An analytical model for the prediction of load distribution in highly torqued multi-bolt composite joints

This paper presents the development of an enhanced analytical approach for modelling the load distribution in multi-bolt composite joints. The model is a closed-form extension of a spring-based method, where bolts and laminates are represented by a series of springs and masses. The enhancement accounts for static friction effects between the laminates, a primary mechanism of load transfer in highly torqued bolted joints. The method is validated against detailed three-dimensional finite element models and where possible, experimental results. The effect of varying bolt-torque and bolt-hole clearance on the load distribution in a three-bolt, single-lap joint is investigated and the method proves to be robust, accurate and highly efficient. Finally, the method is employed in a parameter study, where increasing bolt torque levels can be used for achieving a more even load distribution in multi-bolt joints.     

GBJM方法的改进及其在含钉群复合材料结构钉载分配和承载能力分析中的应用

为了分析含钉群复合材料结构的钉载分配及承载能力问题,首先对Globle Bolted Joint Model(GBJM)方法进行了改进,然后采用改进的方法对复合材料多钉连接结构的钉载分配和承载能力进行了预测,并与试验结果进行了比较。结果表明:当孔边复合材料未出现损伤时,该方法对多钉载荷分配的预测和试验结果比较接近;而对结构承载能力的预测,该方法偏于保守,比试验结果约低15%。同时该方法具有两个显著优点:一是计算结构钉载分配时效率高,和三维有限元模型相比提高约75%;二是能够对含钉群复合材料结构的失效载荷进行有效的预测。     

An analytical model for the prediction of through-thickness stiffness in tension-loaded composite bolted joints

This paper presents the development of an analytical model for replicating the through-thickness stiffness of single-bolt, single-lap composite joints subjected to secondary bending. The model is an extension of a spring-based method, where bolts and laminates are represented by a series of springs and masses. The model accounts for extension of the bolt, the stiffness of the clamped region of the joint due to bolt torque, as well as the flexural stiffness and anticlastic curvature within the laminates. In order capture bolt extension and the stiffness of the clamped region, a closed form approach is used. An approximation approach is used to model flexural stiffness and anticlastic curvature within the laminates. The method is validated against detailed three-dimensional finite element models of bolted composite plates and good agreement was obtained. The method is subsequently employed to calibrate the through-thickness stiffness of single-bolt, single-lap joints in highly-efficient numerical models.     

Hybrid titanium–CFRP laminates for high-performance bolted joints

This paper presents an experimental and numerical investigation of the mechanical response of bolted joints manufactured using new hybrid composite laminates based on the substitution of CFRP plies with titanium plies. The local hybridization of the material is proposed to increase the efficiency of the bolted joints in CFRP structures. Two modeling strategies, based on non-linear finite element methods, are proposed for the analysis of the bolt-bearing and transition regions of the hybrid laminates. The bolt-bearing region is simulated using a three-dimensional finite element model that predicts ply failure mechanisms, whereas the free-edge of the transition region is simulated using plane stress and cohesive elements. The numerical and experimental results indicate that the use of hybrid composites can drastically increase the strength of CFRP bolted joints and therefore increase the efficiency of this type of connection. In addition, the numerical models proposed are able to predict the failure mechanisms and the strength of hybrid composite laminates with a good accuracy.     

考虑间隙配合的复合材料钉载分配均匀化方法

针对多钉连接中因复合材料脆性等因素导致结构中的钉载分配不均匀,以及接头在承载较大的钉位置易发生过早破坏的问题,提出了调整钉孔配合间隙改善钉载分配的不均匀性的优化方法。首先,基于弹簧质量模型,以钉孔间隙为设计变量,建立了多钉连接钉载分配的二次规划优化模型。然后,采用内点法对优化模型进行了求解,得到了优化模型的全局最优解。最后,以复合材料5钉双剪接头为例,对钉孔间隙进行了优化,将计算结果与有限元预测结果进行对比。结果表明:模型优化结果与有限元结果吻合较好,优化后最大钉载比例由41.1%降低到了20%。采用该模型可以高效、准确地实现复合材料多钉连接钉载分配比例的均匀化设计。      

