NUMERICAL MODELLING OF BOLTED JOINTS FROM COMPOSITE. THE MESSAGE 2. EFFECT OF THE BACKLASH AND PCM STRUCTURE ON THE CHARACTERISTICS OF THE STRESS-STRAIN STATE OF BOLTS

In modern finite element class PLM programs have opportunity to create mixed finite element model by gluing. It allows to create, in particular, for calculations on PC rather small 3D-models of polymeric composite materials (PCM) in bolt joints in which composite in zones of bolt-holes is body-sectional modelled, and behind them – approximately, according to theory of the effective module. Previously it demonstrated possibility of using a mixed 3D-models of PCM in bolt joints through simulations to determine minimum size of zones of more precise PCM simulation while providing same accuracy of calculations. The work is dedicated to identification of trends in characteristics of stress-strained state in areas of bolt-holes when composite materials structure is changed, to reduce absolute values of compression stresses in PCM. Created 24 of 3D-models of one shear two-row bolt joints with PCM (contact problem), which ranged PCM structure (6 options), as well as backlash of bolts with holes (4 values). Unchanged were value of bolt tightening force and tensile force specimen. According to results of calculations to determine distribution of minimum stress and contact pressure (tables, graphs). It is concluded that structure of a PCM plate significantly affects characteristics of stress-strained state of PCM in areas of holes; that we can find a structure that will ensure lowest values of absolute values of compression stress and a greater strength.

Problematic. Among the various options for joining parts from layered polymer composite materials (PCM), a significant percentage is bolted joints (BJ). For their proper design, it is necessary, in particular, to carry out strength calculations. In this case, it is desirable to replace complex finite element calculations with express analysis: calculations using simple formulas of sufficient accuracy. One of the main strength calculations of BJ is the calculation of tensile strength of the section weakened by the hole. For BJ plates made from PCM, this question has not been worked out enough.Research objective. Establish of the impact degree of the monolayers stacking sequence of a PCM plate on the value of the stress concentration factor (SCF) near the hole loaded with a bolt.Realization technique. Numerical calculations were carried out using the finite element method (contact problem) for a BJ plate made of layered PCM. A 3D-orthotropy of each monolayer was assumed. Two simple express analysis formulas were tested. Diagrams were built, the presence and impact degree of the monolayers stacking sequence in a laminated PCM plate on the change of the SCF values were established.The results of research. Based on the calculation results, numerical estimates are obtained that characterize the impact degree of the monolayers stacking sequence in a laminated PCM plate and the accuracy of the considered formulas.Conclusions. The calculations showed that change of the monolayers stacking sequence of the layered PCM leads to a significant change of the SCF values near the bolt-loaded hole in the plate section weakened by the hole; that the proposed approximation (17) has insufficient accuracy for the considered materials and monolayers stacking sequences. It is necessary to continue the search for the correction function for (15) on a wider calculation and experimental base of PCM properties.

Bolted joints are widely used in modern engineering structures and machine designs due to their low cost and reliability when correctly selected. Their integrity depends on quantitative representation of the contact pressure distribution at the interface during design. Because of the difficulty in reaching and assessing clamped interfaces with traditional experimental methods, presently bolted joint design and evaluation is based on theoretical analysis, with assumptions to quantify pressure distribution at the clamped interface, which may not represent their true operating conditions. The present work utilises a non-intrusive ultrasonic technique to investigate and quantify the pressure distribution in bolted joints. The effect of variation in plate thickness on the contact pressure distribution at bolted interfaces under varying axial loads is investigated. While it was observed that the contact pressure at the interface increases as the applied load increases, the distance from the edge of the bolt hole at which the distribution becomes stable is independent of the applied load on the bolted joint. However, the contact pressure distribution was observed to vary with the plate thickness. Although the variation in the peak value of the average contact pressure distribution in bolted joints does not depend on the plate thickness, the distance from the edge of bolt hole at which the value of the distribution becomes stable increases as the plate thickness is increased. It was also observed that the edge of the bolt head affected the position of the peak value of the contact pressure distribution at the interface, though its effect was dependent on plate thickness. Furthermore, a model based on a Weibull distribution has been proposed to fit the experimental data and a good correlation was observed.

Contact characteristic parameters modeling for the assembled structure with bolted joints

The dynamic response of complex equipment under mixed-mode loading is significant for structural design. Bolted joints are the primary connection mode of subsystem assembly, and the degradation of bolted joints may reduce the safety and reliability of the equipment. The Iwan model is widely used to describe the degradation of bolted joints, which has been continuously revised and experimentally verified. The classic Iwan model is a static model that lacks predictive ability. The latest dynamic Iwan model can predict the softening process and reveal the physical mechanism of degradation. However, the function of dynamic pressure distribution needs to be determined for the model solution. We analyzed the contact boundary and pressure distribution under mixed-mode loading with the finite element method (FEM) and proposed the dynamic functions. Secondly, we put forward two correction methods to compensate for the loss of preload caused by simplification and to achieve consistency between the pressure distribution function and the contact boundary function. Finally, the influence of discrete order on the correction of pressure distribution was analyzed. The results show that the constraint method is more suitable for the modification of the pressure distribution. The research results can be applied to the solution of the dynamic Iwan model.

