Local Fracture Energy Distribution Research Articles

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.

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.

Correlation between Cohesive Crack-Tip Local Fracture Energy and Peak Load in Mortar Beams

Mortar, as concrete-like coarse-structured materials, has a fracture process zone ahead of crack tip after the crack initiation. The maximum fracture load must be related to the cohesive crack-tip local fracture energy due to the relatively limited crack growth in the critical state. The intention of this paper is to correlate the local fracture energy with the maximum loads in mortar specimens. An analytical approach is proposed on the correlation between the two parameters. Then a fracture test has been performed on three-point-bending notched mortar beams with a wide range of notch depths. Upon comparison of the predicted and experimentally measured peak loads, it is found that the crack-tip local fracture energy indeed varies with notch depth and beam height. Thus, the trilinear model for the local fracture energy distribution is confirmed in mortar specimens, indicating both the front and back free boundary effects. Based on the trilinear model, the size-independent fracture energy can be obtained if the notch depth and the ligament length are long enough. The proposed approach is analytical and convenient without the load-displacement curves in tests.

Influence of local fracture energy distribution on maximum fracture load of three-point-bending notched concrete beams

The maximum fracture load of a notched concrete beam has been related to the local fracture energy at the cohesive crack tip region analytically in this paper, and then the correlation between the size effects on the maximum fracture loads and the RILEM specific fracture energy is established. Two extreme conditions have been established, namely zero crack-tip bridging with zero local fracture energy and maximum crack-tip bridging with the maximum size-independent fracture energy. It is concluded that the local fracture energy at the crack tip region indeed varies with the initial crack length and the size of specimen. The tri-linear model for the local fracture energy distribution is confirmed by using the proposed simple analytical solution.

Downscaling of fracture energy during brittle creep experiments

We present mode 1 brittle creep fracture experiments along fracture surfaces that contain strength heterogeneities. Our observations provide a link between smooth macroscopic time-dependent failure and intermittent microscopic stress-dependent processes. We find the large-scale response of slow-propagating subcritical cracks to be well described by an Arrhenius law that relates the fracture speed to the energy release rate. At the microscopic scale, high-resolution optical imaging of the transparent material used (PMMA) allows detailed description of the fracture front. This reveals a local competition between subcritical and critical propagation (pseudo stick-slip front advances) independently of loading rates. Moreover, we show that the local geometry of the crack front is self-affine and the local crack front velocity is power law distributed. We estimate the local fracture energy distribution by combining high-resolution measurements of the crack front geometry and an elastic line fracture model. We show that the average local fracture energy is significantly larger than the value derived from a macroscopic energy balance. This suggests that homogenization of the fracture energy is not straightforward and should be taken cautiously. Finally, we discuss the implications of our results in the context of fault mechanics.

Size-independent fracture energy in plain concrete beams using tri-linear model

The boundary effect or the size effect on the fracture properties of concrete has been studied assuming a bi-linear model for the distribution of local fracture energy concept. Boundary effect is observed not only near the back boundary but also near the notch tip, where a fictitious boundary seems to exist, separating the linear and non-linear fracture zones. In this paper a tri-linear function is assumed for the local fracture energy distribution along the ligament and expressions relating RILEM fracture energy and the size-independent fracture energy are developed. Transition ligament length measurements based on the acoustic emission (AE) histogram of events are used to obtain size-independent fracture energy. Length of the fracture process zone is identified in the AE histogram and compared with the value obtained from softening beam model. There seems to be a good agreement between the results.

Boundary effect on concrete fracture and non-constant fracture energy distribution

This paper extends the local fracture energy concept of Hu and Wittmann [29,30], and proposes a bilinear model for boundary or size effect on the fracture properties of cementitious materials. The bilinear function used to approximate the non-constant local fracture energy distribution along a ligament is based on the assumption of the proportionality of the local fracture energy to the fracture process zone (FPZ) height and characterises the FPZ height reduction when approaching a specimen back boundary. The bilinear function consists of a horizontal straight line of the intrinsic fracture energy G F and a declining straight line that reduces to zero at the back boundary. It is demonstrated that using the bilinear model, the size-independent fracture energy G F can be estimated from the fracture energy data measured on laboratory-size specimens, and the intersection of these two linear functions, defined as the transition ligament, represents the influence of the back boundary on the fracture properties. It is also demonstrated that the specimen size alone is not sufficient to characterise the size effect in the fracture properties observed on laboratory-size specimens.

Explanation of size effect in concrete fracture using non-uniform energy distribution

A local fracture energy model originally proposed to explain the influence of fracture process zone (FPZ) on fracture energy of cementitious materials is further developed in this study. By assuming a bilinear distribution for the fracture energy distribution, the ligament-dependent fracture energyGf is obtained. The analytical expression ofGf contains two important prameters: the intrinsic size-independent fracture energyGF and a reference ligament sizeal* which determines the intersection of the two linear fracture energy functions. It is shown that the ligament-dependentGf approaches the size-independentGF asymptotically. As a result,GF can be determined from the ligament-dependentGf results. It is also found that while the reference ligament sizeal* is influenced by the specimen geometry, size and loading conditions, the derived fracture energyGF is virtually constant. The present local fracture energy distribution model is also discussed and compared with the original local fracture energy model.

An asymptotic approach to size effect on fracture toughness and fracture energy of composites

Size effect on fracture toughness and fracture energy of composites is investigated by a simple asymptotic approach. This asymptotic analysis based on the elastic/plastic fracture transition of a large plate with a small edge crack is extended to study fracture of composite. A reference crack length, a *, is used in the model, which indicates an ideal elastic/plastic fracture transition defined by the yield strength and plane strain fracture toughness criteria. Experimental results of cementitious materials available in literature are analyzed and compared. It is shown that the common K R-curves can also be obtained by the current asymptotic model. Furthermore, a local fracture energy distribution concept is also discussed and compared with the present asymptotic approach.