ANALYTICAL ANALYSIS OF INTERFACIAL STRESSES IN FRP-RC HYBRID BEAMS WITH TIME-DEPENDENT DEFORMATIONS OF RC BEAM

In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between an RC beam and FRP plate is presented. For this end, a closed-form solution for such stresses in externally FRP plated RC beams including creep and shrinkage effects is presented. The developed model is formulated to predict the interfacial stresses at time ‘t’, in which the RC beams have been already subjected to creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of the RC beam and the FRP panel. Contrary to some existing studies, the assumption that both RC beam and FRP panel have the same curvature is not used in the present investigation. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP-RC hybrid structures.     

Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate

In this paper, an improved theoretical interfacial stress analysis is presented for simply supported concrete beam bonded with a FRP plate. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of adherends has been noted in the results. Indeed, the resulting interfacial stresses concentrations are considerably smaller than those obtained by other models which neglect adherent shear deformations. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

A three-parameter elastic foundation model for interface stresses in curved beams externally strengthened by a thin FRP plate

Externally bonding of fiber reinforced polymer (FRP) plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are of great importance to the effectiveness of this type of strengthening because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, we develop an analytical solution of interface stresses in a curved structural beam bonded with a thin plate. A novel three-parameter elastic foundation model is used to describe the behavior of the adhesive layer. This adhesive layer model is an extension of the two-parameter elastic foundation commonly used in existing studies. It assumes that the shear stress in the adhesive layer is constant through the thickness, and the interface normal stresses along two concrete/adhesive and adhesive/FRP interfaces are different. Closed-form solutions are obtained for these two interfacial normal stresses, shear stress within the adhesive layer, and beam forces. The validation of these solutions is confirmed by finite element analysis.     

Non-steady-state elastic–plastic behavior of metal forming (rolling) with a generalized friction law

An analytical and generalized friction law is formulated and a three-dimensional large-strain non-steady-state elastic–plastic finite element analysis has been performed for rolling process. The contact/friction problem at the interface between the workpiece and the rolls is treated rigorously by using this new friction law. The numerical results, including the evolutions of roll torque and roll forces, and the interfacial normal and shear stresses, are presented and discussed.     

一种预测颗粒增强复合材料界面力学性能的新方法

界面在颗粒增强复合材料中起到传递载荷的关键作用, 界面性能对复合材料整体力学行为产生重要影响. 然而由于复合材料内部结构较为复杂, 颗粒与基体间的界面强度和界面断裂韧性难以确定, 尤其是法向与切向界面强度的分别预测缺乏有效方法. 本文以氧化锆颗粒增强聚二甲基硅氧烷(PDMS)复合材料为研究对象, 提出一种预测颗粒增强复合材料界面力学性能的新方法. 首先, 实验获得纯PDMS基体材料及单颗粒填充PDMS试样的单轴拉伸应力$\!-\!$应变曲线, 标定出PDMS基体材料的单轴拉伸超弹性本构关系; 其次, 建立与单颗粒填充试样一致的有限元模型, 选择特定的黏结区模型描述界面力学行为, 通过样品不同阶段拉伸力学响应的实验与数值结果对比, 分别给出颗粒与基体界面的法向强度、切向强度及界面断裂韧性; 进一步应用标定的界面力学参数, 开展不同尺寸及不同数目颗粒填充试样的实验与数值结果比较, 验证界面性能预测结果的合理性. 本文提出的界面力学性能预测方法简便、易操作、精度高, 对定量预测颗粒增强复合材料的力学性能具有一定帮助, 亦对定量预测纤维增强复合材料的界面性能具有一定参考意义.      

杂交梁界面剪应力的理论分析和数值模拟

采用解析和数值方法研究FRP-混凝土杂交梁的界面应力问题。提出了杂交梁的新的力学模型和假设,克服了以往的分析模型中界面应力表达式非常复杂和界面应力的解析解与数值解相差较大的缺点,本文得到的FRP板加固梁的界面剪应力表达式与数值结果符合很好,并且具有简捷的表达式。利用有限元法研究了杂交梁各物理参数对界面剪应力的影响。研究表明,界面剪应力在FRP板的端部存在应力集中或应力奇性,这是造成杂交梁界面破坏的主要原因。这项研究对进行杂交结构的工程设计具有理论指导和参考价值。     

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.     

Elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with progressive debonding damage

This paper deals with elastic and elastic–plastic singular fields around a crack-tip in particulate-reinforced composites with debonding damage of particle-matrix interface. Numerical analyses are carried out on a crack-tip field in elastic-matrix and elastic–plastic-matrix composites reinforced with elastic particles, using a finite element method developed based on an incremental damage theory of particulate-reinforced composites. A particle volume fraction and interfacial strength between particles and matrix of the composites are parametrically changed. In the elastic-matrix composites, a unique elastic singular field is created on the complete damage zone in the vicinity of a crack-tip in addition to the conventional elastic singular field on the no damage zone. The macroscopic stress level around a crack-tip is reduced by the debonding damage while the microscopic stress level of the matrix remains unchanged. In the elastic–plastic-matrix composites, the damage zone develops in addition to the plastic zone due to matrix plasticity, and both the macroscopic and microscopic stress revels around a crack-tip are reduced by the debonding damage. It is concluded from the numerical results that the toughening due to damage could be expected in the elastic–plastic-matrix composites, while it is questionable in the elastic-matrix composites.     

