Failure Analysis of Composite Bolted Joints in Tension

Transcription

1 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br>17th 4-7 May 2009, Palm Springs, California AIAA Failure Analysis of Composite Bolted Joints in Tension Ali Najafi*1, Mississippi State University, Mississippi State, MS, 39762, USA Mohit Garg and Frank Abdi3. 2 AlphaStar Corp., Long Beach, CA, 90804, USA The failure of preloaded cross-ply laminated composite has been studied through finite element simulation embedded in Progressive Failure Analysis (PFA). Two modeling strategies including low- and high-fidelity models have been considered for this investigation. The high-fidelity FE model consists of fixture components (bolts and washers). It has been shown that both low- and high-fidelity FE models are capable of predicting the experimentally observed failure modes of bolted joints that depends on the geometric parameters with reasonable accuracy. Two catastrophic failure loads, net-tension and shearout can be predicted using both low- and high-fidelity model while the failure load of bearing mode can only be predicted via high-fidelity model that considers the applied preload of the bolt. However, the overall stiffness in the actual experiment is lower than that of predicted via finite element simulation. A I. Introduction n important consideration in design of built-up structures is the method of assembly. When two structural members are connected together by means of mechanical attachments, the resulting joint strength 1,2 depends largely on the mechanical properties and failure characteristics of the joined materials and the pre-load induced via mechanical attachments. With the growing application of fiber-reinforced polymer composite materials in complex structural systems such as large transport airplanes, the behavior of bolted or fastened joints under different loading conditions have become an important design issue. Early works on the strength and stiffness properties of bolted joints can be found from and followed by many reserachers 4,5. A comprehensive review of the research and development of strength analysis of bolted joints can be found in Camanho and Matthews 6. The experimental study has been performed to investigate the effect of relative positioning of bolted joints on the bearing strength. 7 It has been concluded that the relative location can change the initial failure where as the ultimate failure load will not be affected. 7 Peirson 8, et al. performed a numerical and experimental analysis to investigate the stiffness properties of woven composite bolted joints. They used both linear material properties and nonlinear in-plane shear behavior to investigate the effect of clearance and contact angle between pin and material 8. They have shown that the clearance affected the total joint stiffness properties and failure load 7. However the effect of tightening preload has been disregarded. 8 Goswami 9 investigated the effect of thermal environment on the bearing stress of pined joint using shell elements. The effect of different failure criteria has been investigated and it is been shown that the failure load is sensitive to the damage and failure criteria. 9 Hassani et al. 10 develop a nonlinear material model for normal and shear stress-strain relation and studied a simple pin loaded composite. They have shown that using a nonlinear material model decreases the all the shear stress components while the value of normal stress perpendicular to the composite plane increases 10. Dano et al. 11 studied the effect of different criteria on the failure load prediction of bolted joints using progressive failure analysis based on two dimensional finite element analysis. They found that the calculated displacement to failure is very different from what is reported in the experiment due to the fixture deformation also the shear stress failure criteria 1 * Graduate Research Assistant, Dept. of Aerospace Eng. and Center for Advanced Vehicular Systems, Member AIAA. 2 Research Engineer, Member AIAA. 3 Principal Scientist, Member AIAA. 1 Copyright 2009 by Ali Najafi. Published by the, Inc., with permission.

