多亚层柔性节点模型及其在双材料4ENF试件界面分析中的应用

提出了多亚层柔性节点模型用于分析双材料裂纹尖端的应力和变形。该模型考虑了胶层的变形,各亚层视为独立的剪切变形梁,采用两个界面柔度系数考虑界面应力对各亚层界面变形的影响,界面变形包括双材料界面和胶层的变形。通过对FRP-混凝土末端切口四点弯试件(Four-point bending end-notched flexure specimen,简称4ENF)进行界面分析,并与其他模型和有限元分析对比表明:刚性节点模型忽略了裂纹尖端的应力和变形集中,只能粗略地估计构件的整体变形和界面应力;半刚性节点容许裂纹尖端的转动,对裂纹尖端的变形估计优于刚性节点模型,但精度依然不高;多亚层柔性节点模型反映了裂纹尖端的应力和变形集中,与数值分析结果吻合很好,该研究对进行双材料结构的工程设计具有理论指导和参考价值。     

双材料梁界面力学及其应用:综述

双材料结构在工程中得到了广泛应用,如薄膜涂层、压电材料、复合材料层合板和夹层板、粘结接头、FRP加固混凝土结构等;然而,这些结构的破坏通常是从界面及其附近开始的.通常利用损伤力学的方法(材料强度的方法)来预测裂纹的萌生,利用断裂力学的方法来预测裂纹的扩展;因此,开展双材料结构的界面应力分析和具分层双材料结构的断裂以及相关分析是至关重要的.首先介绍双材料梁粘结界面应力分析的基本模型,从而为预测裂纹的萌生提供了有力工具.然后综述双材料梁界面断裂力学分析的基本方法,并详细介绍解析解求解的裂纹尖端法及其相关模型,重点强调裂纹尖端变形对分析结果的影响.最后介绍界面分层对双材料结构其它力学特性的影响,例如屈曲和振动特性.     

Ⅱ型模态控制下的GFRP-混凝土界面断裂韧度测定

介绍了一种适用于评价GFRP-混凝土界面断裂性能的理论分析模型,并结合端部开口试件的四点弯曲试件(4ENF)试验,测得了该类界面在II型模态控制下的断裂韧度.该模型考虑了试件各子梁中的横向剪切变形对能量释放率的影响,引入一阶剪切变形梁理论对界面断裂过程进行模拟;同时由于混凝土在受剪及受拉区域容易发生破坏,故试件设计过程中引入钢筋进行加强,有效减少了实验数据的离散性;进一步通过与有限元仿真进行对比发现结果吻合较好,这说明本文方法能够有效测定II型模态荷载控制下复合材料-混凝土界面的断裂韧度,评价复合材料增强混凝土结构的界面断裂性能,预测界面的起裂、裂纹扩展和失效容差.     

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究.柔性梁为功能梯度材料(functionally graded materials,FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化.以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应.采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型.基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响.结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响.本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的Timoshenko梁结构的动力学问题求解.     

FRP加固钢筋混凝土梁界面开裂分析

应用理论分析及有限元模拟和模型试验相结合的方法分析了FRP加固钢筋混凝土(RC)梁界面的开裂破坏规律。研究结果表明:FRP加固RC梁界面开裂可以应用断裂力学的方法解析,理论分析结论与有限元模拟结果一致。在FRP的剥离角度较大时界面是Ⅰ型和Ⅱ型混合开裂;同时考虑到混凝土剪切裂缝上下错动的尺寸与构件的尺寸相比很小,FRP-RC梁界面主要表现为Ⅱ型断裂。界面的应力强度因子随着加载的增加分为三个发展阶段,分别以混凝土开裂和钢筋屈服为分界点,界面的临界应力强度因子约为5.91MPa·m0.5。并结合试验给出了FRP的极限剥离应变,在工程应用中控制FRP应变在剥离应变以内可以有效地避免界面开裂破坏的发生。     

双材料界面Ⅰ型扩展裂纹尖端的弹黏塑性场

双材料界面中存在材料黏性效应, 对界面裂纹尖端场的分布和界面本身性能 的变化起着重要的影响. 考虑裂纹尖端的奇异性, 建立了双材料界面扩展裂纹尖端的弹黏塑 性控制方程. 引入界面裂纹尖端的位移势函数和边界条件, 对刚性-弹黏塑性界面I型界面 裂纹进行了数值分析, 求得了界面裂纹尖端应力应变场, 并讨论了界面裂纹尖端场随各影响 参数的变化规律. 计算结果表明, 黏性效应是研究界面扩展裂纹尖端场时的一个主要因素, 界面裂纹尖端为弹黏塑性场, 其场受材料的黏性系数、马赫数和奇异性指数控制.     

