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.     

Analysis of bolted joints in composite laminates: Strains and bearing stiffness predictions

A review of the investigations conducted on mechanically fastened joints is presented. A finite-element model is developed to predict the response of pin-loaded composite plates. The model takes into account contact at the pin–hole interface, progressive damage, large deformation theory, and a nonlinear shear stress–strain relationship. To predict progressive ply failure, four different analyses combining Hashin and the maximum stress failure criteria, and different associated degradation rules are conducted. The objectives of the study are to determine the influence of the failure criteria and the associated degradation rules on the predictions of the strains around the hole and the bearing stiffness. Predictions are compared with experimental results. It appears that agreement between the two depends on an appropriate selection of the failure criterion and the degradation rule. Better agreement between experimental results and numerical predictions is observed with the maximum stress criterion.     

Structural analysis of composite bolted joints using the complex potential method

The problem of a pin-loaded hole in a symmetric composite plate with finite dimensions is considered within the scope of the classical laminate theory. The analysis is performed by means of the Lekhnitskii complex potential method. For the given problem, an appropriate power series expansion of the complex potentials is stipulated, where the coefficients are determined from the underlying boundary conditions. The present approach provides an efficient method for the calculation of stresses and displacements in the neighbourhood of the hole where failure is likely to occur.     

On the prediction of bolted single-lap composite joints

A new set of failure criteria to predict composite failure in single-lap bolted-joints is proposed. The present failure criteria are an extension of Chang–Lessard criteria considering a three-dimensional stress field and including out-of-plane failure modes. The advantage with respect to other three-dimensional failure criteria is the consideration of non-linear shear stress–strain relationship. The failure criteria were implemented in a finite element model and validated through comparison with experiments in literature. Stresses were calculated by a non-linear finite element model developed in ABAQUS/Standard which considers material and geometric nonlinearities. A progressive damage model was implemented in a USDFLD subroutine. The model predicted the effect of secondary bending and tightening torque showing an excellent agreement with experimental results. Moreover, results were compared with those reported in literature using Hashin failure criteria. In addition, a parametric study was carried out to analyse the influence of friction coefficient and tightening torque.     

An analytical solution for the analysis of symmetric composite adhesively bonded joints

Analytical solutions for adhesively bonded balanced composite and metallic joints are presented in this paper. The classical laminate plate theory and adhesive interface constitutive model are employed for this deduction. Both theoretical and numerical (finite element analysis) studies of the balanced joints are conducted to reveal the adhesive peel and shear stresses. The methodology can be extended to the application of various joint configurations, such as single-lap and single-strap joints to name a few. The methodology was used to evaluate stresses in several balanced adhesively bonded metallic and composite joints subjected to the tensile, moment and transverse shear loadings. The results showed good agreements with those obtained through FEM.     

复合材料螺栓连接预紧力松弛的温度-时间依存行为

针对碳纤维增强环氧基复合材料机械连接结构耐久性设计中的2个关键问题:黏弹性预紧力松弛的温度-时间依赖行为及其长期性能预测方法进行研究。建立了以蠕变全应变理论为基础的预紧力松弛预测模型。36 h的恒温耐久试验表明:初始预紧力越大,温度越高,连接件预紧力松弛速率越快;复合材料连接件的松弛速率远大于金属连接件;预紧力松弛主要表现为材料蠕变过程。对比短期试验结果表明:本模型能较好地实现对不同温度、预紧力和连接材料的松弛预测,为确立试验数据的外推方法提供了依据。      

复合材料双面贴补修理拉伸解析分析模型及试验验证

复合材料胶接修理是一种有效并且低成本的修理技术。本文建立了复合材料层合板双面贴补胶接修理解析分析模型。模型中考虑了搭接区阶梯末端截面积变化细节。预测失效时,层合板采用最大应变准则,胶层采用最大剪应变准则和损伤区域理论。定义了残差函数来表征极限载荷解析计算结果与试验值的接近程度。通过试验对解析模型得到的等效刚度与极限载荷进行了验证。解析分析结果与试验数据对比表明:复合材料层合板双面贴补等效刚度随着搭接长度的增加单调增加。解析模型计算的等效刚度与试验结果最大误差不超过15%。当损伤特征长度为4%时,损伤区域理论对应极限载荷残差值最小,仅为4.30%,最大剪应变准则预测极限载荷的残差值为6.41%。解析模型分析表明,双面贴补极限载荷随着搭接长度的增加表现为快速增长、缓慢增长和几乎不增长三个阶段。搭接长度结合结构减重等限制因素应选择15~35mm为宜。     

