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Normal stress ( σ n ) under compression-shear conditions significantly affects crack propagation and failure modes of specimens containing non-persistent joints (NPJs). Crack propagation and failure modes of specimens vary for different σ n . In the present study, we adopt a strength-based local maximum stress criterion (SLMS) to describe tensile and shear cracks formed during shear and model crack propagation processes via the finite element method. Two classical cases are performed to validate the SLMS criterion for describing tensile and shear cracks under shear conditions. After that, crack initiation, propagation, and coalescence processes are modeled for specimens containing a pair of horizontal NPJs in coplanar and non-coplanar cases at different σ n . Variations of crack propagation and failure modes of specimens containing coplanar and non-coplanar NPJs are investigated for σ n ranging from low to high. Effects of rock bridge inclination angle (β ) on crack propagation and failure mode of specimens containing non-coplanar NPJs are investigated. Also, the effects of σ n on critical shear load ( τ sc ) for crack initiation in specimens containing coplanar and non-coplanar NPJs are examined. Results indicate that failure modes of specimens with coplanar NPJs transform from tensile to mixed tensile-shear, then to shear, and finally to pure shear as σ n increases. The increase of β promotes the appearance of tensile failure of specimens containing coplanar NPJs under high σ n while suppressing the appearance of shear failure. The modeling results provide a reference for understanding crack propagation and failure modes in rocks containing NPJs under compression-shear conditions. [ABSTRACT FROM AUTHOR]

AbstractTo study the influence of the thickness effect on the impact performance of ZK61m magnesium alloy plate, the influence of ogival projectile on the impact performance of magnesium alloy plate of different thicknesses is analyzed through experiments and numerical simulations, the ballistic limits and failure modes of different thicknesses of the punch target plate are obtained. The velocity of the plug is analyzed by introducing the extruded chisel block velocity model. The experimental results show that the ballistic limit value of the target plate in a specific thickness interval (7 ∼ 11 mm) increases slowly with the increase of its thickness, and the failure mode is dominated by the shear punching failure and accompanied by the tensile failure. The plugs formed in the experimental process are consistent with the extruded chisel block velocity model. Numerical simulation results show that the MJC fracture criterion predictions deviate from the experimental results due to the overestimation of the material ductility, while the Lode parameter dependent MMC fracture criterion, which can better predict the ballistic behavior and failure modes of the target plate. [ABSTRACT FROM AUTHOR]

When the elastic‐brittle cracked body is subjected to compressive‐shear loading, not only does the phenomenon of wing crack initiation and propagation occur, but there is also a notable incidence of secondary crack initiation and propagation due to shear stress. Moreover, the shear fracture toughness (KIIc) predicted by the fracture criterion in the framework of classical fracture mechanics is usually smaller than the tensile fracture toughness (KIc), which is inconsistent with the actual observations. Therefore, this research firstly establishes a mechanical model of an elastic‐brittle cracked body under biaxial compression considering three kinds of crack parameters and materials' mechanical properties. Then, the stress field characteristics at the crack tip are analyzed. Next, a compression‐shear mixed fracture criterion is proposed. Finally, the effects of the lateral pressure coefficient (λ), critical plastic zone size (rc), friction coefficient (f), and deformation parameters of the crack surface on the failure modes at the crack tip are investigated. Highlights: A distinction is made between the failure and loading modes of the cracked rock mass.The stress field at the crack tip under compression and shear conditions is analyzed.A compression‐shear fracture criterion related to KIc and KIIc of materials is proposed.Conditions for the occurrence of shear failure at the crack tip are discussed. [ABSTRACT FROM AUTHOR]