2 cause the premature failure. 11 A comprehensive experimental and theoretical discussion on the bolt stiffness and failure behavior was performed with Vangrimde and Boukhili 12,13. One major problem in composite bolted joint is to identify the failure mode shapes of the bolted joint based on the geometric parameters that result into a reliable, efficient and optimized design for the composite joints. The focus of this paper is on the performance (failure) characteristics of bolted composite lap joints under axial tension considering tightening preload induced by the mechanical fixtures. The three dominant failure modes that can be encountered are net-tension, shear-out, and bearing, as shown in Fig. 1, although a combined failure mode is also possible. Whereas the net-tension and shear-out are considered as catastrophic failure resulting in total separation of the structural parts, the bearing mode creates a localized damage that is governed by the compressive strength of the composite material. Besides the loading condition, the specimen geometry including the hole location can also influence the joint failure mode. While the net-tension and shear-out failure modes can be avoided through proper geometric modifications, the bearing damage may not. Figure 1: Basic failure modes in composite bolted joint 14 Following a concise identification of the failure mechanism of composite bolted joints 15, progressive failure analysis (PFA) offers a viable approach for prediction of failure load 16 in composite structures. In this study, the PFA of composite bolted lap joints is performed through the finite element analysis (FEA) of the loaded specimen using the GENOA software 11. The objective is to capture the failure mode, load, and displacement field (which can be described by joint stiffness as well). For this, two modeling strategies have been considered: one using a low-fidelity model to capture the failure mode and load, and the other using a high-fidelity simulation of the boundary value problem as encountered in the physical experiments of such bolted joints (Fig. 2). The high-fidelity model also contains additional information about the contact surfaces as well as the bolt-hole fit, which yields a more accurate prediction of failure load and associated mode. Figure 2 (a) Low-fidelity model and (b) high-fidelity model II. Specimen Description The geometry and loading condition of a bolted specimen is shown in Fig. 3. The glass-epoxy (E-glass/Epoxy CY225/HY225) specimen is modeled as a rectangular symmetric cross-ply ([0/90] s ) laminate of thickness t, width W, and length E+L with a circular hole of diameter D located at distance E from the left edge 17. The specimen geometry and properties are selected to match those in a previous experimental study 17. The material properties are listed in Table. 1. In order to capture different failure modes, nominal fixed values are chosen for D=5mm, t=1.6mm and L=70mm while dimensions W and E are allowed to change. The bolt is located at the center of the hole and a uniform tensile load P is applied to the specimen. The load is parallel to the specimen and is symmetric with respect to the center line. Distance-to-diameter (E/D) and width-todiameter (W/D) ratios are changed to study the effects on the failure mode. Figure 3: Geometry and loading of the specimen 17. 2

3 III. Modeling methodology Figure.4 shows the experimental setup for the bolted joint test. Based on the experimental set up, and in order to assess the deformation of the joint at through the interaction between the bolt and specimen, two different three-dimensional FE models are developed. Because of symmetry, only one half of the assembly is modeled in each case using 8 node solid elements 19. In the low-fidelity model, the contact among the different parts is captured through two contact surfaces (on the bolt and the hole) with each having a coefficient of static friction of 0.1. In this model, there is no clearance between the circular bolt and the circular hole. The bolt is held fixed while an axial tensile load is applied as a uniformly incremental displacement on one end of the specimen (Fig. 2-a). The high-fidelity model is set up according to the actual physical experiment (Fig. 4) including all the fixture assemblies (Fig. 2-b) to capture the boundary conditions in the experiment. The actual fixture has not been modeled in the high-fidelity model and for this; the edge of the bottom washer hole is fixed in all translational directions. In this model, six finite sliding 19 contact surfaces are defined: 1) contact between the top and bottom surfaces of the laminate with the top and bottom washers (two surfaces), 2) contact between the bolt head and the upper washer (one surface), 3) contact between the cylindrical surface of the bolt and that of the laminate (one surface), and 4) contact between the cylindrical surface of the bolt and that of each washer (two surfaces). The models were subjected to end displacement as per the experiment setup. In order to model the pre-load in the high-fidelity model, an equivalent force is applied at the end of the bolt which squeezes the specimen through its thickness. In each load increment GENOA 18 runs one finite element simulation using ABAQUS 19 as an FE solver for stresses and strains in the FE model.. GENOA takes the stress and strain information at each iteration and evaluates the composite plies for any damage model. It then updates the stiffness of the damaged plies and leaves the original material properties for the undamaged plies and submits the updated model to ABAQUS FE solver again. The load increment in GENOA is controlled by the number of damaged elements such that the number of damaged element and removed element cannot reach beyond four and two elements respectively 18. Upon violation of these criteria, the equilibrium cannot be achieved. In this case, the load increment will be decreased to achieve the equilibrium. A new finite element model will be created in GENOA to solve the model at the presence of the new damaged/removed element that is called stress redistribution. Total Lagrangian scheme has been used for this analysis that updates the geometry of the model in each iteration. 18 Each ply is defined separately in the high-fidelity model. This can help to get realistic results in probable asymmetric deformation due to hole and washer clearances. The clearance between specimen hole and washer hole with bolt is defined 0.01mm and Table 1: Mechanical properties of material 17. Longitudinal elastic modulus, E1 (MPa) 45,100 Transverse elastic modulus, E2 (MPa) 14,400 In-plane shear modulus, G12 (MPa) 2550 Poisson ratio in 12 direction 0.25 Longitudinal tensile and compressive strength(mpa) 687 Transverse tensile strength (MPa) 65 Transverse compressive strength (MPa) 146 Shear strength (MPa) 55 Fiber volume fraction (%) 55 Figure 4 Test setup of bolted joint [17] Table.2 Damage criteria used in the PFA analysis of bolted joints 18 Mode Name Longitudinal Tensile S11T Longitudinal Compressive S11C Transverse Tensile S22T Transverse Compressive S22C Normal Tensile S33T Normal Compressive S33C In-plane Shear S12 Transverse out of plane shear S23 Longitudinal out of plane shear Fiber relative rotation RROT Modified distortion energy MDE 11 3 S13

