Crack Extension Resistance Curve Research Articles

Investigation on crack extension resistance curve of aligned steel fiber‐reinforced cement‐based composites

AbstractIn this study, an analytical method was proposed to predict the crack extension resistance curve (KR curve) of aligned steel fiber‐reinforced cement‐based composites (ASFRC). The three‐point bending tests were carried out on notched ASFRC specimens. Based on the predicted results, the influence of size effect and fiber dosage on KR curves of ASFRC specimens was discussed. Finally, the relationship between KR curves of ASFRC and steel fiber‐reinforced cement‐based composite (SFRC) specimens was investigated. The results show that the analytical results agree well with the experimental ones. The KR curve of ASFRC specimen has size effect and increases with fiber dosage. The ASFRC specimen shows a 30% improvement in the crack extension resistance at peak load over the SFRC specimen when the fiber volume dosage is 0.8%, and the improvement becomes more pronounced with increasing fiber dosage. When the KR curves of ASFRC and SFRC specimens are the same, the fiber consumption can be reduced by at least 40%.

Crack extension resistance for a general three-point bending concrete beam

Expressions of the crack extension resistance for a general three-point bending (TPB) concrete specimen were developed. Based on the proposed general expressions, the effects of span/height ratios on the fracture processes of TPB concrete beams were studied using two types of specimens, i.e. the beams with the same section but different spans and the beams with the same span but various heights. Results indicate that (1) the crack extension resistance curves (KR-curves) increased with the crack propagation. (2) The KR-curves and fracture process zone curves were not affected by the span/height ratios, i.e. the KR-curve can be considered as a criterion to describe the crack propagation in a structure. (3) The calculated crack tip opening displacement was not affected by the specimen span but increased with increasing the specimen height. (4) The stability analysis of crack propagation was also described based on the KR-curve.

Crack extension resistance of steam-cured concrete under different curing temperature conditions

The influences of curing temperatures on the fracture characteristics for steam-cured concrete were investigated by using three-point bending (TPB) method. The measured load-crack mouth opening displacement (P-CMOD) curves were used to determine the crack extension resistance curves (KR curves) and fracture toughness. The results showed at each curing temperature, the KR curves first increased with crack growth and then approximately remained constant after the fracture process zone (FPZ) was completely developed. The KR curves for the specimens cured at 45 °C were slightly higher than those at 20 °C. However, the KR curves became lower and flatter significantly as increasing the curing temperature ranged from 45 to 95 °C. The fracture toughness also demonstrated an increase–decrease tendency with the increase of curing temperature, which was consistent to the variation of KR curves. The optimum curing temperature was found to be about 45 °C in terms of the fracture properties for steam-cured concrete. In addition, the KR curves based on different FPZ models and the stability during crack growth were also analyzed.

Study of fracture parameters and complete fracture process of concrete at low temperatures using an energy approach

The fracture parameters and complete fracture process of concrete under low-temperature environment were studied by using an energy approach. The fracture parameters including the initial fracture energy release rate GIcini, unstable fracture energy release rate GIcun and critical cohesive energy release rate GIcc were determined, and the accuracy of the double-G fracture model was verified by the unstable fracture energy release rate GIcun∗. Furthermore, the equivalence of the double-G fracture model and double-K fracture model was verified by the effective double-K fracture toughness (KIcini¯ and KIcun¯). Finally, the complete fracture process of concrete was simulated by taking GIcini as the condition of each crack propagation. The availability of the numerical method was proved, and the effect of temperature on the crack extension resistance curve was investigated.

Crack extension resistance of concrete at low temperatures

The process of determining crack extension resistance curves (KR curves) associated with the cohesive stress distribution for the complete fracture process of a three-point bending concrete beam at low temperatures from 20°C to −40°C is presented in this paper. A total of 32 concrete beams were divided into two groups, based on different ages, 28 d and 120 d. The KR curves were calculated from curves of load against crack mouth opening displacement obtained from test results of the concrete beams at low temperatures by considering the variation of the fracture process zone length. The weight function approach was used to replace numerical integration techniques to improve the computational efficiency. The calculation results show that the KR curves became higher with decreasing temperature and that the fracture process zone length had a significant influence on the KR curves. The stability of the KR curve and the influence of temperature on the fracture process zone length were also analysed.

