Tension-softening Curve Research Articles

Numerical simulation on structural behavior of UHPFRC beams with steel and GFRP bars

This study simulates the flexural behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) beams reinforced with steel and glass fiber-reinforced polymer (GFRP) rebars. For this, micromechanics-based modeling was first carried out on the basis of single fiber pullout models considering inclination angle. Two different tension-softening curves (TSCs) with the assumptions of 2-dimensional (2-D) and 3-dimensional (3-D) random fiber orientations were obtained from the micromechanics-based modeling, and linear elastic compressive and tensile models before the occurrence of cracks were obtained from the mechanical tests and rule of mixture. Finite element analysis incorporating smeared crack model was used due to the multiple cracking behaviors of structural UHPFRC beams, and the characteristic length of two times the element width (or two times the average crack spacing at the peak load) was suggested as a result of parametric study. Analytical results showed that the assumption of 2-D random fiber orientation is appropriate to a non-reinforced UHPFRC beam, whereas the assumption of 3-D random fiber orientation is suitable for UHPFRC beams reinforced with steel and GFRP rebars due to disorder of fiber alignment from the internal reinforcements. The micromechanics-based finite element analysis also well predicted the serviceability deflections of UHPFRC beams with GFRP rebars and hybrid reinforcements.

Nonlinear finite element analysis of ultra-high-performance fiber-reinforced concrete beams

A nonlinear finite element analysis was performed to simulate the flexural behaviors of ultra-high-performance fiber-reinforced concrete beams. For this, two different tension-softening curves obtained from micromechanics-based analysis and inverse analysis were incorporated. For micromechanics-based analysis, two-dimensional and three-dimensional random fiber orientations were assumed to obtain the fiber-bridging curve, and a softening curve of matrix in ultra-high-performance fiber-reinforced concrete was used. The use of tension-softening curves obtained from inverse analysis and micromechanics-based analysis using two-dimensional random fiber orientation exhibited fairly good agreement with the experimental results, whereas the use of tension-softening curve from micromechanics-based analysis using three-dimensional random fiber orientation underestimated the experimental results.

Predicting the post-cracking behavior of normal- and high-strength steel-fiber-reinforced concrete beams

In this paper, the results of analytical and experimental analyses for the flexural response of steel-fiber-reinforced concrete (SFRC) beams are presented. In the analytical part, to predict the flexural response of SFRC beams according to the strength of concrete and steel fiber content, a model for compression was adopted from a previous research and a trilinear tension-softening curve (TSC) was suggested based on inverse analysis. To obtain the TSC, a number of notched SFRC beams with two parameters such as (1) strength of concrete (normal- and high-strengths) and (2) steel fiber content (0.0%, 0.5%, 1.0%, 2.0%) were fabricated and tested in accordance with the Japan Concrete Institute (JCI) standard. The suggested models were verified through a comparison of the previous four-point flexural test results and the sectional analyses. For the experimental part, the compressive strength and elastic modulus showed negligible changes with the inclusion of steel fibers, while the strain capacity and post-peak behavior were improved by including steel fibers. The addition of more than Vf of 1.0% steel fibers resulted in the significant improvement of flexural strength, deflection capacity, and post-peak ductility, while the increase of compressive strength led to an increase in the flexural strength and a decrease in the post-peak ductility. Lastly, the fracture energy increased with the increase in the fiber content and the decrease in the strength.

Effect of fiber length and placement method on flexural behavior, tension-softening curve, and fiber distribution characteristics of UHPFRC

This study investigates the effect of fiber length and placement method on the flexural behavior, tension-softening curve, and fiber distribution characteristics of ultra-high-performance fiber-reinforced concrete (UHPFRC). Four different fiber lengths (Lf=13, 16.3, 19.5, and 30mm) were considered for two different placement methods. The ultimate flexural strength increased with increasing fiber length up to 19.5mm, despite no noticeable difference in the first crack strength. Conversely, fiber length of 30mm showed deterioration of flexural performance due to the decrease of fiber number existed across the crack surface. Both of first crack and ultimate flexural strengths were affected by the placement method; the specimen with concrete placed in the center (at maximum moment region) exhibited higher strength than that with concrete placed in the corner. The reasons were confirmed by image analysis that poorer fiber dispersion and fewer fibers across the crack surface were obtained for the specimen with concrete placed in the center than its counterpart. Finally, a tri-linear softening curve for UHPFRC was suggested based on inverse analysis and verified through comparison between the finite element analyses and the test data.

