Effect of the Cyclic Crack Opening-Closure during Epoxy-Curing Period of a CFRP Strengthening System Bonded on Concrete Substrate

This article investigates the potential detrimental effects of cyclic load during the installation of externally bonded (EB) carbon fiber-reinforced polymer (CFRP) on a damaged reinforced concrete (RC) structure. Four RC specimens were tested in three point bending to study the consequences of crack cyclic opening-closure during epoxy-curing period. A first RC specimen (without bonded CFRP) was loaded monotonically up to failure to serve as undamaged control sample. The three other specimens were pre-cracked before being subjected to a fatigue loading procedure to simulate service condition of a damaged RC structure. Two of the three pre-cracked specimens were strengthened by EB CFRP. One specimen was repaired before the fatigue test while the other one was repaired during the fatigue test. Finally, remaining capacities of all three pre-cracked specimens were measured through monotonic bending tests until failure. It was found that, although bonding of CFRP reinforcement during cyclic load can induce some interesting features with regard to serviceability, cyclic crack opening and closing alters the cure process of epoxy located below the initial crack and decreases the effectiveness of the strengthening at ultimate state. Extended experimental studies are then needed to assess reliable safety factor for the design of repairing operations in which the bridge has to be maintained in service during CFRP installation.

A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics

Introducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on crack near-tip fields and crack opening displacements is nonetheless available, while intuitive adaption is required to obtain the full-field solutions. Investigating the cause of prevailing deficiencies inevitably leads to a critical review of classical works by Muskhelishvili or Westergaard. Complex potentials of the mixed-mode loaded Griffith crack, sparing restrictive assumptions or limitations of validity, are finally provided, allowing for rigorous mathematical treatment. The entity of stresses and displacements in the whole plate is finally illustrated and the distributions in the crack plane are given explicitly.

Simplified equations for determining double-k fracture parameters of concrete for compact tension test

Polynomial equations in non-dimensional form for various fracture parameters of double-K fracture model for compact tension specimen have been derived and presented in this paper. These equations can be used for computing different double-K fracture parameters of concrete for known material properties and specimen size having relative size of initial crack length of 0.3 without involving much complexity in numerical computations. Values of peak load and corresponding crack opening displacement as necessary to compute the double-K fracture parameters of concrete have been derived from the established fictitious crack model in the present study. A simplified equation in non-dimensional form between peak load and critical crack opening displacement as obtained from a fictitious crack model has also been presented.

EXPERIMENTAL STUDIES OF DEFORMABILITY AND FRACTURE RESISTANCE OF AIRFIELD SLABS ON MODELS

The results of experimental studies of deformability and crack resistance of models of aerodrome slabs made of reinforced concrete and steel-fiber concrete, made on the basis of serial slab PAG-18 taking into account the scale factor, are presented. Two series of slabs were tested - two models of reinforced concrete and two models with one-percent dispersed reinforcement. The load was applied in steps, the instrument readings were recorded twice at each step and the crack opening width was measured starting from the moment of the first crack formation. Dial gauges, deflectometer and microscope MPB-3 were used as measuring instruments. In accordance with the normative documents acting in Ukraine, one of two possible loading schemes was considered - with the loading by the concentrated force applied in the span part of a plate which had a hinged support along its short sides. Plate models were tested on a specially made stand. Each load step ended with a five-minute dwell time, at the beginning and the end of which readings were taken on the measuring instruments. The deformations at the same levels were measured with dial gauges. The process of crack formation was observed with a Brinell tube in the places of the greatest crack opening. Breaking load for fiber concrete slab was 1.52 times higher than for reinforced concrete slab, and the moment of cracking initiation was 1.22 times higher. The process of cracking in the fiber concrete slab begins at higher loads than in the reinforced concrete slab. The initial crack opening width of the slabs is almost the same, and the final crack opening width of all the cracks in the fiber concrete slab is significantly lower than in the reinforced concrete slab. The deformations in steel-fiber concrete slabs when the load is applied in the span, both for compressed and stretched fibers, are higher than in reinforced concrete slabs. The experimental studies indicate that dispersed reinforcement of airfield slabs with steel fiber leads to their higher crack resistance.

