Crack Bridging Stress Research Articles

Fatigue analysis of orthotropic steel-ultra-high-performance fiber-reinforced concrete (UHPFRC) composite deck considering accelerated deterioration and self-healing of fractured ultra-high-performance fiber-reinforced concrete in surface water condition

In this study, an orthotropic steel bridge deck overlaid with ultra-high-performance fiber-reinforced concrete (UHPFRC) is investigated using the finite element analysis. The composite bridge deck which is undergone moving-wheel load is examined under environmental surface water conditions. Two phases, i.e., Phases 1 and 2, are considered for the material model of the UHPFRC with stagnant water. In Phase 1, mechanical recoveries of the tensile strength and reloading stiffness are considered for the cracked UHPFRC caused by the autogenous self-healing behavior. In Phase 2, under the moving-wheel load, the crack bridging stress degradation in reinforced overlayer accelerates due to the closing–opening actions of surface cracks in water. In both phases, the deformation behaviors of the steel deck plate and UHPFRC overlayer are numerically examined. The results of the current numerical model agree with the experimental data in terms of the strain tendency, wherein the strain range of the steel deck plate and UHPFRC overlayer decreases in Phase 1 and progressively increases in Phase 2. Therefore, it can be asserted that, under the surface water condition, scenarios considering two phases of the material model of cracked UHPFRC, have governed the strain behaviors of the tested composite bridge deck.

Material comparative analysis of crack-bridging degradation of SFRC structural beams under flexural fatigue loading

This study experimentally investigates the influence of several material parameters on steel fiber reinforced concrete (SFRC) structural beams and their crack-bridging degradation over constant and variable amplitudes of flexural cyclic loading. Crack-bridging stress is evaluated using inverse analysis and its degradation against maximum rebars strain is derived. Four series of SRFC beams are prepared and characterized with different concrete compressive strengths, hooked-end steel fiber shapes in two different volume fractions, and two longitudinal reinforcement ratios. The results reveal lower crack-bridging degradation rates, and associated longer fatigue life and higher residual capacity, for beams with higher concrete strength. Further, SFRC fracture energy is shown to have a significant effect on fatigue response, with higher fracture energy associated with lower rates of crack-bridging degradation. However, steel fibers with double hooks are shown to have a relatively insignificant effect on controlling crack-bridging degradation rates and the flexural cyclic responses of SFRC beams as compared to single hook fibers. Also demonstrated is that a lower longitudinal reinforcement ratio leads to higher rebar strain rates with no influence on crack-bridging stress. Crack-bridging degradation diagrams are proposed for SFRC beams that quantitatively capture several material parameters effects based on their mechanical properties over the fatigue life.

Crack-bridging degradation and evolution in SFRC structural beams under variable amplitude flexural cyclic loading

A few studies have demonstrated a degradation in the performance of the steel-fibers in bridging cracks over the lifetime of steel-fiber reinforced concrete (SFRC) structures but only considered for constant amplitude cyclic loading. However, SFRC structures in practice are subjected to variable amplitude loading, thus their crack-bridging would be influenced by the preceding loading history. This concern has so far remained unexplored. This study presents experimental and analytical flexural cyclic responses of SFRC structural beams under constant and variable amplitudes. The crack-bridging stresses are evaluated using a proposed inverse method based on sectional analysis calculations. Besides, the maximum rebar strain level is correlated with the crack-bridging degradation law, aiming at reflecting the beam’s macroscopic response. The results show that crack-bridging stress increases if the fatigue load level increases, indicating that new fibers play a role in bridging cracks along the crack length. Further, decreasing the fatigue load level leads to an instant decrease in crack-bridging, which is followed by a stabilization as the pullout stress applied to the bridging fibers is reduced. Finally, a diagram of crack-bridging degradation and evolution is proposed regarding the maximum rebar strain, which is supposed to be a valuable tool in the SFRC structural design.

Effect of multiple matrix cracking on crack bridging of fiber reinforced engineered cementitious composite

In the present paper, a modified micromechanics based model that describes the crack bridging stress in randomly oriented discontinuous fiber reinforced engineered cementitious composite is developed. In the model, effect of multiple matrix cracking on fiber embedded length, which in turn influencing fiber bridging in the composite, is taken into consideration. First, crack spacing of high strength-low shrinkage engineered cementitious composite was experimentally determined by photographing the specimen surface at some given loading points during uniaxial tensile test. The diagram of average cracking spacing and loading time of each composite is obtained based on above data. Then, fiber bridging model is modified by introducing a revised fiber embedment length as a function of crack spacing. The model is verified with uniaxial tensile test on both tensile strength and crack opening. Good agreement between model and test results is obtained. The modified model can be used in design and prediction of tensile properties of fiber reinforced cementitious composites with characteristics of multiple matrix cracking.

