36 (2002) 47–67. [23]
H.T. Sun, F.K. Chang, X. Qing, The Response of Composite Joints with Bolt-Clamping Loads, Part
II: Model Verification, J. Compos. Mater. 36 (2002) 69. doi:10.1177/0021998302036001302. [24]
G.L. Cloud, X. Ding, S. Thelander, B.B. Raju, Strains beneath washers in thick single-lap composite
bolted joint using embedded DSPI and RSG’s ., in: SEM Annu. Conf. Expo. Exp. Appl. Mech., 2005. [25]
G.A. Isaicu, X. Ding, G.L. Cloud, B.B. Raju, 3-D Experimental and Numerical Analyses of Single-
lap Bolted Joints in Thick Composites, in: SEM Annu. Conf. Expo. Exp. Appl. Mech., 2005. [26]
G. Restivo, G. Marannano, G. a Isaicu, Three-dimensional strain analysis of single-lap bolted joints
in thick composites using fibre-optic gauges and the finite-element method, J. Strain Anal. Eng. Des. 45 (2010) 523–534. doi:10.1243/03093247JSA599. [27]
J.A. Speck, Mechanical fastening, joining, and assembly, Marcel Dekker, 1997.
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displacement and strain measurement: a review, Meas. Sci. Technol. Meas. Sci. Technol. 20 (2009) 62001– 17. doi:10.1088/0957-0233/20/6/062001.
17
Figure Captions Figure 1: Composite plate dimensions. Figure 2: Meshing pattern (The parts do not have the same scale). Figure 3: The areas where contact elements were created. Figure 4: The characteristics of the bolt and washer used for modeling and experiments. Figure 5: Position of installed strain gages. Figure 6: The speckle pattern created around the washer. Figure 7: Bolt pretension vs elapsed time (T represents bolt clamping torque in lb-ft). Figure 8: Comparison of bolt tension relaxation between aluminum and glass/epoxy (Clamping torque is 90 lb-ft). Figure 9: Bolt tension vs clamping torque. Figure 10: Propagation of the tension force in the stud of the bolt. Figure 11: Strains obtained from gages at positions 1 to 6 (refer to Figure 5). Figure 12: Strains obtained from strain gages and ANSYS. (EXP: Gages experiments, ANS: ANSYS). Figure 13: Selected areas to compare ANSYS and DIC results. Figure 14: Strain in axial (fiber) direction between holes 1 and 2 (refer to Figure 13). Figure 15: Strain in transverse direction between holes 1 and 3(refer to Figure 13). Figure 16: Normalized strain in fiber direction (ࣅxx) along line “ab” (refer to Figure 13). Figure 17: Normalized strain transverse to fibers (ࣅyy) along line “cd” (refer to Figure 13). Figure 18: Normalized out of plane deformation (UZ) at top surface, along line “cd” (refer to Figure 13). Figure 19: Interlaminar Normal stress, SZ at X=0. Figure 20: Interlaminar Shear stress, SYZ at X=0.
18
Figures
Figure 1
Figure 2
Figure 3
19
Figure 4
Figure 5
Figure 6 20
12 T = 90 10 Tension force (Klbs.)
T = 70
T = 80
8 T = 60
T = 50 6 T = 30
4
T = 40
T = 25 2 0 0
200
400
600
800
1000
1200
1400
Elapsed time (s) Figure 7 12 11.6 Bolt tension (klbs.)
Glass/Epoxy 11.2
Aluminum
10.8 10.4 10 9.6 0
2000
4000
6000 Time (s) Figure 8
21
8000
10000
12000
12
Exp 1(Tmax=50 lb-ft)
Tension force (Klbs.)