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。     

An analytical modelling technique for predicting the stiffness of 3-D orthotropic laminated fabric composites

A new analytical modelling approach for the prediction of the stiffness of 3-D orthotropic laminated composites is given. The composite, which consists of stacked orthotropic layers which are in turn composed of a number of parallel unidirectional stripes, is assumed to be homogeneous and orthotropic macroscopically. The technique introduced is to discretise the representative unit cell of the composite into slices (layers) and then stripes (elements). The stiffness of each slice can then be obtained under the condition of isostrain or isostress. The final stiffness of the composite is formulated analytically by combining these slices. The model eliminates the inconsistency between macro- and micro-level strains and gives more realistic distributions of strain for the representative unit cell. The results demonstrate that the present model, which is both simple and computationally efficient, can give a very accurate prediction compared with data from experiments and some existing models.     

复合材料层合板多钉连接结构累积损伤过程可视化仿真模拟

建立了分析复合材料层合板多钉连接结构的三维有限元模型, 考虑了接触状态非线性和累积损伤过程非线性的影响, 运用ANSYS 中的APDL 编制程序实现了对复合材料层合板机械连接结构整个承载过程的可视化仿真模拟, 同时进行了T300/ Q Y9512 复合材料层合板多钉单剪拉伸试验。结果表明, 在一定几何尺寸下, 复合材料层合板多钉连接结构钉载分配的不均匀性在整个承载过程中并无明显改善。根据本文中提出的累积损伤模型对各孔位变形进行了计算, 计算结果与试验结果吻合较好。从累积损伤过程的仿真结果可以明显看出, 不同几何尺寸的多钉连接结构中各钉孔附近损伤的起始和发展过程具有明显的区别。优化设计结果表明, 不同钉孔处层合板厚度的改变对各钉钉载分配无明显影响, 但孔边法向和切向应力大小和分布均受到严重影响, 对整个多钉连接结构的损伤程度产生很大变化。      

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.     

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.     

Analysis of the bearing response test for polymer matrix composite laminates: bearing stiffness measurement and simulation

This paper is the first part of a project that aims to investigate the mechanical and fracture behaviour of bolted joints in general purpose glass fibre-reinforced polyesters (GRP). In the present study a procedure is set up to measure the bearing stiffness of a GRP laminate in a single-bolt double lap joint. With a three-dimensional finite element model it is shown that the bolt and fixture deformations affect the stiffness results. Hence the experimental displacement data were corrected before calculating the coupon bearing stiffness. The coupon bearing stiffness was also simulated by a two-dimensional finite element model. Provided that bolt–hole clearance, material non-linearity and bolt–hole friction are taken into account, good agreement is observed with experimental data. Bearing strain and bearing stiffness are based on the bearing deformation of the coupon, not on the hole elongation. This makes the stiffness data useful for design and allows an easy installation of the displacement measurement devices.     

Effect of clamping force on the delamination onset and growth in bolted composite laminates

Clamping force is a key element that alters the mechanism and sequence of failure in bolted joints of composite laminates. The mode of failure in bolted joints can be controlled by geometrical parameters and the preferred fail safe mode of failure is ‘bearing’ which generally consists of matrix cracks, delamination and fibre microbuckling. Three-dimensional (3-D) pinned (without clamping force) and bolted (1 kN clamping force) joint models were developed in [0/90]_s carbon fibre reinforced plastic (CFRP) laminates to show the clamping force effect on the onset and growth of delamination. It is shown that delamination was resulted from the shear stress components (Mode II & III) at the interface and the contribution of the out-of-plane component (Mode I - opening), so the clamping force, was negligible without modelling the in-plane failure modes and their coupling with delamination, which will be considered in future work.     

An analytical model for estimating deformation in laser forming

Laser forming of metal sheets offers the advantages of requiring no external forces and thus reduces cost and increases flexibility. This paper presents an analytical model to estimate the angle bent during the laser forming of a sheet. Plastic deformation is considered during both heating and cooling and is calculated based on a history-dependent incremental stress–strain relationship. On the basis of the proposed model with known temperature distributions, the bending angle induced by laser can be calculated. Comparison of the present model with experiment data is provided to demonstrate the accuracy of the present model under both TGM and BM.     