Fracture toughness behavior of low-C medium-Mn high-strength steel with submicron-scale laminated microstructure of tempered martensite and reversed austenite

Fracture toughness was studied in terms of crack-tip opening displacement (CTOD) in low-C medium-Mn high-strength steel at both room temperature and − 40 °C, and excellent fracture toughness was obtained. The critical CTOD values (δ) and crack extension (∆a) followed the relationship: δ = 0.01343 + 0.62315∆a0.47531 and δ = 0.07391 + 0.48466∆a0.60103 at room temperature and − 40 °C, respectively. With the decrease in test temperature from room temperature to − 40 °C, the corresponding δ when ∆a = 0.2 mm (δ0.2) was reduced from 0.30341 to 0.25813 mm, and intersecting point in the crack extension resistance curve with a 0.2-mm passivation line (δQ0.2BL) was reduced from 0.42132 to 0.33941 mm. The large fraction of high misorientation boundaries between tempered martensite effectively hindered the crack propagation and increased the fracture toughness. Furthermore, the submicron-scale complex laminated microstructure of tempered martensite and reversed austenite refined the effective fracture grain size, which inhibited crack propagation and led to high fracture toughness. Also, the excellent fracture toughness is attributed to strain-induced martensite transformation of reversed austenite in the small plastic deformation zone ahead of the crack tip, which absorbed the strain energy, relaxed the local stress concentration, suppressed the crack propagation, and enhanced the fracture toughness.

A semi-empirical model for structural integrity assessment of defected high density polyethylene pipes

The main objective of this study was to propose semi-empirical models to facilitate the integrity analyze of a defective high density polyethylene (HDPE) pipe. To this end, an experimental compact tension test(CT) was performed to establish the HDPE's crack extension resistance (J-R) curve. This curve was used to determine the fracture toughness JIC-CT. different existing approaches in the literature were considered showing how the gap between JIC values is considerable. In order to designate the adequate value of toughness, a numerical analysis is performed and validated with the experimental test. The developed FE model gives the evolution of the J-integral as well as the distribution of the opening stress in the vicinity of the defect. By analyzing these two results we were able to define the fracture toughness JIC-CT and the ultimate pressure of pipe leading to the crack initiation.In the second part, basing on the J-integral concept, the harmfulness of surface semi-elliptical crack located at PE100 pipe wall under internal pressure has been studied using Abaqus software. The crack and pipe size effect on the fracture toughness has been discussed. Results of the finite element analysis has been used to adjust a semi-empirical model which was developed to determine J-integral variation with pipe internal pressure. In like manner, an approximate formula of PE100 pipe fracture toughness as function of pipe size and JIC-CT has been proposed. This allowed us to define the ultimate pressure of pipe leading to the crack initiation.

An analytical method for predicting mode-I crack propagation process and resistance curve of rock and concrete materials

In this paper, taking into account the fictitious crack model and the closure effect of the crack opening displacement (COD) induced by the cohesive force, an analytical method with the crack mouth opening displacement (CMOD) as the control parameter is proposed to predict the mode-I crack propagation process of rock and concrete materials by using stress intensity factor (SIF)-based criteria. With this method, the load-crack mouth opening displacement (P-CMOD) curve, crack extension resistance curve (KR-curve), and fracture process zone (FPZ) length during crack propagation are analytically obtained. The validity of the proposed analytical method is then verified with the experimental results of three-point bending tests on rock and concrete beams. Therefore, given the tensile strength ft, Young’s modulus E, initial fracture toughness KICini, and fracture energy GF, the complete mode-I crack propagation process of rock and concrete beams under three-point bending can be predicted accurately using the proposed analytical method without iteration in calculating the cohesive stress. Finally, the influence of the closure effect of the COD induced by the cohesive force on the P-CMOD curve, KR-curve, and FPZ length is discussed. The results show that although ignoring the closure effect of the COD induced by the cohesive force has little effect on the shape of the P-CMOD curve, the value of crack extension resistance and the maximum FPZ length are significantly underestimated, and the calculation error increases with the crack propagation and then decreases gradually when the FPZ length reaches the maximum.

