Predicting the flexural response of steel fibre reinforced concrete prisms using a sectional model

The material characterisation of steel fibre reinforced concrete (SFRC) continues to be an ongoing topic of debate in the scientific community. When designing a structural element made of SFRC, its defining characteristic is its post-cracking residual tensile strength. Theoretically, a uniaxial tension test is the ideal test in gathering these parameters; however these tests are expensive in time and testing. Consequently, much effort has been placed on inferring the post-cracking properties of SFRC from simpler tests, such as a notched prism in bending. In this paper, the sectional analysis procedure of Zhang and Stang (1998) is adapted with the inclusion of the variable engagement model to describe SFRC in tension. The model is shown to accurately capture the load–deformation characteristics of the tested specimens and allows for the explicit identification of the components resisting load.     

Effect of steel fibres on mechanical properties of high-strength concrete

Steel fibre reinforced concrete (SFRC) became in the recent decades a very popular and attractive material in structural engineering because of its good mechanical performance. The most important advantages are hindrance of macrocracks’ development, delay in microcracks’ propagation to macroscopic level and the improved ductility after microcracks’ formation. SFRC is also tough and demonstrates high residual strengths after appearing of the first crack. This paper deals with a role of steel fibres having different configuration in combination with steel bar reinforcement. It reports on results of an experimental research program that was focused on the influence of steel fibre types and amounts on flexural tensile strength, fracture behaviour and workability of steel bar reinforced high-strength concrete beams. In the frame of the research different bar reinforcements (2∅6 mm and 2∅12 mm) and three types of fibres’ configurations (two straight with end hooks with different ultimate tensile strength and one corrugated) were used. Three different fibre contents were applied. Experiments show that for all selected fibre contents a more ductile behaviour and higher load levels in the post-cracking range were obtained. The study forms a basis for selection of suitable fibre types and contents for their most efficient combination with regular steel bar reinforcement.     

Implications of test methodology on post-cracking and fracture behaviour of Steel Fibre Reinforced Concrete

It is now universally recognized that the mechanical, cracking and fracture, properties of Steel Fibre Reinforced Concrete (SFRC) are far superior to those of plain concrete. The use of SFRC contributes effectively to preserve the structural stability and structural integrity of concrete elements and improve their ductile behaviour.To optimize the performance of SFRC in structural members it is necessary to establish the mechanical properties very precisely. The best test methodology to evaluate the post-cracking and toughness properties of SFRC is the beam bending test. Design codes recommend one of two bending test configurations: the three-point or the four-point bending test. The results obtained from these two test configurations are not identical.The overall focus of this paper is to evaluate the contributions of fibres to the post-cracking and fracture behaviour of concrete as determined by the two different standard test procedures. To achieve these aims plain and fibre concrete specimens were tested. All the test specimens were extensively instrumented to establish the strength properties, crack tip and crack mouth opening displacement, post-cracking and fracture behaviour. The results of the two types of bending tests were then critically analysed and evaluated to identify the differing effects of the bending load configurations on material and structural behaviour.SFRC specimens subjected to four-point bending test showed higher stress values compared to those obtained from the three-point bending tests. The first crack strength values evaluated following the two standards are close with an improvement of 10% for the European standard.     

Impact of fibre orientation on tensile,bending and shear behaviors of a steel fibre reinforced concrete

Fibre orientation and density are known to have a significant influence on steel fibre reinforced concretes (SFRC) mechanical properties. In practice, parameters such as fresh state properties, restriction to concrete flowability and placing methods are likely to induce different fibre orientations in characterisation specimens and structural components. This difference in fibre orientation can impact the mechanical behavior of the structural component and therefore provide an unsafe design if not considered. This project consisted to produce a large SFRC slab, extract specimens with different fibre orientations, and submit specimens to tensile, bending and shear tests to evaluate the impact of fibre orientation and density on mechanical and post-peak strengths. Test results have shown that tensile and bending behaviors are mainly influenced by the fibre orientation, while the shear behavior is mainly impacted by fibre density. Test results were processed to allow comparison between tensile and bending tests. Linear correlations between tensile residual stresses and fibre orientation where found, linear or power type correlations according to bending residual stresses, as well as linear correlations between shear stresses and fibre density.     