Numerical simulation: The dynamic behavior of reinforced concrete plates under normal impact

This investigation deals with the use of the finite element method on the reinforced concrete structural dynamic response and failure behavior when subjected to the projectile impacts of different velocities, using the test conducted in [S.J. Hanchak, M.J. Forrestal, E.R. Young, J.Q. Ehrgott, Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths, Int. J. Impact Eng. 12 (1992) 1–7]. The Johnson–Holmquist concrete material constitutive law model is employed to simulate the large strains, high strain states and high pressures to which the concrete is subjected. The projectile impact velocity ranges from 381 m/s to 1058 m/s. Numerical simulations demonstrate that the Johnson–Holmquist concrete material constitutive model can describe the different failure modes without any predefined defects in the element mesh, and normally obtain good agreement between the numerical simulations and test results.     

FRP-混凝土界面粘结行为的参数影响研究

FRP-混凝土界面的粘结性能对FRP加固混凝土结构力学行为和破坏模式有着重要影响。本文对表征FRP-混凝土界面粘结性能的三个重要参数(界面初始刚度、最大剪应力、界面破坏能)开展研究,通过13个单剪试件的试验考察了混凝土强度、胶层厚度和粘结长度等因素对界面粘结行为的影响,根据试验结果拟合了界面破坏能、最大剪切应力与胶层剪切刚度、混凝土强度之间的函数关系。在试验研究基础上,构建了外贴FRP-混凝土界面粘结的有限元模型。通过有限元分析考察了界面破坏能等三个参数不变的前提下,不同的局部粘结滑移本构关系对界面粘结行为的影响;进而研究了其中一个参数变化时引起的界面粘结性能改变。研究结果表明:界面粘结承载力随着胶层厚度增加而逐渐提高;胶层厚度与界面破坏能成正比,与峰值剪应力成反比;当界面破坏能等三个参数保持不变时,局部粘结滑移本构关系对FRP-混凝土界面粘结性能的影响较小;三个参数中的一个增大时将延缓界面破坏的过程。     

纤维/金属网增强层板低速冲击损伤机理和演化

本文首先通过落锤低速冲击实验测试了纯玻璃纤维增强环氧树脂复合材料和304不锈钢丝网(SSWM)/玻璃纤维混杂复合材料的力学性能,探究了SSWM嵌入数量对混杂复合材料抗冲击性能的影响．随后采用Abaqus有限元软件建立了混杂复合材料的低速冲击模型,分别采用三维Hashin失效准则和Jason-Cook破坏准则模拟了纤维/基体和SSWM的损伤;建立了基于表面接触的内聚力模型来模拟界面分层;编写了VUMAT用户子程序定义混杂复合材料层合板的渐进失效过程．结果表明：相较于纯玻璃纤维增强环氧树脂层合板,SSWM/玻璃纤维混杂增强环氧树脂层合板的抗冲击性能更优,其中铺层形式为铺层III的混杂复合材料抗冲击性能最佳．通过对比发现有限元仿真结果与实验结果吻合良好,表明建立的模型适用于SSWM/玻璃纤维混杂增强环氧树脂复合材料低速冲击损伤的评估．通过分析仿真结果发现混杂复合材料的低速冲击损伤主要是冲击区域的纤维断裂、基体破坏和层间分层;SSWM通过吸收和传递冲击能量从而提升了混杂复合材料的抗冲击性能．     

双材料界面裂纹的改进广义有限差分法

采用数值方法进行断裂力学分析时,裂纹尖端奇异区域处理的好坏直接关系到最终断裂力学参数的求解精度。与传统均匀介质不同,复合材料界面裂纹渐近位移和应力场表现出剧烈的振荡特性,许多用于表征经典的平方根和负平方根物理场渐近性的传统方法也因此失效。论文提出了一种改进的广义有限差分法,该方法基于多元函数泰勒级数展开和移动最小二乘法的思想,将节点变量的各阶导数由相邻点集函数的加权线性累加来近似,具有无网格、无数值积分、数据准备简单、稀疏矩阵快速求解等优点。为提高该方法求解断裂力学问题的计算精度和数值稳定性,论文引入了裂尖奇异区域局部点簇的自动创建技术和一种基于局部点簇几何尺寸的矩阵正则化算法。数值算例表明,所提算法稳定,效率高,在不增加计算量的前提下,显著提高了裂尖近场力学参量和断裂力学参数的求解精度和数值稳定性。     

Nonlinear proportionality of shear-bond stress to shear force in partially plastic regions of asymmetric FRC-laminated steel members

