Multi-fastener Joints Research Articles

Novel finite element for near real-time design decisions in multi-fastener composite bolted joints under various loading rates

In this paper, a highly efficient and novel user defined finite-element capable of modelling composite bolted joints at various loading rates was developed and validated against experimental data. The element was shown to be capable of producing high-fidelity simulations of joint behaviour up to and including catastrophic failure, with CPU times being orders of magnitude less than that required for full 3-D simulations, but with no loss in fidelity. Hence, this element makes possible for near real-time design decisions to be made for preliminary design and design for manufacture in multi-fastener composite bolted joints subjected to various loading rates. Using this element, this study finds that the load distribution in dynamically loaded multi-fastener joints is temporal and dependent on loading rate. The relative proportion of load carried by fasteners is found to vary due to the propagation of elastic stress waves in the joint. The magnitude of load imbalance between fasteners, an important design consideration to prevent premature joint failure, was observed to increase by up to 85% due to these dynamic loading effects.

Topology optimization of the multi-fasteners jointed structure considering joint load constraint and fatigue constraints

The purpose of this paper is to present an important strength issue in the design of multi-fasteners jointed structures. Multi-fastener joints such as bolts and rivets are widely used in assembled structures and always act as critical elements in damage tolerance design. Therefore, fasteners static strength and fatigue performance are simultaneously considered in this paper. On one hand, constraints on joint loads are issued to avoid the fasteners failure. On the other hand, two multiaxial fatigue criterion, i.e., Sines criterion and Crossland criterion are introduced to avoid the failure in the connection areas around fasteners. In addition, the total material usage is limited for the light-weight design. The standard topology optimization is thus extended to minimize the structural compliance with joint load constraints and fatigue failure constraints. Beam elements are used to model the fasteners. The joint loads can therefore be derived easily based on the finite element formulation. In order to eliminate the high stresses caused by the nodal connections of the beam elements, compositional modeling method is used to evaluate the stress level around the fasteners, in which beam elements are used to simulate the stiffness of fasteners and spring/shell elements are used to simulate the interaction of multi-fastener joints. Fatigue constraints are handled in the context of stress-based topology optimization while the corresponding analysis is based on static finite element due to the decomposition of harmonic loads. To address the singularity problems related to stress constraints, q - p relaxation is used and p ≥ q ≥1. Fatigue constraints should be evaluated in every element which inevitably brings in a large number of constraints. P-norm is therefore used as the constraints aggregation scheme. The aggregation factor of P-norm, i.e., Pn is assigned as 6 in this paper. With respect to the constraints aggregation process, the design sensitivities of fatigue constraints and joint load constraints are derived and calculated. Two numerical examples, namely an assembled I-shape beam and a cabin of the high-speed flight vehicle are tested. Optimized results with the proposed method are compared with standard topology optimization design. All the constraints are completely controlled by the prescribed upper level and the loss of stiffness in the optimized configuration can be seen as a trade-off for the strength. It is shown that the fatigue performance is strongly affected by the structural layout and the load carrying path. The effects of different fatigue constraints on the optimized configuration are studied.

Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads

The purpose of this paper is to present an extended topology optimization method for the stiffeners layout design of aircraft assembled structures. Multi-fastener joint loads and manufacturing constraints are considered simultaneously. On one hand, the joint loads are calculated and constrained within a limited value to avoid the failure of fasteners. On the other hand, the manufacturing constraints of the material distribution in the machining directions of stiffeners are implemented by an improved piecewise interpolation based on a beveled cut-surface. It is proven that the objective function is strictly continuous and differentiable with respect to the piecewise interpolation. The effects of the extended method with two different constraints are highlighted by typical numerical examples. Compared with the standard topology optimization, the final designs have clearly shown the layout of stiffeners and the joint loads have been perfectly constrained to a satisfying level.

A reduced fastener model using Multi-Connected Rigid Surfaces for the prediction of both local stress field and load distribution between fasteners

This paper describes the development of a reduced model of a fastener using Multi-Connected Rigid Surfaces (MCRS). The stiffness of the connectors is determined, based on a physical approach, considering different deformation modes of the bolt. The reduced model is constructed and identified from a numerical simulation of a single lap reference joint under tensile load, with the adherent parts and bolts represented by 3-D solid elements. A single simulation with a given clearance, axial preload and friction coefficient is used to identify equivalent stiffnesses. The reduced model is then compared with the 3-D solid elements model in a two-fastener configuration for different values of clearance, preload and friction coefficient. The comparison covers overall response in terms of stiffness and load distribution between fasteners, local response in terms of stress fields and calculation times. Results show that the reduced model proposed here is able to reduce calculation times while still providing a good estimate of the mechanical quantities needed for the study and dimensioning of multi-fastener joints.

