IMPROVED SIF CALCULATION IN RIVETED PANEL TYPE STRUCTURES USING NUMERICAL SIMULATION

Transcription

1 26 th ICAF Symposium Montréal, 1 3 June 2011 IMPROVED SIF CALCULATION IN RIVETED PANEL TYPE STRUCTURES USING NUMERICAL SIMULATION S.C. Mellings 1, J.M.W. Baynham 1 and T.J. Curtin 2 1 C.M.BEASY, Southampton, England 2 C.M.BEASY, Boston, USA Abstract: As damage tolerance methods continue to evolve it has become possible to evaluate the interaction of riveted connections on the predicted SIF values in airframe structures. This current work is focused on the prediction of SIF values and crack growth paths in riveted structural members subject to complex loading, taking into account the influence of contact loading in the rivet hole, by-pass loading and changes to the load path which occur when a growing crack causes a rivet to completely cease transferring load. The SIF calculation and simulated crack growth trajectory are performed using a boundary element based fatigue and crack growth toolset. Newly developed modelling tools and analysis capabilities are applied to demonstrate how load transfer between different structural members may influence the calculated SIF values and crack growth direction. The results from analysis of different airframe type models are presented. The first study examines the effects of changing the rivet geometry, using perfect fit rivets, clearance fit rivets and push fit rivets, and determining the effect on SIF values calculated for a half-penny shaped crack. A second study looks at load transfer between more complex riveted components, including effects of the significant load redistribution which occurs when a rivet is lost as a result of ligament failure.

2 2 S.C.Mellings INTRODUCTION Many aerospace structures are fabricated using mechanically fastened joints. In order to perform an accurate damage tolerance analysis of a multi-fastener connection it is important to understand how the combined effect of bearing loads and loads that bypass the hole can impact the behaviour of a crack. In most applications there is some degree of clearance between the hole and fastener. This clearance affects the contact area at the fastener-hole interface in a nonlinear manner and influences the stress state around the hole. In order to accurately analyze this behaviour an iterative contact analysis is required. If friction within the fastener hole is considered then the way in which the load is applied also becomes quite important due to the load path dependency associated with frictional contact analysis. The following discussion describes the use of the BEASY Fatigue and Crack Growth software to investigate the damage tolerant behaviour of a mechanically fastened airframe structure. In the first example a simple lap joint example is shown where different contact connection types are represented using different BEASY contact conditions. In the second example, a more detailed connection joint is represented. METHODOLOGY In this paper, the analysis uses the Boundary Element Method rather than the usual finite element method to analyse the behaviour of the structures involved. The Boundary Element Method (BEM) has significant advantages for the modelling of fracture and is also ideally suited for the analysis of multi-body contact. In fracture analysis, the crack is a new surface that is part of the structure and as the crack grows this surface changes and evolves. In the BEM analysis of cracks [2-7], only the surface of the crack itself needs to be modelled. As the crack grows the surface mesh on the crack and the surrounding area is modified, representing the growth of the crack. The simplicity of the boundary element mesh required to represent behaviour of cracks is a major advantage when using BEM for fracture analysis. The method allows very refined meshing near the crack front without any difficulty at all. By contrast FE meshes often suffer from the unwanted side-effect that the refinement tends to propagate through the volume of the structure. The simplicity provided by the BEM can especially be appreciated during the growth of a crack, since the only parts of the model that are affected are the surface mesh on the crack and the mesh on the immediately adjacent surfaces. In the examples presented in this paper, multi-body contact analysis is also included. This type of analysis is also ideal suited to the BEM methodology as contact simulations require information about the surface behaviour of the model. In boundary element analysis, the displacements and stresses are computed directly on the surface with no need to extrapolate from internal results. Some other

3 Improved SIF calculation in riveted panel type structures using numerical simulation 3 methods derive stresses by differentiation of displacement, and often calculate results at Gauss points inside the volume, thereafter extrapolating to the surface. It is well known that differentiation tends to dilute accuracy, reducing the accuracy for the contact simulation. In the examples presented here the BEASY Fatigue and Crack Growth software is used to model and analyse the structures. All computed stress and SIF results are provided using this software. Model description LAP JOINT MODEL In the first example a simple lap joint model has been defined as show in Figure 1. This structure has two flat plates connected by 4 connecting pins. The lower plate is restrained, whilst the upper plate has a traction load applied. Figure 1 Simple lap joint geometry The two plates are connected by slider elements on the shared interface. Pins are used to join the plates together and contact conditions are applied at each of the pin-panel connections. In this model the contact connections are defined using conforming contact this means that the pins are modelled to fit exactly into the holes in each panel. This type of contact allows users to select the exact contact behaviour at each interface. In the analysis 3 different initial contact conditions have been considered as follows: Perfect fit pins: Here the pins are represented with a perfect fit to the panels. This is represented with an initial gap of zero in the model Interference fit pins: Here the pins are assumed to be a push fit so that there is an initial pre-stress in the holes. This is represented with a negative initial gap. Clearance fit pins in one zone: Here the connection between the pins and the restrained plate are modelled with a clearance fit, while those in the loaded plate are represented with a perfect fit.

