Bending analysis of a laminated composite patch considering the free-edge effect using a stress-based equivalent single-layer composite model

The interlaminar stresses of a laminated composite patch, which is made up of reinforcing fibers (carbon/graphite) and epoxy matrix are analyzed using a stress-based equivalent single-layer model under a bending load. The composite patch is frequently used as reinforcement for a metallic adherend of mechanical/aerospace structures (i.e., aluminum alloy, etc) by attaching the film- or paste-type adhesive (i.e., epoxy, BMI, etc). To calculate the adhesive stresses transferred from the substrate, an interlayer model is introduced. The adhesive stresses are obtained by solving the equilibrium equations. The stress fields of the patch are determined by assuming certain stress functions. To satisfy the equilibrium state of the patch, the stress functions are divided into homogeneous and particular parts. The adhesive stresses act as prescribed stress boundary conditions of the laminated composite patch. The stress functions are substituted into a complementary virtual work principle, and from this, two coupled ordinary differential equations are obtained. General eigenvalue problems are derived to solve the coupled governing equations. To demonstrate the validity and efficiency of the proposed method, cross-ply, angle-ply and quasi-isotropic laminated composite patches are studied. From the observations made, the authors found that the stress function-based approach is suitable for solving the stress prescribed boundary value problem with accuracy and efficiency compared to a displacement-based approach such as the finite element method. The proposed method can be used as an efficient tool in the initial design stage of structural components when it is necessary to consider the free-edge effect.     

Three-dimensional contact model for numerically analyzing pressure distribution in wear

Although FEM is adequate in solving most elastic and rough surface contact problems with acceptable accuracy, its requirement for a large number of elements jeopardizes its effective use in analyzing real surface contacts, the contact stresses and the surface profile over a finite area between two rough contact surfaces. To overcome this problem, a technique, for constructing 3D surface in a computer by modifying the available 2D finite impulse response (FIR) digital filter methods and using the fast Fourier transform (FFT) procedure, is proposed, by referring to SEM morphology and experimental results. The technique, incorporating the variatonal approach in minimizing the stored contact energy, eliminates the additional iteration needed in determining contact area. It can be used to predict: (i) the contact pressure distribution and contact statistics of 3D real rough surfaces, (ii) the real contact stresses between a rigid flat and various coated specimens, (iii) the contact stress distribution profile, (iv) the role of friction and stress distribution in wear process. This revised version was published online in August 2006 with corrections to the Cover Date.     

一种考虑胶瘤的胶接简化有限元模型:应力与刚度分析

胶接接头中总存在胶瘤,由于建模复杂,胶接接头有限元分析中胶瘤常被忽略.但胶瘤能减少峰值应力,提高结构强度和刚度.为此,提出一种简化的胶接有限元模型,即用壳单元代表胶瘤,体单元代表被粘体和胶层,并用弹性理论建立壳单元等效厚度公式.以体单元精细模型结果作为对比的真实解,考察五种载荷工况下,单搭接头简化有限元模型的胶层应力和刚度.分析表明,壳单元等效厚度公式正确,胶接简化有限元模型精度高,可用于诸如汽车等大型结构中;用壳单元简单模型可定量分析胶瘤大小和形状对接头应力和总体刚度性能的影响.     

齿轮接触安定分析

以Hertz理论为基础,建立齿轮的接触模型.针对齿轮接触表面层变曲率的特点,构造出局部坐标下残余应力应变场的分布状态,分析在此残余应力场分布状态下,齿轮接触的静力安定和机动安定的条件.采用应力应变释放的算法和不同啮合点局部坐标之间的转换法则,模拟齿轮在重复啮合过程中残余应力应变的累积过程,求解安定状态下残余应力的分布状况,确定齿轮接触的安定极限与摩擦因数和齿轮啮合位置之间的变化情况.     

考虑弯曲效应的混元胶接单搭接头应力模型

混元胶接接头是利用多种不同剪切弹性模量的胶层来传递被粘物载荷的单搭接头。它兼具胶层连续性连接和降低端头应力集中等优点,因此能充分利用被粘物材料性能(如复合材料)以提高接头强度。以典型双元胶接接头为对象,考虑加载作用线偏心引起的弯曲效应和胶层剥离正应力,建立被粘物为各向同性的线弹性双元胶接接头应力解析模型。理论模型中的胶层切应力、剥离正应力和上被粘物纵向正应力与精细有限元模型吻合得较好,证实了理论模型的正确性。参数研究中确定了影响混元胶层应力分布的关键耦合参数。     