New design approach for controlling brittle failure modes of small-dowel-type connections in Cross-laminated Timber (CLT)

The introduction of Cross-laminated Timber (CLT) as an engineered timber product has played a significant role in considerable progress of timber construction in recent years. Extensive research has been conducted in Europe and more recently in Canada to evaluate the fastening capacity of different types of fasteners in CLT. While ductile capacities calculated using the yield limit equations are quite reliable for fastener resistance in connections, however, they do not take into account the possible brittle failure mode of the connection which could be the governing failure mode in multi-fastener joints. Therefore, a stiffness-based design approach which has already been developed by the authors and verified in LVL, glulam and lumber has been adapted to determine the block-tear out resistance of connections in CLT by considering the effect of perpendicular layers. The comparison between the test results on riveted connections conducted at the University of Auckland (UoA) and the Karlsruhe Institute of Technology (KIT) and the predictions using the new model and the one developed for uniformly layered timber products show that the proposed model provides higher predictive accuracy and can be used as a design provision to control the brittle failure of wood in CLT connections.

A new approach for evaluating fatigue lives of multi-fastener mechanical joints based on a nominal stress concept and minimal datasets

New formulae are derived to predict the normal bypass, transfer and nominal stresses around the fastener holes on multi-fastener mechanical joints under plane stress conditions. A modified method based on the nominal stress concept is developed to evaluate fatigue lives of complex multi-fastener joints. The method is informed by fatigue characteristics of joints with similar structural details. Fatigue tests on two-rivet, four-rivet and eight-rivet joints were performed and damage mechanisms are deduced from fractographs. Good correlation is achieved between the predictions and actual experiments, demonstrating the practical and effective use of the proposed method.

Net-tension strength of double-lap joints under bearing-bypass loading conditions using the cohesive zone model

Tensile failure is a primary failure mode in structures with multi-fastener joints specially for large bypass loads. Therefore, the precise prediction of the net-tension strength of these joints is essential for reliable design of many engineering structures. In this paper the analytical model presented by Kabeel et al. (2014) has been extended to predict the net-tension strength of double-lap joints under combined bearing-bypass loading conditions. Due to the ability of the cohesive law to predict the effect of the structure size on its strength, the present model is formulated based on the cohesive zone model. The effect of the bypass stresses on the joint net-tension strength has been studied. The present model is able to predict the optimum geometry of the joints and, consequently, its maximum nominal strength. A comparison of the obtained predictions with those of the available experimental work reveals good agreement. The obtained results can be used as design charts for the double-lap joints that are made of isotropic quasi-brittle materials.

An analytical model for strength prediction in multi-bolt composite joints at various loading rates

This paper presents an enhanced analytical model to determine the complete load displacement curve of single- and multi-fastener composite joints. It is an extension of a previous spring-based method, which included the effects of bolt pre-load and clearance, but not local bearing damage. The model has advanced beyond the state-of-the-art as loading rate effects, in addition to bearing damage, are accounted for through a novel conic damage approximation function. Using the developed model, an accurate prediction of the load displacement response of single- and multi-fastener joints to complete failure can be obtained in a matter of seconds. The method is validated against experimental data and excellent correlation was observed. Further studies carried out using the model suggest that slight variations in the energy absorption characteristics at each fastener hole in a multi-fastener joint can significantly alter the bolt-load distribution in the joint.

Modified Stress Severity Factor Method Based on 3D-FEM

The traditional stress severity factor (SSF) approach was applied to analyze the life of aircraft multi-fastener joint. 3-D model was established under simulated state of practical assembling using CATIA, and then the model was imported into ABAQUS to analyze the detail stress state of aircraft multi-fastener joint. The life of aircraft multi-fastener joint was estimated by amending the SSF method. The example shows that the fatigue life by the approach is closer to the experimental result.

Structural topology optimization with constraints on multi-fastener joint loads

This paper addresses an important problem of design constraints on fastener joint loads that are well recognized in the design of assembled aircraft structures. To avoid the failure of fastener joints, standard topology optimization is extended not only to minimize the structural compliance but also to control shear loads intensities over fasteners. It is shown that the underlying design scheme is to ameliorate the stiffness distribution over the structure in accordance with the control of load distributions over fastener joints. Typical examples are studied by means of topology optimization with joint load constraints and the standard compliance design. The effects of joint load constraints are highlighted by comparing numerical optimization results obtained by both methods. Meanwhile, resin models of optimized designs are fabricated by rapid prototyping process for loading test experiments to make sure the effectiveness of the proposed method.

