Stable Crack Research Articles

Method for Determining the Fracture Parameters of Fully Graded Dam Concrete

This paper describes a method for determining the initiation and unstable toughness of fully graded concrete of arbitrary specimen size. The method first predicts the initiation and peak loads of concrete specimens of any size, as well as crack length-to-height ratios based on the fracture test results of concrete specimens with limited sizes or crack length-to-height ratios. Then, combined with the fracture extreme theory, the fracture toughness of concrete with varying size or crack length-to-height ratios is determined. Finally, in order to verify the applicability of the method, it is used to calculate the fracture toughness of small aggregate concrete and fully graded concrete with different sizes or crack length-to-height ratios, and its prediction accuracy is evaluated through indices such as mean absolute percentage error, root mean square error and reliability index a15. The results show that the proposed method can meet the needs of practical engineering applications and can provide theoretical basis for the optimization of the fracture test method of fully graded concrete and the determination of fracture parameters in crack stability or propagation analysis.

Crack propagation velocity and fracture toughness of hydroxyl-terminated polybutadiene propellants with consideration of a thermo-viscoelastic constitutive model: Experimental and numerical study

Solid rocket motors are subject to numerous temperature loads during their service life, so it is essential to investigate the sensitivity of propellant mechanical properties to temperature, particularly fracture properties. This paper presents fracture characteristics of hydroxyl-terminated polybutadiene (HTPB) propellant with mechanical-thermal coupled responses. This work investigated the fracture morphology of the HTPB propellant at different temperatures (233.15 K–333.15 K) using a self-developed thermostatic in-situ video imaging. The crack propagation velocity and J-integral were measured using single-edge notched tension (SENT) specimens. In the numerical study, a thermo-viscoelastic constitutive model combined with 1/r singular elements was used to perform calculations on J-integral. The thermo-viscoelastic constitutive model combined with a cohesive zone model was used to simulate crack propagation; meanwhile, load–displacement curves and crack propagation velocity were obtained. All simulation results were analyzed in comparison to the experimental results. The results revealed that temperature could significantly affect the fracture properties of the HTPB propellant. The fracture morphology of the HTPB propellant changed significantly at different temperatures. As the temperature decreases, the strength of the material gradually increases, with a consequent increase in the critical J-integral and a decrease in the average crack propagation velocity. The time ratio governed the regularity of average instantaneous crack propagation velocity with temperature. Furthermore, three simulation methods for calculating the J-integral were analyzed and discussed.

Mechanical Characteristics of Pre-Peak Unloading Damage and Mechanisms of Reloading Failure in Red Sandstone

The mining of deep coal resources occurs in a high-stress geological environment as well as an engineering environment of rock excavation and unloading. Research on the re-bearing capacity characteristics and damage mechanism of rock masses damaged by peak front unloading is critical in revealing the destabilization and rupture law of deep rock bodies. The triaxial pre-peak unloading point was controlled to prepare damaged sandstone specimens, and the RMT-150C rock mechanics test loading system and the AEwin USB-type acoustic emission monitor were used to perform uniaxial reloading tests on the pre-peak unloading-damaged sandstone and to monitor the acoustic emission signals during the rupture process. Among them, the peak front unloading point was set to 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, and 90% of the peak strength at 10 MPa of the surrounding pressure for a total of 11 working conditions. The test results show that: (1) The degree of unloading before the peak controls the uniaxial reload deformation characteristics of sandstone. The higher the unloading point, the faster the deformation of the rock sample, even directly into the crack instability extension stage, and the sandstone deformation characteristics transform from plastic—elastic to elastic—viscous. (2) The cumulative energy characteristics of the 40% to 60% sandstone at the unloading point are comparable to those of the complete sandstone and are separated into smooth, steady growth, and secondary smooth phases. The acoustic emission energy characteristics of the 65% and 70% sandstone at the unloading point are mostly focused on during the crack expansion stage. The sandstone’s acoustic emission energy characteristics exhibit a “double peak” occurrence at 75% of the unloading point. The cumulative energy characteristics of the 80% to 90% sandstone at the unloading point reveal a “stepped” rise. (3) Sandstone’s pre-peak unloading rupture morphology influences the reload damage characteristics: 40% to 70% of the specimens at the unloading point exhibit “Y”-type double-slope shear damage features. The predominant cause of specimen damage in 75% of the specimens at the unloading point is secondary primary cracks based on the pre-peak tensile rupture pattern. The damage path of 80% to 90% of the specimens at the point of unloading occurs in shear damage along the pre-peak unloading rupture pattern. (4) A closed crack mechanics analysis model under uniaxial reload was established, and the basic solution of pseudo-force for fine microcracks subjected to far-field stress, the stress intensity factor at the crack tip, and the crack fracture angle were theoretically derived. Furthermore, the relationship between the fracture angle θ of rock compression-shear cracks, the crack angle β, and the friction coefficient f at the crack surface was clarified.

