Local Fracture Energy Research Articles

Experimental investigation and numerical modeling of effect of specimen size on microwave-induced fracturing of diorite

The effect of specimen size on microwave-induced fracturing of rocks has not been well understood. In this study, the experimental tests using open-ended microwave and numerical simulations coupling COMSOL Multiphysics and four-dimensional lattice spring model (4D-LSM) were carried out to investigate the evolution process of microwave-induced cracks, and to elucidate the mechanisms responsible for size-dependent microwave-induced fracturing. The experiments show that with the increase of the specimen dimension, the number of microwave-induced cracks is almost constant, and the total crack length first increases and then decreases, while the maximum crack width and maximum crack depth decrease gradually. A comparison of the experimental and numerical temperature characteristics as well as cracking characteristics indicates that the models established in this study are reasonable in the simulation of the rock fracturing behaviours. The numerical results show that the crack initiation time increases logarithmically with the increase of the specimen dimension. For the small-sized specimens, the microwave-induced cracks started from the outer boundary of the specimen and propagated toward to specimen center and into the depth. For the medium-sized and large-sized specimens, the microwave-induced cracks initiated near the outer boundary of the antenna aperture, and then propagated toward to the center of the specimen and the outer boundary of the specimen. The main reason for the size-dependent of fracturing behavior is that the local fracture energy will dramatically decrease when the crack is approaching the specimen boundary.

Energy Storage and Release of Class I and Class II Rocks

As underground excavations become deeper, violent rock failures associated with the sudden release of elastic energy become more prevalent, threatening the safety of workers and construction equipment. It is important to figure out the energy-related failure mechanisms of rocks. However, the energy evolution across the complete deformation of different types of rocks and the effect of high confinement on energy storage and release are not well understood in the literature. In this study, a series of cyclic triaxial compression tests were conducted for Class I and Class II rocks to investigate the confinement-dependent characteristics of energy evolution. The results showed that three types of energy evolution were identified as the rock behavior changed from brittle to ductile. The energy storage limit was linearly enhanced by confinement. The nonlinear increase in dissipated energy at peak stress with increasing confinement was suggested to indicate the start of the brittle–ductile transition. The post-peak fracturing process was characterized using the ratio of the local withdrawn elastic energy and fracture energy, and a novel energy-based index was proposed to quantify the failure intensity of the rock. This paper presents a complete investigation of the energy conversion characteristics of the rock, which may shed light on the failure mechanisms of violent rock failures in underground projects.

How regularization concepts interfere with (quasi-)brittle damage: a comparison based on a unified variational framework

Three regularization concepts are assessed regarding their variational structure and interference with the predicted physics of (quasi-)brittle damage: the fracture energy concept, viscous regularization and micromorphic regularization. They are first introduced in a unified variational framework, depicting how they distinctively evolve from incremental energy minimization. The analysis of a certain time interval of a one-dimensional example is used to show how viscous and micromorphic regularization retains well-posedness within the softening regime. By way of contrast, the fracture energy concept is characterized by ill-posedness—as known from previous non-variational analyses. Numerical examples finally demonstrate the limitations and capabilities of each concept. The ill-posed local fracture energy concept leads by its design to a spatially constant fracture energy—in line with Griffith’s theory. The viscous regularization, in turn, yields a well-posed problem but artificial viscosity can add a bias to unloading and fracture thickness. Furthermore, and even more important, a viscous regularization does not predict a spatially constant fracture energy due to locally heterogeneous loading rates. The well-posed micromorphic regularization is in line with the underlying physics and does not show this undesired dependency. However, it requires the largest numerical efforts, since it is based on a coupled two-field formulation.

