Fracture Energy Distribution Research Articles

CFD‐Discrete Element Method Simulations Combined with Compression Experiments to Characterize Stirred‐Media Mills

AbstractMicromechanical aggregate properties are correlated with stress conditions during the dispersion process in a stirred‐media mill. The fracture energy distribution of the aggregates measured via micro‐compression tests is compared with the stress energy distribution in a stirred‐media mill determined by CFD‐discrete element method simulations and by an analytical model. The simulations are likened with a previously conducted one‐way coupling. Furthermore, the rotor speed is varied to identify its influence on stress energy and number of contacts. Using the stress energy distribution and the measured fracture distribution, an effective dispersion fraction can be calculated and correlated with the dispersion progress.

THE EFFECT OF FRACTURE AND CRACK GROWTH OF STEEL AND POLYPROPYLENE FIBERS IN THE ORDINARY AND HIGH STRENGTH CONCRETE

Today, high performance concrete can be produced as easily as normal strength concrete. Concretes are expected to have ductile behavior and have compressive strength, as well. In the recent years, in order to have ductile behavior, researchers have started to strengthen concrete using fibers and have done lots of researches. In this study, normal and high strength concrete with steel and polypropylene fiber are produced, the compressive strength and the tensile strength in split of these concrete is investigated and the fracture energy and crack distribution of notching samples are examined.

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.

THE EFFECT OF FRACTURE AND CRACK GROWTH OF STEEL AND POLYPROPYLENE FIBERS IN THE ORDINARY AND HIGH STRENGTH CONCRETE

Gunumuzde geleneksel betonlar kadar yuksek performansli betonlar da kolaylikla uretilebilmektedir. Betonlarin basinc dayaniminin yuksek olmasi kadar, belli oranda sunek davranis gostermesi de istenmektedir. Bu amacla, son yillarda, sunekligi saglayabilmek icin uretimlerinde betonu liflerle takviye etmeye baslamislar ve bu konuda da bir cok arastirma yapmislardir. Bu liflerin basinda celik lifler gelmektedir. Bu calismada celik ve polipropilen lif katkili geleneksel ve yuksek dayanimli betonlar uretilerek, bu betonlarin merkezi basinc, yarmada cekme dayanimlari arastirilarak, centikli numunelerde betonlarin kirilma ve catlak gelisimleri incelenmistir.

Re-examination of possible great interplate earthquake scenarios in the Nankai Trough, southwest Japan, based on recent findings and numerical simulations

Abstract Great earthquakes have occurred repeatedly along the Nankai Trough in southwestern Japan with recurrence intervals of 100–200 years. The magnitudes of Nankai earthquakes have historically varied, with many studies to date asserting that an event's magnitude is controlled only by the number of broken segments arranged along the trough. Recent evidence suggests that large tsunami with recurrence intervals of several hundred years have occurred along the Nankai Trough. Therefore, it is now essential to reconsider the scenario of the Nankai earthquakes, including the possibility of seismic slip on the shallow subduction interface. Recently, model calculations of interplate seismic cycles have been conducted using rate- and state-dependent friction. In these calculations, assuming heterogeneous distribution of fracture energy in the seismogenic zone and its shallower extension, both massive earthquakes with slips up to the trough and ordinary earthquakes in the seismogenic zone can occur. Here, we apply a heterogeneous distribution of fracture energy in the shallow plate interface of the Nankai Trough. In the model, we represent the difference in fracture energy by the difference in the characteristic slip distance L . To model the conventional seismogenic zone as a zone of low fracture energy, we set L to be 5 cm at depths of 10–20 km. Conversely, the shallow plate boundary near the trough is modeled as a zone of high fracture energy by setting L to 5 m. As a result, two types of earthquake with different moment magnitude occur alternately. The recurrence interval of the larger type is about 370 years, which is comparable to the recurrence of larger tsunami deduced from geological findings. Large coseismic slip extends to the trough during the larger types. In contrast, the smaller one, whose seismic slip is distributed along the seismogenic zone, occurs after ~ 200 years of the larger one.

Compression and breakage behavior of γ-Al2O3 granules

Abstract The material behavior of dominant elastic–plastic, spherical γ-Al2O3-granules at compression until primary breakage has been experimentally studied. For this, the mechanical properties of the granules were determined using recorded force–displacement-curves. The influence of particle size and moisture content on the compression behavior has also been investigated. Additionally, the specific fracture energy distribution and the distribution of the equivalent impact velocity at fracture were derived from the force–displacement-curves. The work provides a basis for understanding the influence on the material behavior at wetting of hygroscopic and highly porous granules.

Compression Behavior of Moist Spherical Zeolite 4A Granules

AbstractThe material behavior of elastic‐plastic zeolite 4A granules has been experimentally studied using compression tests. The influence of particle size and moisture content has been investigated. Furthermore, the specific fracture energy distribution and the distribution of the equivalent breakage velocity at impact on a rigid target have been determined.