Derivation of crack bridging stresses in engineered cementitious composites under combined opening and shear displacements

The mechanical behavior of Engineered Cementitious Composites (ECC) is strongly dependent on the bridging of cracks by fibers. Due to the bridging action of fibers, tensile and shear stresses can be transferred through cracks in ECC members. In this study, a micromechanics based theoretical model is proposed to describe the shear transfer mechanism on the crack surface due to fiber bridging effect. The model focuses on flexible fibers and both the normal stress along the crack opening direction and the shear stress transferred across the crack surfaces are derived under the coupled effect of crack opening displacement (COD) and shear sliding. With the proposed model, the mechanism of fibers contributing to the shear transfer can be understood and the effect of various micromechanical parameters can be investigated. The simulation results can provide insight on the behavior of ECC under shear loading when cracks are propagating under mixed mode.

Experimental study on crack bridging in engineered cementitious composites under fatigue tensile loading

The crack bridging behaviour of Engineered Cementitious Composites (ECCs) under fatigue tensile loading is investigated experimentally in this paper. Uniaxial fatigue tension tests were conducted on pre-cracked specimens under deformation control with constant crack opening displacement amplitude. The crack bridging stress at the maximum crack opening displacement was obtained against the number of loading cycles. Eight maximum crack opening displacement levels were tested in total. The crack bridging stress was found to decrease with the increase of loading cycles. The crack bridging stress degradation is generally more significant in ECCs than in steel fibre reinforced concrete. In addition, the crack bridging stress degradation behaviour of ECCs reinforced with polymeric fibres was found to be distinct from that of steel fibre reinforced concrete with presence of accelerated stress degradation. The experiment demonstrates that it is important to take the fibre fatigue rupture into account in the analysis of mechanical behaviour degradation of ECCs and that the crack opening affects the crack bridging degradation behaviour.

Shear behavior of steel fiber reinforced concrete using full-field displacements from digital image correlation

Reinforced concrete beams with discrete hooked-end steel fibers at 0.5% volume fraction are tested with a shear span to depth (a/d) ratio equal to 1.8. Digital image correlation (DIC) technique was used to obtain the full-filed displacements from the beam. The formation and propagation of a shear crack which directly influences the load response and the peak load in the load response of the beam is monitored using the displacement information available from DIC. There is a continuous increase in slip across the crack faces with increasing load, which produces an increase in the crack opening. The dilatant behavior indicated by the proportion of crack opening to slip displacement obtained from the control and the SFRC beams is identical. Failure in control beams is brittle and was produced by the opening of dominant shear crack within the shear span. At the peak load, the shear crack pattern in fiber reinforced concrete is identical to the crack pattern in the control beam. The fiber reinforced concrete beams exhibit post peak load carrying capacity with continued slip of the dominant shear crack. The crack bridging stress provided by the fibers results in a significant increase shear transfer across the crack which provides significant post-peak load carrying capacity with increasing slip of the shear crack.

Reinforcing mechanism of graphene at atomic level: Friction, crack surface adhesion and 2D geometry

Owing to its superior mechanical properties, graphene has been used to reinforce and substantially improve the strength of composite materials. Still lacking, however, is a clear understanding of graphene's reinforcing mechanism at the atomic level, especially in relation to its pull-out behavior. By molecular dynamics (MD), it is found that pull-out of graphene, different from that of micro fibers, is not governed by friction only. Rather, the pull-out force is revealed to be governed by a “crack surface adhesion” phenomenon due to unbalanced adhesion at the crack surface when graphene is not functionalized and the crack opening rate is small. Crack surface adhesion produces a constant pull-out force (about 0.2–1 N per meter width) regardless of the embedded length. There is a transition from crack surface adhesion governed pull-out to friction governed pull-out when the crack opening speed, graphene size and degree of functionalization increase. A new model is developed to integrate friction and crack surface adhesion with the 2D geometry of graphene. The new model can be used to predict the crack bridging stress for 2D graphene (or other 2D atomic thin reinforcements). The outcome of this study benefits the understanding and design of new graphene composites.