Fracture characteristics analysis of FRP-reinforced concrete based on acoustic emission

To study the acoustic emission (AE) characteristics of fibre-reinforced polymer (FRP)-reinforced concrete during the fracture process, three-point bending tests of FRP-reinforced concrete beams with cracks were carried out. The AE characteristics of FRP-reinforced concrete beams with different bonding lengths and different bonding layers were analysed based on the AE parameters, and the effect of the fracture parameters was studied. The test results reveal that the crack initiation load and peak load of single-layer FRP-reinforced concrete beams first increase and then decrease with the increase of bonding length. The failure mode of multi-layer FRP-reinforced concrete beams is a kind of dangerous brittle failure, which easily forms the ‘super-reinforcement failure’ mode. The ductility of single-layer FRP-reinforced concrete beams with a bonding length of 25 cm is optimal, which can effectively delay crack propagation. By combining the load–time curves, AE ringing count–time curves and AE energy–time curves, the time points of crack initiation load and instability load can be accurately determined. The analysis of RA–AF (ratio of ringing count to duration–ratio of rise time to maximum amplitude) and clearance factor index can be used to evaluate the damage state of FRP-reinforced concrete beams.

Numerical studies on rebar-concrete interactions of RC members under impact and explosion

In order to reproduce the dynamic behaviors of RC structures under intensive loadings, e.g., impact and blast, more realistically and accurately, the dynamic interactions between the embedded rebar and concrete matrix are studied numerically. Firstly, the validations of the concrete model and corresponding parameters are verified by comparing with the available empirical formulae, related specification and tests results. Secondly, based on the calibrated concrete model, the applicability of seven interaction methods in program LS-DYNA and relevant parameters are verified and determined by simulating the pull-out and three-point flexural tests. Finally, concerning four typical intensive loading scenarios, i.e., low- and high-velocity impacts, short- and long-duration blast loadings, the simulated results such as the deflection, instantaneous crack, damage evolution and distribution derived by adopting different approaches are compared and evaluated. It demonstrates that, (i) concerning above-mentioned scenarios, the dynamic bond-slip behavior has the most significant influence on the dynamic response of the RC member under high-velocity perforation scenario, and more desirable results can be obtained without considering the bond-slip behavior under the deformable projectile high-velocity impact and long-duration explosion; (ii) for the considered scenarios, the CBISF method considering bond-slip behavior is recommended for RC member exhibiting bending failure mode under low-velocity impact, hard missile high-velocity impact, and short-duration explosion; the perfect-bond CBISP and SN approaches are suggested for the deformable missile impact and long-duration explosion conditions, respectively. The present study can provide helpful references in the numerically evaluation and design of impact and blast resistant structures.

Experimental Study on the Crack Initiation and Propagation of Unequal Cracks in Rock-Like Materials

The crack in the rock is a system that coexists with multiscale and interaction cracks, and it is necessary to evaluate the deformation, stability, and strength of rock mass in many engineering projects and the failure of rock are related to the distribution of cracks in the rock. Cracks of different lengths were set in rock-like materials, and uniaxial loading experiments were carried out under 30 test conditions by changing the length of the rock bridge and the short crack as well as the crack angle. During the experiment, a high-speed camera system was used to record the failure process of the specimens. The following conclusions were obtained: when the crack angle is in the range of 30°to 60° with the loading direction, the shorter cracks are more likely to propagate and coalesce. Most of the specimens initiate cracking from the outer tip of the longer crack and the key point of crack instability is the outer tip of the longer crack. The coalescence mode of the cracks is mainly related to the length of the rock bridge length and the crack angle.