多轴应力应变的一种新的计算方法

计算缺口件缺口处的应力应变方法有多种,其中应用较广的是具有能量观点的Neuber法和等效应变能密度法。通常Neuber法过高地估计应力和应变,等效应变能密度法过低地估计应力和应变。通过分析研究,文中引进屈服强度参数,提出一种新的计算方法。通过对同一构件缺口处的应力应变的计算结果进行比较可知,文中提出的新的计算方法是合理可行的,有较好的精度。     

A flat punch pressed against an elastic interlayer under conditions of slip and separation

The problem of a square-ended rigid punch bearing on an elastic half-plane through the medium of an elastically dissimilar interlayer is considered, under plane deformation. The interlayer is in frictional contact with both the punch and half-plane. Regions of slip and separation along the interface are found, and it is shown how these phenomena affect the stress state in the immediate neighbourhood of the contact. This problem is of direct, practical interest to the design of interfacial bearing pads employed in supporting glass plates in structural applications.     

弹性接触问题有限元分析的一个新方法

小变形弹性接触问题属于边界条件几何非线性问题弹性接触问题的非线性,是由于接触点的接触条件引起的。本文提出的有限元混合法适于求解此类局部非线性问题。该方法是利用弹性体的刚度矩阵求出接触边界的接触内力的影响系数矩阵,再由接触边界的连续性条件求解接触内力,从而把非线性问题转化到局部求解。计算表明：对求解此类复杂非线性问题,该方法在计算速度和机器存贮上仅比求解一般线性问题的花费略有增加甚至相当。     

Pre-stressed adhesive strap joints for thick composite sandwich structures

A simple but effective design to improve the strength of thick adhesive composite strap joints is validated with experiment and finite element method. The strap joint under investigation, with a particular application to naval ship structures, consists of two thick woven E-glass/vinyl ester laminates joined together with two steel doublers. Longitudinal tensile loads are applied to the joints, resulting in large concentrated shear and peel stresses near the free edges of bondlines. The new design intends to reduce the adhesive peel stress by application of through-the-thickness compressive pre-stress along the bondline and thus leads to an increase of joint strength. Experiment results show that all the joint failures are delamination of the top layer of the laminated adherends. The test further confirms that joint strength increases significantly by applying the transverse pre-stress. Finite element analysis reveals that the pre-stress can effectively reduce the magnitude even reverse the sign of the peel stress in the adhesive layer and the adherends. Recessing the adhesive leading edge could magnify the pre-stress effect and reduce the adhesive peel stress, but would increase the shear stress. For those composite joints with low transverse interlaminar strength and susceptible to delamination, this simple design/technique can considerably improve their joint strength.     

Stresses in hard coating due to a rigid spherical indenter on a layered elastic half-space

The axisymmetrical contact problem of elasticity connected with an indentation of a rigid spherical indenter in an elastic semi-space covered by an elastic layer is considered. Stress tensor components in interior points of the non-homogeneous half-space by numerical calculation of some integrals was obtained. Detailed analysis of the maximal tensile stress distributions and Huber-von Mises reduced stress distributions produced by contact pressure is presented. The dependence between these stresses and the ratio between the layer thickness and contact area width is explored. The obtained results for stresses are compared with results obtained for half-space loaded by the Hertz pressure.     

The Subsurface Stress Field Created by Three-Dimensionally Rough Bodies in Contact with Traction

A numerical simulation technique for calculating the complete subsurface stress field for three-dimensionally rough bodies in sliding contact is described. The stresses are calculated using real digitized three-dimensional surface profiles. The effects of the surface roughness and the sliding friction are presented. Using an existing contact simulation code, the digitized surfaces are mathematically pressed together and the real areas of contact and the asperity pressures are calculated. The surfaces are assumed to remain elastic throughout the contact simulation process. The shear forces at the asperity contact interfaces are assumed to be proportional to their calculated normal pressures. The subsurface stresses are then determined with these known normal and tangential forces at the surface.     

FEM Comparison of Ball and Roller Bullgears

A structural finite element model has been developed for calculating the forces transmitted through the rolling elements (load distribution) in a bullgear assembly. The elastic structural model consists of 3-D beam elements used to approximate the global race deflection and non-linear springs that approximate the combined rolling element/raceway contact deflections. For rollers, an upperbound on the contact stress (assuming linear variation of force along the length of the roller) is estimated by modeling the rollers as pairs of nonlinear springs. The finite element approach iteratively solves the contact forces at each, rolling element. Contact stresses are then calculated from the contact, forces using Hertz contact theory. This approach is applied to analyze two proposed designs of ball and crossed roller bearing, bullgear assemblies used for rotating the radar antenna on top of a ship's mast. The loads analyzed include those arising from wind loading and from out-of-flatness of the inner race of the bearings due to deflection of the mast. The distribution of the load and the maximum contact stresses for the proposed bullgear assemblies are estimated and compared. It is found that the maximum contact stress in the crossed roller bearing is less than that in the ball bearing for both types of loads. Furthermore, the analysis shows that the out-of-flatness loading produces significantly higher stresses than wind loading.     