Modeling ore degradation during handling using continuum damage mechanics

Degradation of steelmaking materials during handling causes a significant economic impact, given the higher prices achieved by lump ore in comparison to finer products. It is relevant to model the amenability of ores to degradation, since it may be used to simulate the response of ores to different sequences of handling and transportation events from mine to port. The paper presents a mechanistic model to describe degradation caused by transfers and drops of particulate materials. The model is based on damage mechanics and the distribution of fracture energies of the original particles, using data collected in impact load cell and tumbling tests. This model, which is capable of predicting the proportion of particles broken and the entire size distribution resulting from any sequence of drops, has been validated at a preliminary level using data from drop tests of a Brazilian iron ore.

Coarse particle fracture with the ultrafast load cell

Microscale information about single particle fracture can be incorporated into the macroscale model of the whole size reduction process in the mill. The ultrafast load cell (UFLC) device provides a substantial amount of information about fracture characteristics of a particle under impact loading. UFLC captures high-resolution compressive force signals during particle breakage. The measurement of the compressive force at the instant of fracture of the particle allows computation of a number of comminution-related particle properties, as well as the energy absorbed during fracture. In the current study, limestone particles 50 mm in size were fractured to obtain specific fracture energies. Then, based on the experimental data, two models were proposed to quantify the fracture process. The specific fracture energy distribution of the particles in the range of 6 to 50 mm was defined by the well-known Weibull distribution. The other model is a probabilistic fracture model. This model is a link between energy events occurring in a grinding mill and the breakage rates of particles. The impact energy spectra or energy events occurring in a grinding mill can be obtained with a discrete element method (DEM) simulation. One can model the breakage rates of the mill material by combining the energy spectra with the probabilistic fracture model. This novel approach for the modeling of breakage rates via DEM and UFLC is shown here.

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.

Numerical modelling of intergranular fracture in polycrystalline materials and grain size effects

In this paper, the phenomenon of intergranular fracture in polycrystalline materials is investigated using a nonlinear fracture mechanics approach. The nonlocal cohesive zone model (CZM) for finite thickness interfaces recently proposed by the present authors is used to describe the phenomenon of grain boundary separation. From the modelling point of view, considering the dependency of the grain boundary thickness on the grain size observed in polycrystals, a distribution of interface thicknesses is obtained. Since the shape and the parameters of the nonlocal CZM depend on the interface thickness, a distribution of interface fracture energies is obtained as a consequence of the randomness of the material microstructure. Using these data, fracture mechanics simulations are performed and the homogenized stress-strain curves of 2D representative volume elements (RVEs) are computed. Failure is the result of a diffuse microcrack pattern leading to a main macroscopic crack after coalescence, in good agreement with the experimental observation. Finally, testing microstructures characterized by different average grain sizes, the computed peak stresses are found to be dependent on the grain size, in agreement with the trend expected according to the Hall-Petch law.

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.

G030074 き裂を有する異種材料の破壊靭性評価([G03007]材料力学部門一般セッション(7):はく離と異材 )

A method of strength evaluation based on fracture mechanics is important to analyze the fracture strength of material with crack. The heterogeneity of mechanical property in dissimilar materials causes change of fracture behavior. Analysis of mechanical property and fracture strength in dissimilar materials is important to evaluate fracture toughness with accuracy. The purpose of this paper is experimentally to analyze correlation between Young's modulus ratio and fracture toughness in dissimilar materials with a single edge crack. 4 kinds of specimen were used in this experiment. One was homogeneous material, the others were 3 kinds of dissimilar materials. The fracture behavior of dissimilar materials was analyzed by high-speed video camera and digital image correlation method. Then, specimens were bended and displacement near the crack was measured. Fracture toughness was experimentally calculated based on fracture mechanics. The experimental results showed that fracture energy and strain distribution around a crack tip were same values at all specimens. We conclude that relationship between Young's modulus ratio and fracture toughness in dissimilar materials is uncorrelated. Then, the heterogeneity of Young's modulus causes the change of crack opening displacement.

Modeling ore degradation during handling using continuum damage mechanics

Degradation of steelmaking materials during handling causes a significant economic impact, given the higher prices achieved by lump ore in comparison to finer products. It is relevant to model the amenability of ores to degradation, since it may be used to simulate the response of ores to different sequences of handling and transportation events from mine to port. The paper presents a mechanistic model to describe degradation caused by transfers and drops of particulate materials. The model is based on damage mechanics and the distribution of fracture energies of the original particles, using data collected in impact load cell and tumbling tests. This model, which is capable of predicting the proportion of particles broken and the entire size distribution resulting from any sequence of drops, has been validated at a preliminary level using data from drop tests of a Brazilian iron ore.

Modeling breakage rates of coarse particles in ball mills

Breakage rates of coarse particles in ball mills generally follow non-first-order kinetics and the distribution products from batch milling are often characterized by significant contributions of abrasion besides breakage by impact, which are not well described using traditional size–mass balance formulations. Under such conditions, particles are often subject to impacts of insufficient magnitude to produce breakage in each stressing event, so that they are broken by a combination of abrasion and impact and also particles undergo weakening due to unsuccessful stressing events. The paper presents a mathematical model of batch grinding which takes into account the distribution of stressing energies in the mill, the distribution of fracture energies of particles contained in the charge, describing breakage by impacts from grinding media producing catastrophic breakage, abrasion and weakening from repeated impacts. The model has been applied to describe the rate of disappearance of two materials in batch grinding with good results.