10
Exp 2(Tmax= 70 lb-ft)
8
Exp 3(Tmax =90 lb-ft)
6 4 2 0 0
10
20
30
40 50 60 Clamping torque (lb-ft)
Figure 9
1 0.9 Bolt stud length (inch)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 8
10
12
14
16
18
Tension force (Klbs.) Figure 10
22
20
70
80
90
1200 G4
ሺ )
1000
800 G2 600
G1
400
G6
G5
200
G3
0 0
10
20
30 40 Clamping Torque (lb-ft)
50
60
70
Figure 11 600
1000
G1 EXP
G2 EXP
800
G1 ANS
450
G2 ANS
600
300
400 150
200
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
1200
160
G4 EXP G4 ANS
G3 EXP
120
900
G3 ANS
80
600
40
300
0
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
23
0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
600
400
G6 EXP
G5 EXP G5 ANS
320
450
G6 ANS
240 300 160 150
80
0
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
Figure 12
Figure 13
Figure 14
24
0
10
20 30 40 50 60 Clamping toque (lb-ft)
70
Figure 15 1.0 ANS
0.9
DIC
Normalized strain in axial direction
0.8 0.7 0.6 0.5 0.4 0.3 0
20
40 60 Distance percentage from "a" to "b" Figure 16
25
80
100
1 ANS
Normalized strain in transverse direction
0.8
DIC 0.6 0.4 0.2 0 -0.2 0
20
40 60 Distance percentage from "c" to "d"
80
100
Figure 17
Distance from hole center along line "cd" (inch)
Normalized deflection, Uz (inch/inch)
0.1 0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
-0.1
-0.3
-0.5
-0.7
Beneath the washer
Outer region
-0.9
-1.1
12 Layers UZ-12
40 Layers UZ-40
Figure 18
26
80 Layers UZ-80
0.70
0.75
-10
40 Layers
-11 -12 -13
12 Layers
-14 -15 0 Top surface
2 1
12 Layers
0 -1 -2
40 Layers
-3
80 Layers
-4 -5
10 20 30 40 50 Thickness percentage Middle (Y = 0.4 inch) plane
0 Top surface
10
12 Layers
0
40 Layers
-1 -2
80 Layers -3
0 Top surface
10
20 30 40 50 Thickness percentage Middle (Y = 0.65 inch) plane
Figure 19
27
20
30
Thickness percentage (Y = 0.53 inch)
1 Normal stress, SZ (ksi)
Normal stress, SZ (ksi)
-9
3
80 Layers Normal stress, SZ (ksi)
-8
40
50 Middle plane
0.9
0.5
0.1
80 Layers
40 Layers
80 Layers
2 1
40 Layers
0 12 Layers
-1
12 Layers
-0.3
-2 0 Top surface
10 20 30 40 50 Thickness percentage Middle (Y = 0.4 inch) plane
10
20 30 40 50 Thickness percentage Middle (Y = 0.53 inch) plane
1.1 Shear stress, SYZ (ksi)
0 Top surface
Shear stress, SYZ (ksi)
Shear stress, SYZ (ksi)
3
80 Layers 0.7 0.3 12 Layers
-0.1
40 Layers -0.5 0 Top surface
10
20 30 40 50 Middle Thickness percentage plane (Y = 0.65 inch)
Figure 20
28
Alireza Gorjipoor, Suong Van Hoa, Rajamohan Ganesan
PII: DOI: Reference:
S1270-9638(16)30848-3 http://dx.doi.org/10.1016/j.ast.2016.10.008 AESCTE 3794
To appear in:
Aerospace Science and Technology
Received date: Revised date: Accepted date:
7 July 2016 6 September 2016 10 October 2016
Please cite this article in press as: A. Gorjipoor et al., Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads, Aerosp. Sci. Technol. (2016), http://dx.doi.org/10.1016/j.ast.2016.10.008
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Numerical model for investigation of the strain distribution in thick composite plates subjected to bolt loads Alireza Gorjipoor a, Suong Van Hoa b, Rajamohan Ganesan c
Department of Mechanical Engineering, Concordia Center for Composites, Concordia University, Montreal, Canada, H3G1M8.
a
Corresponding Author: Alireza Gorjipoor, [email protected] b
[email protected], c [email protected]
1
Abstract In this study, strain distributions in a thick composite plate subjected to bolt loads have been investigated both numerically and experimentally. Recently, major industries such as aerospace, automobile and marine are interested in development of thick composites applications. One of these applications is the yoke of the helicopter, which connects main blades to the rotor hub using bolt joints. In the present work, a three dimensional finite element model of a thick composite plate subjected to bolt loads is created using ANSYS 14.5. Strains at the surface (around the washer) and along the laminate thickness have been measured using strain gages and Digital Image Correlation method, in order to verify simulation results. The model is used to investigate the effect of thickness on distributions of interlaminar stresses. Keywords: Thick composite laminate; Finite element analysis (FEA); Bolt loads; Digital Image Correlation.