BOLJAT: a tool for designing composite bolted joints using three-dimensional finite element analysis

This paper discusses the development of a software tool for design of composite bolted joints, using three-dimensional finite element analysis. The tool allows the user to create the joint geometry through a menu-driven interface and then generate a customised mesh according to the user's needs. Contact parameters are defined automatically, which shields the user from the most difficult part of the process. Boundary conditions, bolt pre-loads, and material properties can also be set. Only a few manual steps are necessary to complete the finite element code generation process. By automating the time-consuming model creation process, the tool facilitates the increased use of three-dimensional finite element analysis in the design of composite bolted joints. A case study is shown to demonstrate the usefulness of the tool.     

A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures

This paper presents the development of a highly efficient user-defined finite element for modelling the bolt-load distribution in large-scale composite structures. The method is a combined analytical/numerical approach and is capable of representing the full non-linear load-displacement behaviour of bolted composite joints both up to, and including, joint failure. In the elastic range, the method is generic and is a numerical extension of a closed-form method capable of modelling the load distribution in single-column joints. A semi-empirical approach is used to model failure initiation and energy absorption in the joint and this has been successfully applied in models of single-bolt, single-lap joints. In terms of large-scale applications, the method is validated against an experimental study of complex load distributions in multi-row, multi-column joints. The method is robust, accurate and highly efficient, thus demonstrating its potential as a time/cost saving design tool for the aerospace industry and indeed other industries utilising bolted composite structures.     

Progressive failure analysis of bolted single-lap composite joint based on extended finite element method

In this paper, extend finite element method (XFEM) is used to predict the failure of single-lap bolted joints. To simplify calculation of XFEM model, composite laminates of joint are modeled using linear elastic properties. Three-dimensional equivalent material properties are calculated by the MATLAB code written by author. Progressive failure of bolted single-lap composite joint is investigated, and the failure load of joint simulated by XFEM is compared with experiments in literature. Then the influences of geometric parameters on failure load of one bolt single-lap composite joint are studied. Two geometric parameters include plate width-to-hole diameter ratio (W/D) and the edge-to-hole diameter ratio (E/D). At last the failure of single-lap joints with one bolt and two bolts are compared.     

分析复合材料螺栓连接接头静强度的一种方法

根据复合材料机械连接区逐点逐层破坏的物理本质,采用了每层破坏单元刚度退化和应力空间二阶张量破坏准则,用有限元素法,计算了T300/648碳纤维复合材料21种不同铺层情况的接头强度,分析了它们的破坏模式和破坏过程并与试验结果进行了比较.      

复合材料单螺栓双剪搭接干涉配合疲劳强度评价

该文采用有限元软件ANSYS,建立了复合材料单螺栓双剪搭接干涉配合的三维有限元模型,研究了当连接模型中施加了预紧力时,预紧力对干涉配合的影响.首先分析了无载荷作用下复合材料板在干涉配合孔边切向应力分布特点;之后比较了双剪搭接在10kN 和15kN 两种远程纵向载荷作用下,孔边切向应力的分布情况.结果表明:远程纵向循环载荷作用下,预紧力能有效均匀各板所受载荷,并可消除在无预紧力时中板上的局部应力集中点,而且适当增大预紧力能提高干涉配合连接的效率;此外研究显示双剪搭接连接在不同的载荷下,疲劳危险点也不同;最后研究了复合材料干涉配合连接时,各板的交叉区域孔边切向应力分布,因此得出各板在高低不同的载荷下疲劳危险点的分布.     

A three-dimensional progressive damage model for bolted joints in composite laminates subjected to tensile loading

A three-dimensional progressive damage model was developed to simulate the damage accumulation and predict the residual strength and final failure mode of bolted composite joints under in-plane tensile loading. The parametric study included stress analysis, failure analysis and material property degradation. Stress analysis of the three-dimensional geometry was performed numerically using the finite element code ANSYS with special attention given to the detailed modelling of the area around the bolt in order to account for all damage modes. Failure analysis and degradation of material properties were implemented using a set of stress-based Hashin-type failure criteria and a set of appropriate degradation rules, respectively. In order to validate the finite element model, a comparison of stress distributions with results from analytical models found in the literature was carried out and good agreement was obtained. A parametric study was performed to examine the effect of bolt position and friction upon damage accumulation and residual strength.     