A Plasticity-Like Discontinuous FE Approach for Plain and Fiber-Reinforced Brittle Materials

Fiber-reinforced composites are attractive materials due to their good mechanical behavior under general stress states and to their fracture and fatigue resistance. The use of reinforcing fibers is a well-known mechanical-enhancing technique, especially in brittle or quasi brittle materials, and allows us to obtain a better performance with respect to traditional materials. In the present article, a continuum finite element (FE) formulation to analyse fracture mechanics problems in fiber-reinforced or in plain brittle or quasi-brittle materials involving a displacement field discontinuity—produced by crack formation and propagation—is discussed. By employing a cohesive crack approach, an appropriate stress field correction in the above FE formulation is used to simulate the displacement discontinuity (crack), whereas the effect of reinforcing fibers is considered through a micromechanical model, based on energy concepts, which is able to take into account the fiber debonding. The crack bridging stress enhanced due to the fibers is herein determined and considered in the model. Finally, some 2D examples involving plain, fiber and steel rebar reinforced brittle materials are presented in order to evaluate the capability of the proposed computational approach.

Theory of inverse problems for crack bridging stresses determination

A new mathematical procedure has been proposed for the determination of crack bridging stresses from perturbed crack opening displacements (COD) in fiber composites. The problem is an ill-posed inverse problem and the proposed procedure exploited concepts from functional analysis and the theory of inverse problems. The transformation from crack bridging stress into COD has been linearized, where the continuous crack bridging stresses functions of infinite dimensional vector spaces were approximated into finite dimensional subspaces. The coordinate representation of functions and the matrix of the transformation facilitated a numerical solution to the inverse problem. Self consistent direct and inverse problems were solved numerically in context to an example. Results establish that the proposed mathematical procedure produces fairly accurate results for engineering application.

Simulation of crack propagation of fiber reinforced cementitious composite under direct tension

Mode I crack propagation in fiber reinforced cementitious composite is simulated based on fracture mechanics criteria. To analyze crack propagation, a superposition method is employed to calculate the stress intensity factor at the crack tip resulted from both the applied load and the crack bridging stress. Using the model, the effects of various material parameters on the tensile performance are investigated. The requirements for tensile strain-hardening and multiple cracking are analyzed and possible methods for material performance optimization are discussed. Finally, predicted behavior is verified by tensile and bending tests performed on two fiber reinforced cementitious composite beams.

Bridged crack models for the toughness of composites reinforced with curved nanotubes

In this work, the effect of nanotube curvature on nanocomposite toughness is studied by considering a matrix crack bridged by curved nanotubes. The bridging nanotubes undergo a pull-out process as the crack opening displacement increases. An approximate analytical form for the pull-out force versus displacement relationship for a single curved fiber is derived here based on the numerical pull-out model of Chen et al. (2009b). This new analytical description accounts for the sequential elastic, debonding, and sliding response of the interface. When incorporated into a crack bridging model it becomes possible to predict the crack bridging stress and nanocomposite toughness as a function of nanotube curvature, nanotube strength, and interfacial friction resistance. Model predictions indicate that increases in nanotube curvature increase the peak bridging stress, but also decrease the average pull-out lengths. The overall effect can be a reduction in toughness as nanotube curvature increases depending on chosen parameters including interfacial friction properties, nanotube and matrix modulus, and even crack opening.

High resolution COD image analysis for health monitoring of reinforced concrete structures through inverse analysis

Direct and inverse problems of a fracture mechanics based RC beam model are solved. Solution of the direct problem that maps crack bridging stresses into crack opening displacements (COD) is straightforward, but the inverse problem is ill-posed, and better solved by the theory of inverse problems. This paper exploits the Tikhonov regularization method to solve the inverse problem, and estimates the force and location of rebar in buried concrete from CODs. Bending tests are carried out on model RC beams in the laboratory to demonstrate the applicability of the method. During the tests, a microscopic camera snaps high resolution digital pictures of cracked concrete surface. The images are analyzed by a software to measure surface CODs that are input into the inverse problem. The practical CODs inevitably include noise due to experimental error, which makes the inverse problem ill-posed, and necessitates regularization. In the current inverse analysis by the Tikhonov regularization method, bridging stress profiles, i.e. variation of the crack bridging stress along the crack length, has been figured out. Results are compared with those from other theoretical methods of analysis as well as with the readings from strain gauges. The method is a suitable non-destructive means for existing structures in cases where the section information is inadequate, or damages/repairs have altered the designed cross-section.