2
1. Introduction High specific strength and high specific stiffness of composite materials make them an appropriate choice for many industrial applications. Designers and manufacturers are able to replace parts made of common materials like steel and aluminum with composite materials. The specific benefit of composite materials is their ability to be designed in a way to achieve specific material properties in a desired direction. So far, thin composite plates have been widely used in different industries. Therefore, design and analysis methods for thin composites have been widely developed [1,2] and several techniques have been invented by manufacturers to produce more complicated parts [3]. One of major applications of composite materials is in aerospace structures where weight reduction has been always the most challenging endeavor. Aerospace structures are always made up of several components which should be assembled using methods. Joint design has its own significance and complexity especially when composite materials are engaged in the structure. The most common method for composite parts assembly is mechanical fasteners. Bolt joint, which is considered as a type of mechanical fasteners, is more popular and practical since it is inspectable, repairable and undoable. Some of the applications of bolt joints in aerospace industry are such as wing to fuselage joint in Boeing/MDD Harrier, Boeing/Bell V-22 Osprey, Boeing 777 and Grumman X-29 (NASA) [4]. This study is motivated based on the application of thick composite laminates as the yoke of helicopter. Yoke is the part which connects main rotor blades to the hub. It is made of thick tapered composite laminate which is connected to the other parts of the system using bolt joints. Bolts are considered as the most vulnerable parts of the assembly. The failure of the yoke may cause the helicopter to stall. This paper focuses on introducing an effective model for the stress analysis of a thick composite plate subjected to bolt loads. The proposed model is a part of a holistic model which includes all major concepts in design process of the yoke such as bending loads and centrifugal forces. The holistic model will be utilized for failure prediction and fatigue analysis in design process to reduce the number of iterative costly experimental tests. The significant amount of transverse normal and shear stresses along thickness make stress analysis in thick laminates more complicated in comparison with thin laminates, where plane stress assumption is applicable in most study cases [5–7]. Two dimensional methods which have been developed so far are not suitable for prediction of structural behavior in thicker laminates, hence more advanced experimental and analytical methods have been utilized in the literature for stress analysis of thick composite plates [8]. In analytical approach finite element simulation was performed by using either brick elements provided by commercial software or the new elements introduced and developed by researchers [5,6,8–12]. For experimental investigation Digital Image Correlation method and strain gages were utilized to verify finite element simulation results [8]. For thick composites bolt joint is the most frequent assembly method [13]. Several researches have been performed in order to study the effect of bolt joints in composite structures [14]. Some researchers used two dimensional analysis [15]. However, it is shown by Ireman [16] that in the vicinity of the bolt hole, the field of stress is three dimensional and significant interlaminar stresses exist at the free edges. It was shown by 3
Ireman that the distribution of bolt-hole contact pressure is not uniform along the thickness of the composite plate. Therefore, three dimensional finite element analysis is critical when through the thickness effect of composite bolt joint is the study subject. More recently, finite element simulation and experimental tests were implemented in order to investigate the effect of different parameters such as washer size, clamping torque, bolt stiffness, friction coefficient, bolt-hole clearance, plate geometry and layers sequences on the stress and strain distribution in a composite bolt joint [17–20]. Progressive damage model was utilized to predict the failure initiation point and propagation pattern in composite bolt joint with different joint configurations and layer orientations [21–23]. However, the previous studies did not take into account composite laminates with higher thicknesses (more than 15 mm). Recently some studies focused on effect of bolt joints on thick composite structural behavior. In a study by Cloud et al. [24], strains beneath the washer were detected using Digital Speckle Pattern Interferometry (DSPI) method. In this work, to investigate strains beneath the washer, a transparent washer was manufactured from polycarbonate sheet. The polycarbonate washer was made with a thickness of about 4.3 times of a steel washer with the same inner and outer diameters, in order to provide the same stiffness. In another study by Isaicu et al. [25], embedded fiber optic strain gages and finite element simulation were utilized to find strain distributions in a thick composite bolt joint. A very rough estimation was utilized in this research, to convert the clamping torque to bolt preload. A study was done by G. Restivo et al. [26], in order to find through thickness stress distribution in a composite laminate connected to aluminum plate using single-lap bolt joint. In this study the preload was measured using a load cell transducer. In all three above studies a single-lap bolt joint was considered and joint is subjected to axial tension. However, studies on the effect of the bolt joint itself on a thick composite laminate are still lacking. What is studied in this paper is the first step in introducing a numerical model to predict failure behavior and fatigue life in the yoke of the helicopter considering all including aspects such as centrifugal forces, bending moments and clamping loads. The model was developed fully parametric to provide adequate design flexibility. In this first step, the principle goal is to introduce an effective three dimensional finite element model which is able to simulate the structural behavior of a thick composite plate subjected to bolt loads. In addition, two experimental approaches are implemented to validate the finite element simulation results.