A predictive model for determining shear strength and shear fracture energy of FRP bars in alkali-activated slag seawater coral aggregate concrete

Bond parameters between alkali-activated slag seawater coral aggregate concrete (ASSCAC) and fiber reinforced polymer (FRP) bars are necessary to be determined rationally for future service of the new concrete structures in marine environment. The intention of this paper is to develop a predictive model for determining the realistic local shear strength and shear fracture energy incorporating the heterogeneity and discontinuity in the interface region. First, central pull-out tests were performed to study the bond properties between FRP bars and ASSCAC. Ordinary Portland cement CAC (OPCAC) was prepared for comparison. It is found that the ribs on the bar surfaces were seriously abrased and the extent of damage was more serious in the ASSCAC. Subsequently, a microstructure characteristic parameter was introduced indicating the heterogeneity of the interface region and determined as the rib spacing on the bar surface according to the analysis of failure process. The shear crack propagation was discretized by a discrete number. The local shear strength and shear fracture energy were then linked to the maximum pull-out load via the microstructure characteristic parameter and discrete number. Once the maximum load was given from the test, the two bond parameters were conveniently predicted from each specimen. The results indicated that the predicted local shear strength was apparently higher than the maximum average bond stress which was usually used to represent the local shear strength in traditional methods. As the bond length-to-microstructure characteristic parameter ratio increased, the predicted local shear strength showed a certain reduction but the predicted local shear fracture energy was significantly enhanced because of the reduced boundary effect. Moreover, the predicted bond parameters of the FRP bars in the ASSCAC were generally larger than those in the OPCAC.

Combination of acoustic emission and digital image correlation monitoring for wedge splitting tests on large concrete specimens

Acoustic emission (AE) and digital image correlation (DIC) techniques are combined to monitor wedge splitting tests performed on very large concrete specimens made of mass concrete mixture with 100 mm maximum aggregate size. It is shown that cumulative acoustic energy recorded by AE is closely correlated to cumulative fracture energy when only the acoustic events related to microcracking in the local fracture process zone (FPZ) are considered. A new post-processing methodology is presented for DIC, and allows to assess the evolution of the local fracture energy and the length of FPZ during the wedge splitting test. Application of this methodology on WS test results allowed to visualize the boundary effects only on the length of FPZ. Contrary to what was expected, the local fracture energy evolution does not seem to be affected by boundary effect.

Local bond strength prediction of deformed reinforcing bars in concrete considering heterogeneity at interface regions

An analytical model is proposed to predict local bond strength (τf) by incorporating heterogeneity at interface regions for deformed reinforcing bars centrally anchored in concrete. The rib width on the bar surface is introduced as an interfacial characteristic parameter G in the proposed model; this accounts for the heterogeneity. Both τf and the local interfacial fracture energy (GIIf) of each specimen were found to be linked to G and can be determined analytically from the maximum pull-out loads (Fmax) from tests. It was found that the predicted τf was larger than the maximum average bond stress (τavg-max); the discrepancy between the two values reduced with an increase in L/G. Moreover, with an increase in L/G, the predicted τf showed a certain decrease, with the reduction decreasing with stronger interfacial homogeneity. The predicted GIIf was found to be significantly increased because of the weaker boundary effect. The validity of the proposed model was verified using comparisons of predicted Fmax (using the determined values of τf and GIIf) and the experimental Fmax, with the only failure mode being bar pull-out. Moreover, the model can be applied to steel or fibre-reinforced polymer bars and the concrete refers to all types of cementitious materials.

Local bond strength prediction of deformed reinforcing bars in concrete by considering heterogeneity at interface regions

An analytical model is proposed in this paper to predict the local bond strength τf by incorporating the heterogeneity at interface regions for deformed reinforcing bars centrally anchored in concrete. The rib width on bar surface is introduced as an interfacial characteristic parameter G in the proposed model accounting for the heterogeneity. Both the τf and local interfacial fracture energy GIIf from each specimen are linked to the G and determined analytically if the maximum pull-out loads Fmax are given from the test. It is found that the predicted τf is larger than the maximum average bond stress τavg-max. The discrepancy between the two values is reduced with the increasing of L/G. Moreover, as the L/G increases, the predicted τf shows a certain decrease and the reduction becomes smaller with stronger interfacial homogeneity. The predicted GIIf is significantly increased because of the weaker boundary effect. The validity of the proposed model is verified upon the comparisons between the predicted Fmax using the determined τf and GIIf and the experimental ones with the only failure mode of bar pull-out. Moreover, the bars here can be steel or FRP (fiber-reinforced polymer) bars, and the concrete refers to all types of cementitious materials.