Analysis of bolted–bonded composite single-lap joints under combined in-plane and transverse loading

A semi-analytical solution method is developed for stress analysis of single-lap hybrid (bolted/bonded) joints of composite laminates under in-plane as well as lateral loading. The laminate and bolt displacements are based on the Mindlin and Timoshenko beam theories, respectively. For the adhesive, the displacement field is expressed in terms of those of laminates by using the shear-lag model. The derivation of the governing equations of equilibrium of the joint is based on the virtual work principle, where the kinematics of each laminate are approximated by local and global functions and the bolt kinematics is assumed in terms of cubic Hermitian polynomials. The capability of the present approach is justified by validation and demonstration problems, including the analysis of bolted and bonded joints and hybrid joints with and without considering a disbond between the adhesive and laminates.     

Numerical analysis of damage progression and strength of countersunk composite joints

A numerical investigation is conducted into the damage progression and strength of bolted joints between fibre-reinforced composite laminates using countersunk fasteners. Experimental tests were previously conducted on a bearing test specimen and countersunk fastener single-lap joints. In this work, computational models are developed for Abaqus/Explicit, with continuum shells employed to model in-plane ply failure. The bolt-nut assembly is modelled with rigid elements, and the models account for bolt torque and frictional contact. The material properties required in the computational model are determined from standard tests, with the compression fracture toughness of composite plies calibrated against experimental data from the bearing test. The analysis approach captures the load-carrying capability of all configurations, and provides reasonable accuracy in predicting damage patterns. The effects of bolt torque, clearance and countersink height ratio are investigated, and the analysis results compare well with experimental findings. Furthermore, the analysis provides rich insight into the damage progression and joint behaviour at the ply level, with the in-plane and through-thickness damage patterns mapped for increasing applied load. Delamination is incorporated using a cohesive element layer at the start of the countersunk region, though has minimal influence on damage progression and load-carrying capability, which agrees with the experimental results.     

Experimental and numerical investigation on bolted joint in glass–fiber reinforced composites

In this paper, vacuum assisted resin injection technique was employed to prepare the composite laminates with different plies ways. The macro-mechanical performances of the bolted joint of the composite laminates were investigated by experimental and finite element simulation. The influence mechanism of different parameters on the joint performance and failure models of the composite laminates were analyzed. A VUMAT subroutine was developed, according to the failure criteria and corresponding stiffness degradation criteria, to describe the progressive damage process of bolted joint composite laminates through finite element analysis method. The results indicated that the failure strength of composite laminates would be improved with the increasing of tightening torque, and the strength of three-ply-way hybrid composite laminates is higher than that of two-way hybrid laminates. The comparisons between numerical simulation results and experimental results showed that the developed subroutine can effectively predict the macroscopic response of bolted joint glass–fiber reinforced composite laminates.     

A Stacked-Shell Finite Element Approach for Modelling a Dynamically Loaded Composite Bolted Joint Under in-Plane Bearing Loads

This paper presents the results of a study into a novel application of the “stacked-shell” laminate modelling approach to dynamically loaded bolted composite joints using the explicit finite element code PAM-CRASH. The stacked-shell approach provides medium-high fidelity resolution of the key joint failure modes, but is computationally much more efficient than full 3D modelling. For this work, a countersunk bolt in a composite laminate under in-plane bearing loading was considered. The models were able to predict the onset of damage, failure modes and the ultimate load of the joint. It was determined that improved debris models are required in order to accurately capture the progressive bearing damage after the onset of joint failure.     