Structural health monitoring of fatigue crack growth in plate structures with ultrasonic guided waves

Fatigue crack growth in plate structures is monitored with ultrasonic guided waves generated from piezoelectric transducers. Cracks initiate in the vicinity of fastener holes due to cyclic in-plane loading. Ultrasonic guided waves that are partially obstructed by the fastener holes are investigated. Since fatigue crack growth increases the obstruction, these waves are effective for monitoring fatigue crack growth in a pitch-catch mode. The transmission coefficient (TC), which is defined essentially as the current-to-baseline amplitude ratio, and the transmission coefficient ratio (TCR), which is based on amplitude ratios from a single wave, are signal features used for crack characterization. The TCR is well suited for structural health monitoring. The excellent agreement between experimental results and finite element analysis of wave propagation corroborates the experiments. A sparse array of transducers is shown to effectively monitor a multifastener joint. The approach using obstructed ultrasonic guided waves has strong potential for prognostics-based structural health management due to the linear relationship between crack size and the TC.

Thermo-mechanical fatigue analysis of liquid shim in mechanically fastened hybrid joints for aerospace applications

As resin-infused composite laminates continue to replace alloy components in modern commercial aircraft, liquid-shim is often necessary to compensate for assembly tolerances occurring in mechanically-fastened primary structures. This paper evaluates the structural performance of aerospace-grade liquid-shim in double-bolt composite-aluminium alloy ‘hybrid’ joints representative of multi-fastener joints found in the primary structures of modern commercial aircraft. Hybrid joints with liquid-shim were subjected to simultaneous thermal and mechanical-fatigue (TMF) loading conditions representative of those experienced over the lifetime of a commercial aircraft. The joints were subjected to 200,000 fatigue load cycles at −59°C and 100,000 fatigue load cycles at +85°C to simulate service conditions. Key variables investigated were shim material and shim thickness. The main conclusions from this study are: (i) there was no degradation of the liquid-shim in terms of a loss of mechanical stiffness and, secondly, no significant damage was observed on the bearing-plane; (ii) a reduction in joint stiffness due to the presence of liquid-shim was observed using high magnification 2D digital image correlation (DIC) and the reduction was dependent on the thickness of liquid-shim employed; and (iii) joints with second generation liquid-shim exhibited marginally lower stiffness relative to joints manufactured with third generation liquid shim.

Pattern optimization of eccentrically loaded multi-fastener joints

For structural joints subject to dynamic loading, the fatigue strength is controlled by local stresses. For steel plate structures joined with fasteners, fatigue is governed by local friction and slip near the fasteners. As a working hypothesis for this study, a “weakest link” approach has been adopted. An optimum fastener pattern is attained by reducing the shear load in the most severely loaded fastener in the group. In this study, a typical eccentric multi-fastener bracket-to-beam joint was studied using constrained geometric optimization. Alternate assumptions concerning the distribution of the direct shear force between fasteners in a group were assessed. An analytical expression for non-uniform direct shear force resulted in an optimized fastener pattern with approximately 20% lower von Mises equivalent strain. The comparative finite element method based topology optimization analysis resulted in a contour, which was in close agreement with the fastener pattern attained analytically by exploiting geometry optimization.

Finite element modeling and optimization of load transfer in multi-fastener joints using structural elements

A computationally effective model of a multi-fastener, single-lap, composite-to-aluminium joint has been developed by means of structural finite elements. The model is geared towards accurate pre ...

Empirical Models Depicting Grain Angle Effects on Load-Embedment Response of Dowel-Type Fasteners in Wood

Abstract Predicting the moment-rotation response of a multifastener timber joint requires the use of empirical models that describe adequately the influence of load-to-grain angle on embedment response of wood under a dowel fastener. This paper presents two models. The first model describes the relationship between load, embedment, and load-to-grain angle, and can be used for predicting moment-rotation response of a multifastener joint. The second model relates the ultimate embedment at failure to load-to-grain angle. This second model is intended for predicting failure of timber joints. Comparison with test data confirms the suitability of these models to describe the influence of load-to-grain angle on embedment response of wood.

Analysis of composite laminates with multiple fasteners

Fatigue- and fracture-related cracks are to be expected with the large number of fasteners present in aircraft structures. Therefore, contact stresses around the fastener holes and stress intensity factors associated with edge cracks are critical concerns in damage-tolerant designs. Mechanical joints consisting of many fasteners with a staggered pattern further complicate the already rather complex analysis for single-fastener joints. Load distribution among the fasteners significantly influences the failure load of multi-fastener joints. Most existing analyses are confined to single-fastener joints, and the data available for multi-fastener joints are rather limited. Very few experimental and/or analytical/numerical investigations of contact stresses for mechanical joints with staggered fasteners exist in the literature. Therefore, the accurate prediction of contact stresses (load distribution) and stress intensity factors associated with edge cracks is essential for the reliable design of such mechanical joints. This study concerns the development of an analytical methodology, based on the boundary collocation technique, to determine the contact stresses and stress intensity factors required for strength and life prediction of bolted joints with many fasteners. It provides an analytical capability for determining the contact stresses in mechanically fastened composite laminates while capturing the effects of finite geometry, presence of edge cracks, interaction among fasteners, material anisotropy, fastener flexibility, fastener-hole clearance, friction between the pin and the laminate, and by-pass loading. Also, it permits determination of the fastener load distribution, which significantly influences the failure load of a multi-fastener joint.