This paper focuses on the elastic–plastic flexural characteristics of hybrid members comprising I-section steel beams with adhesively bonded fiber reinforced composite (FRC) laminates. Specifically, predictive models are presented for the shear-bond stresses developed within the adhesive layer. The asymmetry of the hybrid section, due to the presence of the laminate, is shown to have two important consequencies, namely that two parameters are required to fully define the elastic–plastic behavior, and that there is a progressive migration of the neutral axis towards the laminate as elastic–plastic flexure of the section increases. Five different phases of elastic–plastic flexure are identified. Analytically exact two-parameter predictive models, which incorporate the nomadic tendencies of the neutral axis, are derived for the shear-bond stresses associated with each phase. The models reveal that, in contrast to fully elastic flexure, shear-bond stress is nonlinearly proportional to shear force during elastic–plastic behavior. Predictions from the models are compared with test data from the laboratory and with predictions from a finite element program, for FRC-laminated I-section steel beams under both distributed loads and point loads. These comparisons show that two elastic–plastic phases, each defined by axial stress redistribution within the tension steel flange, stimulate rapidly varying shear-bond stresses in the adhesive. The capabilities of the models are highlighted, and areas open for further work are discussed.     

纤维增强韧性基体界面力学行为

分析了纤维增强韧性基体的界面力学行为及其失效机理,按剪滞理论和应变理化规律研究微复合材料的弹塑性变形和应力状态,讨论了幂硬化和线性硬化基体的弹塑性变形和界面应力分布,并给出纤维应力和位移的表达式。按最大剪应力强度理论建立了纤维／基体界面失效准则,推导出弹塑性界面失效的平均剪应力随纤维埋入长度的变化关系。     

Elastodynamic Green’s function for reinforced concrete beams

A semi-analytical solution procedure for three dimensional wave propagation in reinforced concrete (RC) beams has been presented in this paper. Elastodynamic Green’s function has been derived by employing the compatibility conditions and utilizing the symmetry conditions at the loaded cross section. Numerical procedure developed for the Green’s function has been validated using results available in the literature for an infinite laminated composite plate. Three-dimensional wave propagation analysis has been performed for reinforced concrete beam sections of T and L shapes which are common forms of structural elements. Steel reinforcement has been modeled in the finite element mesh. Effect of corrosion has also been included in the finite element model. Green’s function for reinforced concrete sections affected by corrosion of steel unit normalized frequency has been evaluated for illustration. Accuracy of the solution technique has been evaluated in terms of the percentage error in energy balance between the input energy of the applied unit load and the output energy carried by the propagating wave modes. The percentage error has been found to be negligible in all the cases considered here. A simple and accurate numerical method has been presented here as a tool to evaluate Green’s function for RC beams and can be used to detect corrosion.     

断裂过程的有限元模拟

讨论了材料断裂过程的有限元模拟技术。基于自适应有限元的一般原理，并针对多相材料的裂纹扩展的特点，提出了一种简化的高精度和高效率有限元网格的动态重新划分策略。裂纹被假设沿着单元之间的路径连续扩展，利用节点力释放技术生成新的裂纹自由表面，发展了一种可随裂尖连续移动的网格动态加密和释放方法。这种方法已在各种裂纹问题中得以实现与应用。     

Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating

In this paper, the three-dimensional (3D) interfacial fracture is analyzed in a one-dimensional (1D) hexagonal quasicrystal (QC) coating structure under mechanical loading. A planar interface crack with arbitrary shape is studied by a displacement discontinuity method. Fundamental solutions of interfacial concentrated displacement discontinuities are obtained by the Hankel transform technique, and the corresponding boundary integral-differential equations are constructed with the superposition principle. Green’s functions of constant interfacial displacement discontinuities within a rectangular element are derived, and a boundary element method is proposed for numerical simulation. The singularity of stresses near the crack front is investigated, and the stress intensity factors (SIFs) as well as energy release rates (ERRs) are determined. Finally, relevant influencing factors on the fracture behavior are discussed.     

纤维复合材料界面横向拉伸分析

以单纤维十字型横向拉伸试验为研究对象,对纤维/基体界面采用弹性-软化双线性内聚力模型,建立了纤维复合材料在横向拉伸作用下界面法向失效过程的解析模型。得到了沿纤维/基体圆周界面的法向应力分布,纤维/基体界面的状态与界面承载力和单纤维复合材料承载力的关系,以及内聚力参数和试件几何尺寸对它们的影响。结果表明:纤维/基体圆周界面在脱粘前经历全部弹性及弹性+软化两种状态;当界面为弹性状态时,界面法向应力随界面强度线性增加;当界面为弹性+软化状态时,界面软化范围随界面裂纹萌生位移的增加而增大;界面初始脱粘位置与拉伸荷载方向重合;界面初始脱粘时的界面承载力随界面强度及界面裂纹萌生位移的增加而增加,随界面裂纹生成位移的增加而降低;单纤维复合材料的脱粘荷载受基体截面尺寸的影响,当纤维体积含量相同时,沿荷载方向截面尺寸的增大对提高脱粘荷载更显著。     

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。