Measurement of crack bridging stresses in environment‐assisted cracking of duplex stainless by synchrotron diffraction

ABSTRACTCrack propagation studies have been conducted in age‐hardened Zeron 100 duplex stainless steel, which in the 475 °C embrittled condition exhibits environment‐assisted cracking under cathodic conditions in aqueous 3.5% NaCl solution. Values of the threshold stress intensity for environment‐assisted cracking, K1SCC, measured by crack arrest, show R‐curve behaviour. Diffraction experiments on the high‐energy beamline ID15A at the European Synchrotron Radiation Facility (ESRF) were performed to measure the crystal lattice strains in ferrite and austenite in wedge open loaded (WOL) stress corrosion specimens. The observations demonstrate that significant crack bridging stresses develop in the wake of the crack. This is due to branching of the environment‐assisted crack. Simple bridging models for the effect of the measured stresses are in agreement with the observed R‐curve behaviour.

Fatigue threshold R-curves for predicting reliability of ceramics under cyclic loading

For monolithic, grain-bridging ceramics, the crack-size dependence of the fatigue threshold during bridging zone development presents a difficulty in its application in design. This paper demonstrates how a fatigue threshold R-curve may express this crack-size dependence, analogous to the traditional fracture toughness R-curve, and may be used to predict the endurance limit and retained strength under cyclic loading conditions. Furthermore, the fatigue threshold R-curve may be deduced from the behavior of millimeter-scale, through-thickness, fatigue cracks via an accurately measured crack bridging stress profile. Both an alumina ceramic with large steady-state bridging zones (∼2 mm), where the predicted and experimentally measured fatigue threshold R-curves agree well over a range of crack sizes from 0.06 to 7 mm, and a (Y 2O 3-MgO)-doped Si 3N 4 ceramic, where bridging zones are much shorter (∼100 μm), are investigated. The approach provides a useful alternative to performing difficult short-crack fatigue experiments, particularly for materials with small bridging zones.

Dynamic visualization of crack propagation and bridging stress using the mechano-luminescence of SrAl 2O 4: (Eu,Dy,Nd)

The goal of the present investigation was to visualize the propagating crack in a mechano-luminescence (ML) material to enable the measurement of instantaneous R-curves and directly observe the bridging (shielding) stress in a fast-propagating crack system. The well-known ML compound, SrAl 2O 4: Eu 2+, was used as a model test material. Two additional trivalent rare earth elements, Dy and Nd, were introduced as co-dopants to improve the luminescent efficiency. The initiation and growth of a crack from the mechanically machined sharp notch tip in a disc shaped compact tension (CT) specimen at a relatively high loading rate were found to be associated with the extent of light emission around the crack. An in-situ measurement of crack length and applied load for 0.3 sec yielded an instantaneous R-curve at the conventional crack propagation speed.

R-curve evaluation and bridging stress determination in alumina by compliance analysis

A procedure is proposed which allows for bridging stress determination and R-curve evaluation from compliance data. R-curves were obtained on the single edge notched beam (SENB) and double torsion (DT) specimens by in situ and direct measurements of crack lengths. The compliance of DT specimens with different successive re-notching and without re-notching was compared. An approach for determining crack bridging stresses of the crack wake from the results of compliance measurements was extended for different grain sizes of alumina ceramics. By this compliance analysis, the KR- curve of alumina ceramics can be predicted from the compliance function, φ(Δa), versus the crack extension, Δa. The results show that compliance analysis can be a powerful tool for crack bridging stresses evaluation and even for R-curve prediction.

Weight Function Analysis on the R-Curve Behavior of Multilayered Alumina-Zirconia Composites

The single-edge V-notched-beam (SEVNB) testing geometry was used to measure the crack growth resistance (R-curve) behavior of multilayered alumina–zirconia composites. Fracture mechanics weight function analysis was applied to predict the R-curve behavior of multilayered composites having a stepwise change in composition. These results were then used to differentiate the influence of residual stresses from crack-bridging stresses on the measured R-curve behavior.

Microprobe fluorescence spectroscopy evaluation of stress fields developed along a propagating crack in an Al2O3/CaO 6Al2O3ceramic composite

The fracture behavior upon stable crack propagation in bending was investigated for a ceramic matrix composite comprising 15 vol% of calcium hexaluminate (CaAl12O19 or “CA6”) in an Al2.O3 matrix and compared to the crack bridging stresses as measured by microprobe fluorescence spectroscopy. In addition, piezospectroscopy coefficients of -4.57 and -3.79 cm-1 GPa-1 were determined for the peaks located at 14488 and 14528 cm-1, respectively, for monolithic CA6. It was concluded that the macroscopic R-curve behavior of the composite could be predicted from microscopic bridging stress data and indicated microprobe fluorescence spectroscopy to be a significant experimental tool for the investigation of fracture micromechanisms in ceramic materials.

Crack bridging stresses in alumina during crack extension

Crack bridging stresses in alumina during crack extension