Crack Extension Resistance Research Articles

On fracture process zone and crack extension resistance of concrete based on initial fracture toughness

In this paper, a numerical approach is developed to investigate the evolution of fracture process zone (FPZ) during the complete fracture process in concrete structures by using stress intensity factor-superposition method. In this approach, the initial fracture toughness KICini, as an inherent material property, is introduced to form a crack propagation criterion for concrete. The developed numerical approach is then employed to analyze the complete fracture process of three series of notched concrete beams under three-point bending. It is found that the numerical results agree well with experimental ones published in literature through which the developed numerical approach, with an initial fracture toughness based crack propagation criterion, for fracture analysis of concrete is validated. The verified numerical approach is then utilized to simulate the complete fracture process of a series of concrete square plates with different sizes and/or initial crack length-to-depth ratio (a0/D). The effects of a0/D on evolution of FPZ length (aFPZ), especially after the FPZ is fully developed, are examined based on numerical analysis results. It is found that there are three different types of aFPZ variation with respect to a0/D, viz. (i) aFPZ keeps increasing after FPZ is fully developed. (ii) aFPZ turns to decrease from the peak value after FPZ is fully developed. (iii) FPZ is not fully developed. Finally, features of KR-curve for concrete are investigated based on the developed numerical method, and it is found that KR-curve of concrete is size-dependent when the effects of FPZ variation are taken into account.

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.

Closure to “Calculating crack extension resistance of concrete based on a new crack propagation criterion” by Wei Dong, Zhimin Wu, Xiangming Zhou

Closure to “Calculating crack extension resistance of concrete based on a new crack propagation criterion” by Wei Dong, Zhimin Wu, Xiangming Zhou

Discussion of “Calculating crack extension resistance of concrete based on a new crack propagation criterion” by Wei Dong, Zhimin Wu, Xiangming Zhou

Based on the original paper, a revised Young’s modulus E and a more accurate calculation of initial fracture toughness are proposed in present discussion.The main contribution of the discussed paper is to develop a numerical method to simulate the whole crack propagation in concrete by considering the variation of FPZ length. Notched concrete beams were tested under three-point bending with P-CMOD curves obtained which were then compared with the numerical ones to validate the proposed numerical method. After that, the proposed method was employed to obtain KR-curve for the complete fracture process, taking into consideration the cohesive stress acting on FPZ. Finally, the effect of variation of FPZ length and fracture energy on KR-curve, as well as size effect on KR-curve, was discussed. The discusser appreciates the authors’ meaningful work. However some findings are interesting to the discusser and are worthy of further discussion.

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.

Fracture toughness of the molten zone of resistance spot welds

A methodology for measuring the fracture toughness at crack initiation and the crack extension resistance of the molten zone of resistance spot welds under Mode I loading has been developed. The cross tensile test of U-shaped specimens was modified by crack growth monitoring and stress intensity factor determination. The resulting values of fracture toughness at crack initiation are independent of the nugget diameter and of the base material mechanical properties. The crack extension resistance seems to depend on base material mechanical properties and nugget diameter. Mixed cleavage + ductile mode associated to medium values of fracture toughness (54–90 $$\text{ MPa }\,\text{ m }^{0.5}$$ ) suggested a ductile to brittle transition behaviour. The relatively low fracture toughness (55–59 $$\text{ MPa } \,\text{ m }^{0.5}$$ ) associated to full interfacial ductile failure was quantitatively related to the high number density of small particles in the molten zone. This study opens the possibility to apply the local approach to fracture under monotonic loading to interfacial failure of resistance spot welds.

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.

OS1530 ISB法による部分安定化ジルコニアのR曲線挙動

R-curve and crack propagation behabior were studied for partially stabilized zirconia. R-curve obtained by the indentation strength in bending method, where beam strength measurements were made using the specimens with indented loads in the range of48-294 N, indicated that there was no increasing crack extension resistance, i.e. flat R-curve behavior. On the other hand, .KI-V curve obtained by constant stress rate tests using indented beam specimens indicated that there was a large effect on fatigue fracture of slow crack growth, i.e. the small crack propagation parameter of n=7.3. As a result, it is considered that the high fracture toughness value in partially stabilized zirconia is not caused by process zone wake, but is done by only frontal process zone produced in the crack tip.

Calculating crack extension resistance of concrete based on a new crack propagation criterion

A crack propagation criterion was proposed for model I crack in concrete by using the initial fracture toughness KICini as an inherent material property. Based on this criterion, crack begins to propagate when the difference, between the stress intensity factors caused by the applied load KIP and that by the cohesive stress KIσ, exceeds KICini. Finite element analyses was then carried out to calculate the complete load vs. crack mouth opening displacement (P-CMOD) curve, the critical crack propagation length ΔaC and the unstable fracture toughness KICun for notched beams under three-point bending. It was found that numerical results showed a good agreement with the experimental ones. Based on this crack propagation criterion, crack extension resistance, in terms of stress intensity factor, KR being able to consider the variation of fracture process zone (FPZ) was employed for describing crack propagation in concrete. KR is composed of KICini and KIσ, which is actually equal to the driving action of crack extension. It was concluded that given the elastic modulus E, the uniaxial tensile strength ft, the fracture energy GF and KICini, the complete fracture process in concrete and the KR-curve of concrete can be calculated based on the numerical method. Finally, discussion was made on the effects of fracture process zone, GF and specimens geometries on KR-curve.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

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.