Pre- and post-peak toughening behaviours of fibre-reinforced hot-mix asphalt mixtures

Recycled plastic fibre-reinforced hot-mix asphalt (HMA) mixtures have better fatigue resistance than plain HMA. The toughening effects of recycled plastic fibre-reinforced HMA were characterised using direct tensile loading tests. Adding a small quantity of recycled plastic fibres to HMA was found to significantly increase the mixture's fracture energy and toughness, which were calculated using the pre- and post-peak stages of tensile force–displacement curves. A theoretical model representing the pre-peak behaviour of fibre-reinforced HMA with direct tension-softening curves for various fibre contents is presented here. The enhanced toughness through post-peak analysis was also observed using toughness indices associated with fibre-bridging effect after the pre-peak composite stress. The pre-peak fracture energy model and post-peak toughness indices appeared to be governed by the direct tensile toughening of fibre-reinforced HMA's enhanced fibre-bridging effects. The pre-peak fracture energy model demonstrates the effect of fibre content on the strain energy density during the pull-out process within the pre-peak composite stress region. The maximum pre-peak fracture energy of a coarse-graded HMA mixed with recycled plastic fibres is achieved at a fibre content of 0.4% of the total weight of the HMA. The increases in the toughness indices within the post-peak composite stress region indicate that the fatigue resistance of fibre-reinforced HMA is at least 30% greater than that of control HMA.

Tension softening curves of plain concrete

The tension softening curves (TSCs) of plain concrete with compressive strengths varying between 40 and 90MPa were estimated by performing three-point bending tests on pre-notched beams. Crack evolution and full-field deformation in the beams were measured using the electronic speckle pattern interferometry technique. The crack characteristics, including the crack opening displacement profiles, the width of the fracture process zone and the length of the crack, were evaluated. By using a newly developed incremental displacement collocation method, the TSCs of plain concrete were determined. To facilitate the use of TSCs by commercial finite element packages, the estimated TSCs were simplified to bilinear and exponential curves, and the related parameters were determined.

Determination of the tension softening curve of nuclear graphites using the incremental displacement collocation method

The fracture properties of two nuclear-grade graphites, the Japanese IG11 graphite and Chinese NG-CT-01 graphite, were evaluated under flexural conditions. Three-point bend tests were performed on centre-notched beams to determine the tension softening curve (TSC), Mode-I fracture toughness KIC and the fracture energy GF. The TSC of the nuclear graphites was originally determined by a newly developed incremental displacement collocation method, and was shown to be able to predict the post-peak behaviour accurately. The TSC was simplified to the bilinear, tri-linear and exponential curves. The tri-linear curve was found to be the best approximation for modelling the tension softening of these nuclear graphites. Furthermore, scanning electron microscope images of their microstructures showed that the difference in brittleness and fracture behaviour between the two graphites was probably caused by a difference in grain size and the degree of binder infiltration.

混凝土断裂模量的尺寸与强度效应

本文用有限元数值模拟的方法研究了混凝土的断裂模量，建立了断裂模量与试件尺寸以及混凝土强度等级的关系。数值试件采用了不同尺寸的三点弯曲混凝土简支梁。在数值模拟中采用弥散裂缝模型模拟混凝土开裂，用非线性拉应力与开裂应变软化曲线模拟混凝土裂缝的进一步扩展。数值试验中考虑影响混凝土断裂模量的因素为混凝土强度等级和梁的高度，最后在数值结果的基础上建立了混凝土断裂模量与脆性指标之间的关系。 In this paper, the flexural strength of plain concrete beams subjected to three-point bending was numerically studied using the finite element program DIANA. Instead of using a discrete crack model, a smeared crack model is adopted in the numerical simulation. A non-linear tension softening curve was used to model the gradually diminishing tensile strength of concrete upon further crack opening. The factors influencing the flexural strength of plain concrete beams considered in this paper are the concrete strength grade and the beam depth. These two factors can be combined into one material parameter and the brittleness index. A relationship between the ratio of flexural strength to the tensile strength and the brittleness index was proposed based on the numerical results.