深梁理论的研究现状与工程应用

综述了深梁理论、截面剪切修正系数计算理论、深梁线性与几何非线性有限元、深梁材料非线性分析、深梁振动理论、深梁稳定理论、箱梁结构分析中弯曲、剪力滞、畸变分析时考虑剪切变形影响的计算理论、钢腹板桥梁考虑剪切变形的研究成果、弹性地基深梁、深梁理论在工程结构中的应用等. 提出了杆系结构的静力、振动和稳定分析方法都可用Timoshenko 深梁理论进行重建和重写.     

基于不同板理论的嵌于柔性层中薄膜的皱曲分析

论文对于柔性层-薄膜-柔性层三层结构系统,基于经典板理论、一阶剪切变形理论和高阶剪切变形理论,分别推导给出薄膜皱曲的控制方程。对于两个柔性层,则把它们处理成具有有限厚度的平面应变弹性体。针对上下柔性层固支边界或自由边界条件,利用线性扰动动方法得到柔性层对薄膜的横向压力差,最终获得确定薄膜具有周期性正弦型皱曲的临界载荷方程。同时,对结构系统建立了有限元数值模型,通过模拟结果与三种板理论的结果进行了比较,验证了理论解的精确性和适用性。最后,进行了参数和极限情况分析,阐述了上下层边界条件、薄膜和柔性层的材料和几何参数对临界值的影响。     

复合材料梁Ⅱ型裂纹的有限元分析

对三点弯曲梁端部层间裂纹的Ⅱ型断裂性能进行了有限元分析。为克服裂纹面两岸节点相互嵌入问题，采用了界面元素，计算结果与理论预测进行了比较．     

Mechanics and fracture of crack tip deformable bi-material interface

Novel interface deformable bi-layer beam theory is developed to account for local effects at crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable sub-layers with consideration of crack tip deformation. Unlike the sub-layer model in the literature in which the crack tip deformations under the interface peel and shear stresses are ignored and thus a “rigid” joint is used, the present study introduces two interface compliances to account for the effect of interface stresses on the crack tip deformation which is referred to as the elastic foundation effect; thus a flexible condition along the interface is considered. Closed-form solutions of resultant forces, deformations, and interface stresses are obtained for each sub-layer in the bi-layer beam, of which the local effects at the crack tip are demonstrated. In this study, an elastic deformable crack tip model is presented for the first time which can improve the split beam solution. The present model is in excellent agreements with analytical 2-D continuum solutions and finite element analyses. The resulting crack tip rotation is then used to calculate the energy release rate (ERR) and stress intensity factor (SIF) of interface fracture in bi-layer materials. Explicit closed-form solutions for ERR and SIF are obtained for which both the transverse shear and crack tip deformation effects are accounted. Compared to the full continuum elasticity analysis, such as finite element analysis, the present solutions are much explicit, more applicable, while comparable in accuracy. Further, the concept of deformable crack tip model can be applied to other bi-layer beam analyses (e.g., delamination buckling and vibration, etc.).     

COUPLED THERMO-MECHANICAL ANALYSIS OF FUNCTIONALLY GRADIENT WEAK/MICRO-DISCONTINUOUS INTERFACE WITH GRADED FINITE ELEMENT METHOD

Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.     

General analytical solution to bending of composite laminated beams with delaminations

Based on the first-order shear deformable beam theory, a refined model for composite beams containing a through-the-width delamination is presented, and the deformation at the delamination front is considered. Different from the ordinary delami- nated beam theory, each of the perfectly bonded portions of the new model is constructed as two separated beams along the interface without assuming a plane section at the de- lamination front. The governing equations of the delaminated portions and bonded ones are established, combined with continuity conditions of displacements and internal forces. Solutions of delaminated composite beams with different boundary conditions, delamina- tion locations and sizes axe shown in excellent agreement with the finite element results, showing efficiency and applicability of the present model.     