Fiber Bridging Effect on In-Plane-Shear Mode Crack Extension Resistance of Unidirectional Fiber-Reinforced Composites

The fiber bridging effect, which affects the crack extension resistance in fibrous composites, is discussed in the case of in-plane-shear mode crack extension parallel to fibers in unidirectional fiber-reinforced composites. We first make a model of the bridging of a single fiber and estimate the force acting on the crack surface through a bridging fiber. Then, introducing the stochastic process of fiber breakage, we obtain the quantitative relationship between the relative crack surface displacement and the equivalent cohesive stress which is the probabilistic expectation of forces acting on the crack surface through a large number of bridging fibers. We numerically simulate the crack extension behavior with the equivalent cohesive stress acting on the crack surface. Then the simulated results are consistent with the experimental results. We finally conclude that the in-plane-shear mode crack extension is greatly affected by the stochastic process of fiber breakage.

Remaining life assessment and optimal design of statically indeterminate pipe system with circumferential crack

This paper examines the J–R curve theory in elastic-plastic fracture mechanics and crack extension resistance in order to analyze the large-scale yielding of statically indeterminate pipe structure with a circumferential crack. The dJ/da characteristic can be utilized to measure that the crack is stable ductile fracture or unstable ductile fracture and to analyze the crack growth rate. The total propagation time of the crack until collapse can be computationally estimated by numerical analysis that is presented in this paper. The further analysis of dJ/da and optimization is to maximize the crack propagation time during the crack growth before reaching plastic collapse. Both of the center-point crack and end-point crack are investigating cases for analyzing the mechanics and engineering design. These analysis and design strategies developed in this paper are useful for the safety performance of a structural pipe under crack deformation.

Fabrication of nature-inspired bulk laminar composites by a powder processing

Among many kinds of “nano-laminar” composites inspired by the brick and mortar structure of nacre in mollusk shells, a bulky, dense and ceramics–base composite has been a missing piece despite its importance. Here we report that such a composite with a submicron-order layered structure can be fabricated by a simple method, sintering aligned flake-like inorganic powder coated with ductile matrix material. The composites fabricated by this method had crack extension resistance by interface delamination, crack deflection, and ligament bridging by the ductile matrix. They showed non-brittle fracture behavior in a bending test despite a quite high flake volume fraction of over 80%, and had a work of fracture (WOF) of more than 300 J/m 2, several hundreds times as large as that of monolithic glass.

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.

Weight function approach for determining crack extension resistance based on the cohesive stress distribution in concrete

The use of universal form of weight functions for determining the K R -curves associated with the cohesive stress distribution for complete fracture process of three-point bending notched concrete beam is reported in the paper. Closed form expressions for the cohesion toughness with linear and bilinear distribution of cohesive stress in the fictitious fracture zone during monotonic loading of structures are obtained. Comparison with existing analytical method shows that the weight function method yields results without any appreciable error with improved computational efficiency. The stability analysis and the size-effect study using K R -curves of crack propagation are also described.

Fracture stability and residual strength assessment of reinforced concrete beams

In conventional analysis and design procedures of reinforced concrete structures, the ability of concrete to resist tension is neglected. Under cyclic loading, the tension-softening behavior of concrete influences its residual strength and subsequent crack propagation. The stability and the residual strength of a cracked reinforced concrete member under fatigue loading, depends on a number of factors such as, reinforcement ratio, specimen size, grade of concrete, fracture properties, and on the tension-softening behavior of concrete. In this work, a method is proposed to assess the residual strength of reinforced concrete beams subjected to cyclic loading. The crack extension resistance based approach is used for determining the condition for unstable crack propagation. The effect of reinforcement is modeled as a closing force counteracting the effect of crack opening produced by the external moment. The effect of percentage reinforcement and specimen size on the failure of reinforced beams is studied. Finally, the residual strength of the beams are computed by including the softening behavior of concrete.

Study of the resistance to crack propagation in alumina by acoustic emission

The resistance to crack propagation or R-curve effect is still extensively studied in polycrystalline ceramic materials. This effect is shown in the literature by the increase of the stress intensity factor K I versus crack extension, or by the decrease of crack velocity versus K I under flexure tests. We have studied this fracture resistance by using the acoustic emission and the Hertzian indentation technique. It was found that the acoustic emission count rate decreases, like crack velocity in conditions of sub-critical crack growth before the failure is reached. Two specimen of alumina, respectively with small and coarse grains, were tested. A high crack extension resistance is obtained for coarse-grained alumina. Mechanisms of crack bridging and crack shielding are responsible for the R-curve effect. These mechanisms are also operating during cyclic loading. The resistance to crack propagation increases more and more after each cycle. Also we obtain R-curve effect during static loading. On the other hand, toluene or silicone oil corrosive environment delays the crack propagation. But water medium has a reverse effect and the apparent toughness is reduced in this case.

Experimental Study on the Material Response of Laser Weldment under Dynamic Loading

The materials response of a laser beam welded joint from hot rolled DP600 steel plate to the dynamic loading has been experimentally studied by instrumented Charpy impact testing. Based on the impact force-displacement curve, Critical Crack Length, i.e. CCL and dynamic crack extension resistance curve, i.e. J-a were determined, describing the welding joint’s crack formation toughness and the dynamic crack behavior. It is shown that the difference of crack initiation and propagation between the HAZ and BM is not significant. In addition, the CCL of Welding Area, i.e. WA is multiple higher than that of HAZ and BM, which is also less dependent of low temperature. Moreover, the J-a curve of WA consists of two segments, the initial sudden ascending with linear feature and the subsequent slow rising. Furthermore, tearing module derived from the slope of J-a curve was discussed, indicating the material microstructure mechanism affected by the thermodynamic process of laser beam welding.