4
2. Finite element simulation The dimensions of the modeled plate are illustrated in Figure 1. It is made of 80 layers of glass epoxy. Each layer has a thickness of 0.009 inch (0.23 mm), therefore total thickness of the plate is 0.72 inch (18.3mm). All layers are made of unidirectional prepregs provided by Cytec Engineered Materials company (product number: FX E773/S-2). Four holes were drilled at each side of the plate using diamond twist drills. The inner surface of holes was inspected visually to make sure that drilling process did not cause any damage at this area. The dimensions of the plate and the configuration of the holes are selected regarding the application of the structure as the yoke of helicopter. In order to study the effect of the bolt, a full three dimensional finite element model is created using finite element software ANSYS 14.5. The model is created fully parametric to make it suitable for sensitivity analysis which is the point of interest for future studies. Figure 1
All parts of the model were meshed using a specific solid element (Solid185) from the software element library. This element can be used to model both structural and layered solid parts. It has 8 nodes and three translation degrees of freedom at each node and can use both reduced and full integration methods. In order to define the layers thicknesses and orientations, a shell section was associated with the solid element. Since in this study the laminate is made of 80 unidirectional layers, a section consisting of 4 unidirectional layers was defined and 20 elements were created along the thickness. Material properties of glass epoxy, washer and bolt are defined according to the material library of the finite element software (ANSYS) and summarized in Table 1. Table 1: Material properties (extracted from ANSYS workbench 14.5 material library) Glass/Epoxy Plate
E1
E2 = E3
7.25 (Msi)
1.16 (Msi)
50 (GPa)
8 (GPa)
Technical
7-9 (Msi)
1-2 (Msi)
Data Sheet*
48-62 (GPa)
7-14 (GPa)
ANSYS
Washer Bolt Nut
v23
v12 = v13
0.4
0.3
-
-
G23
G12 = G13
0.56 (Msi)
0.73 (Msi)
3.8 (GPa)
5 (GPa)
-
-
Steel E
v
29 (Msi)
0.30
200 (GPa)
* www.cytec.com-CYCOM E773 Epoxy Prepreg Data Sheet (Page 4)
5
Figure 2 shows the mesh pattern created for each part. Similar mesh pattern and sizing were implemented in contact areas between washer, bolt and plate. The created mesh improves the accuracy of contact simulation between these parts and facilitates the convergence of nonlinear contact analysis. Elements TARGE170 and CONTA174 were created at the mentioned areas to model three dimensional contact. Figure 3 demonstrates contact definition at corresponding areas. Contact behavior between bolt head-washer, washer-plate and bolt stud-hole inner area were all defined as flexible surface-to-surface contact. Figure 2
Figure 3
Mesh sensitivity analysis was done in order to find the optimum mesh sizing. In this analysis, number of elements along the thickness remained constant and the meshing pattern on the surface of the plate was changed. The contact force between washer and plate was calculated and considered to perform mesh sensitivity analysis. A very simple static analysis of the bolt and washer shows that the contact force between washer and plate should be theoretically equal to the pretension force applied in the stud of the bolt. Table 2 summarizes the results obtained from three different meshing patterns (different number of elements). In all three cases of Table 2, the same preload (8700 lbs. or 38.7 KN) was applied to the bolt. As it is illustrated in Table 2 mesh pattern 2 improved the accuracy by about 60%, considering that the time of solving increased by 40%. Comparing patterns 2 and 3 shows that the running time increased about 5 times and the accuracy improved up to 47%. In addition by using mesh pattern 3, software did not show any warning or error about the aspect ratio of elements. Therefore it was decided to use mesh pattern 3. In this pattern elements sizes vary between 0.18 to 24.25 mm3 for the plate. Table 2: Mesh sensitivity analysis results Mesh
Total
Number of contact
Solving
Calculated
Difference between contact
pattern
elements
elements washer-plate
time
contact force
force and bolt preload
1
22880
80
5 min
8624
0.90%
2
41118
160
7 min
8670
0.35%
3
128084
320
40 min
8684
0.18%
The dimensions of the bolt and washer used in the simulation and experiments are shown in Figure 4. To reduce the complexity of the finite element model, the hexagonal shape of the bolt head and nut was replaced with a circle with the same area. The thickness of the nut and bolt head are both 0.35 inch and bolt and nut were glued to each other. The thickness of the washer was selected as the average of the range introduced by
6
the manufacturer. To model the tension force propagated in the stud of the bolt due to clamping torque, a pretension section was created at the axial middle section of the shaft of the bolt. The nodes of the pretension elements (PRETS179) are able to collapse into each other. Since the bolt is constrained at each side by the contact with washers, collapsing of pretension nodes into each other produces tension in whole length of the shaft of the bolt. Figure 4
To calculate the bolt preload due to clamping torque, a simple approximation introduced by Speck [27] was used. Based on the mentioned method, the load can be obtained using Equation 1, where T is clamping torque, D is thread pitch diameter and K is friction coefficient. During experimental tests, the bolt tension was measured by a load transducer installed in the shaft of the bolt. Also a calibrated torque meter was utilized to apply different clamping torques. The experiments results were utilized with Equation 1, to find the relation between the force and the torque for this type of joint. ܶ ൌ ܭൈ ܦൈ ܨ
Equation 1
7