Problems. When designing bolted joints (BJ), it is necessary, in particular, to carry out their verification calculations for strength. At the same time, it is desirable to use express analysis: calculations by simple formulas of sufficient accuracy. For BJ of plates made of layered polymer composite materials (PCM), the problem has not yet been solved. The aim of the study. The task is to test the accuracy of three known formulas for quick calculation of the value of the stress concentration factor (SCF) in zone of contact of bolt-hole with a rigid cylinder (bolt). The study was carried out on contrasting examples of materials and schemes of reinforcement of plates made of PСM, taking into account possible clearance between bolt and hole in the real range: from zero to 1% of diameter. Methodology of implementation. Numerical calculations were made using the finite element method (contact problem) for the BJ of plates made of layered PCM. 3D orthotropy of each monolayer was provided. Three simple formulas of express analysis were tested. The results are summarized in the tables and many illustrations are given. Research results. Numerical estimates of depending of the SCF in zone of the surface of the bolt-hole from considered factors are obtained. The factors are the material characteristics, the schemes of reinforcement of plates made of layered PСM and the values of the clearance between bolt and hole in the plates, as well as the accuracy of the considered formulas. Conclusions. Changing the material and the scheme of reinforcement of plate made of layered PСM leads to a significant change in the values ​​of maximum stresses and SCF in zone of the bolt-loaded hole in the weakened by hole cross section of a plate. Considered formulas of the express analysis have insufficient accuracy for consideration of contrast properties of materials and schemes of reinforcement of a plate. Changing size of clearance between bolt and hole in the range from zero to 1% of the diameter leads to relatively small changes in SCF: up to 10% maximum. Additional research is needed.

The formulas are proposed to describe the contact pressure distribution on the nut bearing surface and on the threads in bolted joints. The reaction forces in three axes directions and reaction moments about them are investigated for a bolted joint during the tightening process. Finite element analysis (FEA) is used to analyse and evaluate the contact pressure and those forces and moments. To acquire more accurate results, a parametric effective 3D finite element (FE) modelling scheme, which takes account of the helical geometry, is developed. Effects of contact radii ratios of the nut bearing surface on the contact pressure distribution are investigated.

Physicomechanical and tribotechnical properties of structural composite materials based on thermoplastic polymer and organomineral ingredients operating under friction and wear conditions during contact with pulp (raw cotton) have been investigated. The regularities of changes in the physical, mechanical and tribotechnical properties of structural composite materials during contact interaction with raw cotton were determined, the dependence of their properties on the type and content of graphite, mineral and fibrous fillers in structural composite materials was studied. It has been established that the nature and structure of fillers has a certain effect on the physical and mechanical properties of composite materials based on polypropylene. At the same time, fiber-filled compositions have the highest mechanical strength. It was also found that when mineral fillers are introduced into composite polymer materials, their coefficient of friction with raw cotton increases significantly, while the wear rate decreases, except for fillers with a plate structure (kaolin, talc), when used, a decrease in the coefficient of friction is observed. The introduction of carbon-graphite fillers into the composition of composite materials leads to a significant decrease in the coefficient of friction, temperature and static electricity charge in the friction zone with raw cotton. The introduction of fillers with a fibrous structure leads to a significant decrease in the rate of wear of the composites. It provides high strength and resistance of the material under thermomechanical action. Effective compositions of structural composite materials for work under conditions of contact interaction with fibrous mass have been developed, and their physical, mechanical and tribotechnical properties have been investigated.

Accurate modeling of contact interface in bolted joints is crucial in predicting the dynamic behavior for bolted assemblies under external load. This paper presents a contact pressure distribution based non-uniform virtual material method to describe the joint interface of assembly structure, which is connected by sparsely distributed multi-bolts. Firstly, the contact pressure distribution of bolted joints is obtained by the nonlinear static analysis in the finite element software ANSYS. The contact surface around bolt hole is divided into several sub-layers, and contact pressure in each sub-layer is thought to be evenly. Then, considering multi-asperity contact at the micro perspective, the relationship between contact pressure and interfacial virtual material parameters for each sub-layer is established by using the fractal contact theory. Finally, an experimental platform for the dynamic characteristics testing of a beam lap structure with double-bolted joint is constructed to validate the efficiency of proposed method. It is found that the theoretical results are in good agreement with experimental results by impact response in both time- and frequency-domain, and the relative errors of the first four natural frequencies are less than 1%. Furthermore, the presented model is used to examine the effect of rough contact surface on dynamic characteristics of bolted joint.