Wear stability of polymer nanocomposite coatings with trilayer architecture

A polymer trilayer (sandwiched) film with a thickness of 20–30 nm has been designed to serve as a wear resistant nanoscale coating for silicon surfaces. These surface structures are formed by a multiple grafting technique applied to self-assembled monolayers (SAM) and functionalized tri-block copolymer, followed by the photopolymerization of a topmost polymer layer. The unique design of this layer includes a hard-soft-hard nanoscale architecture with a compliant rubber interlayer mediating localized stresses transferred through the topmost hard layer. This architecture provides a non-linear mechanical response under a normal compression stress and allows additional dissipation of mechanical energy via the highly elastic rubber interlayer. At modest loads, this coating shows friction coefficient against hard steel below 0.06, which is lower than that for a classic molecular lubricant, alkylsilane SAM. At the highest pressure tested in this work, 1.2 GPa, the sandwiched coating possesses four times higher wear resistance than the SAM coating. The wear mechanism for this coating is stress and temperature induced oxidation in the contact area followed by severe plowing wear.     

弹性接触问题的计算机辅助分析

论述了两个弹性体之间点或线接触问题的理论及其计算机算法关键 ,表明完全可以采用计算机辅助分析手段直接进行求解。通过对各种主要弹性趋近量算式来源的阐述和相应计算结果的对比分析 ,得出了几条相关结论。这些结论可供相关工程研究人员尤其是轴承工作者参考     

Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit [P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]     

Models of adhesive contact between rough elastic solids

Adhesion of rough elastic solids is considered. Roughness is simulated by the Winkler–Fuss nonlinear elastic layer, which can be stretched. Mechanical properties of the layer are determined by statistical theories of adhesive contact between nominally flat rough surfaces. The contact of solids is described by the nonlinear boundary integral equations with non-monotonic operators, whose solutions determine reduction of effective thickness of the rough layer, nominal contact stresses, nominal contact regions and relation between applied force and approach of solids. The theoretical background and numerical implementation of the models are given. Both a full model and its simplified version are analyzed.     

微动接触应力的有限元分析

以方足微动桥,试样接触几何条件为研究对象,应用ANSYS有限元分析软件对其接触面上的应力分布进行弹性有限元分析,验证用ANSYS所建计算模型的正确性,分别计算不同名义接触压力和不同摩擦因数条件下接触状态（粘着区、滑动区、张开区）和接触面应力分布,选取不同水平的循环载荷进行计算,研究接触状态和应力分布随循环载荷的变化情况。结果表明,微动疲劳过程中接触表面拉应力与剪应力在接触面的粘,滑交界区存在突变,微动疲劳裂纹正是在这一区域内萌生并扩展,计算结果与实验结果吻合很好。     

Gauging Persson Theory on Adhesion

In this work, we propose three amendments to Persson’s contact mechanics theory, the most important one being a modification of the way in which the stress distribution broadens with increasing resolution of random roughness features. The three adjustable coefficients of our treatment are gauged on existing reference data and tested against results of the contact mechanics challenge and a new set of data for adhesive slabs of finite width. Although the coefficients turn out to be of order unity, their problem-specific tuning is required to achieve highly accurate results, such as an essentially perfect dependence of contact area on load for non-adhesive, self-affine solids. Despite an overall convincing agreement between theory and full simulations, we find it to be intrinsically impossible to make the theory reflect the exact asymptotics of the stress distribution at small and large stresses. In addition, we find that the transition from small to large contact happens too abruptly with decreasing thickness of the elastic slab.     

The adhesive scarf joint in pure bending

The stress distribution in a scarf joint subjected to pure bending, and with arbitrary angle of scarf, is analyzed as a two dimensional elasticity problem in plane stress. Both the adherend and the adhesive are assumed to be elastic and isotropic. The two adherends may have differing moduli of elasticity. Numerical results are given.     

Shakedown theory for elastic-perfectly plastic bodies revisited

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter shakedown theory. Classical shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-shakedown collapse modes of elastic plastic structures.