Complexity in earthquake sequences controlled by multiscale heterogeneity in fault fracture energy

A series of dynamic rupture events under constant tectonic loading is simulated on a fault with multiscale heterogeneity and a stochastic rupture initiation process. The fracture energy of the fault plane is assumed to have multiscale heterogeneous distribution using fractal circular patches. The stochastic rupture initiation process as a function of the accumulated stress is introduced in order to take account of unknown smaller‐scale heterogeneity and variability. Five realizations of a statistical spatial distribution of fracture energy (fault heterogeneity maps) are tested for the simulations of earthquake sequences during a few seismic cycles. The diversity of earthquake sequences is principally controlled by the spatial distribution of the patches. The effect of dynamic rupture appears in the residual stress after the characteristic events because of their directivity and this localizes the subsequent sequences. Although the characteristic earthquakes occur rather regularly in time and similarly in different seismic cycles, some irregular behavior is found based on the heterogeneity maps and the randomness of the preceding earthquake sequence, leading to a visible anomaly in the seismicity. Such anomalies are not predicable but understandable through the analysis of the considered earthquakes during the cycle. The similarity and the diversity simulated in this study, governed by the structure of an inherent distribution of multiscale heterogeneity, suggest the importance of the pre‐existing heterogeneity field along the fault for the appearance of earthquake sequences, including those that are characteristic.

Statistical evaluation of anisotropic fracture behavior of ODS ferritic steels by using small punch tests

Small punch (SP) tests were performed to evaluate the anisotropy in the ductile–brittle transition behavior for the oxide dispersion strengthened (ODS) ferritic steel for the advanced nuclear systems. The upper-shelf energy and scattering of SP fracture energy for the specimens where the surfaces are perpendicular to the extruded direction was larger and smaller than that for the other direction, respectively. The anisotropic fracture behavior appears to be mainly caused by the favorable cracking path along the elongated grain. Data scattering of SP fracture energy could be explained by combination of microstructural observations and the statistical evaluation method based on the Weibull distribution of SP fracture energy, indicating that brittle inclusions along elongated grain was responsible to the unexpected initial failure type fracture mode.

Size effect on specific fracture energy of concrete

Size effect on the specific fracture energy G F of concrete can be adequately modelled by an uneven fracture energy distribution along the crack path induced by the specimen boundary influence. The boundary influence on G F can be neglected only if a specimen is very large so that the boundary region is a very small portion of the total fracture area. The underlying principle on the specimen boundary induced size effect provides a simple and logical explanation for the commonly observed size effect on G F. The boundary effect model recently proposed by the authors is used in this paper to quantitatively evaluate the specimen boundary influence so that the size-independent fracture energy is derived, which otherwise can only be measured with very large concrete specimens. New experimental results from a very different material system, polymer, are analysed together with concrete results by the simple boundary effect model.

Distribution of stress drop, stiffness, and fracture energy over earthquake rupture zones

Using information provided by slip models and the methodology of McGarr and Fletcher (2002), we map static stress drop, stiffness (k = Δσ/u, where Δσ is static stress drop and u is slip), and fracture energy over the slip surface to investigate the earthquake rupture process and energy budget. For the 1994 M6.7 Northridge, 1992 M7.3 Landers, and 1995 M6.9 Kobe earthquakes, the distributions of static stress drop show strong heterogeneity, emphasizing the importance of asperities in the rupture process. Average values of static stress drop are 17, 11, and 4 MPa for Northridge, Landers, and Kobe, respectively. These values are substantially higher than estimates based on simple crack models, suggesting that the failure process involves the rupture of asperities within the larger fault zone. Stress drop as a function of depth for the Northridge and Landers earthquakes suggests that stress drops are limited by crustal strength. For these two earthquakes, regions of high slip are surrounded by high values of stiffness. Particularly for the Northridge earthquake, the prominent patch of high slip in the central part of the fault is bordered by a ring of high stiffness and is consistent with expectations based on the failure of an asperity loaded at its edge due to exterior slip. Stiffness within an asperity is inversely related to its dimensions. Estimates of fracture energy, based on static stress drop, slip, and rupture speed, were used to investigate the nature of slip weakening at four locations near the hypocenter of the Kobe earthquake for comparison with independent results based on a dynamic model of this earthquake. One subfault updip and to the NE of the hypocenter has a fracture energy of 1.1 MJ/m2 and a slip‐weakening distance, Dc, of 0.66 m. Right triangles, whose base and height are Dc and the dynamic stress drop, respectively, approximately overlie the slip‐dependent stress given by Ide and Takeo (1997) for the same locations near the hypocenter. The total fracture energy for the Kobe earthquake, 3.7 × 1014 J, is about the same as the seismic energy (Ea = 3.2 × 1014 J).