Multi-bolt Composite Joints Research Articles

A characteristic curve including hygrothermal effects for predicting the failure of composite multi-bolt joints

A characteristic curve that considers hygrothermal effects was developed based on the traditional characteristic curve. A nondimensional temperature was introduced to represent the severity of seven hygrothermal conditions experienced by primary aircraft structures. The tensile characteristic lengths and compressive characteristic lengths under the seven conditions were determined using a numerical strategy. Expressions between the characteristic lengths and the nondimensional temperature were established by fitting the data with exponential functions. Consequently, an equation of the characteristic curve formulated as a function of the nondimensional temperature and the angle, was established. The developed characteristic curve can be used to predict the failure of composite multi-bolt joints under any hygrothermal environment.

Analysis of multi-bolt composite joints with a user-defined finite element for the evaluation of load distribution and secondary bending

The present paper aims to demonstrate the capabilities of the Composite Bolted Joint Element (CBJE) methodology in the framework of single-lap multi-bolt joints analysis. This FE modeling approach exploits the CBJE, a user-defined finite element. It is founded on the complete elastic characterization of the bolted region through analytical models. The elastic behavior of a circular portion of the laminates enclosing the bolt is determined in the context of thick composite plate mechanics; a set of radial beam elements is made structurally equivalent through the custom definition of their stiffness matrix . The interaction between the bolt and the plates is modeled as a beam on elastic foundation. The stiffness contributions of the bolt and the specific properties of the joint, such as preload, bolt-hole clearance, contact stiffness , and friction effects are simulated utilizing an assembly of beam and spring elements. In this way, it is created a FE model from the theoretical solution of the bolted region featuring high fidelity and computational efficiency, as it requires a low amount of degrees of freedom. Experimental data are used to validate the FE model with CBJE of the single-lap three-bolt composite joint. Specimens with varying lay-up, radial clearances , bolts preload and bolt number are also analyzed to evaluate the bolt load distribution and out-of-plane behavior. The CBJE results are successfully compared with those of reference solid models. • FE approach derived from the theoretical model to consider the joint key features. • Bolt-load distribution precisely determined for the subsequent strength analysis. • Remarkable computational savings are obtained together with high accuracy. • Especially useful for the preliminary design to assess different joint configurations.

Extended spring–mass method for joint stiffness prediction of single-lap multi-bolt composite joints considering assembly gap and gap shimming

A multi-bolt spring–mass method considering assembly gap and shim was developed to predict the shear stiffness and bolt stiffness of the single-lap composite joints. Based on the premise that the highly stressed portions of adjacent holes have no overlap, multi-bolt joints can be converted into individual single-bolt joint with considering the conical and spherical stress envelope, gradual elimination of the bolt-hole clearances, and irregular assembly gap shape. The proposed method was validated by both experiment and finite element method for typical three-bolt composite joints with relative error of shear stiffness <3%, and that of bolt stiffness <20%.

A Two-Dimensional Model for Pin-Load Distribution and Failure Analysis of Composite Bolted Joints.

Multibolt composite joints are widely used in aircraft structures. The determination of the pin-load distribution among the bolts is a critical step in the failure prediction of bolted joints. In this paper, a two-dimensional model of the multibolt composite structure is established for the pin-load distribution analysis. Its accuracy is validated by experimental results and the results from a 3D finite element model. Based on the determined pin-load distribution, FE models for a laminated plate with three-row fastener joints are built for failure prediction. Hashin stress criteria and the degradation guidelines of the material stiffness with respect to the different failure modes proposed by Tserpes are applied for the failure evaluation and the material degradation, respectively. The failure location and ultimate load are well predicted, which further validates the effectiveness and applicability of the proposed model for the pin-load distribution analysis.

Prediction of net-tension failure of multi-bolt composite joints: A fast approach for laminates with arbitrary layup

In this study, a new fast approach to predict the net-tension failure strength of multi-bolt composite joints was developed based on finite fracture mechanics and p-version parametric finite element methods. In the proposed approach, stress distribution and stress intensity factor are obtained using the principle of superposition, based on which the problem can be divided into open hole tension and hole bearing problems. The stress distribution and stress intensity factor are determined by using p-version parametric finite element models, which is very computational efficient and can address laminates with arbitrary layup. For the validation purpose, the failure strengths of three multi-bolted joints were predicted and compared to the test data from public literatures, and good agreements were obtained. In addition, the effects of typical parameter variations on the net-tension failure strength were presented by performing a series of parametric studies, which would be a reference for engineering design of multi-bolt composite joints.