3. Experimental investigation Verification of the finite element simulation accuracy was done using two experimental methods. First, strain gages were used to measure strain at critical points around the washer and along the thickness of the laminate. The gage measurements were compared with the results obtained from finite element model. Second, Digital Image Correlation method was used to find the strain field at the surface. For the first step, six Tee Rosettes (Vishay WK-06-030WT-120) were installed around the washer using M-Bond 200 Adhesive from MicroMeasurements Company. The gage sensitivity for this type of strain gage is 50×10-6 (50 micro) strain. The gages were positioned at the points where the maximum and minimum strains (along fibers and in transverse direction) were obtained from finite element analysis. Figure 5 shows the positions and orientations of the installed strain gages. Gages numbered 1, 3 and 5 (G1, G3 and G5) measured the strain in fiber direction and gages numbered 2, 4 and 6 (G2, G4 and G6) measured strain transverse to the fibers. Although the critical points were positioned at the edge of the washer according to analysis, during experimental investigation the gages were placed at a distance of 0.2 in (5 mm) from the edge to prevent gage damages. Hence, the radial distance of the center of G1 to G4 to the center of the hole was 0.825 in (21 mm). Center point of G5 and G6 were positioned at the middle thickness and along the central axis of the hole. To find the relation between applied torque and the tension force in the stud of the bolt, a special bolt equipped with a transducer gage installed in its shaft was utilized. The output of the transducer gage is helpful to modify the load calculation done in numerical analysis. Figure 5
Digital Image Correlation (DIC) method was utilized to find strain distribution pattern around the hole in upper surface. DIC is a practical tool for full-field in-plane strain investigation. The method is based on comparison between digital images taken before and after loading. The whole process consists of three main steps: 1) preparing the specimen and imaging setup, 2) capturing photos before and after load application and 3) image processing using computer. During the last step the computer tracks the different node displacements during loading and interpolates the displacement between these nodes to find the full displacement and strain fields [28]. To make the specimen ready for test it is required to make random black and white spots in order to provide trackable patterns for the image processing. As Figure 6 shows a speckle pattern was created on the desired surface using paint spray. Cameras with the resolution of 5 mega pixels were used to capture images. The resolution of images was 289855 dpi and the field of view was 3.1 inch ൈ 2.6 inch. Figure 6
8
4. Results 4.1.Bolt preload The bolt preload versus the elapsed time is shown in Figure 7. As it was expected the tension force was zero at the beginning because there was no clamping torque. As a clamping torque of 25 lb-ft was applied in the first step the tension force increased to 3.2 Klbs. During several steps the tension force increased when higher torque was applied. At the very first few seconds of each torque increasing step, the tension jumped to a high level but in a few seconds it released until reaching a steady value. This phenomenon is highlighted for clamping torque of 90 lb-ft in Figure 7. The mentioned tension reduction varied between 5% for 25 lb-ft of torque to 15 % at the clamping torque of 90 lb-ft. This behavior reveals the viscoelastic reaction of thick composite laminates when they are subjected to bolt clamping pressure. Right after applying a higher torque, the plate resists against deformation which causes higher tension to be produced in the bolt shaft. Then the contact pressure of washer pushes the material away in radial direction, therefore the material beneath the washer moves to the sides and resistance against washer will decrease. As a consequence the tension in the bolt shaft releases. Figure 7
Although the effect of the thickness and material properties on the viscoelastic behavior of thick composites requires further investigation (which is not the subject of the present study), a simple comparison between the sample made of 80 unidirectional layers of glass/epoxy and an aluminum plate with the same dimensions has been performed. Figure 8, compares the relaxation of the bolt tension between aluminum and composite plate at the clamping torque of 90 lb-ft. As it can be seen in Figure 8, for composite laminate higher tension was produced in the bolt while in case of aluminum plate, the tension relaxation occurred with a faster rate. The reduction in the force until reaching the steady value was 12.5 % for composite plate and 5.3% for the aluminum one. Figure 8
To find a single value for bolt tension at each clamping torque, the test was duplicated while the load was monitored continuously during the whole test process. When the load reached a steady value, that value was selected as the preload at the specific applied torque. Figure 9 illustrates the pretention force as a function of clamping torque in three experiments with different maximum clamping torques. As it is illustrated in Figure 9, the relation between torque and bolt preload is linear with a good approximation. Based on the results, the friction coefficient (refer to Equation 1) obtained from experiments is 0.197, 0.194 and 0.195 for three different test cases. The average of these values was used with Equation 1 to calculate bolt tension load at any clamping torque desired for finite element analysis. 9
Figure 9
Figure 10 illustrates the tension force propagation in the stud of the bolt obtained from ANSYS. As it is indicated the tension force due to clamping of the bolt has a sharp drop at both stud ends while it reaches an approximately uniform distribution in the middle section. In Figure 10, the dashed lines represent the position of the thickness of the washers at each side. It is obvious that between two washers the tension force does not have significant variation comparing to the top and bottom sections. For the analysis represented in Figure 10 the defined pretension was 8700 lbs. (38.7 KN) and the average of tension force obtained after analysis was 8635 lbs. (38.4 KN) which shows only 0.75% of difference. Figure 10