Laser powder bed fusion (L-PBF) 3D printing thin overhang walls of permalloy for a modified honeycomb magnetic-shield structure

Modified honeycomb parts of Ni-15Fe-5Mo permalloy for magnetic shielding applications were designed and fabricated via laser powder bed fusion (L-PBF) 3D printing. We focused on the L-PBF process and performances of the thin-walled samples with different overhangs. After temperature-field numerical simulations and mechanism analyses on the L-BPF molten pools, the process optimizations were conducted to achieve a high bulk relative density. The thin walls with different wall thicknesses (0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 mm) and overhanging angles (10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°, and 90°) were printed without any supporting struts. The structures, mechanical properties, and formation mechanisms of the thin-walled overhangs were studied. We roughly gained some such trends or inferences about the tensile properties of the thin-walled overhangs. The microstructural anisotropies and surface “step effects” were the primary factors affecting the tensile properties. The numerical simulation and experiment of compression on the modified honeycomb parts with several sidewall inclination angles were performed. The modified honeycomb structures transferred stress and premature failure to other local structures far away from the compression face. The preferential plastic deformation of the modified honeycomb structures occurred at the inclined corners, exhibiting good plastic deformation buffering effect and thus avoiding instantaneous cracking. This work presented some reference significance for high-quality formation and performance evaluation of thin-walled overhanging structures via L-PBF.

Study on Crack Development in Red Clay from Guangxi Guilin with Different Clay Grain Content

In order to study the influence of different clay contents on the fractality of red clay, specimens having four different water contents were prepared. The cracking characteristics of the specimens were observed at 20 °C and 60 °C. Image J software was used to measure and calculate the crack area, crack ratio, crack length and width of each sample. The test results showed that the development of cracks in red clay could be divided into three stages: crack generation, crack development and crack stabilization. The clay particle content, temperature and water content have significant effects on crack development, and from the test analyses, it was determined that for construction in the Guilin area, it is necessary to pay attention to drainage protection.

Asphalt complex cracks' sensitivity to temperature and crack depth and adjustment of the composite stress intensity factor

This paper is based on the fracture mechanics K-criterion with the composite stress intensity factor solution formula. The influence of temperature and depth in developing complex crack instability and diffusion in asphalt pavements is investigated. The crack composite stress intensity factor and development pattern are analyzed. The finite element modeling analyzes the change in stress intensity factor values at different temperatures and cracks depths. The composite stress intensity factor's temperature effect factor (t*) and crack depth effect factor (d*) are derived, and the calculation formulae are optimized. The study results show that among the complex cracks in asphalt pavements, the type I crack tip stress intensity factor (KⅠ) is the most seriously affected by temperature and crack depth and is also the main controlling factor of crack development. Type II crack tip stress intensity factor (KⅡ) is not significantly influenced by temperature but tends to rise and fall as the crack depth increases. Type III crack tip stress intensity factor (KIII) is smaller than KⅠ and KⅡ. It has less influence on the development of complex cracks in asphalt pavements. t* and d* were introduced to derive the formula for the modified composite stress intensity factor (Keff*). The formula was verified to calculate the composite stress intensity factor at different temperatures and crack depths and to study the cracking pattern of asphalt pavements.

Modeling Atomistic Dynamic Fracture Mechanisms Using a Progressive Transformer Diffusion Model.

Dynamic fracture is an important area of materials analysis, assessing the atomic-level mechanisms by which materials fail over time. Here, we focus on brittle materials failure and show that an atomistically derived progressive transformer diffusion machine learning model can effectively describe the dynamics of fracture, capturing important aspects such as crack dynamics, instabilities, and initiation mechanisms. Trained on a small dataset of atomistic simulations, the model generalizes well and offers a rapid assessment of dynamic fracture mechanisms for complex geometries, expanding well beyond the original set of atomistic simulation results. Various validation cases, progressively more distinct from the data used for training, are presented and analyzed. The validation cases feature distinct geometric details, including microstructures generated by a generative neural network used here to identify novel bio-inspired material designs for mechanical performance. For all cases, the model performs well and captures key aspects of material failure.