A modified stiffness method considering effects of hole tensile deformation on bolt load distribution in multi-bolt composite joints

The bolt holes of multi-bolt composite joints have bearing deformation caused by bolt loads and hole tensile deformation resulted from bypass loads. However, the hole tensile deformation was neglected in the existing stiffness method, because the stiffness formula of laminates without hole was applied for the joined hole laminates, which leads to a relatively rough prediction of the bolt load distribution, especially for the multi-bolt joints with larger numbers of bolts, in which the bypass loads are much bigger than the bearing loads. To improve the accuracy of the existing stiffness method, a modified stiffness method was proposed. In this method, based on the effect mechanism of the hole tensile deformation on the deformation compatibility condition, a concept of an additional stiffness corresponding to the hole tensile deformation and its calculation method were presented to modify the deformation compatibility equation. The bolt-load ratios predicted by the modified method and the existing method were compared with those obtained from FE models. It follows that the modified method possesses higher precision, and the improvement of the prediction accuracy is more conspicuous as the number of the bolts increases. The presented method shows overwhelming advantages over the existing method.

Effects of Laminate Thickness and Tapering on the Behavior of FRP Composite Multibolt Joints

AbstractThis paper presents a numerical study to show the effects of laminate thickness and tapering on the performance of composite bolted joints made of carbon fiber–reinforced polymer (CFRP) mat...

A hybrid approach for global sensitivity analysis of FRP composite multi-bolt joints

This paper presents a hybrid approach for global sensitivity analysis of FRP composite multi-bolt joints. The proposed approach integrates a spring-based analytical model with moment-independent sensitivity analysis. The homogenized properties within the spring-based analytical model are computed by utilizing a novel homogenization technique for FRP composites. The proposed model has been utilized for stochastic sensitivity analysis of a generic double-lap multi-bolt FRP composite joint where, both material and geometric properties are uncertain. The importance of the input parameters with respect to structural responses of the bolted joint has been computed. The proposed approach is found to be highly efficient, even for realistic composite model with significant number of layers. This indicates that the proposed model can be used to save computational time and design effort by identifying the most important design parameters.

A progressive failure analysis of all-C/SiC composite multi-bolt joints

A progressive damage model (PDM) was proposed to analyse the failure of plain-weave carbon fibre-reinforced silicon carbide (C/SiC) composite joints with C/SiC bolts, which were manufactured by the chemical vapour infiltration (CVI) technique. A bilinear constitutive model was established to describe the pseudo-plasticity of the C/SiC composites. Several failure criteria, including the maximum stress failure criterion, Tsai-Wu failure criterion, and Hashin-type criterion, and several material degradation models were compared. Moreover, the deposition models accounting for the deposition effects of CVI in the all-C/SiC composite joints were discussed. A series of comparative failure analyses of a C/SiC open-hole composite laminate with available experimental data in the literature was conducted to determine the most suitable combination of the Hashin-type criterion and the combined material degradation model was filtered for C/SiC composite structures. Based on the PDM, the failure strength and failure pattern of an all-C/SiC composite single-lap, three-bolt joint were predicted. Static tension experiments testing the all-C/SiC composite single-lap, three-bolt joints fabricated by the CVI technique were also conducted. Good consistency between the numerical failure predictions and the experimental outcomes was obtained, indicating the effectiveness of the proposed PDM for failure analyses of all-C/SiC composite multi-bolt joints.

Investigation of bolt load redistribution and its effect on failure prediction in double-lap, multi-bolt composite joints

A test method was presented to measure the bolt load distribution in the progressive damage process of multi-bolt composite joints, which exhibits continuous changes with the damage propagation in composite laminates. Based on the repeated loading-unloading cycles, bolt shear loads of a double-lap, three-bolt joint were tested by alternately using modified instrumented bolt-nut pairs and aircraft-grade fasteners, from which the bolt load redistribution history was achieved. In addition, a progressive damage method was adopted to trace the load redistribution history of the joint. The numerical predictions were in good agreement with the experimental outcomes, both of which show that the load distribution tended toward equal proportions before the final failure of the joint. Using a modified failure envelope method, the failures of two-, three- and four-bolt composite joints were predicted based on the uniform load distribution and actual load distribution, and compared with that based on the traditional load distribution calculated by a traditional stiffness method (TSM). It follows that the effect of the actual load distribution on the failure of the multi-bolt joints can be more faithfully reflected by adopting a uniform load distribution than by the traditional one.