Micromechanics of crack bridging stress-displacement and fracture energy in steel hooked-end fiber-reinforced cementitious composites

This paper presents a probabilistic micromechanical framework for analyzing crack bridging stress-displacement in short steel hooked-end fiber-reinforced cementitious composites, featuring the fiber length/diameter aspect ratios of 45 and 80, with varying fiber volume fractions and varying snubbing coefficients. The proposed formulation is constructed based on the randomly located, randomly oriented distribution of steel fibers. This random nature accounts for the dominant features of the composite failure mechanisms. The composite fracture energy dissipation may be obtained from the area under the tension-softening curve. The fracture energy dissipations contributed by the fiber interfacial debonding and fiber pullout of both the straight-part and the hooked-end element are systematically investigated. Further, the fiber bridging micromechanical mechanism and the bridging stress-displacement are accommodated. The fracture energy dissipation attributable to the hooked-end element is shown to be smaller than that of the straight element, but still remains significant. Comprehensive comparisons between the constant shear model predictions and experimental data manifest significant improvements when the hooked-end effects are incorporated into the composite fracture energy dissipation analyses. Based on the experimental data and micromechanical predictions, we recommend the range of the fiber volume fraction to be from 0.75% to 1%.

Incremental displacement collocation method for the evaluation of tension softening curve of mortar

The tension softening curve (TSC), showing the relationship between the cohesive tensile stress and crack opening displacement, is the constitutive law of the cohesive crack model. Due to the difficulties in measuring local deformations around the crack tip, the TSC is usually determined inversely from the global responses such as load–deflection curve or load–crack mouth opening displacement curve of pre-notched specimens. However, the use of global responses alone in the inverse analysis usually causes problems that may affect the reliability and accuracy of the TSC which is basically a local material property. To overcome these limitations, an incremental displacement collocation method (IDCM) that is able to evaluate the TSC in a step-by-step manner is proposed in this paper. Both global and local responses of a pre-notched mortar beam, which are measured using an electronic speckle pattern interferometry technique, are used in the displacement collocation process. Furthermore, the finite element model (FEM) is utilized to simulate the response of the beam. The TSCs evaluated in this study are verified through the comparisons of the global and local displacements as well as the fracture energy. A tri-linear curve was found to be the best approximation of the TSC of mortar.

Nonlinear Analysis of RC Structures Using Isotropic Damage Model

This article proposes a simple isotropic damage model within damage mechanics framework to represent the behavior of concrete in tension. Macroscopic evolution of tensile crack is considered as damage and is mathematically defined using an exponential function of tensile strain. A damage evolution law is formulated by applying strain equivalence principle to hyperbolic tension-softening curve. Value of damage variable is assumed theoretically to vary between ‘0’ and ‘1’ to denote uncracked and ruptured states, respectively. A smeared rotating crack model is coupled with damage formulation to simulate crack propagation effects in nonlinear finite element analysis of reinforced concrete (RC) structures. Many deficiencies of smeared crack model such as stress locking, mesh-induced directional bias, and instability in response computation for near-ultimate load are overcome using the coupled model. To verify the proposed model, nonlinear static response behavior of a RC beam is computed and compared with experimental and analytical results reported in literature. Effectiveness and applicability of the model to analyze practical structures are proved by analyzing a RC chimney. Nonlinear response of RC chimney is reviewed at global level while damage states of finite elements are studied at local level.

Prediction of the Tension Softening Curve of Dam Concrete Based on BP Neural Network

This paper predicted the tension softening curves of dam concrete by employing the BP neural networks based on the experimental data of direct tension tests of dam concrete. This approach can predict the tension softening curves for the same component material but different mixtures dam concrete without performing the direct tension tests which are complex and expensive.

EVALUATION OF SHEAR CARRIED BY STEEL FIBERS OF REINFORCED CONCRETE BEAMS USING TENSION SOFTENING CURVES

The aim of this paper is to propose the method for evaluating the shear carried by steel fibers of reinforced concrete with steel fibers (RSF) beams. Ten RSF beams with various steel fiber volume fraction, stirrup ratio and specimen size were tested by a four-point bending test. The crack surface displacement was examined by the image analysis. Length of the diagonal crack was measured. The tension softening curves were used to calculate the stress transferred across the diagonal crack. The contribution of steel fibers on the shear resistance of RSF beams has been investigated based on the fracture mechanics. The shear carried by steel fibers calculated from the proposed method showed good agreement with experimental values.

Correlation between tension softening relation and crack extension resistance in concrete

Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve, one of the fundamental fracture criteria in crack mechanics. Recently, experimental observation of the fracture behavior in concrete was used to develop a new fracture criterion, the crack extension GR resistance curve, to analyze crack propagation during the entire concrete fracture process. The variation of the crack extension resistance is mainly associated with the energy consumption in the fracture process zone ahead of the stress-free crack tip. The crack extension resistance is then a function of the softening curve, which is a basic mechanical property in the fracture process zone. The relationship between the softening curve and the crack extension GR resistance curve is then analyzed based on results of three-point bending beams tests. The results indicate that the characteristic points of the crack extension resistance GR curve is closely related to the characteristic point on used tension softening curve.

