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The establishment of a rock constitutive model considering microcrack propagation characteristics is an important channel to reflect the progressive damage and failure of rocks. The prepeak crack strain evolution curve of rock is divided into three stages based on the triaxial compression test results of granite and the definition of crack strain. According to the nonlinear variation characteristics of crack strain in the stage of rock crack stable propagation, rock deformation is expressed as the sum of matrix strain and crack strain. Then, the exponential constitutive relationship of rock crack stable propagation is deduced. The axial crack strains of the rock sample and its longitudinal section are equal. Thus, the longitudinal symmetry plane of the rock sample is abstracted as a model containing sliding crack structure in an elastic body, and the evolution equation of crack geometric parameters in the process of stable crack propagation is obtained. Compared with the experimental data, results show that the rock crack stable propagation model based on crack strain can adequately describe the evolution law of crack strain and wing crack length. In addition, the wing crack propagates easily when the elastic body with small width contains an initial crack with a large length and an axial dip angle of 45° under compressive load. This study provides a new idea for the analysis of the stable propagation characteristics and laws of rock cracks under compressive load.

This paper presents the investigations of the tension-softening constitutive relation of concrete and the numerical method for mode I fatigue crack propagation in concrete. Firstly, the static loading, fatigue loading, and fatigue–static loading were carried out on 191 notched three-point bending (TPB) beams. With the experimental results, the tension-softening constitutive relation of concrete under fatigue loading was proposed from the view of energy conservation, where the equilibrium relation between the energy dissipated by crack propagation and the external work was established. Secondly, by combining the constitutive relation with the stress intensity factor (SIF)-based crack propagation criterion, the numerical method for mode I fatigue crack propagation in concrete was developed. Finally, the applicability of the numerical method was validated by comparing the numerically derived fatigue life, fatigue crack propagation length, crack mouth opening displacement (CMOD), and SIF with the experimental results. It is concluded that the numerical method proposed in this paper is significantly helpful in evaluating the fatigue performance of concrete structures.

A thermal–mechanical coupled phase field fracture model is developed to study the complex dynamic crack propagation path in brittle material under thermal shock loading. By introducing a global continuum phase-field variable to describe the diffusive crack, the coupling between heat transfer, deformation and fracture is conveniently realized. A novel elastic energy density function is proposed to drive the evolution of phase-field variable in a more realistic way. The three-field coupling equations are efficiently solved by adopting a staggered time integration scheme. The coupled phase field fracture model is verified by comparing with three classical examples and is then applied to study the fracture of disk specimens under central thermal shock. The simulations reproduce the three different types of crack paths observed in experiments. It is found that the crack grows through the heating area straightly at lower heating body flux, while branches into two at higher heating body flux loading. The crack branching prefers to occur in the heating area with larger heating radius and prefers to occur outside the heating area with smaller heating radius. Interestingly, the crack branches when propagation speed is at its lowest point, and it always occurs close to the compression region. It is shown that the heterogeneous stress field induced by temperature inhomogeneity may have a strong influence on the crack branching under the thermal shock loading.

The low-temperature fatigue crack propagation rate of 925A steel, as a rudder steel for polar special ships, has a crucial impact on the evaluation of the fatigue strength of polar ships. The purpose of this article is to study the fatigue crack propagation rate of 925A steel under different low-temperature conditions from room temperature (RT) to −60 °C. The material was subjected to fatigue crack propagation tests and stress intensity factor tests. The experimental tests were conducted according to the Chinese Standard of GB/T6398-2017. The results show that as the temperature decreases, the lifespan of 925A increases. Within a certain stress intensity factor, as the temperature decreases, the fatigue crack propagation rate decreases. At −60 °C, it exhibits ductile fracture; within normal polar temperatures, it can be determined that 925A meets the requirements for low-temperature fatigue crack propagation rates in polar regions. However, in some extreme polar temperatures below −60 °C, preventing brittle failure becomes a key focus of fatigue design. Finally, the fatigue crack propagation behavior at the microscale of 925A steel at low temperatures was described using fracture morphology. The experimental data can provide reference for the design of polar ships to further resist low-temperature fatigue and cold brittle fracture.

The phase field method is a very effective method to simulate arbitrary crack propagation, branching, convergence and complex crack networks. However, most of the current phase-field models mainly focus on tensile fracture problems, which is not suitable for rock-like materials subjected to compression and shear loads. In this paper, we derive the driving force of phase field evolution based on Mohr–Coulomb criterion for rock and other materials with shear frictional characteristics and develop a three-dimensional explicit parallel phase field model. In spatial integration, the standard finite element method is used to discretize the displacement field and the phase field. For the time update, the explicit central difference scheme and the forward difference scheme are used to discretize the displacement field and the phase field respectively. These time integration methods are implemented in parallel, which can tackle the problem of the low computational efficiency of the phase field method to a certain extent. Then, three typical benchmark examples of dynamic crack propagation and branching are given to verify the correctness and efficiency of the explicit phase field model. At last, the failure processes of rock-like materials under quasi-static compression load are studied. The simulation results can well capture the compression-shear failure mode of rock-like materials.