Shear deformation effect in plates stiffened by parallel beams

In this paper a general solution for the analysis of shear deformable stiffened plates subjected to arbitrary loading is presented. According to the proposed model, the arbitrarily placed parallel stiffening beams of arbitrary doubly symmetric cross section are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The analysis of the plate is based on Reissner’s theory, which may be considered as the standard thick plate theory with which all others are compared, while the analysis of the beams is performed employing the linearized second order theory taking into account shear deformation effect. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The effectiveness, the range of applications of the proposed method and the influence of shear deformation effect are illustrated by working out numerical examples with great practical interest.     

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR (Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto~plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack’ was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.     

3D printed,bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometries (trapezoidal, rectangular, anti-trapezoidal, and triangular) are studied and characterized by several important geometric parameters: the presence or absence of a bonded tip region, the tip angle, and the geometry. It is shown that a wide range (in some cases as great as an order of magnitude) in stiffness, strength, and toughness is achievable dependent on tip bonding, tip angle, and geometry. Suture interfaces with a bonded tip region exhibit a higher initial stiffness due to the greater load bearing by the skeletal teeth, a double peak in the stress–strain curve corresponding to the failure of the bonded tip and the failure of the slanted interface region or tooth, respectively, and an additional failure and toughening mechanism due to the failure of the bonded tip. Anti-trapezoidal geometries promote the greatest amplification of properties for suture interfaces with a bonded tip due the large tip interface area. The tip angle and geometry govern the stress distributions in the teeth and the ratio of normal to shear stresses in the interfacial layers, which together determine the failure mechanism of the interface and/or the teeth. Rectangular suture interfaces fail by simple shearing of the interfaces. Trapezoidal and triangular suture interfaces fail by a combination of shear and tensile normal stresses in the interface, leading to plastic deformation, cavitation events, and subsequent stretching of interface ligaments with mostly elastic deformation in the teeth. Anti-trapezoidal suture interfaces with small tip angles have high stress concentrations in the teeth and fail catastrophically by tooth failure, whereas larger tip angles exhibit a shear failure of the interfaces. Therefore, larger tip angles and trapezoidal or triangular geometries promote graceful failure, and smaller tip angles and anti-trapezoidal geometries promote more brittle-like failure. This dependence is reminiscent of biological systems, which exhibit a range of failure behaviors with limited materials and varied geometry. Triangular geometries uniquely exhibit uniform stress distributions in its teeth and promote the greatest amplification of mechanical properties. In both the bonded and unbonded cases, the predictions from the presented analytical models and experimental results on 3D printed prototypes show excellent agreement. This validates the analytical models and allows for the models to be used as a tool for the design of new materials and interfaces with tailored mechanical behavior.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

Energy release rate and phase angle of delamination in sandwich beams and symmetric adhesively bonded joints

Delamination in sandwich structures along the interface between the face sheet and the core, or along the adherend/adhesive interface in adhesively bonded joints, is one of the most common failure modes of this type of tri-layer structure. This delamination is usually modeled as an interface crack problem, for which the energy release rate and phase angle can be calculated using interface fracture mechanics solutions. Existing interface fracture mechanics solutions, however, ignore the effect of transverse shear deformation, which can be significant for short crack. In an effort to overcome this shortcoming, this study presents new analytical solutions for the energy release rate and for the phase angle of the interface crack in sandwich structures or adhesively bonded joints. Since the new solutions incorporate relative rotation at the tip of the delamination, transverse shear effects are taken into account in this study. Typical delaminated sandwich and adhesively bonded joint specimens are analyzed by using the new solutions, as well as by the existing solutions. The energy release rate predicted by the present model agrees very well with that predicted by FEA, and furthermore it is considerably more accurate relative to existing models. As the existing model neglects the transverse shear force, it underestimates the total energy release rate. A stress field analysis is also conducted in this study in order to clarify some misunderstandings in the literature on the determination of the phase angle of adhesively bonded joints using an interface stress-based method.