Steel-to-concrete bond after concrete splitting: test results

The definite trend towards the use of large-diameter rebars and the introduction of high-strength steels (f _y=500 to 600 MPa) make it necessary to study the effects of longitudinal splitting on the steel-to-concrete bond. The study of splitting effects requires firstly basic tests to be performed in order to gather experimental information on bond and confinement stresses acting at the bar-to-concrete interface. For this purpose, three series of tests were recently carried out at the Politecnico di Milano. The results make it possible to ascertain a few basic properties of the bond after concrete splitting, and to formulate empirical constitutive laws regarding the stresses and the displacements (bar slip and opening of the splitting crack). All specimens consisted of a short deformed bar embedded in a concrete block, which had a preformed splitting crack in the plane passing through the bar axis: twelve specimens (Tests A and C) were fitted up with a round deformed bar having crescent-shaped lugs (D_b=18 mm); seven specimens (Tests B) were fitted up with a specially machined deformed bar having a rectangular cross-section and straigth, lugs, so that concrete deterioration close to the bar could be investigated at the surface of the specimen, by means of the moiré technique. The tests were carried out at constant slip rate, up to very large slip values ( ); both the ascending and the descending branches of the stress-slip curves were measured, for four different values of the opening of the splitting crack. The agreement among the results of the three series is generally satisfactory and often very good: consequently, constitutive laws regarding the four main variables (crack opening and bar slip, shear and confinement stresses) can be worked out, as will be shown in a companion paper on constitutive relationships and on concrete deterioration at the bar-to-concrete interface.     

基于Najar能量法的混凝土分形损伤本构模型研究

混凝土损伤模型的研究,实质上是研究损伤变量对混凝土材料本构关系的影响。在外界因素作用下,材料的累积变形引起结构内部损伤的发展,最终将产生宏观裂缝直至破坏。在混凝土损伤破坏过程中,"凹凸无序"的断裂面和"杂乱无章"的裂缝是对混凝土宏观力学性能离散化、非线性、随机性的最直接的体现和表征。基于断裂面和裂缝的分形特性,得到了分形应力、分形应变的基本概念,使之能更为准确地描述混凝土的宏观力学性能。通过Najar能量损伤理论,利用分形应力与表观应力、多重分形应变与表观应变之间的关系,推导得出了混凝土分形损伤本构模型,重新定义了Weibull概率分布的混凝土损伤扩展规律,得到了基于压缩变形分形特性的损伤演化方程。     

Comparative analysis and critical issues of the main constitutive laws for concrete elements confined with FRP

This paper presents and compares the results of an analysis dealing with various constitutive laws for reinforced concrete elements confined with FRP. One of the main problems of such constitutive laws is their dependence not only on concrete class, fiber type and wrapping’s number of sheets, but on cross-section’s size too. Because of the great number of parameters involved in the different analyzed constitutive laws, it is very difficult to predict the effects both in terms of ultimate strength and/or ultimate strain of the different assumptions and calibration option. A comparative analysis is herein presented aiming to point out the “critical issues” affecting the constitutive laws.     

Nonlinear isotropic constitutive laws: choice of the three invariants, convex potentials and constitutive inequalities

The aim of this paper is a new formulation of nonlinear isotropic constitutive laws. Our main hypothesis claims that the eigenvalues of stress and strain tensors are classified in the same order (the eigenvector associated to the highest eigenvalue of the stress tensor is also associated to the highest eigenvalue of the strain tensor, etc.). Further, we assume the existence of a differentiable convex isotropic potential. By introducing three new invariants for each tensor (called X, Y, Z for the stress tensor S and x, y, z for the strain tensor E) a constitutive law is revealed to be a simple duality between the chosen invariants: (x, y, z) and (X, Y, Z) look like Cartesian coordinates of E and S. We look at several potentials chosen as polynomials of these invariants. Finally, first and third order isotropic elasticity laws are reviewed and convexity of the potentials is discussed.     

The effect of surface preparation on the bond interface between FRP sheets and concrete members

Fiber-reinforced polymer (FRP) composite wraps have been established as an effective method for rehabilitation and strengthening of concrete structures. They are being increasingly used as an alternative to steel for reinforcing and strengthening of concrete structures. This paper presents the experimental and analytical results of the influence of concrete surface treatment and the type of FRP sheets on the bonding strength of concrete-FRP sheet. The FRP sheets were bonded to concrete beams in two opposite sides using an epoxy resin. Variables included the type of fiber (C1, C5, and GE) and the surface treatment (water jet and sanding). With changing the surface treatment of concrete surface preparation and the type of fiber sheets, the bonding strength, bonding load–strain response and failure modes were investigated. The concrete specimens with surface roughened with water jet showed much better bonding strength than those roughened with an ordinary sander. Equations for predicting the bond load failure of concrete specimens externally bonded with carbon and glass fiber sheets compared well with those of experimental.     