An investigation on strain/stress distribution around the overlap end of laminated composite single-lap joints

The damages of laminated composite single-lap joints often begin from their overlap ends because strain/stress concentrations often occur at the overlap ends. This paper presents the results of a combined experimental and finite element (FE) investigation on the strain/stress distributions around the overlap ends of laminated composite single-lap joints. Digital image correlation (DIC) technique is used to measure the strain fields near the overlap ends. A three-dimensional geometrically nonlinear FE model based on the submodel technique is developed to predict the deformation of single-lap joints. A reasonable agreement is achieved between the results from experimental measurements and FE analysis. Additionally, some FE models are built to investigate the effects of the mesostructures at the overlap ends on the stress concentrations around the overlap ends.     

An analytical model for the vibration of a composite plate containing an embedded periodic shape memory alloy structure

This paper explores the integration of a periodic repeating arrangement of shape memory alloy (SMAs) within a composite plate, with a view to active control of the vibrations of the plate by means of a controllable activation strategy for the SMA elements. The benefits of this configuration are that ‘antagonistic’ operation of SMAs on the plate allows the significantly longer cooling time constant of previously activated elements to be shortened by means of active elements working against them during that phase. This concept dramatically shortens the cooling time constant and brings it into the same order of magnitude of the heating phase. The paper examines the mathematical modelling of such a plate, and offers an approximate analytical solution by means of a hybrid WKB–Galerkin method. The antagonistic operation of the system is represented mathematically by terms in which the stiffness and damping are both time dependent. Therefore the equation of motion contains terms with time variant coefficients and is impossible to solve without recourse to specialised methods. Comparisons with numerical methods are given and it is shown that good similarity can be obtained for judicious choice of practical values for the time variant stiffness and damping functions.     

Investigation of precipitate refinement in Mg alloys by an analytical composite failure model

An analytical model is developed to simulate precipitate refinement in second phase strengthened magnesium alloys. The model is developed based on determination of the stress fields inside elliptical precipitates embedded in a rate dependent inelastic matrix. The stress fields are utilized to determine the failure mode that governs the refinement behavior. Using an AZ31 Mg alloy as an example, the effects the applied load, aspect ratio and orientation of the particle is studied on the macroscopic failure of a single α-Mg₁₇Al₁₂ precipitate. Additionally, a temperature dependent version of the corresponding constitutive law is used to incorporate the effects of temperature. In plane strain compression, an extensional failure mode always fragments the precipitates. The critical strain rate at which the precipitates start to fail strongly depends on the orientation of the precipitate with respect to loading direction. The results show that the higher the aspect ratio is, the easier the precipitate fractures. Precipitate shape is another factor influencing the failure response. In contrast to elliptical precipitates with high aspect ratio, spherical precipitates are strongly resistant to sectioning. In pure shear loading, in addition to the extensional mode of precipitate failure, a shearing mode may get activated depending on orientation and aspect ratio of the precipitate. The effect of temperature in relation to strain rate was also verified for plane strain compression and pure shear loading cases.     

复合材料层合板单钉双剪连接挤压强度的一种工程估算方法

将上限理论应用到复合材料层合板单钉双剪连接挤压强度分析中, 把连接结构的位移场划分为动态区域(层合板)和静态区域(紧固件), 并认为失效发生在位移可动场和不动场之间的钉孔边受挤压部分。由于受挤压孔孔边各层应力状态不一样, 受挤压孔边各层的失效区域和失效模式也各不相同。从宏观上研究复合材料层合板单钉连接孔边的失效区域和失效模式, 结合上限理论提出了一种估算复合材料单钉连接挤压强度的工程算法。通过与试验结果对比, 发现该方法能较好地预测出复合材料单钉双剪连接挤压强度。     

Nonlinear finite element analysis of stress and strain distributions across the adhesive thickness in composite single-lap joints

A geometrically nonlinear, two-dimensional (2D) finite element analysis has been performed to determine the stress and strain distributions across the adhesive bond thickness of composite single-lap joints. The results of simulations for 0.13 and 0.26 mm bond thickness are presented. Using 2-element and 6-element mesh schemes to analyze the thinner bond layer, good agreement is found with the experimental results of Tsai and Morton. Further mesh refinement using a 10-element analysis for the thicker bond has shown that both the tensile peel and shear stresses at the bond free edges change significantly across the adhesive thickness. Both stresses became increasingly higher with distance from the centerline and peak near but not along the adherend–adhesive interface. Moreover, the maximum shear and peel stresses occur near the overlap joint corner ends, suggesting that cohesive crack initiation is most likely to occur at the corners. The dependence of stress and corresponding strain distributions on bond thickness and adhesive elastic modulus are also presented. It is observed that the peak shear and peel stresses increase with the bond thickness and elastic modulus.