4 4 S.C.Mellings Initial crack added to model The model has a single half-penny shaped crack positioned on the side of one of the interface holes at the point with peak maximum principal stress value. The crack has been added into the lower, restrained plate as shown in Figure 2, which also shows contours of stress. Figure 2 Stresses around half-penny-shaped crack in bore of rivet hole in the lap joint assembly Stress intensity factors caused by the three different contact conditions The SIFs are computed directly from the stresses and displacements in the BEM analysis by using a decomposition of the J-Integral, to give the three required SIF values [8-9]. Variation along the crack front of the mode 1, 2 and 3 stress intensity factors for the three different contact assumptions are shown in Figures 3 to 5. Figure 3 Variation along the crack front of Mode 1 Stress Intensity Factor (K1) for different assumed rivet sizes

5 Improved SIF calculation in riveted panel type structures using numerical simulation 5 Figure 4 Variation along the crack front of Mode 2 Stress Intensity Factor (K2) for different assumed rivet sizes Figure 5 Variation along the crack front of Mode 3 Stress Intensity Factor (K3) for different assumed rivet sizes

6 6 S.C.Mellings BEAM FASTENER MODEL Model description The component geometry shown in Figure 6 consists of a beam cap fastened by rivets to a lower panel and vertical web. Figure 6 Mechanically fastened structural panel geometry A simulation model was created using a short section (3.2 inch) of this geometry to represent the load interaction between the various mechanically fastened components when load is transferred from the beam cap to the lower panel and vertical web. Cracks of different size were inserted into the model and stress intensity factor (SIF) solutions were obtained. This approach offers significant advantage in terms of accuracy compared to current handbook based solutions. Loading and Boundary Conditions The model shown in Figure 7 is a boundary element surface mesh. Only 7500 elements were required to accurately model the three structural plates and 12 rivets. A perfect fit (i.e. no initial gap) and frictionless contact boundary conditions were applied at all rivet locations. Rivet contact boundary condition were applied under the rivet heads and along the shank of the rivet. Applying contact boundary conditions to all the rivet surfaces was numerically more intensive than for example the methods used in the study by Evans [1] but provides a different insight into the actual load transfer mechanisms active in this particular structural assembly. A rivet pre-stress was not applied in this modelling exercise although it could easily be implemented through a simple change in the contact gap parameter applied under the rivet head. A slider boundary condition (allowing in-plane displacement without any transfer of shear stress) was applied on the contacting regions between the beam-lower panel and beam-vertical web surfaces. This is a numerically more efficient

7 Improved SIF calculation in riveted panel type structures using numerical simulation 7 approach compared to an iterative contact solution and may be appropriate when in-plane loading is the dominant mode of stress transfer. Figure 7 BEASY Model Geometry Showing Loading and Restraint A traction of 10,900 psi is applied to one end of the beam cap as shown in Figure 7. The panel/web sections are restrained at the other end to prevent axial displacement. Additional restraints, provided to prevent rigid body motion, are not shown in the figure. Rivet Loading Load transfer through the rivets from the beam to the panel (and similarly to the web) is automatically taken care of in the model, including redistribution of load as the crack grows. However, it is assumed that when a ligament fails the local rivet will no longer transfer load, and the rivet is therefore removed from the model. The by-pass loading ratio occurring in the model is the real value, which corresponds to the geometry, loading, and crack location and size. It would of course be possible to model a single panel and to load it with both remote traction and rivet pin loads, to determine effects of specific by-pass ratios, but that process is not covered in this paper. Crack location The various cracks assumed in the beam cap are in the plane of the rivets shown in red in Figures 8 and 9. The first of these figures shows the rivets (in the plane of the crack) which are transferring load in crack cases 1 and 2, while the second shows those which are transferring load in crack cases 3 and 4.