4 0.001mm, respectively where all of these components are concentric. The damage criteria that are used in this analysis are listed in table.2. The longitudinal, transverse and normal directions represent the directions along, transverse and normal to the fibers in each ply. The damage criteria has been assigned to degrade the ply stiffness to 1%, 20% and 15% for tensile, compressive and shear of the original values. It means that the tensile damage assumed to be catastrophic while in the compression and shear loading there is residual stiffness in the material which can carry more load. Once all the plies have failed in one element, it can be chosen to be removed from the FE model. In this study, the element removal criteria is activated only for tensile damage criteria in all directions (longitudinal, Transverse and normal). IV. Results The failure mode shapes in the low-fidelity versus high-fidelity models and experiment have been shown in Fig.5. The red region represents the damaged plies that are taken place in the elements. Once all the plies in an element are Experiment 17 High-fidelity model Low-fidelity model 4 Figure 5 Basic failure American modes Institute from low- of Aeronautics and high-fidelity and Astronautics GENOA-PFA and experiment 17

5 damaged the element will be either removed or degraded by a knockdown factor. The critical criteria in this analysis are chosen to be tensile in all directions. The location of the removed element represents the failure mode shape. The low-fidelity model can approximately capture the localized behavior of failure mode shape. Where as in the high fidelity model the localized area are clearly captured. As the washer-lug contact is effective under preload in the high fidelity model, the net-pure tension mode shape is appeared more dominantly than the low fidelity model. Because of the fact that there are no element removal criteria for the shear in the element, the only way for element to remove is through the tensile modes. So the pure shear-out mode cannot easily be captured in the high fidelity model. It is followed by localized region similar to the net tension mode shape that may be treated as mixed mode shape but the shear-out seems to be more dominant since all the elements in the region have failed. An actual shearout mode shape is predicted in the low fidelity model shows. Catastrophic failure mode can be avoided as the distances of the hole to the edge increase. This mode shape considered as bearing mode shape. The main feature of bearing mode shape in the bolted joint is that the localized damage region is located in a small area around the hole. The localized area cannot easily develop due to the existence of contact surfaces between bolt assembly components. Fig. 5 shows that the damage area is more confined around the hole. Both modeling strategies can capture the observed failure mode; however, the ultimate load predicted in the low-fidelity model is much lower than that of high-fidelity model that is addressed later in this section. In order to assess the damage propagation, the half model is divided into three separate regions as depicted in Fig.6. For the net-tension mode in low-fidelity model, the damage starts due to the in-plane shear stresses in all four layers in region II (Fig.7). The in-plane shear damage develops in the joint until the axial force of 356kN causes the transverse tensile stresses in two mid-layers (90 degree layers) located in region III to reach their critical value. The in-plane shear in all layers and transverse tensile damages in two mid-plies expands by increasing the load Region I Region II Region III Figure 6: Breakdown of the domain for damage mechanism identification in region II up to 690kN where the tensile stress in the external layers (0 degree layers) of the region III meets its strength and starts to damage in which the first total failure-reported ultimate load- of the laminate is occurred and (a) Figure. 7: The damage state in low-fidelity starts with (a) in-plane shear in region I & II (b) transverse tensile mode in region II & III the element removed from the model. This point represents the maximum load reported as the strength of the joint. The final accumulated damage distribution at the end of simulation is shown in Fig.5. In the high-fidelity model, the damage initiates with the transverse tensile damage of mid-layers in region III. Transverse tensile damage expands in the region III till the in-plane shear damage of plies in region II starts to grow (Fig.8). The in-plane shear damage dominates the damage area in region I and II until load reaches 850 kn and the two outer plies (0 degree plies) totally fail due to the longitudinal tensile stresses in region III. The load drops to 600kN to achieve the equilibrium of incrementally applied displacement. This mechanism is extended up to a point (b) 5