Dynamic Versus Quasi-Static Analysis of Crack Propagation in Soft Materials

Abstract Cracks usually propagate dynamically that makes them so dangerous. However, most crack simulations are based on quasi-static analyses because they are simpler than the dynamic ones. Is it correct to use quasi-static analyses instead of the dynamic ones? Will the quasi-static and dynamic simulations provide similar results? We try to answer these questions in the present work. We compare results of quasi-static and dynamic simulations of crack propagation in aneurysm material. We use the material-sink (MS) approach, which is based on the notion of the diffused bond breakage. The latter feature implies a local loss of material and, consequently, decrease of mass density, which, in its turn, means that both stiffness and inertia go down in the damaged zone. The cancellation of inertia is an important feature of the MS approach in contrast to more formal regularization theories as phase field, gradient damage, and other nonlocal formulations. The MS approach is implemented within commercial finite-element software abaqus. A reduced mixed finite-element formulation is adopted to circumvent the volumetric locking and an implicit staggered solution algorithm is developed via the user-defined element subroutine UEL. Considered examples show that the onset of crack instability under static loads is followed by the dynamic rather than quasi-static crack propagation. Moreover, dynamic and quasi-static simulations, generally, provide different results.

Damage mechanism of Al2O3f/Al2O3 composites by acoustic emission technology

Continuous alumina fiber-reinforced alumina matrix composites (Al2O3f/Al2O3 composites) were produced via sol-gel process, the structure, micromorphology, and matrix properties of the composites were characterized, and then the damage mechanism was investigated using acoustic emission (AE) technology. The results showed that the composites were mainly composed of α-Al2O3. When the load first increased with time in the tensile test, the composites showed low AE signal energy, and cracks started and expanded in Al2O3 matrix. When the load reached its peak and abruptly declined, the number of AE signal events and accumulated energy increased dramatically. The proportion of AE signal events in the Al2O3f/Al2O3 composites was 0.37, and the proportion of accumulated energy was as high as 0.79, indicating that most of the fibers and the matrix were destroyed at this time. During the short-beam shear test, almost no AE signal was generated when the load rise reached the peak, and the crack instability expanded along the interlayer, resulting in delamination failure. After the initial load decreased, numerous high-energy AE signals were generated with increasing specimen deformation, and many fibers in Al2O3f/Al2O3 composites were crushed synchronously with the matrix.

Variation of Fracture Toughness with Biaxial Load and T-Stress under Mode I Condition

The effect of a biaxial load on brittle fractures of solids under predominantly elastic deformation and mode I loading conditions is studied in this article. A cross-shaped specimen is used in this work, and the variation of T-stress is achieved by changing the load applied to the arm parallel to the crack. In the tests, under a series of different loads parallel to the crack, a series of load values perpendicular to the crack are obtained, and the stress intensity factor is calculated by FEM (Finite Element Analysis). The test data demonstrate that the apparent fracture toughness of the material varies with the load parallel to the crack and the T-stress, since the T-stress is directly related to the load parallel to the crack. If only the first term of the Williams series solution is used to describe the stress field near the crack tip, the variation of KC is unexplained; therefore, more than one term in the Williams series solutions is used to develop the theory of biaxial effect on solid fracture behavior. The fracture criterion based on this consideration is also used to predict crack instability or crack curving under mode I load conditions. Experimental data are presented and compared with the theory.

Evaluations on Ceramic Fracture Toughness Measurement by Edge Chipping

Advanced ceramics, such as alumina and zirconia, are widely used in modern industries, due to their superior properties, such as high hardness and strength. Fracture toughness is a significant property that describes the capability of materials to resist crack instability and expansion to failure, and also helps when calculating the allowable working stress, and crack size, of the component. This paper comprehensively lists the current toughness-testing methods. With comparative investigations of various methods, edge chipping is found to be the simplest way of measuring the ceramic fracture-toughness, in terms of the dominant median crack, chip geometrical similarity, and force-distance relations, giving consideration to its potential application in industry. Moreover, to avoid the data variance from crack-length measurement in edge chipping, it is further proposed that the energy analyses can be used to improve the way in which the toughness expression is formulated.