Towards brittle materials with tailored fracture properties: the decisive influence of the material disorder and its microstructure

Considering a semi-infinite crack propagating within a plane where the local fracture energy fluctuates due to the presence of microstructural heterogeneities, we emphasize the decisive influence of the material disorder on the effective fracture energy of the composite at a macroscopic scale. Through the use of large-scale numerical simulations of a crack interacting with tough inclusions of varying shape, we show how the disorder intensity and the inclusion geometry modify both quantitatively and qualitatively the toughening behavior with respect to the periodic case, where the inclusions are arranged in an ordered manner. This disorder-induced toughening is then rationalized using a theoretical homogenization framework borrowed from statistical physics. It ultimately allows to propose strategies for the design of disordered composites with improved crack growth resistance and tailored asymmetric fracture properties.

Influences of Steel Fiber Content on Size Effect of the Fracture Energy of High-Strength Concrete

Quasi-brittleness is an important factor affecting the size effect of concrete, and the addition of steel fiber can effectively change this effect in concrete. The size effect on the fracture energy of steel fiber reinforced high-strength concrete was investigated in this paper. A total of 156 concrete single-edge notched beams (SENB) of various span-to-depth ratios, crack-to-depth ratios and steel fiber contents were tested to study the size effect of fracture energy of the high-strength concrete added steel fibers. The parameters of fracture in the boundary effect model (BEM) and size effect law (SEL) were deeply analyzed. The results show that the addition of steel fiber will generate significant influence on the parameter values obtained from both BEM and SEL. Based on the BEM, the relationship among Gf (experimental test fracture energy), gf (local fracture energy), and GF (fracture energy unaffected by specimen boundary) could be obtained. Thus, a method for analyzing the influence of steel fiber on GF was proposed using small-size SENB specimens at laboratory. In addition, based on the SEL, the impact of size effect on the fracture energy was effectively mitigated by the addition of steel fibers in high-strength concrete to a certain extent.

The disturbed fracture process zone theory for the assessment of the asymptotic fracture energy of concrete

The fracture energy constitutes an important input parameter for non-linear finite element analysis of concrete structures. Characterization of such parameter based on standard RILEM three-point bending test or wedge splitting test is known to depend on the size of the specimen. For the assessment example of large hydraulic structures using non-linear finite elements, it is important to develop an experimental protocol for characterizing a size-independent fracture energy, or asymptotic fracture energy representative of the size of these structures.Characterization of the asymptotic fracture energy requires specimens with very large sizes and thus represents an important experimental challenge. This work aims to develop a new experimental protocol based on wedge splitting test on specimen with moderate size and using digital image correlation technique.The new protocol is based on the disturbed fracture process zone (DFPZ) theory developed in this work, as an interpretation theory for the boundary effect theory of Duan et al. [8]. It uses the same hypothesis of bilinear distribution of the local fracture energy as in the simplified boundary effect method (SBEM) (Abdalla and Karihaloo [1], Karihaloo et al. [21]) but requires only one set of specimens with a specific notch over depth (a/D) ratio rather than two sets of specimens with two different a/D ratios.In order to validate the developed approach and theory, an experimental programme of 14 concrete specimens is conducted. Two concrete mixtures are considered with two maximum aggregate sizes: 38 mm and 76 mm, representative of hydraulic structures.Assessment of the fracture energy using the new protocol and the protocol based on SBEM resulted in similar values for both mixtures and thus validates the new developed theory.

Fracture energy and tensile strength depending on stress triaxiality along a running crack front in three-dimensional cohesive modeling

It is known that the critical fracture energy value decreases with specimen thickness, whereas the local tensile strength of the material increases with the stress triaxiality. In the present work, the critical fracture energy and the tensile strength depending on stress triaxiality are experimentally investigated and identified with the help of finite element computations. It is found that the fracture energy distributes in a running crack front very differently from that in a straight through-crack. The maximum crack driving force appears near the free surface in the plane stress state, whereas the maximum tensile stress is in the specimen middle. The local fracture energy is monotonically decreasing in the form of an exponential function, while the local tensile strength linearly increases with the stress triaxiality.

