A Point‐wise Approach to the Analysis of Complex Composite Structures Using Digital Image Correlation and Thermoelastic Stress Analysis

Thermoelastic stress analysis (TSA) and digital image correlation (DIC) are used to examine the stress and strain distributions around the geometric discontinuity in a composite double butt strap joint. A well‐known major limitation in conducting analysis using TSA is that it provides a metric that is only related to the sum of the principal stresses and cannot provide the component stresses/strains. The stress metric is related to the thermoelastic response by a combination of material properties known as the thermoelastic constant (coefficient of thermal expansion divided by density and specific heat). The thermoelastic constant is usually obtained by a calibration process. For calibration purposes when using orthotropic materials, it is necessary to obtain the thermoelastic constant in the principal material directions, as the principal stress directions for a general structure are unknown. Often, it is assumed that the principal stress directions are coincident with the principal material directions. Clearly, this assumption is not valid in complex stress systems, and therefore, a means of obtaining the thermoelastic constants in the principal stress directions is required. Such a region is that in the neighbourhood of the discontinuities in a bonded lap joint. A methodology is presented that employs a point‐wise manipulation of the thermoelastic constants from the material directions to the principal stress directions using full‐field DIC strain data obtained from the neighbourhood of the discontinuity. A comparison of stress metrics generated from the TSA and DIC data is conducted to provide an independent experimental validation of the two‐dimensional DIC analysis. The accuracy of a two‐dimensional plane strain finite element model representing the joint is assessed against the two experimental data sets. Excellent agreement is found between the experimental and numerical results in the adhesive layer; the adhesive is the only component of the joint where the material properties were not obtained experimentally. The reason for the discrepancy is discussed in the paper.     

Strain energy release rate determination of prescribed cracks in adhesively-bonded single-lap composite joints with thick bondlines

An analytical model for determining the strain energy release rate due to a prescribed crack in an adhesively-bonded, single-lap composite joint with thick bondlines and subjected to axial tension is presented. An existing analytical model for determining the adhesive stresses within the joint is used as the foundation for the strain energy release rate calculation. In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory. In order to simulate the thick bondlines, the field equations of the adhesive are formulated using the linear elastic theory to allow non-uniform stress distributions through the thickness. Based on the adhesive stress distributions, the equivalent crack tip forces are obtained and the strain energy release rate due to the crack extension is determined by using the virtual crack closure technique (VCCT). The specimen geometry of ASTM D3165 standard test is followed in the derivation. The system of second-order differential equations is solved to provide the adherend and adhesive stresses using the symbolic computational tool, Maple 7. Finite element analyses using J-integral as well as VCCT are performed to verify the developed analytical model. Finite element analyses are conducted using the commercial finite element analysis software ABAQUS™. The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses. It can be seen that the same prescribed crack has a higher strain energy release rate for the joints with thicker bondlines. This explains the reason that joints with thick bondlines tend to have a lower load carrying capacity.     

New Initiatives on Comparison of Whole-field Experimental and Numerical Results

Abstract: A simple approach to plot photoelastic fringes in grey scale and also in colour from finite element (FE) results is presented for better recognition and comparison with experiments. This requires proper identification of the plotting variable from FE results. For comparison with transmission photoelasticity, post-processing of principal stress difference is needed and for reflection photoelasticity the principal strain difference is to be used. The importance of the use of appropriate correction factors for comparison with reflection photoelastic results is emphasised. A newer approach to evaluate R _f for complicated geometries is indicated. Plotting of experimental fringes from finite elements is useful not only for validating the numerical model based on experiments but also for validating the experiments. To illustrate this, the problem of an interfacial crack in a bi-material Brazilian disc is discussed.     

Photoelastic Investigation of Bimaterial Interfacial Stresses Induced by Thermal Loading

Abstract:  In this paper, the photoelastic technique and finite element method were employed to investigate the interfacial stresses induced by thermal loading in bimaterial structures. By observing the photoelastic fringe patterns, in comparison with those theories developed by other investigators, severe temperature and stress gradients were found across the specimens' heights. The maximum fringe order near the interface was six times that near the top surface of the photoelastic material when the temperature was raised to 65 °C. Furthermore, for the bimaterial structures, differences were found between measured stress fields as a result of increasing and decreasing temperature differences.     