Fatigue behaviour of the bond interface between carbon fibre‐reinforced polymer sheets and concrete

Externally bonded carbon fibre‐reinforced polymers (CFRPs) have been applied to retrofit and strengthen civil structures. In this study, four‐point bending beams were manufactured and tested to examine the fatigue behaviour of the CFRP–concrete interface. The results indicated that the specimens exhibited debonding failure in the concrete beneath the adhesive layer under static loading. However, when cyclic loads were imposed on the small beams, debonding failure may occur in the adhesive layer. Moreover, fitting expressions were proposed to predict the shear stress–slip relationship between the CFRP sheets and concrete and the flexural strength of the CFRP‐strengthened beams under static loads, and good agreement with the test data was obtained. Finally, a fatigue life prediction model was also presented to capture the fatigue life of the CFRP–concrete interface under cyclic loads. The calculation results showed that the fatigue strength of the CFRP–concrete bond interface was approximately 65% of the ultimate load capacity.     

Environmentally induced deterioration of concrete: physical motivation and numerical modeling

This paper is concerned with the effects of moisture, heat and chemical dissolution processes on the long-term behavior of concrete structures. Motivated by experimental findings described in this paper, numerical models for durability analysis of concrete structures, taking hygrally, thermally and chemically induced degradation processes into account, are described. As an example for chemically corrosive mechanisms in concrete structures, the material degradation due to calcium leaching and mechanical loading is considered in a coupled chemo-mechanical model. Furthermore, the interactions between mechanically induced damage, moisture and heat transport are taken into account in a coupled hygro-thermo-mechanical model for concrete. Results from two-dimensional simulations of a concrete panel subjected to coupled mechanical, hygral and thermal loading and coupled chemo-mechanical loading, respectively, are included as representative numerical examples.     

Evaluation of bond quality at the interface between steel bar and concrete using the small-dimension break-off test

This paper investigates the feasibility of using the small-dimension break-off test for evaluation of the bond quality at the interface between steel bar and concrete. Experimental studies were performed on bar-type concrete specimens and reinforced concrete beams. Twelve bar-type concrete specimens containing plain and deformed steel bars with different diameters were used to develop the relationship between the break-off moment and the adhesive strength at the steel bar/concrete interface. Subsequently, three reinforced concrete beams containing normal reinforcing bars, epoxy-coated reinforcing bars, and bars smeared with oil to simulate various adhesive conditions at the bar/concrete interface were used to study how the break-off moment and the bond strength were affected by the different adhesive conditions. In addition, two beam specimens containing normal reinforcing bars were vibrated severely on a self-made shaking table shortly after initial setting of concrete to simulate the bond damage in fresh reinforced concrete beams due to unexpected vibration or impact. Experimental results show that the effective break-off moment has a good correlation with the adhesive strength at the interface between steel bar and concrete. The break-off moment increases with an increase in bond strength. It is demonstrated that the small-dimension break-off test is capable of evaluating damage at the steel bar/concrete interface.     

A concise interface constitutive law for analysis of delamination and splitting in composite materials and its application to scaled notched tensile specimens

A concise constitutive law for cohesive interfaces is proposed in this paper. A new state variable is introduced to track the extent of damage accumulated at the interface. The constitutive equations not only account for mixed‐mode delamination propagation in composite materials, but also satisfactorily deal with mode ratio change during the debonding process. The interface model is implemented in the LS‐DYNA explicit finite element code. The model has been applied to scaled open hole tension tests on laminated composite material. Comparison between numerical results and experiments shows good correlation for failure modes and strengths for a range of different specimen sizes. Copyright © 2006 John Wiley & Sons, Ltd.     

Bond and splitting in reinforced concrete: test results on bar pull-out

The test results regarding the pull-out of 16 large-and small-diameter bars (d_b=18 mm), embedded in presplit specimens, are presented here, at the conclusion of a systematic research project on the deterioration, confinement-sensitivity and path-dependency of bond, caused by concrete splitting. The 16 tests carried out at constant width of the splitting crack show that the role of the diameter is not negligible and that small-diameter bars have the edge in terms of bond strength and stiffness, while crack opening is always detrimental to bond efficiency. In all cases, the bond stress-slip curves exhibit a welldefined softening branch, and the bond stress-confinement envelopes are characterized by limited cohesion, a mostly linear ascending branch and a sort of plateau. As for bond confinement-sensitivity and path-dependency, 4 tests on medium-diameter bars were carried out at constant confinement: bond peak-strength turns out to be an almost linear function of the confinement stress, and path-dependency is very limited at high confinement levels. The results are intended to contribute to the formulation of more reliable laws regarding the governing parameters of bond-splitting interaction, in order to quantify and control the unfavorable effects of concrete splitting.     