4.2.Strain gages Figure 11 represents the results obtained from strain gages at different clamping torques at positions 1 to 6 (refer to Figure 5). In Figure 11 and Figure 12 the amount of strain is represented in terms of micro strain (strain × 106). Results show that under a single bolt clamping force, strain in fiber direction at top surface was higher in G1 comparing to G3. Also, it is obvious that G4 has higher lateral strains in comparison with G2. In general, it could be concluded that lateral strains at the surface are higher compared to longitudinal strains. This was expected since the plate is unidirectional and the material is stiffer along fibers rather than transverse direction. G5 and G6 measured strains at the plate thickness. Because the loading (bolt force) is along the thickness of the plate and plate is unidirectional, the strain in thickness direction (G6) was higher compared to the longitudinal strain (G5). Considering the fact that no failure was observed up to the clamping torque of 70 lb-ft, a linear relation between strains and clamping torque was obtained. Figure 11
Figure 12 compares strains obtained from gages with ANSYS results at different clamping torques. For G1, maximum difference between experimental and finite element is 9% (35 micro strain) at clamping torque of 50 lb-ft. Hence the gages sensitivity was 50 micro strain, it can be said that ANSYS and experiment values correlate very well at this position. The same investigation for G2 reveals that the maximum difference is 9% (55 micro strains) at the torque of 70 lb-ft which also represents the good correlation between results at this position. For G3 the amount of strain was not considerable comparing to the other positions. Although the maximum difference is 35%, it is only 35 micro strains which is less than the gage sensitivity. For G4 and G6 the maximum difference is less than 5% (40 micro strains) and finally for G5, the difference is 20% (35 micro strains). All the results show that the maximum difference between strain gages and finite element analysis
10
was in the order of the gages sensitivity. This fact shows that the finite element model can predict the strain with good accuracy within the gage sensitivity. Figure 12
4.3.Digital image correlation (DIC) Comparing strains fields obtained from ANSYS simulation and DIC method reveals that the model is able to predict strains accurately in thick composite plates subjected to the clamping forces induced by the bolt. Results obtained from DIC showed that structure encountered a very small rigid body motion during the test, which caused discrepancies between deformations fields obtained from DIC and ANSYS. Since the strain is not affected by rigid body motion, the verification of the finite element analysis results were done based on the strain fields comparison. Here, strains obtained at clamping torque of 70 lb-ft are reviewed to show the achieved agreement between these two methods. Figure 13 represents the areas under consideration to compare ANSYS and DIC results. In this figure the dotted line represents the outer edge of the washer. Figure 14 illustrates the distribution of the strain in axial direction (along the fibers) at the top surface between holes number 1 and number 2. Distribution of the strain in transverse direction (perpendicular to the fibers) between holes number 1 and number 3 is shown in Figure 15. Comparison between strains distribution patterns obtained from ANSYS and DIC reveals that there is a good qualitative coordination between results. Figure 13 Figure 14 Figure 15
To compare the results quantitatively, strain along lines “ab” and “cd” (refer to Figure 13) have been extracted from both DIC and finite element simulation results. Figure 16 shows the distribution of strain in axial (along fibers) direction from point “a” to point “b” (refer to Figure 13). The amounts of strains obtained from both ANSYS and DIC were normalized according to the maximum strain obtained in this direction which wasͳʹͲͲ ൈ ͳͲି ݄݅݊ܿȀ݄݅݊ܿ. Also Figure 17 illustrates the distribution of the strain in transverse direction (perpendicular to fibers) from point “c” to point “d” (refer to Figure 13). Similar to axial strain the transverse strain was normalized using the maximum value which wasʹͳʹͲ ൈ ͳͲି ݄݅݊ܿȀ݄݅݊ܿ. It is obvious from Figure 16 and Figure 17, not only ANSYS model correlates qualitatively with DIC results but also there is a good match between the strains quantities obtained from these two analysis. Unfortunately the test setup did not provide enough space to install the camera close enough to the thickness side to perform DIC on the thickness. Figure 16 11
Figure 17
4.4.Thickness effect In order to demonstrate the effect of thickness on stress distribution in a composite plate under bolt load, three plates with different number of layers were considered. As it is indicated in finite element simulation section, the thickness of each layer is 0.009 inch (0.23 mm). Three numbers of layers 12, 40 and 80 were considered to investigate the effect of the plate thickness. For all analyses the material of the plate, unidirectional layers sequence, bolt and washer configurations and bolt preload remained constant. Table 3 shows the characteristics of selected plates. Table 3: Characteristics of plates considered for thickness effect investigation Number of unidirectional layers
Total thickness
Plate 1
12
0.108 in (2.74 mm)
Plate 2
40
0.36 in (9.145 mm)
Plate 3
80
0.72 in (18.29 mm)