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。      

复杂受力大直径焊接空心球节点的有限元分析与足尺试验研究

针对某体育馆拱形屋盖的超大直径焊接空心球节点设计的需要,对该球节点进行了有限元非线性分析和足尺模型试验研究。首先采用ANSYS软件的shell143弹塑性壳单元,同时考虑几何和材料双重非线性,通过有限元分析得到了该节点的应力分布规律,且在1.5倍设计荷载作用下,四号锥管根部首先屈服。然后,对该节点进行了足尺模型试验,试验结果表明:在1.4倍设计荷载作用下,四号锥管根部首先进入屈服,试验结果和有限元结果基本一致。基于研究结果,为工程节点设计提供了重要建议。     

Process parameters design of a three-dimensional and five-directional braided composite joint based on finite element analysis

This paper presents an analytical method for designing the configuration of composite joint with three-dimensional (3D) five-directional braided composites. Based on the analysis of 3D braided structure characteristics, the elastic properties of the 3D five-directional braided composites were determined by the volume averaging method. The effects of the braiding angle and fiber volume fraction on the elastic constants of the braided composites were also discussed. Finite element analysis on the load capacity of the 3D five-directional braided composite joint was implemented using the software ANSYS Workbench 14.0. The influence of braiding angle on the stress, strain and deformation of the composite joint under tensile loading were calculated. The results show that when the fiber volume fraction of the 3D five-directional braided preform is given, the equivalent stress of the composite joint decreases monotonically as the braiding angle increases, while the normal stress, maximum principal stress and total deformation firstly decreases and then increases. Based on the finite element analysis, we found that at the fiber volume fraction of 60%, the braiding angle within the range of 30–35° are the optimum processing parameters for the 3D five-directional braided composite joint structure that used in the tensile load 320 N condition.     

On design methods for bolted joints in composite aircraft structures

The problems related to the determination of the load distribution in a multirow fastener joint using the finite element method are discussed. Both simple and more advanced design methods used at Saab Military Aircraft are presented. The stress distributions obtained with an analytically based method and an FE-based method are compared. Results from failure predictions with a simple analytically based method and the more advanced FE-based method of multi-fastener tension and shear loaded test specimens are compared with experiments. Finally, complicating factors such as three-dimensional effects caused by secondary bending and fastener bending are discussed and suggestions for future research are given.     

Multiphase hybrid stress finite element analysis of heterogeneous media by simple mesh: One element with one interface

In this paper, a finite element method is proposed to analyze the microscopic and macroscopic mechanical behaviors of heterogeneous media with randomly distributed inclusions. A simple mesh partitioned the domain into regular quadrilateral or triangular elements, where one element may contain two phases. An assumed stress hybrid formulation is implemented in the finite element model and the functional is derived for an element containing two phases. Numerical examples were used to study the microscopic and macroscopic properties of the composites, such as the effective modulus, to validate of the proposed model. The results show that the proposed multiphase hybrid stress finite element model can accurately measure the stress fields of materials with arbitrary microstructural distributions and improve computational efficiency by about 30 to 1500 times in comparison with the traditional displacement based finite element method.     

钢框架梁柱端板连接的非线性有限元分析

运用通用有限元软件ANSYS建立三维有限元模型,对8个不同形式、不同构造的钢框架梁柱端板连接进行了非线性有限元分析(FEA),并与相应的试验结果进行了全面对比分析。比较结果表明:该文的有限元模型不但能够准确地分析计算各种类型和不同构造的钢框架梁柱端板连接节点的整体受力特性,包括承载力、弯矩-转角(M-φ)曲线、极限变形状态等,还能有效地分析计算节点及其组件的细部受力特性,包括高强度螺栓的预拉力,端板和柱翼缘之间的接触状态,以及节点域、端板、螺栓、端板加劲肋、节点域加劲肋等组件的受力状态,为进一步运用该模型对各种形式和构造的端板连接进行全面的有限元参数分析计算提供了正确性依据。同时,有限元分析还给出了螺栓预拉力引起的接触面预压力分布、荷载作用下接触面的摩擦力分布以及节点的主应力流分布等对于全面和深入理解端板连接节点受力特性非常有意义但是又难于通过试验进行测量的结果。     

An analytical and experimental study of the plate tearing mode of fracture

Certain analytical and experimental aspects of the fracture of cracked thin plates subjected to pure twisting moments are examined. A simplified analytical and finite element approach to evaluate plate tearing mode stress intensity factors is proposed. A photoelastic study was also performed to observe the crack-tip fringe patterns and evaluate the plate tearing mode stress intensity factors. Although the observed fringe patterns differed considerably from the predictions obtained using Williams' analysis, they were much closer to the predictions obtained using Reissner's bending theory and the approach proposed in this paper. The finite-element study using the proposed method as well as the Kirchoff bending theory showed that the stress intensity factors obtained using the proposed method agree more closely with the photoelastic results.     

Stress and failure analysis of crimped metal–composite joints used in electrical insulators subjected to bending

Experimental and numerical investigations are carried out on metal/fibreglass-reinforced-plastic joints integrated in electrical insulators subject to bending. Numerical stress and strain distributions through the bond are calculated with a solid 3D finite element model and the damage initiation in the composite is highlighted. The simulations are compared to experimental data obtained from several joint specimens tested under bending on an experimental setup equipped with strain gauges and a six-channel acoustic emission system. Good correlation between the finite element predictions and the test results is found. The investigations have identified the stress concentrations in the rod, the onset of damage when the load–displacement curve characterizing the bending test deviates from linearity, and the different failure mechanisms.     

On the determination of interfacial stresses in a composite material

The conventional finite element method has been modified to allow the elastic stresses along the fibre matrix interfaces of a composite to be determined with improved accuracy. The results obtained by this 'modified' method are compared with both a photoelastic and some traditional finite element solutions.     