DEFORMABILITY AND CRACK RESISTANCE OF AIRFIELD SLABS

The results of experimental studies of deformability and crack resistance of models of airfield slabs made of reinforced concrete and steel fiber concrete are presented. Two series of plates were tested ‒ three models of reinforced concrete and three models with steel fiber added to the concrete mixture in amount of 1% of the total volume of the product. The load was applied in small steps, the instrument readings were recorded twice at each step, and the crack opening width was measured starting from the moment of the first crack formation. Dial gauges and deflectometers were used as measuring instruments. According to the normative documents acting in Ukraine, one of two possible loading schemes was considered ‒ with the loading by the concentrated force applied on the cantilever part of a plate. The plate models were tested on a specially made stand which consisted of four supporting struts connected in pairs by beams. The airfield slab was supported by the beams. The load was applied along the width of the plate in steps ‒ 0.05 of the destructive load, along two concentrated vertical strips. Each degree of load ended with a five-minute dwell time, at the beginning and end of which readings were taken on the measuring instruments. The deformations at the same levels were measured with dial gauges. The process of crack formation was observed with a Brinell tube in the places of the greatest crack opening. It follows from the obtained results that the process of cracking in the fiber concrete slab begins at higher loads than in the reinforced concrete slab. The final and initial crack opening widths of all cracks in the fiber concrete slab are significantly lower than in the reinforced concrete slab. The deformations in steel-fiber concrete slabs during the application of load in the cantilever part, both for compressed and stretched fibers are higher than in reinforced concrete slabs. At the initial stages of load application in the cantilevered part of the slabs, the deflections increase in a linear relationship. The curves get non-linear character for airfield slabs made of reinforced concrete when the load reaches the level of 10÷25 kN, for steel-fiber-concrete slabs ‒ 15÷30 kN. In reinforced concrete slabs, the non-linearity starts a little earlier and is expressed more clearly. Experimental studies show that dispersed reinforcement of airfield slabs with steel fiber leads to their higher crack resistance.

Model of normal cracks level formation and opening in stretched reinforced concrete elements

The article highlights the most important studies results of the mechanism of normalcracks formation and opening in stretched reinforced concrete elements during their deformation. Acritical analysis of the existing methods and ways for calculating normal cracks level formation andopening, in which the reinforcement to concrete adhesion is taken into account directly or indirectly,is carried out. The main advantages and disadvantages of each of these methods are indicated. It hasbeen experimentally confirmed that the crack formation process is generally leveled. The mainfeatures and patterns of cracking in stretched reinforced concrete elements and structures arerevealed. The main characteristics of the prototypes are given, according to the test results of whichit was established that in practical calculations of the reinforced concrete elements crack resistance,it is usually possible to restrict oneself to two levels of normal cracking. For the indicated crackinglevels, the corresponding load level, step and crack opening width are established. The expediencyof using in practical calculations the nonlinear function of the reinforcement with concrete averageadhesion stresses is also substantiated. Based on the studies results carried out, the existing methodsfor calculating the normal cracks formation and opening in reinforced concrete elements andstructures were evaluated from the standpoint of local disadvantage of the reinforcement to concreteadhesion.General and simplified methods for calculating normal cracks level formation and opening inreinforced concrete elements have been developed. In them, the direct integration of the expressionfor the concrete and reinforcement mutual displacements is proposed to be replaced not by thenumerical integration of the indicated expression, but by the successive accumulation of the indicateddisplacements. Corresponding statistical comparisons of the calculations results by these methodswith experimental data are carried out. The effectiveness of the developed methods for calculatingnormal cracks level formation and opening by comparing them with existing methods is estimated.