Figure 18 shows the out of plane deformation (ܷ ) at top surface and along line “cd” (refer to Figure 13). In Figure 18, the dotted line represents the position of the edge of the washer. It can be observed that for plates with higher thickness the effect of the washer contact propagated over a larger area around the washer. In addition for the same preload in the bolt, the plate with higher thickness had higher deformation in the area beneath the washer as well as in outer region. The values of out of plane deformation (ܷ ) at the distance of 0.4 in (10.16 mm) from the hole center along line “cd” (refer to Figure 13) showed that Plate 3 deformation is 4.8 times higher than Plate 1 deformation. For all three plates the deformation changed linearly in the area beneath the washer except at regions close to the washer inner and outer edges. Since the inner diameter of washer is 0.53 inch while the hole diameter is 0.5 inch, the material at the vicinity of the hole edge is not in contact with washer and it can flip up. This phenomenon causes the nonlinear behavior which can be observed at the first points of all three graphs in Figure 18. Figure 18
As can be seen from Figure 18, the effect of washer load started to vanish at the point located on the washer outer edge (at the distance of 0.53 inch from the hole center). Therefore the edge of the washer was set as one of the critical reference points. Also two other points were selected to study the distribution of interlaminar normal and shear stresses along the thickness of the plate. The position of the mentioned points were selected in way to include the interlaminar stresses distribution investigation beneath, at the edge and in outer region of the washer. A coordinate system was defined to simplify results representation. The origin of the 12
coordinate system was placed at the center of the hole at the top surface, “X” was defined in fiber direction and “Y” was in transverse to the fibers. “Z” was considered along the thickness. According to the above coordinate system, the distribution of ܵ and ܵ at X=0 and Y= 0.4, 0.53 and 0.65 (in) through the thickness of the plate were investigated. Figure 19 presents the distribution of interlaminar normal stress (ܵ ሻ along the thickness at X=0 and Y= 0.4, 0.53 and 0.65 (inch). Since plates were unidirectional, the distribution of the stresses along thickness were symmetric. Therefore the stresses are plotted from top surface up to middle plane of the thickness. Figure 19 shows that for all three selected locations the variation of the normal stress along thickness is higher for plates with higher thicknesses. For the thinnest laminate (Plate 1) the normal stress (ܵ ሻ was almost constant at Y= 0.4 inch (beneath the washer) and the compressive stress was higher than the other two plates. At the edge of the washer (Y = 0.53 inch), Plate 2 and Plate 3 still have compressive stress along 80 to 90% of their thickness, while Plate 1 encountered tensile stress at all points. Finally, for the thinnest plate the effect of the bolt load does not propagate up to the point selected in outer region (Y = 0.65 in), while there is still a significant amount of compression at the same location inside thicker laminates. Figure 19
Figure 20 shows interlaminar shear stress ሺܵ ሻ distribution through the thickness. Comparison between plates revealed that higher interlaminar shear stress produced in plates with higher thicknesses. Similar to the normal stress, the variation of shear stress ሺܵ ሻ along thickness was much higher for the Plate 3 compared to Plate 1. This phenomenon was observed at all selected three different Y positions. Figure 20 indicates that at the outer region (Y=0.65 inch), the amount of interlaminar shear stress ሺܵ ሻ is relatively higher in thicker plates across the whole thickness (i.e. for plate with 80 layers at 20% of thickness the shear stress is 1 ksi). At this point (Y=0.65 inch) Plate 1 showed very small interlaminar shear stress (22 psi) which remained constant through the thickness. As it can be seen in Figure 20, the position through the thickness where maximum shear stress ሺܵ ሻ is occurred, varies with the plate thickness. Figure 20
13
5. Conclusion and discussion This paper proposes a full three dimensional finite element model to predict the strain in a thick unidirectional composite laminate subjected to a single bolt load. Two experimental approaches including strain gages and digital image correlation have been utilized to validate the model accuracy both qualitatively and quantitatively. It has been found that in case of unidirectional thick composite laminate subjected to clamping bolt forces, since the material is stiffer in axial direction (fiber direction), the axial deflection is less than transverse deflection. As a consequence the axial strain is less than transverse strain too. This behavior was observed in results obtained from both experimental and numerical studies. Results obtained from ANSYS and strain gages were in a close agreement at critical positions in axial and transverse directions. For the top surface the strain values and distributions obtained from DIC correlate well with both ANSYS simulation and strain gages. Experimental test results demonstrates that the developed finite element model is able to predict the structural behavior of a thick composite subjected to bolt loads, both in the magnitudes of strains and also the strain distribution pattern. The effect of number of layers was studied comparing plates with 12, 40 and 80 layers. Results showed that interlaminar stresses values and their variation along thickness for thick composites are more significant compared to thin laminates. In addition, for thicker plates the effect of bolt load propagates in a larger zone around the washer. Results showed that thickness has a significant influence on interlaminar stresses values and distributions. The holistic investigation of the thickness effect requires more detailed analysis which is the subject of the future studies.
14
Acknowledgement This research is conducted by financial supports of Natural Sciences and Engineering Research Council of Canada (NSERC), Ministère du Développement économique de l'Innovation et de l'Exportation (MDEIE), Le Consortium de recherche et d'innovation en aérospatiale au Québec (CRIAQ) and Bell Helicopter Textron Inc.