Mechanics of longitudinal joints in segmental tunnel linings: Role of connecting bolts

This paper proposes the use of the Weibull probability density distribution to predict the shape of the contact pressure distribution in bolted metal joints. Contact pressure distributions in bolted joints were measured using a commercially available pressure-sensitive film. Three different joint materials were analyzed: aluminum- aluminum, stainless steel-stainless steel, and aluminum-stainless steel. The metal plates were circular and bolted together through a hole at their center. Two bolt head radii were employed. Five different axial loads were applied for each bolted joint configuration. The agreement was very good between the correlations, based on the Weibull distribution and the data. The results indicate that the Weibull function is an adequate model for the shape of the contact pressure distribution of bolted joints.

Quantitative characterization of contact pressure distribution in bolted joints directly influences the calculation accuracy of connection stiffness. In this paper, a three-dimensional finite element model of the bolted joints is established using the software ANSYS, and pretension force and contact between the joint components are accommodated in the model. Then, parametric studies are carried out to investigate the effects of the material properties, preloads, bolt sizes, grip lengths and hole clearances on the contact pressure distribution. According to the finite element analysis results, a polynomial equation system is derived for mathematical representation of contact pressure distribution in bolted joints. Furthermore, the conical envelope angle used in the mathematical characterization is identified for the bolted joints with different bolt sizes and grip lengths. Finally, an experimental platform is constructed for the measurement of contact pressure distribution, and then the applicability of mathematical characterization is validated by comparison with a series of experiment results.

<div class="htmlview paragraph">Energy dissipation due to micro-slip in joints is the primary source of damping in many vehicle and space structures. This paper presents results on how the surface topology may be modified to increase the energy dissipation in joints. An analytical solution for general forms of contact pressure of a one-dimensional micro-slip problem is presented. The solution indicates how the contact pressure should be distributed to maximize the energy dissipation. Two dimensional contact pressures are optimized using finite element methods in combination with numerical optimization methods and the results are used to modify the surface topology in bolted joints in order to increase the energy dissipation during loading. The predicted increase of energy dissipation is validated with physical testing. A direct result of the study is a washer with varying thickness increasing the energy dissipation in joints and hence the structural damping of joined structures.</div>

Distinctive mechanical behaviors of bolted joints are caused by the helical shape of thread geometry. Recently, a number of papers have been published to elucidate the strength or loosening phenomena of bolted joints using three-dimensional finite element analysis. In most cases, mesh generations of the bolted joints are implemented with the help of sophisticated commercial software. Therefore, the mesh patterns thus obtained are not necessarily adequate for analyzing the stress concentration and contact pressure distributions, which are the primary concerns when designing bolted joints. In this paper, an effective mesh generation scheme is proposed, which can provide helical thread models with accurate geometry in order to analyze such important characteristics as the stress distribution along the helix and the contact pressure distributions on the pressure flank. Using the FE models constructed according to the proposed procedure, it is shown how the thread root stress and contact pressure vary along the helix. Also shown is how the imperfect engagement of the mating threads, around the top and bearing surfaces of the nut, affects the circumferential contact pressure distribution at the nut loaded surface and the axial load distribution along engaged threads.

When designing bolted joints (BJ), it is necessary, in particular, to carry out their verification calculations for strength. At the same time, it is desirable to use express analysis: calculations by simple formulas of sufficient accuracy. For BJ of plates made of layered polymer composite materials (PCM), the problem has not been solved yet. Objective. To revise, to rethink and structure the formulas for the express calculation of the maximum stress when the hole is in contact with a rigid cylinder (bolt). Carry out a review on contrasting examples of materials and schemes of PCM plate reinforcement, taking into account possible lateral bolt/hole clearances in a practically relevant range, based on previously obtained and new results. Numerical calculations were carried out using the finite element method (contact problem) for the BJ plate made of laminated PCM. 3D orthotropy of each monolayer was assumed. Several simple express analysis formulas were checked, and their structuring was carried out. The results are summarized in a table, illustrations are given. Five factores influencing the value of the maximum tensile stress near the hole in the laminated PCM plate are separated. Numerical estimates were obtained that characterize the degree of influence on the stress concentration on the surface of the hole: material characteristics, reinforcement scheme, and bolt/hole gap sizes in the laminated PCM plate, as well as the accuracy of the considered formulas. A change in the material and scheme of reinforcement of the layered PCM leads to a significant change in the values ​​of the maximum stresses and stress concentration factor (SCF) in the bolt-loaded hole in the cross-section of the plate weakened by the hole. The considered express analysis formulas have insufficient accuracy for contrasting cases of materials and plate reinforcement schemes. Additional research is needed, especially for the reinforcement scheme [φ/-φ]2s at 0<φ<90.