Study of some three dimensional effects in bolted joints

Abstract

Joints are essential to connect parts of structural components and to interconnect subassemblies of largescale structural systems. Various types of structural joints are used in technological practice; among these, bolted joints are the most commonly used wherever periodic assembly and disassembly are needed, and whenever articulation is to be provided. These joints are sources of high stress concentration and are often potential locations of failure. Accurate analysis of these joints is of considerable significance for structural design purposes. The problem of load transfer in a doubleshear lap joint is dealt with in this thesis. The joint consists of three flat plates with a central circular hole clamped by a bolt and a nut, and the load is transferred from the central plate to the two outer plates. The joint could be of an interference, neat, or clearance fit, depending on the bolt diameter being larger, equal to, or smaller than that of the hole. The bolt is tightened by application of torque on the nut to provide clampup pressure between the plates. A complete understanding of the stress and deformation pattern in such a joint requires a threedimensional analysis. The major problem in developing analysis of these joints is the requirement of multibody contact stress analysis. Progressive application of load in these problems would lead to changes in contact/separation areas, resulting in a nonlinear movingboundary value problem. The complexity of the structure requires a finiteelement approach for the stress analysis, and this must be coupled to an iterative routine to determine the changing contact/separation boundaries. Various aspects of load transfer in bolted joints were studied earlier by simplified approaches. Considering each plate in a state of twodimensional plane stress, load transfer through bearing was studied, including partialcontact behaviour. Such analysis does not consider plate clamping by the bolt and ignores thicknesswise variation of stress distribution. The effects of bolt clampup pressure alone were studied by some earlier workers in an axisymmetric joint between circular plates, and this work is related to flange joints where there is no inplane load transfer between the plates. In these studies, the modelling of selfequilibrating clampup load involved certain assumptions. Wherever the bolt could be considered rigid, it was modelled as uniform indentation on the plates, and cases of long elastic bolts were modelled as uniform stress on the bolt at the centre section. Such models are not acceptable in short elastic bolts as those in shear joints considered in the present thesis. To study the doubleshear lap joints including the effects of bolt clampup pressure, the following two special developments are carried out regarding the use of the frontal solver in the finiteelement software and the modelling of bolt clampup load transfer. The iterative method of analysis for contactstress problems in bolted joints could be expensive unless special features are introduced into the technique. For this purpose, computationally efficient software using a frontal solver is developed along with appropriate pre and postprocessors. The frontal solver is used to eliminate all degrees of freedom except those needed for contactstress analysis. A dummy element is introduced into the element library whose connectivity is identified with the degrees of freedom where conditions could be either contact or separation and where external load is applied on the joint. This element has zero stiffness so that the total stiffness is not altered, and only the reduced stiffness is conveniently generated with respect to those degrees of freedom. The iterative process is carried out on smallerorder matrices, and the appropriate boundary conditions, including multipoint constraints in the contact region, are imposed during this process. The pre and postprocessors have special modules for automatic mesh generation, mesh viewer, throughthickness stress chart, polar chart, stresssurface chart, XY charts, and colourshaded stress contours. The mesh generator has special features to automatically identify the degrees of freedom of the dummy element (for contactstress analysis) for threedimensional problems based on experience gained from simpler axisymmetric analysis. Torque tightening results in load transfer along the interface between the bolt shank and the nut interface. Based on experimental results available in literature and the physics of the problem, load transfer across this interface is idealised as a parabolic pressure distribution. The constants of the parabolic distribution are determined such that they ensure the bolt to be in tension and the nut to be in compression due to clampup load. This model is validated by (i) a sensitivity analysis and (ii) by comparing results using this model with earlier experimental results. The sensitivity analysis showed that any deviation in the assumed distribution at the boltnut interface affects only the results in the close vicinity of this interface, and the overall loadtransfer mechanism in the joint and the stress and deformation pattern away from this interface are not affected. This bolt clampup pressure model is used to carry out parametric study on axisymmetric joints between two or three plates, and some results are compared with earlier analytical and experimental results. Using the software tools developed and the clampup pressure model, threedimensional effects in doubleshear lap joints are studied in two stages. In the first stage, the joint is considered with an interferencefit bolt where there is full contact along the bolthole interface to start with. The inplane loads on the joint are restricted to the range that do not cause bolthole interfacial separation. For this case, an axisymmetric part of the joint with the outer circular boundary being nearly twenty times the diameter of the hole is analysed under nonsymmetric loading. On each plate of the joint, the stress boundary conditions on this notional outer boundary are determined from the wellknown Kelvin’s solution for a point load in an infinite plate. When the outer boundary is considered large, it is assumed that the details of the bolthole interface do not influence stresses on this outer boundary. Harmonic analysis of such a configuration provides significant information on thicknesswise variation of stresses, bending of the elastic bolt, loads for onset of separation, and certain solutions in the preseparation zone to compare with full threedimensional solutions. Numerical studies showed that clampup load and the elasticity of the bolt play a significant role in load transfer in the joint. The clampup load causes bending of the plates and early initiation of separation. Similarly, bolt flexure results in early initiation of separation so that separation initiates at much smaller loads for an elastic bolt compared to a rigid bolt. The gradient of maximum hoop stress, an important parameter for fatigue behaviour of the joint, however improves with bolt clampup pressure. The choice of bolt clampup load for a given inplane load transfer in the joint can be evaluated from this analysis. In the second stage, a threedimensional finiteelement analysis of the doubleshear lap joint is carried out. Eightnode isoparametric brick elements are used to model the joint, and the benefits of computational economy with the developed software tools are utilised to the maximum extent. A comparison of these results with those obtained earlier showed that axisymmetric analysis under nonsymmetric loading predicted the maximum stresses in the joint within 17% of the threedimensional analysis, but the distributions differ by up to 30% at certain locations. The postseparation behaviour of the joint is analysed by threedimensional analysis and results are presented on the growth of separation and stress variations. Stresses in the elastic bolt are evaluated for a particular configuration for which experimental results are available in the literature, and the comparison is excellent. Computational limitations restricted the study of finite friction effects. The effects of finite friction, joints between composite plates, analysis of multiplefastener joints, and analysis in thermal environments are identified as areas for further research.