Shear capacity of steel and polymer fibre reinforced concrete beams

This paper deals with the application of a plasticity model for shear strength estimation of fibre reinforced concrete beams without stirrups. When using plastic theory to shear problems in structural concrete, the so-called effective strengths are introduced, usually determined by calibrating the plastic solutions with tests. This approach is, however, problematic when dealing with fibre reinforced concrete (FRC), as the effective strengths depend also on the type and the amount of fibres. In this paper, it is suggested that the effective tensile strength of FRC can be determined on the basis of the tensile stress-crack opening relationship found from wedge splitting tests. To determine the effective compressive strength of FRC, it is proposed to adopt the formula used for conventional concrete and modify it by introducing a fibre enhancement factor to describe the effect of fibres on the compressive softening behaviour of FRC. The enhancement factor is determined as the ratio of the areas below the stress–strain curves for FRC and for conventional concrete. The outlined approach has been verified by shear testing of beams containing no fibres, 0.5% steel fibre volume and 0.5% polymer fibre volume. The tests results are compared with estimations and show satisfactory agreements, indicating that the proposed approach can be used.     

Predicting the flexural load–deflection response of steel fibre reinforced concrete from strain, crack-width, fibre pull-out and distribution data

A semi-analytical model is presented, based on conventional principles of mechanics, to predict the flexure behaviour of steel fibre reinforced concrete. The model uses a stress-block approach to represent the stresses that develop at a cracked section by three discrete stress zones: (a) a compressive zone; (b) an uncracked tensile zone; and (c) a cracked tensile zone. It is further shown that the stress-block, and hence flexural behaviour, is a function of five principal parameters: compressive stress–strain relation; tensile stress–strain relation; fibre pull-out behaviour; the number and distribution of fibres across the cracked section in terms of their positions, orientations and embedment lengths; and the strain/crack-width profile in relation to the deflection of the beam. An experimental investigation was undertaken on both cast and sprayed specimens to obtain relationships for use in the model. The results of the study showed a reasonable agreement between the model predictions and experimental results. However, the accuracy of the model is probably unacceptable for it to be currently used in design. A subsequent analysis highlighted the single fibre pull-out test and the sensitivity of the strain analysis tests as being the main cause of the discrepancies.     

Post-cracking strength and ductility of glass–GFRP composite beams

This paper presents results of experimental and numerical investigations on the structural behaviour of composite beams made of annealed glass panes and glass fibre reinforced polymer (GFRP) pultruded profiles. The main goal of the transparent structural solutions presented here is to increase the post-cracking residual strength and ductility of glass by using GFRP strengthening laminates. The experimental programme included (i) tensile tests on double lap joints between glass and GFRP pultruded laminates, bonded with different types of structural adhesives, and (ii) full-scale flexural tests on glass beams and glass–GFRP composite beams, with different strengthening geometries and structural adhesives. Results obtained in this study show that, unlike glass beams, in glass–GFRP composite beams it is possible to obtain relatively ductile failure modes, with a significant increase of both strength and deformation capacity after the initial cracking of glass. The stiffness of the structural adhesive used, together with the geometry of the GFRP strengthening element, have a major influence on the structural response of the composite beams. Finite element models were developed for all tested beams, allowing to simulate their serviceability behaviour (prior to glass cracking) with fairly good accuracy, namely in what concerns the degree of shear interaction at the bonded interfaces.     

Strength and fracture properties of industrially prepared steel fibre reinforced concrete

The paper reports on a study of steel fibre reinforced concrete (SFRC) which was prepared using normal industrial mixing, compaction and curing conditions. Both strength (compressive and tensile) and fracture (toughness measurements) characteristics have been investigated with test specimens prepared from 5 m long SFRC piles. The piles contained only steel fibre reinforcement and were manufactured in exactly the same way as ordinary piles.Slight differences in the tensile strengths (determined via torsion tests) were observed due to the existence of preferential fibre orientation. Flexural tests on notched beams (to evaluate fracture characteristics) produced a much more stable, reproducible, test than that observed for un-notched beams. Hence, it is concluded that the notched beam is a better geometry in terms of test stability and reliability. The results showed that tests specimens taken from industrially prepared SFRC displayed similar characteristics compared to that observed with test specimens prepared under laboratory conditions, with regards to the strength, fracture characteristics and, in particular, the variation observed.     