15
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Figure Captions Figure 1: Composite plate dimensions. Figure 2: Meshing pattern (The parts do not have the same scale). Figure 3: The areas where contact elements were created. Figure 4: The characteristics of the bolt and washer used for modeling and experiments. Figure 5: Position of installed strain gages. Figure 6: The speckle pattern created around the washer. Figure 7: Bolt pretension vs elapsed time (T represents bolt clamping torque in lb-ft). Figure 8: Comparison of bolt tension relaxation between aluminum and glass/epoxy (Clamping torque is 90 lb-ft). Figure 9: Bolt tension vs clamping torque. Figure 10: Propagation of the tension force in the stud of the bolt. Figure 11: Strains obtained from gages at positions 1 to 6 (refer to Figure 5). Figure 12: Strains obtained from strain gages and ANSYS. (EXP: Gages experiments, ANS: ANSYS). Figure 13: Selected areas to compare ANSYS and DIC results. Figure 14: Strain in axial (fiber) direction between holes 1 and 2 (refer to Figure 13). Figure 15: Strain in transverse direction between holes 1 and 3(refer to Figure 13). Figure 16: Normalized strain in fiber direction (ࣅxx) along line “ab” (refer to Figure 13). Figure 17: Normalized strain transverse to fibers (ࣅyy) along line “cd” (refer to Figure 13). Figure 18: Normalized out of plane deformation (UZ) at top surface, along line “cd” (refer to Figure 13). Figure 19: Interlaminar Normal stress, SZ at X=0. Figure 20: Interlaminar Shear stress, SYZ at X=0.
18
Figures
Figure 1
Figure 2
Figure 3
19
Figure 4
Figure 5
Figure 6 20
12 T = 90 10 Tension force (Klbs.)
T = 70
T = 80
8 T = 60
T = 50 6 T = 30
4
T = 40
T = 25 2 0 0
200
400
600
800
1000
1200
1400
Elapsed time (s) Figure 7 12 11.6 Bolt tension (klbs.)
Glass/Epoxy 11.2
Aluminum
10.8 10.4 10 9.6 0
2000
4000
6000 Time (s) Figure 8
21
8000
10000
12000
12
Exp 1(Tmax=50 lb-ft)
Tension force (Klbs.)
10
Exp 2(Tmax= 70 lb-ft)
8
Exp 3(Tmax =90 lb-ft)
6 4 2 0 0
10
20
30
40 50 60 Clamping torque (lb-ft)
Figure 9
1 0.9 Bolt stud length (inch)
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 8
10
12
14
16
18
Tension force (Klbs.) Figure 10
22
20
70
80
90
1200 G4
ሺ )
1000
800 G2 600
G1
400
G6
G5
200
G3
0 0
10
20
30 40 Clamping Torque (lb-ft)
50
60
70
Figure 11 600
1000
G1 EXP
G2 EXP
800
G1 ANS
450
G2 ANS
600
300
400 150
200
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
1200
160
G4 EXP G4 ANS
G3 EXP
120
900
G3 ANS
80
600
40
300
0
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
23
0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
600
400
G6 EXP
G5 EXP G5 ANS
320
450
G6 ANS
240 300 160 150
80
0
0 0
10
20 30 40 50 60 Clamping torque (lb-ft)
70
Figure 12
Figure 13
Figure 14
24
0
10
20 30 40 50 60 Clamping toque (lb-ft)
70
Figure 15 1.0 ANS
0.9
DIC
Normalized strain in axial direction
0.8 0.7 0.6 0.5 0.4 0.3 0
20
40 60 Distance percentage from "a" to "b" Figure 16
25
80
100
1 ANS
Normalized strain in transverse direction
0.8
DIC 0.6 0.4 0.2 0 -0.2 0
20
40 60 Distance percentage from "c" to "d"
80
100
Figure 17
Distance from hole center along line "cd" (inch)
Normalized deflection, Uz (inch/inch)
0.1 0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
-0.1
-0.3
-0.5
-0.7
Beneath the washer
Outer region
-0.9
-1.1
12 Layers UZ-12
40 Layers UZ-40
Figure 18
26
80 Layers UZ-80
0.70
0.75
-10
40 Layers
-11 -12 -13
12 Layers
-14 -15 0 Top surface
2 1
12 Layers
0 -1 -2
40 Layers
-3
80 Layers
-4 -5
10 20 30 40 50 Thickness percentage Middle (Y = 0.4 inch) plane
0 Top surface
10
12 Layers
0
40 Layers
-1 -2
80 Layers -3
0 Top surface
10
20 30 40 50 Thickness percentage Middle (Y = 0.65 inch) plane
Figure 19
27
20
30
Thickness percentage (Y = 0.53 inch)
1 Normal stress, SZ (ksi)
Normal stress, SZ (ksi)
-9
3
80 Layers Normal stress, SZ (ksi)
-8
40
50 Middle plane
0.9
0.5
0.1
80 Layers
40 Layers
80 Layers
2 1
40 Layers
0 12 Layers
-1
12 Layers
-0.3
-2 0 Top surface
10 20 30 40 50 Thickness percentage Middle (Y = 0.4 inch) plane
10
20 30 40 50 Thickness percentage Middle (Y = 0.53 inch) plane
1.1 Shear stress, SYZ (ksi)
0 Top surface
Shear stress, SYZ (ksi)
Shear stress, SYZ (ksi)
3
80 Layers 0.7 0.3 12 Layers
-0.1
40 Layers -0.5 0 Top surface
10
20 30 40 50 Middle Thickness percentage plane (Y = 0.65 inch)
Figure 20
28