Fracture properties of jointed rock infilled with mortar under uniaxial compression

Grouting is commonly used to fill rock joints to provide reinforcement in geotechnical engineering. Understanding the fracture behavior of grouted rock joints depends on the characterization of infilled rock joints. In this work, mortar-filled rocks with grooved granite joints an inclination of 45° and infilling mortar layer between granite joints were simulated and a pre-existing cracks were assumed in mortar layers. Uniaxial compressive tests were performed on 20 specimens with different initial crack lengths a. Mix mode I-II fracture occurred in joints due to compression-shear condition. Peak load Pmax and fracture energy G0 were determined based on experimental load-deformation curves. The obtained results showed that both peak load Pmax and specific volume fracture energy Gf-V were observed to decrease with increasing initial crack length a. A simple bilinear distribution of local volume fracture energy gf-V was assumed to evaluate the effect of front boundary on specific volume fracture energy Gf-V to obtain the size-independent real fracture parameter of mortar-filled rock joints GF-V. Experimental results were also obtained by the established front boundary effect. It was observed that volume fracture energy and front boundary zone length were GF-V = 1.7 N/mm2a* = 17.5 mm, respectively, which were consistent with experimental observations.

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.

An analytical approach to predict fracture parameters of coral aggregate concrete immersed in seawater

An analytical approach is proposed to predict the fracture parameters of coral aggregate concrete (CAC). Both the size-independent tensile strength and fracture toughness are related to the maximum fracture load linearly based on the boundary effect model by incorporating the average aggregate size. Moreover, an explicit expression is derived to correlate the maximum fracture load with the local fracture energy at the crack-tip region. The local fracture energy distribution and size-independent fracture energy are then determined by virtue of the maximum fracture load. Four groups of three-point-bending notched CAC beams are tested by considering two ages and two environmental conditions (immersion in seawater or not) and the initial crack length-to-beam depth ratios are set from 0.1 to 0.7 in each group. Results show that the failure modes of all the specimens are coral coarse aggregate fracture without interfacial debonding between the aggregate and surrounding mortar. The average values of tensile strength, fracture toughness and fracture energy can be obtained in each group by using the experimentally measured maximum fracture loads and the experimental scatters were analyzed based on normal distribution analysis. All the fracture parameters increase with the age and become larger if the specimens were immersed in seawater.

Evaluation of fracture properties of cancellous bone tissues using digital image correlation/wedge splitting test method

The fracture mechanics (FM) parameters of cancellous bone tissues are very important from a clinical point of view especially for the bone cement augmentation. From the literature review, one can observe that the experimental determination of fracture mechanic parameters of cancellous bone are still lacking. This can be due to the conditions associated with the unstable crack propagation in the cancellous bone and lack of tools to extract and measure the parameters (like crack opening displacement (COD) and crack length) in the course of fracture tests, which are necessary to evaluate the fracture properties. To address above mentioned, a platform was developed integrating an optical measurement technique like digital image correlation (DIC) with classical wedge splitting test (WST) method to extract precise and real crack tip positions, crack opening displacement (COD) at each load step. These indeed used for the evaluation of the fracture mechanic properties (fracture toughness, specific fracture energy (Gf)) of the cancellous bone. Two approaches were used to evaluate the fracture mechanic properties of the bone. The first method is based on the global approach, which was widely used in the literature and the second method is based on the local approach. In this local approach, the local fracture energy (Gi) during the course of the test was evaluated, which give access to local fracture mechanics. The results evaluated by both the methods were in good accordance and compared with available literature. In addition, an attempt made to retrieve the real crack tip position at each load step during the test.

Effect of micro-macro crack interaction on softening behaviour of concrete fracture

During the fracture of concrete the formation of microcracks is a continuous process where new microcracks are formed in the vicinity of the macrocrack. As the fracture grows, these microcracks interact with the macrocrack and disrupt its smooth opening. In fracture mechanics based approaches; a smooth stress-crack opening softening behaviour is generally used to describe the local fracture process, where the effect of micro-macro crack interactions is lacking. This paper presents firstly an experimental study on the interaction between microcracking and the macrocrack opening (COD) in concrete using digital image correlation and acoustic emission techniques. The study reveals a transient behaviour of macrocrack opening as microcracks are formed in the surrounding. Based on the experimental results, the paper presents a new approach based on fracture mechanics to consider the effects of micro-macro crack interaction on the stress-crack opening softening behaviour. Local fracture energy is determined using the new softening model with micro-macro crack interaction for different geometrically similar sizes of the beams and at different locations on the crack profile.