Fatigue life estimation of coach peel riveted joints using multi-axial fatigue criteria

This study investigates fatigue behaviour of riveted joints in a coach peel configuration under various load ranges and load ratios. Three well-known multi-axial fatigue criteria of Smith–Watson–Topper, Glinka and Fatemi–Socie are used to predict the fatigue life of the joint based on the stress and strain components obtained from a finite element analysis. A three-dimensional finite element model was developed with considering elastic–plastic behaviour of aluminium alloy 2024-T3 for the joint plates as well as frictional contact between all the contacting parts. Fatigue life estimation results agreed well with existing experimental data for the same joint. This verifies the finite element results and shows how well the multi-axial fatigue equations can predict fatigue life of the riveted joints. The finite element modelling approach may be then used with confidence for fatigue life estimations of different configurations of riveted joints.     

Two- and three-dimensional elastic-plastic stress analysis for a double edge notched tension specimen

This paper describes an elastic-plastic stress analysis for a double edge notched tension specimen, a specimen used for the determination of the microscopic cleavage fracture stress. The analysis was performed numerically using the finite element method. First, a study of the finite element modelling is presented in order to demonstrate the requirements on a three-dimensional finite element structure leading to accurate stress distributions in the whole specimen. On the other hand possible restrictions are shown, if only a certain parameter, e.g. the maximum tensile stress has to be evaluated. Then the global response of the three-dimensional structure is compared with results of two-dimensional calculations assuming plane stress and plane strain, respectively. Subsequently the most interesting stress and strain distributions are discussed. The maximum value of stress concentration in front of the notch is given as a function of the applied stress. Additionally the state of deformation at fracture load is characterized by the plastic zone size, too. All three-dimensional results are compared with results of a plane strain model.     

Thermally induced birefringence in Nd:YAG slab lasers

We study thermally induced birefringence in crystalline Nd:YAG zigzag slab lasers and the associated depolarization losses. The optimum crystallographic orientation of the zigzag slab within the Nd:YAG boule and photoelastic effects in crystalline Nd:YAG slabs are briefly discussed. The depolarization is evaluated using the temperature and stress distributions, calculated using a finite element model, for realistically pumped and cooled slabs of finite dimensions. Jones matrices are then used to calculate the depolarization of the zigzag laser mode. We compare the predictions with measurements of depolarization, and suggest useful criteria for the design of the gain media for such lasers.     

The multi-load method of determining discrete system parameters in a loaded three dimensional photoelastic model

The determination of the secondary principal stress difference and their orientations for a discrete slice of thickness dz along a particular light path in a loaded three dimensional photoelastic model is discussed in this paper. It is well known that once the geometry of the loaded member and the geometry of loading on the member are fixed, the secondary principal stress directions at any particular point along any line of consideration remain constant. The secondary principal stress values will get multiplied by the factor through which the loading on the component is increased. This has been made use of in the present method and from the characteristic parameters obtained at the end of any light path for different loadings on the three dimensional model, the secondary principal stress difference and their orientations are obtained. The method proposed is a fully non-destructive method of testing and involves measurements only on a transmission polariscope.     

Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.     

Influences of heat source model on welding residual stress and distortion in a multi-pass J-groove joint

Welding mechanical behaviors including residual stress and distortion are highly non-linear phenomena in nature. When numerical simulation methods such as thermal elastic plastic finite element method (FEM) are used to quantitatively predict welding residual stress and distortion, a long computational time is required especially for multi-pass joints. In real engineering structures, many weldments have large dimensions and complex shapes, and they are usually assembled by a multi-pass welding process. Therefore, it is necessary to develop time-effective computational approaches for practice engineering analysis. In this study, a method based on variable length heat sources was proposed for the analysis of thermo-mechanical behaviors for multi-pass joints. The welding residual stress field in a dissimilar metal J-groove joint with axis-symmetric geometrical shape, which was performed by a semi-circle balanced welding process, was investigated using the proposed method. The simulation results were compared with the measured data as well as the simulation results computed by a moving heat source. Meanwhile, the instantaneous line heat source was also employed to estimate the welding residual stresses in the same joint in an extreme case. The influences of heat source model (type) on welding residual stress and distortion were discussed.     

复合材料管接头与钢管间摩擦力及其对管接头强度的影响——数值分析

通过定义接触单元, 建立了复合材料套管接头与钢管连接的有限元分析模型。分析了在钢管端部受到弯曲、压缩和扭转载荷条件下, 复合材料管接头的应力状态, 并采用Tsai-Wu 强度准则对复合材料管接头进行了强度分析。重点研究了随着摩擦系数的变化复合材料管接头与钢管间摩擦力的变化规律及其对复合材料接头强度的影响。结果表明, 随着摩擦系数的增大, 复合材料管接头与钢管间最大正应力减小, 最大摩擦力增大; 在以弯曲载荷为主的组合载荷作用下, 复合材料管接头的安全裕度增大。