8 8 S.C.Mellings Figure 8 Rivets in the plane of the crack which are assumed to be transferring load for Crack Cases 1 & 2 (4 rivets active in cross section) Figure 9 Rivets in the plane of the crack which are assumed to be transferring load for Crack Cases 3 & 4 (3 rivets active in cross section)

9 Improved SIF calculation in riveted panel type structures using numerical simulation 9 Crack Case Scenarios and SIF Solutions Four different crack sizes were studied ranging from a 0.1 inch radius corner crack to a 0.6 inch through crack with an adjoining failed ligament (Figure 10). A rivet was removed from the model once a crack grew to a size large enough to completely fracture a ligament in the beam. The coupled contact and SIF solution method used improved the understanding of the impact of load redistribution on SIF values as crack lengths were increased in size. Figure 10 Different Crack Cases Investigated A plot of the stress intensity factor solutions (K I ) along the crack front is shown in Figure 11. The plot in Figure 11 indicates the magnitude of K I increases as the initial corner crack (Crack Case 1) grows to the point of becoming a through crack (Crack Case 2). However once the remaining ligament in the beam fails and a secondary corner crack initiates (Crack Case 3) there is a reduction in the magnitude of K I. The corresponding break in the beam ligament at this location also results in a redistribution of load. It can be seen from Figure 12 that the rivet holes closest to the beam connection with the lower panel experience an increase in stress whereas the upper row of rivets perpendicular to the crack surface show a corresponding decrease in stress. As this secondary corner crack then continues to grow eventually becoming a large through crack (Crack Case 4) there is another phase of increasing K I as this crack front approaches a second highly stressed rivet hole in the beam.

10 10 S.C.Mellings Crack Case 1 Crack Case 2 Crack Case 3 Crack Case 4 Figure 11 SIF Solutions for Crack Cases 1-4 Crack Case 1 PSI Crack Case 2 Crack Case 3 Crack Case 4 Figure 12 Change in Maximum Principal Stress on Beam for Different Crack Cases Benefits of BEASY SIF Solution Method The coupled contact and SIF solution methodology used in this work automatically accounts for the interrelationship between the contact stress state and increasing component compliance caused by an opening crack. This capability provides an

11 Improved SIF calculation in riveted panel type structures using numerical simulation 11 added degree of accuracy in terms of analyzing mechanically fastened plates since the presence of a crack at the edge of contact may alter the contact solution. It is likely that the compliance of the component will change once a crack begins to open and propagate and this will impact the contact length and contact stress state (i.e. pressure and shear traction). This effect is not accounted for using simplified fracture mechanics approaches such as generalized weight functions or the method of distributed displacement discontinuities. Previous work by the authors also suggests that friction can dramatically influence the crack growth life estimates. Although this analysis assumed frictionless contact the modelling method used could be easily adapted to investigate the impact of frictional loading in the rivet holes. REFERENCES [1] Evans, R., Gravina, R., Heller, M., Clarke, A., Rock, C., Burchill, M. (2010). In Proceedings of the Aircraft Airworthiness & Sustainment Conference, vol. I, pp , Rouchon, J. (Ed.), Cépaduès Editions, Toulouse. [2] Mellings, S., Baynham, J., Adey, R.A., Advances in crack growth modelling of 3D Aircraft Structures, International Committee on Aeronautical Fatigue, Rotterdam, Netherlands, May [3] Mellings, S.; Baynham, J.; Adey, R.A.; Curtin, T.; Durability Prediction Using Automatic Crack Growth Simulation, International Committee on Aeronautical Fatigue, Toulouse, France, June [4] BEASY User Guide, Computational Mechanics BEASY Ltd, Ashurst, Southampton, UK, [5] Portela, A.; Aliabadi M.H; Rooke, D.P., The Dual Boundary Element Method: Efficient Implementation for Cracked Problems, International Journal for Numerical Methods in Engineering, Vol. 32, pp , (1992). [6] Mi Y; Aliabadi M.H., Three-dimensional crack growth simulation using 6EM, Computers & Structures, Vol. 52, No. 5, pp , (1994). [7] Neves A.; Niku S.M., Baynham J.M.W., Adey, R.A., Automatic 3D crack growth using BEASY, Proceedings of 19th Boundary Element Method Conference, Computational Mechanics Publications, Southampton, pp , [8] Rigby R.; Aliabadi M.H; Mixed-mode J-integral method for analysis of 3D fracture problems using BEM ; Engineering Analysis with Boundary Elements, Volume 11, Issue 3, 1993, Pages [9] Rigby R.; Aliabadi M.H; Decomposition of the mixed-mode J-integral revisited ; International Journal of Solids and Structures, Volume 35, Issue 17, June 1998, Pages