The development and extension of microcracks in rocks affect the integrity and stability of rock mass construction. External dynamic loads with different loading rates lead to different dynamic fracture characteristics of rock fractures. In this study, a large-sized PMMA specimen with an arc boundary was proposed. The time at which the crack started and spread was determined using drop hammer impact testing and crack growth meter testing. Subsequently, the microscopic characteristics of the crack fracture surfaces were analyzed using a scanning electron microscope. Finally, the dynamic fracture toughness of the crack tip of the PMMA specimen was calculated using the finite-element method. Both experimental and numerical studies indicated that the arc boundary of the specimen demonstrated effective capabilities for arresting propagating cracks, and as the loading rate increased, the crack velocity also increased, while the crack initiation time decreased. The crack no longer propagated along the original crack surface after the crack arrest. The peak compressive stress along the crack trajectories increased with the loading rate. During the early stages of crack propagation, the highest compressive stress was observed for the 65° specimen. Conversely, during the later stages of the crack propagation, the 125° specimen exhibits the highest compressive stress. The dynamic arrest toughness of the crack is greater than the dynamic initiation and propagation toughness of the crack. As the loading rates increased, the dynamic initiation and propagating toughness of the crack also increased, while the dynamic arrest toughness of the crack changed little with the loading rate.

Microwave energy can be used to assist mechanical rock breakage for civil and mining engineering operations. To assess the industrial applicability of this technology, microwave heating of basalt specimens in a multi-mode cavity (a microwave chamber) at different power levels was followed by conventional mechanical strength and fragmentation effect tests in the laboratory. X-ray diffraction and scanning electron microscopy/energy-dispersive X-ray spectroscopy were used to determine the mineral composition and distribution of the basalt, to aid interpretation of crack propagation patterns and the associated strength reduction mechanism. These analyses demonstrated that cracks mainly occurred around olivine grains, primarily as intergranular cracks between olivine and plagioclase grains and intragranular cracks within olivine grains. Strength reduction during microwave fracturing of basalt is driven by heat from enstatite (a microwave-sensitive mineral) and volumetric expansion of olivine (a thermally expansive mineral). Uniaxial compressive, Brazilian tensile, and point load strengths all decreased with increasing microwave irradiation time at rates that were positively related to the power level. For a given power level, mechanical strength reduction can be estimated from linear relationships with irradiation time. On the other hand, a power function best described burst time (the irradiation time at which the specimen burst into fragments) vs. power level (for a given specimen size) and burst time vs. specimen size (for a given power level) relationships. Microwave-induced hard rock fracturing can be an integral part of new methods for rock breakage and tunnel excavation.

Interest in adhesively bonded joints has significantly increased due to their numerous advantages over other joining techniques. However, they are frequently used in structures subjected to fatigue loading, which might cause defects such as cracks within the bondline. Thus, timely detection, localization, and size estimation of such defects are crucial for ensuring structural safety. This study focused on experimentally investigating crack length estimation in adhesively bonded joints under mode II fatigue loading. To analyze the crack growth, a comprehensive comparison was conducted between various techniques, such as visual testing, digital image correlation, optical backscatter reflectometry, and the analytical compliance-based beam method. In interrupted fatigue tests (static acquisition), digital image correlation and optical backscatter reflectometry exhibited consistent damage sensitivity, estimating larger crack lengths compared to visual testing by approximately 3 mm and 5 mm, respectively. The optical backscatter reflectometry in uninterrupted tests (dynamic acquisition) showed significantly larger estimations, approximately double those of static ones. This demonstrated its potential to detect possible damage within the adhesive that might not be detected by other methods, as shown previously for quasi-static loading conditions. Its capability in early damage detection under the dynamic regime makes it a valuable tool for continuous monitoring. Furthermore, a comparison of optical backscatter reflectometry’s performance in quasi-static, static, and dynamic acquisitions indicated a potentially larger process zone under quasi-static loading, a finding confirmed by the compliance-based beam method.

This work reports a selective median crack propagation phenomenon in glass, leading to a novel glass cutting process. We found that by scribing a glass sample to the extent of plastic deformation with a deformation depth of 100–400 nm, followed by inducing an initial crack, a subsurface crack with a depth of ~ 10 μm was propagated backward along the centerline of the scribed region with a speed of 1 μm/s order. The crack depth and propagation speed were increased by increasing the scribing load. We conclude that the propagation direction was determined by the effect of the shear stress caused by a scribing tip sliding motion.

Fatigue failure is the main type of failure that occurs in gas turbine engine blades and an online monitoring method for detecting fatigue cracks in blades is urgently needed. Therefore, in this present study, we propose the use of acoustic emission (AE) monitoring for the online identification of the blade status. Experiments on fatigue crack propagation based on the AE monitoring of gas turbine engine blades and TC11 titanium alloy plates were conducted. The relationship between the cumulative AE hits and the fatigue crack length was established, before a method of using the AE parameters to determine the crack propagation stage was proposed. A method for predicting the degree of crack propagation and residual fatigue life based on the AE energy was obtained. The results provide a new method for the online monitoring of cracks in the gas turbine engine blade.