Hot-forming technology for 22MnB5 hot-forming steel (22MnB5 HF steel) plates has been widely used in the automobile manufacturing industry in recent years. Physical simulation and numerical modeling were carried out in order to determine the forming limit of a 22MnB5 steel plate for the stamping process. The deformation experiments were performed in a temperature range of 600~900 °C and a strain rate range of 0.1~10 s−1. In the uniaxial tensile tests, it was found that at the forming temperature of 600 °C, the condition of dynamic recrystallization was not fully reached, and thus the corresponding tensile strength was much larger than that at other deformation temperatures. In the numerical simulation of bulging experiments, it was found that 22MnB5 steel had good formability when the initial deformation temperature was high and the forming speed was low by using the instability criterion, combining the maximum punch force and strain path transition. The forming limit diagram of 22MnB5 steel at a temperature of 700 °C and tool speed of 25 mm/s was obtained by means of simulation and a hot stamping experiment. The establishment of the forming limit of the 22MnB5 steel plate can provide theoretical and technical guidance for the hot-forming process. [ABSTRACT FROM AUTHOR]

In this paper, a novel calculating method for the three-dimensional stress intensity factor (SIF) was put out. By using the finite element approach, it was possible to compute the Mode I, Mode II, and Mode III SIF under the impact of a single factor (height, width, thickness, crack length, and inclination angle) and derive its variation rule. The SIF was computed by using the uniform design method, which also yielded the fitting formula that could determine the fracture at any geometric position on any plate. Then, a new three-dimensional penetrating crack fracture criterion was established to forecast both Mode I, Mode II, and Mode III initiation parameters of three-dimensional penetrating oblique crack. Uniaxial compression tests were done in order to validate the forecasted outcomes, including the crack initiation angle and load. The results demonstrate that the normalized KI always decreases with z/t (the crack front spacing), while the normalized KII and KIII increase first and then decrease. KI and KIII increase with the crack length 2a, while KII decreases first and then increases with the crack length. KI and KII both increase with the plate height. KI rises with the crack inclination angle, while KII and KIII initially raise and then lower. Along with the crack inclination angle, the crack initiation angle decreases, and the crack initiation stress rises. All of fracture mechanisms are Mode I. [ABSTRACT FROM AUTHOR]

During the hydraulic-fracturing process, stress interference occurs among multiple wells and fractures, potentially affecting the trajectory of hydraulic fracture propagation. Previous studies have largely overlooked the influence of proppant support stresses on the trajectories of fracture propagation. This paper establishes a mathematical model, grounded in the boundary element method, designed to compute the propagation of multiple fractures, considering both proppant support on the fracture surface and dynamic perturbations within the local stress field. The findings of this research reveal that the stress field induced by hydraulic fracturing exhibits dynamic evolution characteristics, necessitating a comprehensive study of the fracture initiation and extension across the entire fracturing time domain. The effect of the residual fracture width under proppant action on the in situ stress field cannot be ignored. During simultaneous fracturing, hydraulic fractures are inclined to propagate in the direction of the maximum horizontal principal stress, particularly as the in situ differential stress escalates. Staggered fracturing between wells has been proven to be more effective than head-to-head fracturing. Simply increasing the well spacing cannot solve the problem of inter-well fracture interference. In zipper fracturing, adjusting the fracturing sequence can inhibit the fracture intersections between wells, thereby controlling the trajectory of fracture propagation. The aforementioned research has considerable significance in guiding the control of fracture morphology during hydraulic-fracturing processes. [ABSTRACT FROM AUTHOR]

In this work, different stages of gas production in shale reservoirs are modelled. First, hydraulic fracturing is considered by injecting water at high pressures to crack the formation and increase the flow capacity of the reservoir. During the fluid injection, rock properties are modified and water appears in the stimulated area. Then, these changes can be detected through seismic monitoring. Finally, once the fracking stage is completed, the simulation of gas production begins. The simultaneous gas–water flow in the injection and production stages is modelled using the Black‐Oil formulation. Furthermore, a fracture criterion is applied under the hypothesis of constant temperature and constant stress field in this first analysis of the problem. The numerical simulations allow us to analyse the propagation of the fracture and the behaviour of the pore pressure and water saturation in the stimulated area. The advance of the fracturing fluid is delayed in relation to the breakdown of the rock. Besides, the presence of new fractures is detected by applying a poroviscoelastic wave propagation simulator that considers mesoscopic losses induced by heterogeneities in rock and fluids. After the fracture network is created, the injection well becomes a producer, allowing the extraction of gas and the flowback of the injected fluid. The simulated gas flow rates are compared with those obtained by a simplified single‐phase analytical solution used for practical applications, achieving optimum matching results. [ABSTRACT FROM AUTHOR]

