Flexural time-dependent cracking and post-cracking behaviour of FRP strengthened concrete beams

The time-dependent flexural cracking behaviour of reinforced concrete beams strengthened with externally bonded composite materials is investigated with a focus on the creep effects. A theoretical model is developed, which accounts for the creep of the different materials involved, and which also accounts for the time-dependent cracking and the tension-stiffening phenomenon. The deformability of the adhesive layer in shear and through its thickness, as well as its ability to transfer shear and vertical normal stresses, is considered in the model. The incremental governing equations are formulated via the variational principle of virtual work based on an incremental exponential algorithm for the creep modelling. The capabilities of the model are demonstrated through numerical examples including a comparison with test results available in the literature. The results show that creep causes a significant redistribution of the internal forces and the interfacial stresses at the adhesive interfaces with time, which should be carefully considered in the design of FRP strengthened members.     

Nonlinear long-term behaviour of spherical shallow thin-walled concrete shells of revolution

The nonlinear long-term buckling behaviour (creep buckling) of spherical shallow, thin-walled concrete shells of revolution (including domes) subjected to sustained loads is investigated herein. A thorough understanding of their nonlinear time-dependent behaviour, as well as the development of comprehensive analytical models for their analysis, has hitherto not been fully established and further studies are required. A nonlinear axisymmetric theoretical model, which accounts for the effects of creep and shrinkage, and which considers the ageing of the concrete material and the variation of the internal stresses and geometry in time, is developed for this purpose. The governing field equations are derived using variational principles, equilibrium requirements, and integral-type constitutive relations. A systematic step-by-step procedure is used for the solution of the integral-type governing equations. First, the nonlinear short-term behaviour is studied to provide a benchmark for the long-term analysis. Different theories for the analysis of the shell structure are examined for this purpose and compared with results obtained by the finite element method. A numerical study, which highlights the capabilities of the nonlinear theoretical model and which provides insight into the nonlinear long-term behaviour of shallow concrete domes, is presented. The results show that long-term effects are critical for the design and structural safety of shallow, thin-walled concrete domes, and so these effects need to be fully understood and quantifiable.     

钢-混凝土组合梁收缩徐变效应的随机分析

钢-混凝土组合梁是由混凝土板和钢梁通过剪力键连接而成的组合结构。由于混凝土的收缩徐变,将引起结构内力和应力重分布。混凝土收缩徐变具有离散性大的特点,进而导致结构长期响应表现出随机性。本文综合考虑徐变模型、收缩模型、混凝土抗压强度、混凝土弹性模量、环境湿度、钢材弹性模量、荷载以及剪力键刚度的随机性对钢-混凝土组合梁结构响应的影响。利用拉丁超立方抽样技术和基于响应面方法的蒙特卡洛抽样,研究了钢-混凝土组合梁挠度和应力时变效应的概率问题。     

A homogenized microstructural approach to creep fracture

A two-dimensional nonlocal continuum model is proposed in this paper for creep damage in polycrystalline materials. Starting from previous micromechanical modeling, a heuristic homogenization approach is adopted to derive a theory for the macroscopic response. The model accounts for the main damage mechanisms (grain boundary sliding, nucleation, growth and coalescence of cavities along the grain boundaries) responsible for the creep fracture process. The resulting constitutive law takes into account the nonlocalities expressed through the gradients of the stresses and the damage variables.     

施工期混凝土浇筑块的脆弹性徐变应力分析

本文将线性徐变理论和脆弹性破坏模型相结合,推导出计算混凝土浇筑块温度徐变应力的非线性有限元递推公式,并编制了计算机程序。最后以东江拱坝基础部分浇筑块为例进行了分析计算。     

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.     

On the use of solid- and shell-type finite elements in creep-damage predictions of thinwalled structures

Summary  Solid- and shell-type finite elements available for plasticity and creep analysis are applied to the creep-damage prediction of a thinwalled pipe bend under uniform internal pressure. Conventional creep-damage material model with scalar damage parameter is used. Based on the comparative numerical study, performed using solid and shell elements, the applicability frame of the shell concept is discussed. Particularly, if a dependence on the stress state is included in the material model, the cross-section assumptions of the first-order shear deformation theory should be refined. The possibilities to modify the through-thickness approximations are demonstrated on the beam equations. The first-order shear-deformation beam theory is discussed in detail. It is shown that if the damage evolution significantly differs for tensile and compressive stresses, the classical parabolic transverse shear-stress distribution and the shear-correction coefficient have to be modified within time-step simulations. Received 30 January 2000; accepted for publication 30 May 2000     