Stress analysis and strength prediction of mechanically fastened joints in FRP: a review

A review of the investigations that have been made on the stress and strength analysis of mechanically fastened joints in fibre-reinforced plastics (FRP) is presented. The experimental observations of the effects of joint geometry, ply-orientation, lay-up and through-thickness pressure on the joint behaviour are described briefly for both single and multi-fastener joints. The analytical and numerical methods of stress analysis required before trying to predict failure are discussed. The numerical approaches cover both two and three-dimensional models and the effects of clearance, friction and geometry are assessed. The several methods that have been used to predict failure in single or multi-fastener joints are described. It is concluded that there are some issues that require further investigation. There is no general agreement about the method that should be used to predict failure, but progressive damage models are quite promising since important aspects of the joint's behaviour can be modelled using this approach. In order to take into consideration several factors related to joint strength the use of three-dimensional models is suggested. These models require a three-dimensional failure criterion and an appropriate property degradation law.

Load distribution in composite multifastener joints

This paper focuses on studying the load distribution of multifastener composite joints under the applied shearing load or off-axis tensile load. In this paper, the models of multifastener joints for the finite element analysis are discussed. An idealization model under the shearing load is set up and the difference between two models under the shearing load and the tensile load are compared. The presented method in the paper can be used to compute bolt loadings, which include their magnitudes and directions. The radial forces on contact boundary can be solved by the displacement coordination equation. In illustrative examples the joints with four fasteners, six fasteners and eight fasteners in two rows under the shearing load are computed. The computation results are coincident with experiment data. In addition, this method is used to compute the load distribution of a joint with three fasteners in a row under off-axis tensile loading. The computation results show that the load distribution has many characteristics under off-axis loading compared with that under on-axis tensile load. The method presented by this paper can be used to predict in engineering.

Failure Criterion for Thick Multifastener Graphite-Epoxy Composite Joints

A method for accurately predicting the strength of multifastener, thick composite joints is discussed. The method is based on the average stress criterion applied around the hole circumference. Basic laminate strength data are obtained from single-fastener and reduced-section notched specimens. Using ABAQUS finite element analyses (FEA), the stress-field distribution around the fastener-loaded hole in both the single-fastener and multifastener joints is determined. The single-fastener test data in conjunction with this FEA and the average stress criterion are then used to predict the multifastener joint strength. Multifastener joint strength of three different laminate lay-ups is predicted to within 1% accuracy. However, the results show that the average stress criterion cannot accurately predict the location of failure initiation. In the current investigation, the maximum strain criterion is used to locate possible sites of failure initiation. When this information is used in conjunction with the average stress criterion, the predicted multifastener joint strength based on single-fastener net-tension data is reasonably accurate.

Stress analysis method for clearance-fit joints with bearing-bypass loads

Within a multi-fastener joint, fastener holes may be subjected to the combined effects of bearing loads and loads that bypass the hole to be reacted elsewhere in the joint. The analysis of a joint subjected to search combined bearing and bypass loads is complicated by the usual clearance between the hole and the fastener. A simple analysis method for such clearance-fit joints subjected to bearing-bypass loading has been developed in the present study. It uses an inverse formulation with a linear elastic finite-element analysis. Conditions along the bolt-hole contact arc are specified by displacement constraint equations. The present method is simple to apply and can be implemented with most general purpose finite-element programs since it does not use complicated iterative-incremental procedures. The method was used to study the effects of bearing-bypass loading on bolt-hole contact angles and local stresses. In this study, a rigid, frictionless bolt was used with a plate having the properties of a quasi-isotropic graphite/epoxy laminate. Results showed that the contact angle as well as the peak stresses around the hole and their locations were strongly influenced by the ratio of bearing and bypass loads. For single contact, tension and compression bearing-bypass loading had opposite effects on the contact angle. For some compressive bearing-bypass loads, the hole tended to close on the fastener leading to dual contact. It was shown that dual contact reduces the stress concentration at the fastener and would, therefore, increase joint strength in compression. The results illustrate the general importance of accounting for bolt-hole clearance and contact to accurately compute local bolt-hole stresses for combined bearings and bypass loading.