Effect of acid corrosion on crack propagation of concrete beams

The effect of acid corrosion on crack propagation of concrete beams was theoretically studied by the method of crack extension resistance curve. Based on this method, a calculation approach was proposed to determine fracture stress intensity factors in crack propagation of concrete beams. Loop iteration analysis was carried out to calculate maximum bearing capacity load, unstable crack toughness, resistance toughness curve, cohesive toughness curve and load–crack mouth opening displacement. Both bilinear and nonlinear softening traction–separation curves were adopted for each of these calculation parameters. The analysis results of each showed the effect of acid corrosion degrees. The influence of acid corrosion on fracture properties was discussed through the calculated results of cohesive toughness curves. These five kinds of simulated results were basically consistent, before the load attained the maximum value. However, with further crack propagation, cohesive toughness of nonlinear softening model was significantly larger than that of bilinear softening model, and the descending branch of P–CMOD curve by nonlinear law is higher than that by bilinear law. To validate the approach, tests of specimens under six different corrosion periods were experimentally studied, using three-point bending notched concrete beams soaked in sulphuric acid solution. The Double-K fracture parameters were investigated based on the test results, and load–crack mouth opening displacement curves for different acid conditions were obtained using synchronous sampling of a load sensor and clip-gauge. Numerical results by bilinear softening model showed a good correlation with the experimental ones.

Study of mechanical properties and cracking extension resistance behavior of C/SiC composites by single edge notched beam and digital image correlation techniques

The carbon fiber reinforced silicon carbide matrix (C/SiC) composites were prepared by using precursor infiltration and pyrolysis method. Fracture characteristics of C/SiC materials were studied by single edge notched beam with the aid of digital image correlation (DIC) technique. It was found that DIC played an important role in in-situ monitoring full/local strain evolution and cracking growth during bending tests, which was useful for revealing potential failure micro-mechanisms of C/SiC composites. The results showed that the average fracture toughness KIC and fracture strength of C/SiC were estimated as 7.81±0.12MPam1/2 and 223.23±3.5MPa, respectively. Moreover, the crack extension resistance curves (R-curve) in terms of stress intensity (KR-curves) were determined on the basis of the crack initiation toughness KIC. The values varied from 4.68MPam1/2 to 16.83MPam1/2 during the R-curve tests.

An analytical method for determining the crack extension resistance curve of concrete

Owing to its importance in evaluating the fracture behaviour of concrete, crack extension resistance has been studied based mainly on experimental results. In this paper, an analytical method is developed for determining the crack extension resistance curve of concrete. It is assumed that, when the difference in stress intensity factor caused by external forces and by the cohesive stress within the fracture process zone is equal to the initial cracking toughness, crack propagation is initiated. According to this assumption, the crack extension resistance curve of concrete is expressed analytically as either the stress intensity factor caused by external forces, or the sum of the initial cracking toughness and the stress intensity factor by the cohesive stress within the fracture process zone. One advantage of this method is that, unlike other methods, the experimentally measured load–crack mouth opening displacement curve is not required in calculating the crack extension resistance curve. Based on numerical results, it is found that the crack extension resistance curve is independent of initial crack length. Also, for a given fracture energy, the shape of the cohesive stress–crack opening displacement curve exhibits no significant effect on the crack extension resistance curve. It is concluded that the proposed method can predict the crack extension resistance curve of concrete with reasonable accuracy.