Dynamic splitting tensile properties of concrete and cement mortar

To investigate the dynamic tensile behaviours of concrete and cement mortar, a 50‐mm split Hopkinson pressure bar was applied on Brazilian disc specimens for dynamic tensile experiments, in which strain rate varied from 10^?5 to 20 s^?1. The high‐speed camera testing technique was used to capture the dynamic fractured process of the specimens at relative high strain rate. The experimental results revealed that the dynamic tensile strength of concrete specimens has a stronger strain rate effect than that of cement mortar specimens. Then three typical failure patterns of the specimens were confirmed in dynamic experiments. In addition, one‐parameter semi‐empirical relation between dynamic tensile strength and strain rate was established. Finally, the limitation of dynamic splitting experiments on Brazilian disc specimens was discussed in detail at high strain rate, in which the crack initiates from the contact point between the incident bar and specimens rather than the centre of the specimens.     

Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates

One objective of the present study is to use arbitrary complete 3-dimensional constitutive equations without reduction or manipulation in nonlinear plate and shell analysis. The obvious consequence, namely the extension of a conventional 5-parameter shell formulation with Reissner-Mindlin kinematics to a 6-parameter formulation including the full set of stress and strain state does not solve the problem because a significant error in bending dominated cases occurs. To avoid this error the transverse normal strain is allowed to vary linearly across the thickness. This so-called 7-parameter theory recently proposed in the group of the authors resorts to the Enhanced Assumed Strain concept and preserves the basic features of a displacement formulation.The 7-parameter formulation is extended to the simulation of the response of laminated structures with arbitrarily large displacements and rotations. Following the main idea of the concept, it is sufficient to formulate a complete 3-dimensional material law which considers the layered setup of the shell.Finally, a layer-wise so-called multidirector model is developed which is well suited to grasp local interlaminar effects. In this formulation the displacement interpolation across the thickness is extended to a C⁰-continuous field described by a layer-wise Reissner-Mindlin kinematics. The purpose of the multidirector formulation is twofold: Firstly the higher order kinematics satisfies the same requirements discussed for the 7-parameter theory and allows also to use complete 3-dimensional material laws. Secondly it is appropriate to simulate laminates with extreme differences of the thicknesses or dissimilar material properties of each layer with sufficient accuracy. These are situations where formulations with C¹-continuous displacement fields across the thickness fail.The present study is supported by a grant of the German National Sciences Foundation (DFG).Dedicated to Professor Hans Bufler, University of Stuttgart, for his invaluable contributions in applied mechanics     

Effect of constitutive laws on plane strain ideal flow design: an analytical example

Summary. The major objective of this paper is to clarify the effect of constitutive laws on bulk forming design based on the ideal flow theory. The latter theory is in general applicable for perfectly/plastic materials. However, its kinematics equations constitute a closed-form system, which are valid for any incompressible materials, therefore enabling us to extend design solutions based on the perfectly/plastic constitutive law to more realistic laws with rate sensitive hardening behavior. In the present paper, several constitutive laws commonly accepted for the modeling of cold and hot metal forming processes are considered and the effect of these laws on one particular plane strain design is demonstrated. The closed form solution obtained describes a nontrivial nonsteady ideal process. The design solutions based on the ideal flow theory are not unique. To achieve the uniqueness, the criterion that the plastic work required to deform the initial shape of a given class of shapes into a prescribed final shape attains its minimum is adopted. Comparison with a non-ideal process is also made.     

Drying creep of concrete: constitutive model and new experiments separating its mechanisms

A new experimental method which allows the direct separation of the components of drying creep due to microcracking and stress-induced shrinkage is developed, demonstrated and validated. The basic idea is to compare the curvature creep of beams subjected to the same bending moment but very different axial forces. The results confirm that drying creep has two different sources: microcracking and stress-induced shrinkage. The latter increases continuously, whereas the former first increases and then decreases. The test results are fitted using a finite element model. The results validate the present model for drying creep. The microcracking is described by an established model, and the free (unrestrained) shrinkage of a material element is shown to depend approximately linearly on the humidity drop.     

钢筋混凝土微平面本构模型及其算法研究

阐述文献[1]的第二部分。第一部分在Ba ant Z.P.等人提出的混凝土微平面模型的基础上引入钢筋的影响提出了一个适用于配筋混凝土的微平面动态本构模型。混凝土模型采用能够反映各种复杂受力行为并被试验充分验证的微平面模型,钢筋采用Cowper-Symonds型率相关的双线性模型。该模型可用于钢筋混凝土的静力和动力显式分析。这一部分将给出模型的显式算法和试验验证。     

Multiscale modeling of intergranular fracture in aluminum: constitutive relation for interface debonding

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics—finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction–displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum–atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum–atomistic interface, and continues its propagation in the atomistic environment. This study is a step toward relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.