Shear behavior model for steel fiber-reinforced concrete members without transverse reinforcements

Due to the complex shear mechanism of steel fiber-reinforced concrete (SFRC) members, there is lack of comprehensive shear behavior models for SFRC members. The shear behavior model, based on a smeared crack model, requires the tensile stress–strain constitutive equation of SFRC membrane subjected to biaxial stresses. After SFRC panel tests under biaxial stresses were recently conducted, it has been possible to create a more complete smeared crack model for estimating the shear behavior of SFRC members. It is, however, very difficult to conduct such experiments for different types of steel fibers, various amount of steel fibers, different ranges of concrete strengths, etc. Thus, in this study, steel fibers are modeled as average direct tensile contribution elements in a modified smeared crack truss model, considering directionality and distribution of fibers. In this way, only simple bond tests are required to reflect the effects of different characteristics of SFRC. In addition, the shear contribution of steel fibers can be obtained considering the bond failure of steel fibers. The proposed model was compared to the test results of 8 SFRC panels and 80 SFRC beams, and the shear behavior of the SFRC members was well estimated.     

Tensile behaviour of nonwoven structures: comparison with experimental results

Nonwoven structures have been recently explored for numerous novel applications ranging from composites to scaffolds. The tensile property of nonwovens is a pre-requisite and indeed, one of the main parameters to determine their performance for such applications. In the first part, a modified micromechanical model describing the tensile behaviour of thermally bonded nonwovens was proposed by incorporating the effect of fibre re-orientation during the deformation (Rawal et al., J Mater Sci 45:2274, 2010). In this study, an attempt has been made to compare the theoretical and experimental stress–strain curves of thermally bonded and spunbonded nonwoven structures. These theoretical findings have been obtained from the most popular analytical tensile models of nonwovens available in the literature in addition to our modified tensile model. Poisson’s ratio has also been determined experimentally in order to predict the stress–strain behaviour of nonwoven, and its relationship with longitudinal strain has clearly distinguished between the randomly and preferentially orientated types of structures. In thermally bonded nonwovens, the tensile strength in various test directions is computed through pull-out stress and a comparison is made with the experimental results.     

Tensile stress–crack width law for steel fibre reinforced self-compacting concrete obtained from indirect (splitting) tensile tests

In this work, mode I fracture parameters of steel fibre reinforced self-compacting concrete (SFRSCC) were derived from the numerical simulation of indirect splitting tensile tests. The combined experimental and numerical research allowed a comparison between the stress–crack width (σ–w) relationship acquired straightforwardly from direct tensile tests, and the σ–w response derived from inverse analysis of the splitting tensile tests results. For this purpose a comprehensive nonlinear 3D finite element (FE) modeling strategy was developed. A comparison between the experimental results obtained from splitting tensile tests and the corresponding FE simulations confirmed the good accuracy of the proposed strategy to derive the σ–w law for these composites. It is concluded that the post-cracking tensile laws obtained from inverse analysis provided a close relationship with the ones obtained from the experimental uniaxial tensile tests.     

Design of SFRC structural elements: flexural behaviour prediction

Practical steel fibre reinforced concrete (SFRC) applications in load-carrying structural members have yet to gain wide acceptance in design codes. This is partly explained by the lack of a unified design philosophy adapted to this material. A model based on simple and widely accepted assumptions is proposed for the analysis and the design of SFRC members subjected to bending moments. In order to evaluate the accuracy of the analytical model predictions, an extensive experimental program was conducted on 21 rectangular and T-beams of various sizes produced with five different types of SFRC. The contribution of fibres at different loading phases in bending is described in detail. The analytical model accuracy to predict maximum crack opening applicable in service conditions and at the ultimate flexural strength are compared to experimental measurements. Discrepancies observed are related to the dispersion of the material properties and the difference of fibre orientation in beams and characterization specimens. Finally, the proposed design approach is applied to the design of a realistic T-beam subjected to positive and negative bending moments.     