Anchorage of naturally corroded bars in reinforced concrete structures

The bond properties of naturally corroded reinforced concrete members were experimentally investigated. Thirteen specimens were taken from the northern edge beam of Stallbacka Bridge, a girder bridge in Sweden. The specimens exhibited different levels of corrosion-induced damage, including concrete cracking and cover spalling. The damage was carefully documented and the specimens were tested in suspended four-point bending tests. Their general behaviour was monitored through measurements of applied loads and vertical deflections. At the same time, the local anchorage behaviour was recorded at the end regions. The test results showed around 5% lower anchorage capacity for damaged specimens compared with the reference ones. The residual bond strength was studied with respect to the observed damage. These tests, and artificial corrosion results from the literature, indicate that the bond strength decreased with increasing maximum splitting crack widths. However, the bond capacity was higher for the naturally corroded specimens. The results thus show an obvious difference between artificial and natural corrosion, and furthermore indicate that the provisions given in fib Model Code 2010 are on the safe side. These test results contribute to further knowledge regarding the structural behaviour of corroded reinforced concrete structures. predict the crack extension resistance curve of concrete with reasonable accuracy.

Residual crack extension resistance of post-fire wedge-splitting normal strength concrete specimen based on the cohesive force function

A comparative study on determining the crack extension resistance curves (KR-curves) for the complete fracture process associated with two functions of the cohesive stress distribution, i.e. Peterson’s softening curve and CEB-FIP Model, 1990 softening curve using an analytical method and the weight function approach is presented in this paper. Fifty wedge-splitting normal strength concrete specimens were prepared to sustain ten different elevated temperatures up to 600°C. The stress intensity factor curves (K-curves) were calculated from the load–displacement curves obtained on these post-fire specimens. At each temperature, the residual fracture toughness KR(Δa) increased with the crack extension length Δa, whereas the KR-curves became lower and flatter with the increasing heating temperatures Tm. It was found that the KR-curve calculated from the weight function method coincided well with the one from the analytical method, whereas different softening curves had observable effects on the KR-curves. The stability of the KR-curve and the influence of temperatures on the crack tip opening displacement–crack extension curves (CTOD–Δa curves) were also analyzed.

Crack Extension Resistance of Normal-Strength Concrete Subjected to Elevated Temperatures

Determination of the residual crack extension resistance curves (KR-curves) associated with cohesive force distribution on fictitious crack zone of complete fracture process is implemented in present research. The cohesive force distributes according to bilinear softening traction-separation law proposed by Petersson. Totally ten temperatures varying from 20°C to 600°C and the specimen size of230×200×200 mm with initial-notch depth ratios 0.4 are considered. The load-crack mouth opening displacement curves (P-CMOD) of postfire specimens are obtained by wedge-splitting method from which the stress intensity factor curves (K-curves) are calculated. In each temperature, with the distribution of cohesive force along the fracture process zone, the residual fracture toughnessKR(Δa) increases with increasing crack lengthΔa, whereas theKR-curves decrease with increasing temperaturesTmfor the thermal damage induced. The stability analysis on crack propagation demonstrates that when the residualKR-curve is higher thanK-curve, the crack propagates steadily; otherwise, the crack propagates unsteadily.

Crack Extension Resistance of Post-Fire Concrete

Wedge-splitting test is carried out in present research.Determination of the residual crack extension resistance curves (KR-curves) associated with cohesive force distribution on fictitious crack zone of complete fracture process is implemented. In each temperature, with the distribution of cohesive force along the fracture process zone, the residual fracture toughness KR (Δ̱) increases with increasing crack length Δ̱. Whereas the KR-curves decrease with increasing temperatures Tm for the thermal damage induced.