PEELING-OFF PHENOMENON IN FRP STRENGTHENED CONCRETE BEAMS DUE TO THERMAL RESIDUAL STRESS

Peeling-off phenomena in FRP strengthened concrete beams are investigated in this paper. Based on the beam theory and the fracture mechanics, a new theoretical model is proposed to analyze the peeling-off behavior near FRP-concrete interfaces, which is governed by residual thermal stresses. Numerical examples are presented to provide a clear insight into the failure mechanism. Some suggestions are provided for the optimal design of FRP strengthened structures.     

钢桁腹-混凝土组合箱梁畸变效应研究

为研究梯形截面的钢桁腹-混凝土组合箱梁的畸变效应,在薄壁箱梁理论的基础上,考虑钢桁腹杆的力学特性,应用改进的板元分析法建立畸变控制微分方程,并给出畸变解析解。通过ANSYS建立实体模型验证所推公式的正确性。结合数值算例,对比分析在均布畸变荷载作用下相同截面参数的钢桁腹-混凝土组合箱梁和传统混凝土箱梁的畸变翘曲正应力,并分析梁宽和钢腹杆俯角对组合箱梁畸变内力的影响。结果表明,相同截面参数下,由于组合箱梁钢桁腹杆的纵向刚度很小,其畸变翘曲正应力为混凝土箱梁的1.71倍;梁宽对畸变内力影响较大,当梁宽增加至4.5 m时,畸变双力矩和畸变矩分别增大至3.68倍和1.36倍,且前者在纵向上双峰的分布趋势逐渐平缓;腹杆俯角对畸变双力矩影响较大,当腹杆俯角增加至27°时,畸变双力矩减小了约14.3%,但其对畸变矩影响很小。     

Superplastic characteristics of high purity yttria-stabilized zirconia polycrystals

The mechanical characteristics of superplastic yttria-stabilized zirconia polycrystals have been analyzed as a function of stress, temperature and grain size. The evolution of the stress exponent n with stress found in high purity materials is similar to that observed in superplastic metals. True creep parameters can be ascribed to the deformation mechanism at high stresses. By contrast, the creep parameters exhibit a continuous evolution with stress, temperature and grain size at low stresses. The threshold stress formalism used in conventional and high strain rate superplastic metals accounts for the mechanical characteristics observed in fine-grained zirconia polycrystals.     

钢筋再生混凝土梁徐变性能试验研究

为揭示钢筋再生混凝土梁的徐变性能,通过三种持荷水平下9根钢筋再生混凝土梁试件的徐变(徐变应变与徐变挠度)对比试验,分析了钢筋再生混凝土梁徐变与时间的相关关系,研究了加荷幅值、初始变形(初始应变、初始挠度)等因素对钢筋再生混凝土梁徐变性能的影响规律,揭示了钢筋再生混凝土梁的徐变机理。研究结果表明:在45%极限荷载水平的持续作用下,钢筋再生混凝土梁总徐变挠度值为初始挠度值的62%左右,并且在前期发展较快,7d发展至总徐变挠度值的64%左右,后期变缓;钢筋再生混凝土梁徐变随着施加荷载幅值、初始变形的升高而有所增加。经历徐变过程后的钢筋再生混凝土梁,其承载性能有所下降,变化趋势为总徐变值越大,降低的幅度也越大。     

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.     

The perturbation finite element method for solving the plane problem in consideration of linear creep

In this paper, a method (PFMC) for solving plane problem of linear creep is presented by using perturbation finite element. It can be used in plane problem in consideration of creep, such as reinforced concrete beam, presiressed concrete beam, reinforced concrete cylinder and reinforced concrete tunnel in elastic or visco-elastic medium, as well as underground building and so on.In the presented method, the assumption made in the general increment method that variables remain constant in a divided time interval is not taken. The accuracy is improved and the length of time step becomes larger. The computer storage can be reduced and the calculating efficiency can be increased.Perturbation finite element formulae for four-node quadrilateral isoparametric element including reinforcement are established and five numerical examples are given. As contrasted with the analytical solution, the accuracy is satisfactory.     