This article, published in the International Journal of Applied Mechanics, explores the relationship between configurational stress/force and material fracture. The study aims to develop a new bridge between these concepts by using migrating control volume and thermodynamics to develop the Eshelby relation. The study also proposes a zero circumferential configurational stress fracture criterion based on the local properties of the crack-tip configurational stress tensor and fracture mechanics. The results indicate that the proposed fracture criterion is in good agreement with experimental observations and other fracture criteria. The study provides valuable insights into the mechanism of crack initiation and propagation in engineering materials. [Extracted from the article]

To study the stressed state and limit equilibrium of a closed elastoplastic cylindrical shell containing a plane longitudinal internal crack of any configuration, we use an analog of the δc-model and represent the resolving system of equations of the problem in the complex form. The obtained system of equations is reduced to a system of nonlinear singular integral equations whose solution is constructed by the method of mechanical quadratures with regard for the conditions of plasticity of thin shells, the conditions of boundedness of stresses, and the conditions of uniqueness of displacements. We also perform the numerical analysis of the dependences of the crack opening displacements and the sizes of plastic zones on the boundary conditions imposed on the shell edges, on the configuration of the crack, and on the geometric and mechanical parameters. [ABSTRACT FROM AUTHOR]

In this work two novel criteria for strength predictions of bearing failure on mechanically fastened composite joints are proposed for preliminary design. These criteria can estimate the bearing strength of hybrid laminates, which makes them innovative and applicable to a much wider range of aircraft structures that usually use this type of laminate in mechanical joints. The new approach uses characteristic lengths d 0 and a 0 to estimate the joint strength in bearing. Three surrogate models based on a linear regression of lamination parameters and AML (Angle Minus Load) parameter are proposed to provide accurate estimates for characteristic lengths d 0 and a 0 for a given set of these parameters. The regression models used three or two lamination parameters or a single parameter AML. They were applied to experimental results of six different laminate families including three hybrid laminates. The modified average bearing stress criterion (ABSC) outperformed the modified point bearing stress criterion (PBSC) in all cases. The results of the ABSC have a maximum discrepancy for the bearing strength of all laminate families of 2.77% and 1.91%, for the three and two parameters, respectively. The single parameter regression model using AML had a maximum discrepancy of 8.83%. All these results compare very favorably with the criteria proposed in the literature, including the AML regression that had the worst accuracy. Therefore, these criteria together with the proposed surrogate models can be used to minimize the number of tests required for the aircraft development, being a good candidate for preliminary design. [ABSTRACT FROM AUTHOR]

Hot-forming technology for 22MnB5 hot-forming steel (22MnB5 HF steel) plates has been widely used in the automobile manufacturing industry in recent years. Physical simulation and numerical modeling were carried out in order to determine the forming limit of a 22MnB5 steel plate for the stamping process. The deformation experiments were performed in a temperature range of 600~900 °C and a strain rate range of 0.1~10 s−1. In the uniaxial tensile tests, it was found that at the forming temperature of 600 °C, the condition of dynamic recrystallization was not fully reached, and thus the corresponding tensile strength was much larger than that at other deformation temperatures. In the numerical simulation of bulging experiments, it was found that 22MnB5 steel had good formability when the initial deformation temperature was high and the forming speed was low by using the instability criterion, combining the maximum punch force and strain path transition. The forming limit diagram of 22MnB5 steel at a temperature of 700 °C and tool speed of 25 mm/s was obtained by means of simulation and a hot stamping experiment. The establishment of the forming limit of the 22MnB5 steel plate can provide theoretical and technical guidance for the hot-forming process.