Brittle fracture studied by ultra-high-speed synchrotron X-ray diffraction imaging.

In situ investigations of cracks propagating at up to 2.5 km s-1 along an (001) plane of a silicon single crystal are reported, using X-ray diffraction megahertz imaging with intense and time-structured synchrotron radiation. The studied system is based on the Smart Cut process, where a buried layer in a material (typically Si) is weakened by microcracks and then used to drive a macroscopic crack (10-1 m) in a plane parallel to the surface with minimal deviation (10-9 m). A direct confirmation that the shape of the crack front is not affected by the distribution of the microcracks is provided. Instantaneous crack velocities over the centimetre-wide field of view were measured and showed an effect of local heating by the X-ray beam. The post-crack movements of the separated wafer parts could also be observed and explained using pneumatics and elasticity. A comprehensive view of controlled fracture propagation in a crystalline material is provided, paving the way for the in situ measurement of ultra-fast strain field propagation.

Split Hopkinson Pressure Bar Test and Its Numerical Analysis Based on Transparent Rock Samples

Rock crack propagation is an important direction in the analysis of rock mechanical properties. However, due to the opacity of rock mass, crack evolution process cannot be directly observed. In this study, a heterogeneous anisotropic transparent rock made by mixture randomly distributed different sizes molten quartz sand and pure epoxy resin. This study aims to provide an intuitive and useful method of observing the characteristics of crack evolution, also crack evolution process is recorded by a high-speed camera based on Split-Hopkinson pressure bar (SHPB) tests. The results show that: change of internal color is monitored during loading, which confirms the visualization of internal crack evolution. Failure occurs along the loading direction, and many cracks are distributed in the center of the sample. When the main crack passes through the broken glass sand, it directly passes through the glass sand, and when it passes through the unbroken glass sand, it extends along the edge of the glass sand. Particle flow code(PFC) is used to simulate crack propagation process of transparent rock sample in the SHPB test, and the process is divided into four stages: no crack, crack initiation, crack coalescence, and crack stability. When the final failure of the sample occurs during loading course, tensile cracks account for 78.3% of the total cracks and shear cracks account for 21.7%. Furthermore, fracture of the sample is dominated by tensile action. Stress—strain curve and failure mode of numerical simulation are in good agreement with laboratory test. The visualization of rock crack propagation is helpful to the follow-up study of hydraulic fracturing of roadway and debonding of bolt.

Analysis of fracture characteristics of thin and thick rim asymmetric spur gear based on strain energy release rate

Gears are one of the most important components in most mechanical machines, automobiles, and other wind mills. The gears are subjected to repeated fillet stress, which causes them to develop root fracture leading to the failure of the power transmission system. Hence, the gear should be resistant to fracture. Furthermore, reduced weight and size of the gear is necessary to reduce the overall weight of the transmission system. The effect of backup ratio on the fatigue crack behaviour of symmetric and asymmetric spur gear under mix mode fracture is investigated in this study. The strain energy release rate (SERR), T-stress, and stress intensity factors (SIFs) of thick and thin rim asymmetric spur gear under mixed-mode condition are determined. Additionally, the effective SIF and the shape factor are evaluated for all spur gears. It is noticed that the fracture resistance of asymmetric spur gear (ANCR) increases with an increase in rim thickness. Further, an increase in backup ratio increases the stability of the crack and hence retards the crack growth. In addition, the influence of backup ratio on fracture resistance decreases with an increase in drive side pressure angle. Hence, an increase in pressure angle at drive side increases the crack stability, and the resistance towards fracture. The inference of this study gives valuable guidelines for designing asymmetric spur gears to reduce the weight without compromising the service life.