6 that the outer plies in region III failed and corresponding elements are removed again due to the specified catastrophic damage (longitudinal tensile). The final failed shape of the joint is illustrated in Fig.5 where it shows a pure net-tension failure mode. (a) Figure. 8: The damage state in high-fidelity starts with (a) transverse tensile mode in region II & III (b) in-plane shear in region I & II The damage growth in other modes including shear-out and bearing is also follows the mechanism described above. The high fidelity model in shear-out mode shows that the failure and element removal started from region III where is identified as the failure of the net-tension mode shape. However, compare to the net-tension mode, the stress distribution in region II starts to grow faster such that the elements are removed because of the smaller ligament (E) and wider width(w) where shows the shear-out mode shape. This failure mode seems to be more pure in low-fidelity model (Fig.5). PFA initiates removal of the elements when all the plies in those elements are damaged due to some failure criteria listed in Table.2. In the low-fidelity FE models, the element removal initiates immediately after the peak load. Further incremental displacement beyond the peak load point does not increase the load since the damage area grows during the simulation, as shown in Fig. 5. On the contrary, in the high fidelity high-fidelity FE model the presence of the fixture components and tightening preload hinders the removal of elements. Fig. 9 (white color bars) illustrates the maximum load in test and PFA simulation based on the low-fidelity and high fidelity model in different geometries. The simulation results are within 7 to 8 percent lower than experimental results in catastrophic failure cases (net tension and shear out failure mode). However, in the bearing failure mode, this difference between loads in the low-fidelity model increases to 25%. The major source of variation in the load prediction validation is coming from the variation in contact area under the washer in different geometries. The contact areas between washers and specimen, in the bearing failure mode case, are much larger than the other configurations. This helps the joint to be able to carry higher load. As mentioned above the area of the damaged element is more localized around the hole. The Figure 9 Maximum load results distance of damaged area from the joint edge provides more potential to carry load. The predicted load in the high-fidelity FE models is much closer to the experimental (b) 6

7 results (gray color bars in Fig. 9). The difference between the predicted ultimate failure load between experiment (blue color bars in Fig. 9) and high-fidelity model is 10%. Based on the experimental results, the load displacement behavior of the bolted joint in experiment can be divided into three parts; loosing part which has concave force-displacement curve and represents the amount of forces and displacements requires to put all the components of assembly in their place and provide the static equilibrium such that the load can be transferred to all the assembly components, sliding part which represents the interaction between contact surfaces and, bearing part that is coming from the loads that are directly transferred through the cylindrical surface of the bolt to the specimen. The load displacement behavior of the specimen with E/D=1 and W/D=2 which represents the net tension failure mode is illustrated in Fig.10. The difference between two slopes is because of the contact between assembly components. Once the load reaches a value which the load can be transferred directly to the specimen, the PFA simulation and test follow the same slopes. Since low-fidelity model does not contain the detail assembly and boundary conditions of experimental setup, the slopes in the load-displacement curve is not comparable with the test. The main source of this discrepancy comes from the assumption of linear material. The nonlinearity of matrix can highly improve the bearing region of load displacement curve. The results of high-fidelity model are show in Fig.10 as well. The load displacement behavior can be divided to three distinct parts. Including; loosing, sliding and bearing. The key factor in the loosing region is the preload which can change the slope in this region. The sliding part can be changed by friction between contact surfaces. The bearing part cannot be easily achieved since three major nonlinearity from the matrix, material degradation due to damage and contacts along with the possible loosing of the joint are existed. However, the trend of the load displacement curve captured through the high -fidelity model. One major difference between the experimental results and simulation is the stiffness of the joint resulting from the load displacement curve. One of the most important source for this discrepancy is the nonlinear material behavior of the matrix. Matrix nonlinear behavior affects the stiffness significantly especially in case of shear and transverse behavior deformation. V. Conclusions Figure 10 Load displacement behavior of bolted joint in net-tension failure mode E/D=1 W/D=2 In this paper, the failure behavior of bolted joints including failure mode, failure load and joint stiffness has been studied and compared with the experimental results. It is seen that the Bolted joint analysis faces several computational challenges including; nonlinearity of material due to damage and failure, contact and surface interaction in the experimental assembly and preload conditions. Also load-displacement behavior of the bolted joints depends on local parameters (hole clearances, friction coefficient, contact area, matrix compression hardening after damage) of the bolted joint assembly which will affect the result of displacement prediction as well. Progressive failure analysis complementing non-linear FE analysis results in enhancement of maximum load prediction, failure mode and load displacement behavior of the bolted joints. Based on the high- and low-fidelity modeling strategy, the performance of bolted joints under standard failure mode shapes studied. The net-tension mode shape can be captured with high-fidelity model. While the shear-out mode shape in the high-fidelity model mixed with net tension mode. However the shear-out mode shape can be capture with low-fidelity model. It is worth mentioning that the net tension mode shape in the preloaded joints usually observed as mixed mode where both nettension and shear-out are appeared because of the presence of the contact interface region. Although the ultimate failure mechanisms in both low- and high-fidelity model are due to the catastrophic mode known as longitudinal tensile, the damage initiation is different. The low-fidelity model starts with in-plane shear where as damage in the high-fidelity model begins with transverse tensile. 7