An improved spring method for calculating the load distribution in multi-bolt composite joints

Abstract Fast and reliable prediction of the load distribution is necessary in the initial design of the composite bolted joint structures. Traditional spring method is time consuming in the modelling of a composite bolted joint structure. In this paper, an improved spring method considering the hole clearance and friction effects is developed for efficient modelling of the composite bolted joint structures. This method is based on spring method and finite element theory. A seven-bolt double-lap joint model is built as an example to study the effects of plate width, plate thickness, bolt pitch and clearances on the load distribution. The improved spring method is also adopted in the Monte Caro simulation with clearances considered as uncertain-but-bounded parameters. The results show that the proposed method is time efficient for the load distribution prediction of the bolted joint composite structures.

Global sensitivity analysis of load distribution and displacement in multi-bolt composite joints

Abstract This paper presents the development of a novel methodology for global sensitivity analysis of multi-bolt composite joints. Two sources of uncertainty were considered, i.e., the mechanical properties of composite plies and the bolt-hole clearance which comes from assembly phase. The uncertainty propagation in the composite plate was derived through the classical laminate theory, while the load distribution within bolts and the joint displacement were determined by an analytical spring-based method. A kind of Monte Carlo simulation was used to calculate the variance-based sensitivity indices. Furthermore, the proposed methodology was applied to a generic single-lap composite joint, which can also be extended to represent double-lap joints, to identify the significant input random variables with respect to structural responses of the joint. Useful conclusions for the design of multi-bolt composite joints were obtained from the computational results and discussions.

Coupled continuum damage mechanics and failure envelope method for failure prediction of composite multi-bolt joints

A numerical strategy, based on continuum damage mechanics and the failure envelope method, is proposed for failure prediction of composite multi-bolt joints. First, the design parameters of the failure envelope are determined by virtual tests of simple structures. Then, a modified failure envelope incorporating the bending effect is constructed. Finally, different bearing-to-bypass stress ratios and the influence of bolt rows on the bending effect are discussed. It is shown that the failure envelope with constant bearing-to-bypass stress ratio, obtained by assuming uniform bolt load distribution, is recommended. And the bending effect of single-lap, composite multi-bolt joints is alleviated by the introduction of more bolt rows. These results indicate that failure prediction of composite multi-bolt joints, using the proposed numerical strategy, exhibits excellent agreement with the experimental outcomes. This demonstrates that the numerical strategy is feasible.

Effect of damage on failure mode of multi-bolt composite joints using failure envelope method

Failure envelope method is comprehensively used in failure mode prediction of multi-bolt composite joints. The method is based on the assumption that bolt load distribution proportion is constant till failure. However, bearing damage and net-section damage must have some influence on the load distribution and then change structure failure mode. In this paper, tensile experiments of two-bolt and three-bolt joints were conducted to obtain the failure modes and other properties. Three dimensional (3D) finite element models involving damage were constructed, and the results were consistent with experimental data. Then, the models were used to study the effect of damage on failure mode of multi-bolt composite joints. The results show that failure mode prediction with failure envelope method should involve the effect of composite damage. Compared with net-section damage, bearing damage has greater influence on failure mode. Based on conventional failure envelope method, a new evaluation procedure involving damage was proposed.

A three dimensional implicit finite element damage model and its application to single-lap multi-bolt composite joints with variable clearance

A three-dimensional, implicit, finite element composites damage model is developed, and applied to a problem involving highly complex, three-dimensional loading, i.e. a single-lap, multi-bolt, composite joint, having variable clearances. The model extends a previous model, adding Puck’s criteria to allow delamination-like, transverse cracking-like or mixed mode failures to be simulated. Plasticity is also added for non-reversible strains in the undamaged parts of the matrix, and a mesh independence strategy is incorporated. A back-up strategy for when the Newton–Raphson method fails to converge, adds significantly to model robustness. The model is implemented in a commercial, implicit solver and demonstrates excellent robustness, being capable of following damage progression from onset, through bearing failure at the holes, to catastrophic, net-tension failure. The predicted failure modes and loads are in good agreement with experiment. The effect of clearance on secondary bending, and consequently on damage progression, is demonstrated. The current model shows better capability than our previous model for predicting matrix damage near the hole, which will be important for future fatigue modelling studies.