Finite element analysis has been carried out to study the effect of stress triaxiality cut-off value in the fracture criterion on the ballistic behavior of 9.94 mm thick Al2024-T351 plates impacted by rigid blunt-, hemisphere- and ogival-nosed projectiles. The plastic and fracture behavior of plates are described by a modified Johnson-Cook (MJC) model and our recently proposed DF2021 criterion, which are implemented into ABAQUS/Explicit finite element code with VUMAT subroutine. The stress triaxiality cut-off parameter in the DF2021 criterion is varied as 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5 with a larger stress triaxiality cut-off parameter corresponding to a lower stress triaxiality cut-off value. The effect of stress triaxiality cut-off values on the ballistic behavior of the targets against three different nose-shaped projectiles is evaluated and compared in terms of ballistic limit velocities, residual velocities, and failure patterns in the impact process. It is observed that the ballistic limit velocity increases with the stress triaxiality cut-off value under the impact of blunt-nosed projectiles while it first decreases and then increases with the stress triaxiality cut-off value under the impact of the hemisphere- and ogival-nosed projectiles. The formed shear plug or fragments exhibit different profiles with variations of the stress triaxiality cut-off value under the impact of hemisphere- and ogival-nosed projectiles, but uniformly exhibit a cylinder shape under the impact of blunt-nosed projectiles. The numerical results are compared with available experiments. It is found that the predictions from the DF2021 criterion with a cut-off parameter of 0.1 have the best agreement with the experiments. The reason causing the difference in the ballistic behavior due to the change of stress triaxiality cut-off value is discussed by analyzing the stress states of failed elements and the energy dissipation. The objective of the study is to evaluate the necessity of considering the stress triaxiality cut-off value in a fracture criterion in predicting ballistic behavior through finite element simulations.

The effect of a hole radius in an elastic layer on a critical external load at the moment of the onset of fracture, determined by the energy criterion, is investigated. A free energy flow through an interaction arc is used as a fracture criterion to describe the dependence of a critical external load on a hole radius. The length of the interaction arc constructed in the vicinity of a free energy peak point is determined using a linear parameter. The introduced linear parameter for a polymethyl methacrylate layer is obtained using known experimental data. The maximum value of the linear parameter can be taken as a material constant. [ABSTRACT FROM AUTHOR]

An experimental study of the ultralow-cycle fatigue of iron-based shape memory alloy (Fe-SMA) in triaxial stress states was conducted. Monotonic tensile tests of specimens with different geometries were carried out to investigate monotonic mechanical properties of Fe-SMA under various triaxial stress states in terms of stress triaxiality and Lode angle, followed by ultralow cyclic tests (cycles <100) which were carried out to study the ultralow-cycle fatigue of Fe-SMA under various loading systems at triaxial stress states. Fe-SMA had nonlinear combined hardening under cyclic loading. A parameter identification method based on an optimization-based algorithm was established to calibrate the constitutive model of Fe-SMA. The initiation and propagation of cracks in the fracture process were different for Fe-SMA under monotonic and cyclic loading. The influences of stress triaxiality and Lode angle on the fracture ductility of Fe-SMA were investigated. An ultralow cyclic fracture criterion, the cyclic Bai–Wierzbicki (CBW) criterion, was established based on the accumulation of ductile damage and the attenuation of ductile damage threshold. The applicability of the calibrated constitutive model and the proposed fracture criterion was validated by simulating the ultralow-cycle fatigue and fracture failures of Fe-SMA. [ABSTRACT FROM AUTHOR]

In this study, a modified maximum tangential stress criterion by considering T-stress and uniaxial compression tests have been utilized to theoretically and experimentally reveal the fracture initiation mechanism of a center-symmetric closed crack in compacted clay. The results show that wing cracks occur in the linear elastic phase of the stress-strain curve. In the plastic phase of the stress-strain curve, the wing cracks extend gradually and the shear cracks occur. The crack initiation stress and peak stress of compacted clay first decrease with the rise in pre-crack inclination angle (β = 0°–40°), and then increase with the rise in pre-crack inclination angle (β = 50°–90°). When the pre-crack inclination angle is relatively small or large (β ≤ 10° or β ≥ 70°), the crack type is mainly tension cracks. Secondary shear cracks occur when the pre-crack inclination angle is 10°–80°. When the dimensionless crack length is larger than 0.35, the crack types include wing-type tension cracks and secondary shear cracks. The experimental results were compared with the theoretical values. It was found that the critical size rc of compacted clay under compression-shear loading was 0.75 mm, smaller than the value calculated by the empirical formula (12 mm). The MTS criterion considering T-stress can be used to predict the compression-shear fracture behavior of compacted clay. [ABSTRACT FROM AUTHOR]