NUMERICAL SIMULATION ON COMPLETE PROCESS OF MODEL I CRACK PROPAGATION OF FULLY-GRADED CONCRETE

The initial fracture toughness was taken as a crack propagation criterion.The Mode Ⅰ crack propagation of fully-graded concrete was simulated by using ANSYS software.Complete P-CMOD curves,critical crack lengths and double-K fracture parameters of the wedge-splitting specimens were calculated respectively.The simulated results show a good agreement with the fracture test data of the Xiluodu dam.Meanwhile,based on the experimental data,the fracture parameters of standard specimens were calculated,using the formulae specified by the Norm for fracture test of hydraulic concrete,and compared to the simulated results.It is concluded that the method proposed by the norm can also be applied to the calculation of non-standard large-size specimens,the error rate of which is within 5%.Besides,if the elastic modulus,the uniaxial tensile strength,the uniaxial compressive strength,and the initial fracture toughness of the fully-graded concrete are measured,the double-K fracture parameters,the complete process of crack propagation and the KR crack extension resistance curves can be obtained by the proposed numerical method.

A Novel Videography Method for Generating Crack-Extension Resistance Curves in Small Bone Samples

Assessment of bone quality is an emerging solution for quantifying the effects of bone pathology or treatment. Perhaps one of the most important parameters characterising bone quality is the toughness behaviour of bone. Particularly, fracture toughness, is becoming a popular means for evaluating bone quality. The method is moving from a single value approach that models bone as a linear-elastic material (using the stress intensity factor, K) towards full crack extension resistance curves (R-curves) using a non-linear model (the strain energy release rate in J-R curves). However, for explanted human bone or small animal bones, there are difficulties in measuring crack-extension resistance curves due to size constraints at the millimetre and sub-millimetre scale. This research proposes a novel “whitening front tracking” method that uses videography to generate full fracture resistance curves in small bone samples where crack propagation cannot typically be observed. Here we present this method on sharp edge notched samples (<1 mm×1 mm×Length) prepared from four human femora tested in three-point bending. Each sample was loaded in a mechanical tester with the crack propagation recorded using videography and analysed using an algorithm to track the whitening (damage) zone. Using the “whitening front tracking” method, full R-curves and J-R curves could be generated for these samples. The curves for this antiplane longitudinal orientation were similar to those found in the literature, being between the published longitudinal and transverse orientations. The proposed technique shows the ability to generate full “crack” extension resistance curves by tracking the whitening front propagation to overcome the small size limitations and the single value approach.

Optimal Design for the Maximum Load of Three-Point Bending Concrete Beam Based on the Analyzing of Critical Crack-Mouth Opening Displacement

An optimal design method for the maximum load of three-point bending concrete beam is proposed in this study. The statistics model is built according to the theory of GR resistance curve. With the help of least square method and Matlab® computing platform, the optimal design results are very similar of the experimental results, and thus a new criterion for unstable fracture in crack extension resistance curve theories is constructed. It can able to monitor safety and stability of specimens in engineering practice at any time.

Crack Extension Resistance Curve of Concrete Considering Variation of FPZ Length

Owing to its importance in evaluating the fracture behavior of concrete, the crack extension resistance curve of concrete has been widely studied, both experimentally and theoretically. In this paper, a numerical approach is developed for the crack extension resistance curve of concrete by considering the variation of the fracture process zone (FPZ) length during the whole fracture process. In this approach, the FPZ length is determined by using the linear asymptotic superposition assumption. Dividing the whole fracture process into three different stages of the cohesive stress distribution within the FPZ, the crack extension resistance curve is formulated by superposition of the intrinsic fracture toughness of concrete and the fracture toughness caused by the cohesive stress within the FPZ. The developed numerical approach is applied to the tested and simulated standard three-point bending notched concrete beams. The effect of the variation of the FPZ length on the crack extension resistance curve is evaluated on the basis of the numerical results. The crack extension resistance first increases with an increase in ratio of the effective crack length to the beam depth and then reaches a plateau value when the FPZ is fully developed. When the effective crack length is normalized to the beam depth, the crack extension resistance is basically independent of the beam depth within the beam size range studied.

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.