An analytical joint stiffness model for load transfer analysis in highly torqued multi-bolt composite joints with clearances

An analytical tri-linear joint stiffness model accounting for the effect of bolt-hole clearances on the bearing chord stiffness is presented. A single-parameter iteration method is also proposed to solve the nonlinear system of equations of the load transfer analysis, in which the recursive formulae are verified to be monotonic. To verify the present joint stiffness model, a series of single-lap, single-bolt joints with various bolt-hole clearances and bolt tightening torques were tested to empirically confirm the influence coefficients of the joint stiffness model. The load distributions in three single-lap, three-bolt joints with various clearances were also tested under finger-tight and highly torqued conditions. The load distributions in multi-bolt joints predicted by the presented joint stiffness model together with the single-parameter iteration method are in good agreement with the experimental outcomes, verifying the accuracy of the presented joint stiffness model and the feasibility of the single-parameter iteration method. In addition, the effects of the friction forces originated from the bolt-tightening torque and bolt-hole clearances on the load distribution in multi-bolt joints are presented.

Investigation on characteristic length testing methods for failure prediction of composite multi-bolt joints

Characteristic lengths (CLs) are key factors in the characteristic curve method (CCM), which is widely used in engineering to predict the failure of composite multi-bolt joints. They directly affect the accuracy of predicting the joint failure. To identify suitable CL testing methods, six schemes have been designed and tested, in which two tensile CL specimens (open- and filled-hole laminates) and three compressive CL specimens (semi-circular notch laminates, pin-loaded hole laminates and single-bolt joints) have been compiled. Additionally, 3D FE analyses on the stress concentration have been performed and a discussion of the unit failure index curves of different specimens has been carried out to explore their load-carrying mechanism and determine why they result in different CLs. Failure predictions of composite multi-bolt joints by using the CCM with different CL testing schemes have been compared and evaluated using related static tensile experimental results. Filled-hole laminates for the tensile CL and single-bolt joints for the compressive CL are recommended because they best approximate the actual structure and obtain accurate failure predictions for composite multi-bolt joints.

Effects of material nonlinearity on load distribution in multi-bolt composite joints

In this manuscript, an analytical approach is presented to determine load distribution in single-column multi-bolt composite joints by taking into account the effect of material nonlinearity of the joint members. For this purpose, an integration of traditional spring–mass model in joints and nonlinear Tsai–Hahn formula in polymeric composites were employed to construct a new computational tool for joint design. Load–displacement curve of the joint by considering material nonlinearity revealed of 3.66% and 3.97% more displacement at constant force in comparison to the linear case of three and five bolted joints, respectively. In addition, it was shown that increasing the degree of material nonlinearity of the members increased and decreased the amount of the load transferred by the outer and inner bolts of the joint, respectively. Findings of this research in comparison to the linear results are a promising step forward in designing of reliable composite joints.

An analytical model for the prediction of load distribution in multi-bolt composite joints including hole-location errors

In the aircraft industry, the method for designing metal-composite joints is mainly based on conservative metallic calculation rules and on applying high safety factors. The reason is that the influence of errors due to manufacturing is not well-known, and few studies deal with this issue. Here, an analytical model is developed to evaluate load distribution in an aluminium-composite double-lap joint, in the presence of clearance and hole-location errors. The model also includes the nonlinear behaviour of the bolt implied by bearing degradation. The analytical model is validated by comparing results obtained by finite element analysis and experiments. Finally, an industrial use of the analytical model is presented.

Determination method of stress concentration relief factors for failure prediction of composite multi-bolt joints

Stress concentration relief factor, which reflects the linear relationship between the stress concentration factors of composite joint and those of elastic isotropic joint, was proposed by Hart-Smith for the failure prediction of composite multi-bolt joints. It is deemed to be determined by experiments from either unloaded- or loaded-hole laminates and is suitable for investigations of bypass and bearing stress concentration factors. To examine this viewpoint, in this paper, the stress concentration relief factor is determined by tensile tests of open-, filled- and loaded-hole laminates failing in tensile mode, respectively. It can be found that the loaded-hole has obviously high-stress concentration level, while the filled-hole has slightly higher stress concentration than that of open-hole. Detailed 3D-FE analyses are performed to disclose the stress concentration mechanisms of three hole-laminates. Various stress concentration relief factors are combined to calculate bearing and bypass stress concentration factors, which provide the failure envelope for the strength prediction of composite joints. Moreover, both conventional and modified failure envelopes are discussed. Experimental results of two-, three- and four-bolt joints are provided to investigate the suitability of different failure envelopes. It follows that the stress concentration relief factor for bearing stress concentration factor needs to be determined by a loaded-hole laminate, while that for bypass stress concentration factor can be determined by each of open-, filled- and loaded-hole laminates.