Strength and Energy Evolution Law of Deep-Buried Granite Under Triaxial Conditions

With the increasing global demand for clean and renewable energy sources, many underground hydropower caverns are built in deep mountain valleys in high-stress regions. The evolution of the mechanical properties of the surrounding rock of underground caverns under high-stress excavation requires urgent investigation. According to the deep-buried granite in the underground caverns of the Shuangjiangkou hydropower station, triaxial tests under confining pressures of 10, 30, 40, and 50 MPa were conducted by the MTS815 rock mechanics test system. Based on the stress–strain curve, the evolution law of the strength parameters of rock samples with the crack volume strain and energy with the energy consumption ratio under different confining pressures was analyzed. Our results showed that the stress–strain curve of the sample is divided into five stages with four characteristic points: the closed point, initiation point, volume expansion point, and peak point. The strength of each stage increases with an increase in the confining pressure. In addition, the failure of this granite is characterized by apparent shear failure. The internal friction angle and the cohesion increase rapidly with the increase in the crack volume strain, and they gradually tend to be constant. Furthermore, the confining pressure profoundly influences energy evolution during the loading in the stable and unstable crack growth stages. In these stages, total energy, dissipated energy, and elastic strain energy increase with an increase in the confining pressure. Finally, the energy consumption ratio can represent the preliminary criterion of rock failure in terms of energy. With the increase in the confining pressure, the energy consumption ratio of rock samples gradually increases to approximately 1.0 at the peak stress point. The research results can provide a reference for the instability prediction of surrounding rock masses of high-stress underground caverns.

Study on Intrinsic Influence Law of Specimen Size and Loading Speed on Charpy Impact Test.

Charpy impact energy/impact toughness is closely related to external factors such as specimen size. However, when the sample size is small, the linear conversion relationship between the Charpy impact energy of the sub-size and full-size Charpy specimens does not hold; the Charpy impact toughness varies with the size of the specimen and other factors. This indicates that studying the internal influence of external factors on impact energy or impact toughness is the key to accurately understanding and evaluating the toughness and brittleness of materials. In this paper, the effects of strain rate on the flow behavior and the effects of stress triaxiality on the fracture behavior of 30CrMnSiNi2A high-strength steel were investigated using quasi-static smooth bar and notched bar uniaxial tensile tests and Split Hopkinson Tensile Bar (SHTP). Based on the flow behavior and strain rate dependences of the yield behavior, a modified JC model was established to describe the flow behavior and strain rate behavior. Charpy impact tests were simulated using the modified JC model and JC failure model with the determined parameters. Reasonable agreements between the simulation and experimental results have been achieved, and the validity of the model was proved. According to the simulation results, the impact energy was divided into crack initiation energy, crack stability propagation energy and crack instability propagation energy. On this basis, the effects of striker velocity and specimen width on the energy and characteristic load of each part were studied. The results show that each part of the impact energy has a negligible dependence on the hammer velocity, but there is a significantly different positive linear relationship with the width of the sample. The energy increment of each part also showed an inverse correlation with the increase in the sample width. The findings reveal that the internal mechanism of Charpy impact toughness decreases with the increase in sample width; to a certain extent, it also reveals the internal reason why the linear transformation relationship of Charpy impact energy between sub-size specimens and standard specimens is not established when the specimens are small. The analytical method and results presented in this paper can provide a reference for the study of the dynamic behavior of high-strength steel, the relationship between material properties and sample size, and the elastic–plastic impact dynamic design.

Analysis of stress intensity factor for a crack emanating from elliptical hole subjected to compressive stress and shear stress

Underground caves often exist in karst areas, which will cause many difficulties in tunnel construction. The underground caves are often subjected to compressive stress, shear stress and internal pressure come from rock, faults and groundwater, respectively. The crack emanating from the cave will propagate under the effect of external forces, leading to the disaster of cave collapse and water gushing. To research the stability of crack emanating from the elliptical cave, a model of a plane containing an elliptical hole with a single crack under the compressive stress, shear stress and internal pressure was established. The theoretical solutions of stress intensity factors (SIFs) for crack tip were derived using complex variable function and conformal mapping function. The theoretical results were compared with the results of numerical simulation to verify the correctness of the theoretical solutions. The effects of crack length, ellipse shape, compressive stress, shear stress, internal pressure and crack inclination angle on SIFs were discussed. We can conclude that when the crack inclination angle is varied from 0° to 30°, the initiation pressure is small, and the cave is easily destroyed by groundwater. The flatter the elliptical hole, the easier the crack propagates. With an increasing of crack length, the value of SIFs at the crack tip increase quickly first and then increase linearly. When the crack inclination angle is 45°, the initiation angle of the crack reaches the maximum value.