8 The ultimate failure load in the net-tension and shear-out mode shapes was described by the low fidelity model. Based on the high fidelity model, three distinct regions in the load displacement curve was observed including loosing part that the load can be transferred to all the assembly components, sliding part which represents the interaction between contact surfaces and, bearing part that is coming from the loads that are directly transferred through the cylindrical surface of the bolt to the specimen. Acknowledgements The authors are grateful to Prof. Masoud Rais-Rohani for discussions and comments on this study. Partial funding provided for this study by the US Department of Energy under Grant No. DE-FC26-06NT42755 is also gratefully acknowledged. References 1 Choi, J.H., Chun Y.J., Failure Load Prediction of Mechanically Fastened Composite Joints, Journal of Composite Materials, Vol. 37, No.24, 2003, pp Tserpesa, K.I., Labeasb, G., Papanikosb, P., Kermanidisa, Th., Strength prediction of bolted joints in graphite/epoxy composite laminates, Composites: Part B, Vol. 33, 2002, pp Whitney, J.M., Nuismer, R.J., Stress Fracture Criteria for Laminated Composites Containing Stress Concentrations, Journal of Composite Materials, Vol. 8, No.3, 1974, pp Chang, F.K., R.A., Scott, Springer, G.S., Strength of Mechanically Fastened Composite Joints. Journal of Composite Materials, Vol. 16, No.6, 1982, pp Hiroyuki Hamada Zen-Ichiro Maekawa Kazushi Haruna, Strength Prediction of Mechanically Fastened Quasi-Isotropic Carbon/Epoxy Joints, Journal of Composite Materials, Vol. 30, No.14, 1996, pp Camanho, P.P., Matthews F.L., Stress analysis and Strength prediction of mechanically fastened joints in FRP: a review., Composites: Part t A, Vol. 28, 1997, pp Tong, L., Bearing failure of composite bolted joints with non-uniform bolt-to-washer clearance, Composites: Part A, Vol. 31, 2000, pp Pierson, F., Cerisier, F. and Grediac, M., A Numerical and Experimental Study of Woven Composite Pin-joints, Journal of Composite Materials, Vol.34, 2000, pp Goswami, S., A Finite Element Investigation on Progressive Failure Analysis of Composite Bolted Joints Under Thermal Environment, Journal of Reinforced Plastics and Composites, Vol. 24, No.2, 2005, pp Hassani, F., Shokrieh, M. M., Lessard, L., A fully non-linear 3-D constitutive relationship for the stress analysis of a pinloaded composite laminate Composites Science and Technology Vol. 62, 2002, pp Dano, M.L., Kamal, E., Gendron, G., Analysis of bolted joints in composite laminates: Strains and bearing stiffness predictions, Composite Structures, Vol.79, 2007, pp Vangrimde, B. and Boukhili, R., Analysis of the bearing response test for polymer matrix composite laminates: bearing stiffness measurement and simulation, Composite Structures, Vol. 56, 2002, pp Vangrimde, B. and Boukhili, R., Descriptive relationships between bearing response and macroscopic damage in GRP bolted joints, Composites: Part B, Vol.34, 2003, pp Murat, B.,,Karakuzu, R., Progressive failure analysis of pin-loaded carbon epoxy woven composite plates, Composites Science and Technology, Vol. 62, 2002, pp Camanho, P.P., Bowron, S., Matthews, F.L., Failure Mechanisms in Bolted CFRP, Journal of Reinforced Plastics and Composites, Vol.17, No.3, 1998, pp Camanho, P.P., Matthews, F.L., A Progressive Damage Model for Mechanically Fastened Joints in Composite Laminates Journal of Composite Materials, Vol. 33, No.24, 1999, pp Sayman, O., Siyahkoc, R., Sen, F. and Ozcan, R., Experimental Determination of Bearing Strength in Fiber Reinforced Laminated Composite Bolted Joints under Preload, Journal of Reinforced Plastics and Composites, Vol. 26, No.10, 2007, pp Abdi F., GENOA4.3 Volume.1 User Manual, 2008, Alpha STAR Corp., USA 19 ABAQUS/Standard version 6.2, user s manual., 2003, Hibbit, Karlsson and Sorensen Inc., Rhode Island, USA 8