Study on fracture properties of alkali-activated slag seawater coral aggregate concrete

Alkali-activated slag was first used as cementing material in seawater coral aggregate concrete (SCAC) production in this paper. It would contribute to both the environmental protection and raw materials obtained locally in island construction far away from the mainland. However, cracks would be harmful to structural durability of SCAC especially under ocean environment. Thus, the present study is mainly aimed at the fracture properties of alkali-activated slag SCAC (ASSCAC) by virtue of three-point-bending tests. Two types of slag (Types A and B) and two types of coral aggregates, namely columnar and crushed coral coarse aggregates (CCA), are considered. Besides, two beam depths of 100 mm and 150 mm are prepared and the initial notch-to-depth ratios are set from 0.1 to 0.7 for each depth. Results show that the failure modes of all the beams are fracturing of CCAs. Then an analytical approach was proposed to predict the fracture parameters of ASSCAC. The size-independent uniaxial tensile strength and fracture toughness are obtained by using the experimental maximum fracture loads and the former proves to be the maximum tensile stress at the fictitious crack-tip. Then the correlation between the maximum fracture load and the local fracture energy at crack-tip region is obtained. The size-independent fracture energy is derived based on the comparison between the analytical and experimental maximum fracture loads. The tensile strengths of ASSCAC mixed by Type A slag and crushed CCAs are larger. But the fracture toughness and fracture energy are slightly higher when the ASSCAC is made by Type B slag.

Fracture energy estimates from large-scale laboratory earthquakes

The dynamics of fault ruptures in natural and laboratory earthquakes is governed by a balance of released elastic energy and dissipated local fracture energy. The latter is the result of various friction weakening processes occurring at the fault and is thus often estimated indirectly and from small-scale friction experiments. We analyze high-frequency strain measurements from large-scale laboratory earthquakes with gages positioned slightly away from a granite fault. The strain measurements present rapid fluctuations during fault rupture propagation, as was also observed in other experiments. Characteristics of these strain fluctuations are compared with fracture mechanics theory to estimate local fault properties. We determine fracture energy for secondary rupture fronts, which appear behind the main front where local slip occurred already. Measured fracture energy is consistent with indirect estimates from rupture termination in independent experiments but is orders of magnitude lower than reported values from rotary shear friction experiments, which may be due to large differences in overall slip.

Fracture Energy Analysis of Concrete considering the Boundary Effect of Single-Edge Notched Beams

The method of determining concrete fracture energy recommended by RILEM has an obvious size effect, so determining fracture energy that is unaffected by size of the test specimen is difficult. In this study, 60 high-strength concrete single-edge notched beams (SENBs) of different sizes, crack length-to-depth ratios, and span-to-depth ratios were subjected to the three-point loading test as recommended by RILEM. Then, the influences of the boundary effect on the fracture energy were identified. Based on the SENB boundary effect model, a piecewise function of the interrelationships between the experimental test fracture energy Gf, the local fracture energy gf, and the fracture energy unaffected by specimen size GF was established. The applicability of the boundary effect model was verified using the test results from this study and from the previously published research. The results show that the local fracture energy distribution in the boundary influence region was nonuniform. The smaller the local fracture energy was, the closer it was to the rear boundary of the specimen. The influence length al∗ of the boundary increased with the increasing specimen size. Based on the bilinear distribution model of the local fracture energy gf, the fracture energy unaffected by beam size GF can be obtained according to the fracture energy Gf measured for laboratory-scale small-sized SENB specimens. Furthermore, the model predictions are in good agreement with experimental observations.

Determination of boundary effect on mode II fracture energy of FRP sheet-to-concrete bonded joints

Fracture energy is a crucial parameter in describing the interfacial debonding process in concrete structures externally bonded with FRP plates or sheets. This paper is mainly concerned with the boundary effect on the mode II (shear) fracture energy of FRP-to-concrete bonded joints. An analytical model was proposed to predict the maximum pull-out load of FRP sheet from concrete, which is then related to the local fracture energy at the shear crack-tip region. Based on the comparisons between the analytically predicted and experimentally determined load-carrying capacity, the crack-tip local fracture energy indeed varies with the initial shear crack length. A bi-linear model was presented to well describe the mode II local fracture energy distribution along the overlapping length indicating the boundary effect. The size-independent mode II fracture energy is 550N/m.