In this article, a new fracture criterion is formulated for a normal rupture crack, the most common in practice, based on the assumption that the tangential stresses in the prefracture zone are equal to the local strength of the material. In this case, the size of the prefracture area and the local strength are determined taking into account the nonsingular Тхx and Тzz stresses included in the asymptotic stress distribution according to Williams and characterizing the two-dimensional local constraint of deformation along the crack front in three-dimensional bodies. An expression for the effective stress intensity factor is obtained. In addition to the classical stress intensity factor, it includes the ratios of the Тxx and Тzz stresses to the yield strength. This makes it possible to take into account the restriction of deformations in the transverse (due to Тxx stresses) and longitudinal (due to Тzz stresses) directions in the vicinity of the crack front. Verification of the developed software tools and the proposed fracture criterion has been carried out. Examples of the implementation of the developed criterion for assessing crack resistance of a plate stretched in one or two directions with a coaxial transverse crack are given. [ABSTRACT FROM AUTHOR]

Mixed mode fracture is a widely studied topic, while the coupling effects of mixed mode cracking are unclear. In this paper, elastic fracture behaviors and the coupling effects of the mixed mode cracks are studied in detail based on the finite element method, experimental study and linear elastic fracture mechanics. Results show that there always exist II-III coupling effects at the crack tips of mixed mode cracks, which have many effects on the crack tip field and crack propagation behavior. It is found that a mode II component at the tip of a mixed mode crack is the main reason for crack deflection, while the mode III components show no effect. For any mixed mode crack, mode II components at the crack tip can be divided as that by mode II loading which causes plane crack propagation, and by the coupling effect which causes spatial crack propagation. On this basis, a new fracture criterion suitable for any mixed mode crack is proposed, combined with the coupling effect and the linear elastic superposition principle. The research in this paper provides a solution to the problem of an II-III coupling effect in mixed mode fracture research and further promotes the development of fracture mechanics. [ABSTRACT FROM AUTHOR]

In order to deeply investigate the tensile properties and fracture behaviors that are obtained by tensile tests of welded joints, constitutive and damage models are imperative for analyzing the tensile behaviors. In this work, the tensile tests are conducted on the T-welded joint specimens of aluminum alloy 6061-T6, which were cut from the T-welded joints of thin-walled parts under different welding currents of Tungsten Inert Gas Welding (TIGW). A modified Johnson-Cook (J-C) model based on the original J-C equation, Swift model, Voce model, and Hockett-Sherby (H-S) model, their linear combination model, and fracture failure model are constructed and applied to simulate tensile behaviors, combined with tensile test data. What is more, the finite element (FE) simulation of tension tests is executed with the VUMAT and VUSDFLD subroutines. Compared to those results simulated with different fracture criteria and tensile experiments, the tensile strength and yield strength of T-welded joint thin-walled parts under different welding currents were achieved, and their best mean errors were only about 1%. Furthermore, the accuracy of different fracture criteria is also evaluated by the correlation coefficient and mean squared error. The results show that the combination model can accurately predict the tensile properties and fracture behaviors of T-welded joints better than the single model, especially the results simulated with the Swift-H-S model and H-S-Voce model, which are in good agreement with tensile test results, which will provide an analysis foundation for enhancing the welding assembly quality and preventing fracture failure for complex thin-walled antenna structures. [ABSTRACT FROM AUTHOR]

Peridynamic formulations of the mean stress and incubation time fracture models are discussed in the paper. Contemporary fracture simulations using the peridynamic theory often rely on critical bond stretch fracture criterion which is known to operate similar to energy-based fracture models. The energy-based fracture criteria—both in classical Griffith's and Irwin's form—are known to be powerful tools for fracture simulations and analysis. However, a number of experimentally observed dynamic fracture effects cannot be captured by these models, e.g. rate sensitivity of the material toughness. Thus, coupling of peridynamic approach with alternative stress-based fracture models would possibly broaden the peridynamics applicability. Here implementation technique of the aforementioned fracture model is discussed and its results for the case of a dynamically propagating crack with relatively low velocity due to quasistatic load appear to be in good agreement with the classical energy release rate approach. [ABSTRACT FROM AUTHOR]