Mechanical properties of steel fibre reinforced concrete exposed at high temperatures

Steel fibre reinforced concrete (SFRC) is an advanced cementitious composite where fibres can act as a profitable replacement for diffused reinforcement, like welded steel mesh, especially for thin cross sections. In this case fire becomes a very important condition in the design. Previous experimental research has shown the benefits in fire resistance of steel fibres, when structural elements are bent. A careful mechanical characterization of a SFRC used for prefabrication after thermal cycles at high temperature is here presented. Three different tests are considered: four point bending, uniaxial compression and fixed-end uniaxial tension. In the paper the decay of peak and post-cracking strengths versus temperature increase for uniaxial compression, uniaxial tension and bending are discussed.     

Constitutive relationship of polyolefin fibre–reinforced concrete: Experimental and numerical approaches to tensile and flexural behaviour

Flexural tensile tests are usually used to evaluate the suitability of fibre‐reinforced concrete (FRC) in structural applications. The constitutive relationships of FRC are derived from such tests by using several inverse analyses. Given that the structural design of FRC is based on the residual load‐bearing capacities obtained under flexural tests, the approach to analyse fracture behaviour by means of uniaxial tensile tests would mean use of more direct and reliable constitutive curves compared with those obtained by indirect means. The significance of this paper lies in the characterisation of polyolefin fibre–reinforced concrete (PFRC) not only by using fracture flexural results tests but also by comparing such results with the direct tensile behaviour of the material obtained from uniaxial tests. This comparison would both extend the knowledge of the PFRC mechanical properties and broaden the reliability of structural design by comparing the behaviour of PFRC under flexural and tensile stresses. Moreover, the suitability of an iterative method proposed by the authors for obtaining the constitutive relations of PFRC from flexural tests has been checked by performing a series of numerical simulations of the tensile tests performed. The differences in the properties obtained in the flexural tests and the tensile tests have been assessed. The experimental results gathered from the tensile tests have been accurately reproduced by using a cohesive crack approach with trilinear softening functions by the iterative inverse analysis proposed.     

Characterization of macrocrack propagation under sustained loading in steel fibre reinforced concrete

Preoccupation for improving concrete infrastructure durability has become just as important as safety issues and concrete cracking plays a key role for durability. Despite various studies carried out in the last decade, very little information regarding the propagation of cracking under sustained loading and the physical mechanisms involved is available. In order to address this problem, an experimental study on the propagation of a macrocrack under sustained loading in steel fibre reinforced concrete (SFRC) beams was completed. This article describes the flexural creep tests carried out on 0.7 m long beams. The evolution of the deflection, the crack width and the crack propagation were measured until the specimens’ failure. The results permit the assessment of the influence of initial CMOD and sustained load levels on crack propagation, damage evolution, and the mechanisms leading to the rupture of the beams. In addition, behaviour of beams in sealed and drying hydric conditions with an identical loading history are compared to determine the influence of hydric conditions. The results show that crack propagation governs the failure mechanisms of SFRC beams subjected to high sustained load levels.     

Constitutive model for cyclic deformation of perfluoroelastomers

Observations are reported in uniaxial cyclic tensile tests with a strain-controlled program on perfluoroelastomer Hyflon MFA. A constitutive model is developed for its viscoplastic response and damage at three-dimensional deformations with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Numerical simulation demonstrates that the constitutive equations adequately describe the mechanical response of perfluoroelastomer in cyclic tests with complicated deformation programs.     

Assessment of the fibre orientation factor in SFRC slabs

The design of steel fibre reinforced concrete (SFRC) structures is evolving towards a new approach that uses correction factors to consider differences between the small-scale characterisation specimens and the real-scale elements. Recently, the Model Code 2010 proposed an orientation factor (K) that accounts for the effects of the orientation in the structural response of elements. The present study focuses on the identification of this factor in SFRC slabs with different dimensions. For that, flexural tests on real-scale slabs were conducted and the fibre orientation was assessed with an inductive method. A finite element analysis showed the differences between the experimental curves and the prediction of the Model Code without considering K. Based on the results obtained, a range of values is proposed for K and validated. This study sheds light on possible modifications that this philosophy of design might require to better reproduce the behaviour of slabs.     