考虑收缩徐变影响的新旧混凝土叠合梁单元刚度矩阵改进

混凝土自身的收缩徐变会在新旧混凝土叠合梁中使应力重分布.为了计算重分布应力,首先推导以挠度表达的叠合梁非线性微分方程,然后通过求解该微分方程,引入位移形函数、刚度形函数和等效节点载荷形函数,最后得出新混凝土梁、旧混凝土梁和Goodman弹性夹层三合一的叠合梁改进型单元刚度矩阵和等效节点载荷,从而为收缩徐变影响下的混凝土的内力计算提供了一种有效的新方法.文中还进行了实例验证分析,并从中得出了一些有益的结论.     

混凝土核安全壳干缩应力的计算

提出内约束干缩应力和外约束干缩应力的概念,利用混凝土的蠕变理论,建立了考虑施工过程的有限元计算模型,编制了电算程序,计算了秦山核安全壳在施工过程中的干缩应力。     

Predictions of nonlinear viscoelastic behavior using a hybrid approach

An approach for nonlinear viscoelastic characterization is presented which uses the combined measurements from creep and dynamic mechanical tests. Although the methodology should extend to several materials and geometries, this research concentrates on thin film polymers used in the manufacture of high altitude scientific balloons. Typically, the constitutive behavior of these materials is characterized through the use of linear viscoelastic techniques. Although this linear approach provides an accurate model for small strains or loads, these materials have been shown to be highly stress dependent and, consequently, it is necessary to identify this nonlinear behavior. Traditional creep measurements require extensive laboratory test times, yet the results obtained from dynamic mechanical analysis provide the capability to predict long term material performance without a lengthy experimentation program. However, dynamic mechanical methods are currently limited to linear response; thus, an approach is presented in which the stress-dependent behavior is derived from short-term creep measurements in a manner analogous to time-temperature superposition. Predictions of material response using linear and nonlinear approaches are compared with experimental results obtained from traditional long-term creep tests. Although linear pre-dictions deteriorate for large stresses, excellent agreement is shown for the nonlinear model.     

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.     

Boundary element approach to creep deformation of edge notched and cracked specimens

A direct formulation of the boundary element method using a complex variable numerical approach is presented for the time-dependent inelastic stresses in edge notched and cracked creeping metallic structural components subject to high temperature gradients. Particular attention is focused on the numerical evaluation of energy rate contour integrals in single edge cracked specimens in tension. The constitutive models used in the numerical calculation are internal state variable creep–plasticity or elastic power law creep model. Numerical results are compared with solution obtained from other methods for different loading rates.     

基于能量守恒理论的带肋钢筋-混凝土粘结滑移本构关系研究

针对钢筋-混凝土粘结滑移的劈裂破坏模式,将整个破坏过程分为未开裂的弹性阶段和带裂缝阶段。弹性阶段采用弹性厚壁圆筒模型,带裂缝阶段采用考虑混凝土软化特性的厚壁圆筒模型。基于这两种模型,研究了粘结滑移劈裂破坏过程的能量变化规律,推导出了两种模型的能量计算公式。利用能量守恒定律建立了钢筋-混凝土粘结滑移本构关系的微分方程,并通过数值积分方法得到了粘结滑移本构模型。该本构模型能够体现混凝土与钢筋材料参数和几何参数的影响,对不同形状的粘结滑移关系曲线具有较好的适应性。最后,将得到的本构关系与文献的试验结果进行对比,并分析了各参数的变化规律。     

Impact of thermal loads on interfacial debonding in FRP strengthened beams

The effect of thermal loads on the debonding mechanisms in beams strengthened with externally bonded composite materials is analytically investigated. The analytical approach adopts a high-order stress analysis model and a fracture mechanics model that uses the concept of the energy release rate through the thermo-mechanical form of the J-integral. The two models are combined to synthesize the relation between the energy release rate, the mechanical loads, the thermal loads, and the interfacial crack length simulating the thermo-mechanical debonding process. The model is supported through comparison with experimental results taken from the literature. The comparison quantifies and explains various phenomena observed in the experiments and mainly the non-monotonic dependency of the debonding failure load on the temperature. The impact of the temperature on the interfacial stresses and on the stability of the debonding process is also studied. Finally, the effect of an uniform thermal load on the debonding behavior of a strengthened beam is studied revealing the impact of the thermal load on the debonding stability and strength characteristics.