Prediction of Tension Softening Curve in Concrete Using Artificial Neural Networks

Knowledge of the tension softening process of concrete is essential to understand fracture mechanism, further to analyze fracture behaviour, and further to evaluate properties of concrete. For the last eight years, many different tests on uniaxial tension with elimination of secondary flexure were performed in Tohoku Institute of Technology. The paper is dedicated to predict tension softening curve of concrete by using artificial neural networks (ANNs) based on experimental data of five different mixtures of concrete (including High Performance Concrete). It is an advantage to predict a proper tension softening curve without performing uniaxial tension tests. Several artificial neural networks with different architectures (with various hidden neurons and layers) were studied using software - Statistica Neural Network. In order to evaluate the prediction accuracy, tension softening curve and other fracture parameters were predicted for each mix from the other four mixes and compared with the omitted data of the relevant mix. High accuracy was obtained in the all predicted tension softening curves and the fracture parameters were also well predicted.

Size Effect of Concrete in Uniaxial Tension

In order to investigate the size effect of concrete, four sizes of rectangular prisms were tested in uniaxial tension. The cross sections of the prisms were 50x100mm, 100x100mm, 200x100mm and 400x100mm. The concrete was an ordinary one with the compressive strength of 34 MPa and the maximum aggregate size of 20mm. Notches were applied on four side faces and secondary flexure was completely eliminated during the test in order to obtain the exact nominal tensile strength. The size effect was analyzed by four factors, namely tensile strength, fracture energy, critical crack opening displacement and tension softening curves. Clear size dependence was observed in critical crack opening displacement and initial convexity of tension softening curves, and a slight size dependence was observed in tensile strength. On the other hand, size effect was unclear in fracture energy and other part of tension softening curves because of their scatters.

コンクリートの直接引張試験における4つの誤解

The best way to investigate the tension softening process is by applying a uniaxial tension force directly on a concrete specimen, because it can measure both tensile strength and the tension softening curve from an identical specimen. However, no standard tests have been adopted to provide a direct measurement of the tension softening curves of concrete, though many inadequate test procedures were proposed until recently. There are four misunderstandings in investigating the tension softening process, concerning the effects of notches, secondary flexure, boundary conditions and specimen geometry. In this paper, the misunderstandings are discussed and clarified in detail with theoretical and experimental considerations. A test procedure free from these misunderstandings is proposed for the uniaxial tension test of concrete and some successful test results are presented.

Fictitious Crack Modeling of the Fracture of a Refractory Ceramic: Fitting through Experimental Measurements of the Displacement Field around the Fracture Process Zone

In this paper, we present the modelling of the fracture of a refractory ceramic using the fictitious crack model. The parameters of the tension-softening curve of the modelling are obtained, not by numerical fitting of macroscopical data, but after observation of the displacement field around the fracture process zone. The modelling obtained is compared with experimental data and previous modelling made by other authors, giving a good fitting of the experimental values and a modelling at least as good as the one obtained by numerical fitting.

A practical method for uniaxial tension test of concrete

A test method for uniaxial tension test of concrete to obtain tension softening curves has not been established yet, because there are several difficulties in performing the test. In the past 40 years, many different test conditions, sometimes even completely opposite conditions have been adopted. In order to show which conditions should be selected and why the conditions should be selected, theoretical and experimental investigation was carried out. For the experiment, prismatic specimens with notches and an originally designed gear system preventing secondary flexure were adopted. It was shown that the tension softening curves were successfully monitored by the present procedure with a high success ratio. A practical test procedure of uniaxial tension test of concrete was proposed based on the investigation.

Crack Growth of Non-Coplanar Parallel Crack Array and Tension-Softening Model(Brittle Fracture)

It is well known that the tension-softening model can describe the macroscopic fracture behavior of quasi-brittle materials containing pre-existing microcracks such as rocks, ceramics and concretes. The problem studied in this paper is a tension-softening behavior in brittle materials based on the growth of a non-coplanar parallel crack array. Crack growth analyses are performed numerically using the body force method. The problem calculated is a non-coplanar crack array subjected to uniform tensile stress at infinity. The plane strain condition is assumed. The maximum principal stress criterion is employed to determine the each crack growth direction and the global stress required for crack propagation. The tension-softening behavior is studied from the remote tensile stress and deformation of the numerical result. The deduced tension-softening curve is consistent with experimental data obtained for granites. This evidence revealed that the overlapping of non-coplanar cracks, i.e. the ligamentary bridging, is the main source of the tension-softening behavior of granites.