Evaluation of the threshold for the development of fatigue cracks in a railway steel under harmonic and operational loading

The results of experimental studies of the fatigue crack development in 20GFL steel specimens cut from a cast bolster of a freight car are presented. The ratio of the threshold stress intensity coefficient Kth determined from the kinetic diagram of fatigue fracture and from the average parameters of the operational loading process is considered using the experimental results with a simulation of operational loading. Tests were carried out upon the development of permanent blocks of crack opening in the specimen (in a rigid loading mode). The operational process is presented in the form of a block of consecutive loading cycles recorded during the test of the car frame in conditions typical for a straight section of the railway track. The threshold operational level is determined by the algorithm of gradual reduction of the loading similar to the original process. The regularities in a decrease of the rate of crack development and corresponding decrease in the load were determined. Subsequent extrapolation of the obtained experimental regularities to zero value of the crack propagation rate provided estimation of the threshold loading level, similar to the initially specified value. It is shown that the value of the threshold level of the fatigue crack development in low-alloy steel 20GFL obtained from the fatigue fracture diagram (i.e., under harmonic loading) is significantly higher than that obtained from the estimate based on the average values of the operational loading process. The considered model of operational loading gives greater damage compared to harmonic loading, on the basis of which the survivability of structural elements is usually assessed.

Experimental and Numerical Investigations on High Performance SFRC: Cyclic Tensile Loading and Fatigue

In the present study, the capability of high-strength short steel fibers to control the degradation in high-performance concrete was experimentally examined and numerically simulated. To this end, notched prismatic high-performance concrete specimens with (HPSFRC) and without (HPC) short steel fibers were subjected to static and cyclic tensile tests up to 100,000 cycles. The cyclic tests showed that the rate of strain increase was lower for HPSFRC specimens and that the strain stagnated after around 10,000 cycles, which was not the case with HPC specimens. The microscopic examinations showed that in HPSFRC, a larger number of microcracks developed, but they had a smaller total surface area than the microcracks in the HPC. To further investigate the influence of fibers on the behavior of HPSFRC in the cracked state, displacement-controlled crack opening tests, as well as numerical simulations thereof, were carried out. Experiments have shown, and the numerical simulations have confirmed, that the inclusion of short steel fibers did not significantly affect the ultimate strength; however, it notably increased the post-cracking ductility of the material. Finally, the unloading/reloading behavior was examined, and it was observed that the unloading stiffness was stable even for significant crack openings; however, the hysteresis loops due to unloading/reloading were very small.

Numerical analysis of fatigue crack growth using a plastically dissipated energy factor based model

The investigation of fatigue crack growth (FCG) behavior may contribute to the assessment of damage tolerance of components. To study the FCG behavior considering the elastic–plastic behavior at the crack tip, a numerical simulation scheme based on compact tension (CT) specimen is developed. Also, an effective plastically dissipated energy (PDE) factor composed of maximum PDE ([Formula: see text]) and PDE range ([Formula: see text]) is proposed to establish the expression for evaluating the FCG rate. The simulation results show good agreement with the results of test under same load conditions. Also, the mesh sensitivity analysis and the comparison with test results confirm the validation of proposed model. Based on the proposed numerical simulation scheme, the FCG behavior is studied by analyzing the influence of plastic wake, mean load, load range, overload, underload, load sequence, and cyclic compression load on FCG from the perspective of crack driving force, FCG rate, and crack opening displacement (COD). It is found from the analysis results that the developed numerical simulation scheme can consider the load history effect and crack closure effect. The mechanisms of these factors on the influence of FCG rate are analyzed in detail.

A Novel Methodology for Calculating Crack Opening Stress under Tension-Compression Cyclic Load

Crack closure model has been used in several applications on the prediction of fatigue crack growth life, with expression of crack opening stress often serving as milestones. A typical difficulty in calculating the crack opening stress is the phenomenon of crack closure caused by the compressive load effect. Compressive load effect, resulting in the change of residual stress status at the unloading stage and the decrease of crack opening stress, is a long-term challenge for predicting fatigue crack growth life. We propose the expression of crack opening stress to predict fatigue crack growth life based on the analysis of compact tensile specimen with elastoplastic element method. It combines the characteristics of material and load to deal with the phenomenon of crack closure and uses stress ratio and normalized maximum applied load variable to construct the expression of crack opening stress. In the study of tensile-compression fatigue crack growth experiments, the proposed expression is proved to improve, by comparative analysis, the predictive ability on the whole range of experiment data. The novel expression is accurate and simple. Consequently, it is conducive to calculate the crack opening stress under tension-compression load.