1060-H112 aluminum alloy with high ductility is widely used in industrial engineering. The study of its dynamic mechanical behavior has theoretical and engineering application value. In this paper, quasi-static tensile tests from room temperature to 250°C and high strain rate compression tests were conducted using a universal material testing machine and a Hopkinson compression bar. By using a hybrid test-numerical simulation method, a modified Johnson-Cook (MJC) strength model and Cockcroft-Latham (C-L) fracture criterion parameters were calibrated. Subsequently, Taylor impact tests were performed on 1060-H112 aluminum alloy specimens with a diameter of 12.66 mm and a length of 50.64 mm in the range of 176.3–483.03 m/s. Upsetting and tensile tearing were observed in the tests. A 12.68 mm diameter blunt nosed projectile impact test on 2 mm 1060-H112 aluminum alloy plate was also conducted with a light gas gun system, and the speed related parameters and failure modes were obtained. Finally, a three-dimensional model corresponding to the test was established in ABAQUS/Explicit finite element simulation software, and the failure modes of the Taylor rod and the velocity parameters and failure modes of the target impact test were predicted. The results show that the MJC strength model and the C-L fracture criterion can predict the experimental results of the two tests accurately. It shows that the MJC strength model and C-L fracture criterion have high accuracy, and they will play an important role in the application of 1060-H112 aluminum alloy in industrial engineering. [ABSTRACT FROM AUTHOR]

The strength of a rectangular plate with two opening-mode (mode I) edge cracks was studied using the Neuber–Novozhilov approach and a modified Leonov–Panasyuk–Dugdale model with a nonzero prefracture zone. A coupled discrete-integral fracture criterion is used since the stress field in the vicinity of the crack tip has a singularity. The ultimate strain fracture criterion is satisfied at the real crack tip, and the normal stress criterion is satisfied at the model crack tip. The constitutive equations of the analytical model are analyzed. Simple formulas for the fracture load are derived for quasi-brittle and quasi-ductile fracture. Plate fracture curves are plotted for a plane stressed state. [ABSTRACT FROM AUTHOR]

A new test specimen is proposed for investigation of mixed mode I/II/III fracture of materials. In the test specimen, by displacing the position of an inclined crack from the middle of the rectangular specimen, in addition to mode II loading, mixed mode I/III loading conditions are created under anti‐symmetric four‐point bending. To examine the applicability of the test set‐up, the specimens made of PMMA (polymethyl‐methacrylate) with three crack angles and three different positions of crack with reference to the middle of the specimen are tested. The experimental fracture loads are compared with the theoretical predictions of the maximum principal stress fracture criterion. There is a satisfactory consistency between the test and theoretical results. Although the proposed test configuration has limitations in applying the mixed modes of I/III and II/III, it is an efficient test configuration easier and less expensive than other configurations utilizing complex crack geometry or complicated loading fixtures. Highlights: A new test specimen under ASFPB loading is proposed to test mixed‐mode I/II/III fracture.Both FE analysis and experiments are used to assess the test specimen for fracture study.Good agreement of the experimental results with the fracture criteria is reported.The method is simple and cheap, but unable to test mixed‐modes I/II, and II/III fracture. [ABSTRACT FROM AUTHOR]

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In order to characterize the Ⅰ-Ⅱ mixed-mode fracture performance of 2D-C/SiC composites, Arcan butterfly specimens with unilateral cracks were used, and the mode-Ⅰ and mode-Ⅱ fracture shape factors of the specimen were calibrated through finite element model. The Arcan disc device was used to carry out mode-Ⅰ, mode-Ⅱ and Ⅰ-Ⅱ mixed-mode fracture tests upon 2D-C/SiC butterfly specimens, and the macroscopic and microscopic fracture modes and strength properties of the specimens under different loading paths were investigated. The results show that the fracture toughness of mode-II of 2D-C/SiC material is higher than that of mode-I. With increasing of the loading angle, the influence of shear stress on the crack propagation path increases, and meanwhile the fracture resistance of the specimens presents a tendency to increase. The applicability of several fracture criteria is demonstrated, and an Ⅰ-Ⅱ mixed-mode fracture criterion for 2D-C/SiC composites is suggested.