Influence of casting condition on the anisotropy of the fracture properties of Steel Fibre Reinforced Self-Compacting Concrete (SFRSCC)

Identification of the tensile constitutive behaviour of Fibre Reinforced Concrete (FRC) represents an important aspect of the design of structural elements using this material. Although an important step has been made with the introduction of guidance for the design with regular FRC in the recently published fib Model Code 2010, a better understanding of the behaviour of this material is still necessary, mainly for that with self-compacting properties. This work presents an experimental investigation employing Steel Fibre Reinforced Self-Compacting Concrete (SFRSCC) to cast thin structural elements. A new test method is proposed for assessing the post-cracking behaviour and the results obtained with the proposed test method are compared with the ones resulted from the standard three-point bending tests (3PBTs). Specimens extracted from a sandwich panel consisting of SFRSCC layers are also tested. The mechanical properties of SFRSCC are correlated to the fibre distribution by analysing the results obtained with the different tests. Finally, the stress-crack width constitutive law proposed by the fib Model Code 2010 is analysed in light of the experimental results.     

An experimental and numerical study of the effects of length scale and strain state on the necking and fracture behaviours in sheet metals

Within sheet metal forming, crashworthiness analysis in the automotive industry and ship research on collision and grounding, modelling of the material failure/fracture, including the behaviour at large plastic deformations, is critical for accurate failure predictions. In order to validate existing failure models used in finite element (FE) simulations in terms of dependence on length scale and strain state, tests recorded with the optical strain measuring system ARAMIS have been conducted. With this system, the stress–strain behaviour of uniaxial tensile tests was examined locally, and from this information true stress–strain relations were calculated on different length scales across the necking region. Forming limit tests were conducted to study the multiaxial failure behaviour of the material in terms of necking and fracture. The failure criteria that were verified against the tests were chosen among those available in the FE software Abaqus and the Bressan–Williams–Hill (BWH) criterion proposed by Alsos et al, 2008. The experimental and numerical results from the tensile tests confirmed that Barba's relation is valid for handling stress–strain dependence on the length scale used for strain evaluation after necking. Also, the evolution of damage in the FE simulations was related to the processes ultimately leading to initiation and propagation of a macroscopic crack in the final phase of the tensile tests. Furthermore, numerical simulations using the BWH criterion for prediction of instability at the necking point showed good agreement with the forming limit test results. The effect of pre-straining in the forming limit tests and the FE simulations of them is discussed.     

Micromechanics of multiple cracking Part II Statistical tensile behaviour

A computational model for fibre-reinforced brittle materials in tension is developed. The model includes multiple cracking and strain-hardening processes, as well as single fracture and strain softening. The composite behaviour is derived from a single-fibre analysis by integrating over all possible fibre locations and orientations. The single-fibre analysis is based on symmetry fibres satisfying the equilibrium condition. The result is a complete constitutive relation: stress–strain or stress–crack width curve, and a prediction of crack spacing. The model is an extension of the ACK theory by Aveston, Cooper and Kelly, as it can be used with discontinuous fibres with different distributions, as well as for analysing hybrid composites. Fibre orientation introduces additional phenomena, which are taken into account with simple models. It was seen that matrix spalling at the fibre exit point may have a considerable effect on the composite strain and the crack width. The effect of fibre aspect ratio on the failure mode was studied, and it was found that with an intermediate fibre diameter the composite fails by fibre pull-out in a multiple-cracking stage, resulting in a strain-hardening material with a high ductility. The proposed model was verified against experimental results of a strain-hardening material, called an engineered cementitious composite. The model can be used in tailoring new materials to meet certain requirements, or in studying the effects of micromechanical properties on the composite behaviour, including the crack width, crack spacing, post-cracking strength, ultimate strain, and ductility. The derived constitutive relationship can further be used in finite element analyses defining the behaviour perpendicular to the crack. © 1998 Kluwer Academic Publishers