Strength prediction in CFRP woven laminate bolted double-lap joints under quasi-static loading using XFEM

The current paper is concerned with modelling damage and fracture in woven fabric composite double-lap bolted joints that fail by net-tension. A 3-D finite element model is used, which incorporates bolt clamp-up, to model a range of CFRP bolted joints, which were also tested experimentally. The effects of laminate lay-up, joint geometry, hole size and bolt clamp-up torque were considered. An Extended Finite Element (XFEM) approach is used to simulate damage growth, with traction–separation parameters that are based on previously reported, independent experimental measurements for the strength and toughness of the woven fabric materials under investigation. Good agreement between the predicted and measured bearing stress at failure was obtained.     

Failure Analysis of Bolted Joints in Cross-ply Composite Laminates Using Cohesive Zone Elements

A strength prediction method is presented for double-lap single fastener bolted joints of cross-ply carbon fibre reinforced plastic (CFRP) composite laminates using cohesive zone elements (CZEs). Three-dimensional finite element models were developed and CZEs were inserted into subcritical damage planes identified from X-ray radiographs. The method makes a compromise between the experimental correlation factors (dependant on lay-up, stacking sequence and joint geometry) and three material properties (fracture energy, interlaminar strength and nonlinear shear stress-strain response). Strength of the joints was determined from the predicted load-displacement curves considering sub-laminate and plylevel scaling effects. The predictions are in a reasonable agreement with the experimental data.     

T800碳纤维增强复合材料双剪单钉连接的拉伸试验及强度估算

为系统地研究T800碳纤维增强复合材料螺栓连接的力学性能,首先,对T800碳纤维增强复合材料双剪单钉连接进行了面内准静态拉伸试验,探讨了铺层比例、铺层顺序、螺栓直径以及固化工艺对复合材料螺栓连接刚度和2%偏移挤压强度的影响;然后,根据试验结果得到了T800碳纤维增强复合材料螺栓连接的应力集中减缓因子;最后,结合相应铺层比例的无缺口层合板的应力集中减缓因子和拉伸强度,建立了复合材料连接最终挤压强度的工程算法。结果表明:当螺栓断裂时,连接的最终挤压强度由螺栓剪切强度和螺栓直径/板厚比决定;连接存在挤压和剪切2种失效形式,与±45°铺层比例有关;工程算法的计算结果与试验结果吻合良好。所得试验结果和工程算法可为T800碳纤维增强复合材料螺栓连接的初步设计提供理论依据和技术支持。      

接头局部增强的复合材料层合板螺栓连接试验与数值模拟

采用真空辅助成型工艺（VARI）制备了四种局部增强的复合材料层合板螺栓连接试件，通过试验及数值模拟对其力学性能进行了研究。数值研究中将复合材料层合板连接件的拉伸作为一个准静态问题，运用ABAQUS的显示分析算法及所编写用户材料子程序VUMAT对连接件进行了三维渐进失效模拟，同时在有限元模型中采用内聚力单元模拟了层合板与所设增强层的界面分层失效。数值计算结果与试验结果取得了较好的一致，验证了本文中数值方法的有效性。研究结果表明，不同的局部增强方案对复合材料螺栓连接性能的影响较大，设置[0/90/0/90]_S铺层的内置纤维增强层能显著提高层合板的螺栓连接性能。     

复合材料3钉单搭连接有限元模拟与钉载分布

进行了复合材料一铝合金三钉单搭连接单向拉伸试验,测量了层合板面内位移、应变和离面位移随载荷的变化关系,建立了复合材料多钉单搭连接的三维累积损伤有限元模型,计算与试验对比结果表明,该模型可模拟大范围损伤发生之前的承载特性。采用试验和数值模拟相结合的方法研究了复合材料一金属三钉单搭连接钉载分布情况,结果表明：试验用复合材料-铝合金三钉单搭连接,螺栓1承载比例最高,螺栓3次之,中间螺栓的承载比例最低,并且螺栓承载比例在加载过程中基本保持不变;随着金属连接板刚度的增加,螺栓1的承载比例增加,螺栓3承载比例降低,中间螺栓2的承载比例变化较小,层合板离面位移减小;金属板配合间隙变化对钉载分布影响很小,但层合板的离面位移随配合间隙的增大而增大。