Based on the fracture mechanics theory of the isotropic Hoek-Brown strength criterion, this paper established the initiation conditions of the bifurcated microcrack along bedding which begins with the meso-fracture mechanism of laminated rocks. Then the author substituted the critical angle which indicates that the initial crack most likely causes the fracture of the rock into above established conditions and derived the anisotropy expression of the parameter m1 for the weak plane of bedding leading to the crack deflection. Through introducing the correction coefficient for the mixed fracture of the rock along the bedding and the matrix, this paper obtained the anisotropic modified model of Hoek-Brown strength criterion. Compared with the established anisotropic Hoek-Brown model and shale triaxial test results, the validity of the model was proved. The modified model inherits the fracture mechanics analysis of the isotropic Hoek-Brown strength criterion for the selection of rock failure characteristic quantity, and reflects the microscopic failure mechanism of the rock, also considers the effect of bedding anisotropy. The parameters in the modified criterion have a clear physical meaning. The parameter m in the model is related to the angle of the bedding plane, the tensile strength, compressive strength and friction coefficient of bedding and matrix. The change in the friction coefficient of the bedding plane will cause the position of the minimum value of m and the rock strength characteristics changed.

The damage and deterioration of jointed rock mass under dry-wet cycling strongly influence the rock fracture characteristics, which threaten the safety of reservoir bank slopes. To explore the effect of dry-wet cycling on the mechanical properties of jointed rock, in the present study, a sequence of uniaxial compression tests were conducted on the jointed sandstone subject to the dry-wet cycles. The deformation and cracking process were quantitatively studied by the digital image correlation (DIC) system. Subsequently, four failure modes after the dry-wet cycles were found. Finally, a rock fracture criterion that considers the effect of dry-wet cycling is established based on the Drucker-Prager criterion. The results show that the compressive strength, elastic modulus, and crack initiation stress level of the jointed rock samples gradually decreased with increasing dry-wet cycle number. Dry-wet cycling aggravated the localized deformation of the jointed sandstone samples prior to failure and drastically reduced the damage degree during failure. The experiments highlight four main failure modes of jointed rock subjected to dry-wet cycling: tensile failure; mixed shear-tensile failure; buckling-shear failure; and mixed buckling-shear-tensile failure. The fracture toughness calculated using the dry-wet cycle fracture criterion is consistent with that obtained from the fracture test. The established fracture criterion can consequently be applied to estimate the fracture toughness of rock under dry-wet action. This study provides important guidance for the stability analysis of slope rock mass and preventing geological disasters in reservoir bank slopes. [ABSTRACT FROM AUTHOR]

Different dimensions of tensile test specimen can be used for qualification of welding procedure according to the existing standard. However, they are found to be dissimilar in tensile properties. In this study, the tensile properties of TIG welded 2219-T8 aluminum alloy joints were tested with different tensile specimen sizes. The welding residual stress releasing, specimen size effect, as well as fracture criteria were taken into account by using a sequential “welding - cutting - tensile” finite element simulating method. Results indicated that the degree of welding residual stress releasing decreased with the increasing of specimen width. For specimens with 250 mm width, over 80% of the residual stresses were kept. Tensile testing result showed that the tensile strength and elongation of joint decreased when the specimen width increased. The differences in tensile properties were proved to result from the size distinctions, rather than residual stress releasing, because the stress triaxialities were different in the specimens with different sizes. This phenomenon was precisely simulated by using the Johnson–Cook fracture criterion. Eventually, the constitutive equations of Johnson–Cook model were established based on the experimental tensile strengths to describe the tensile behaviors of 2219 aluminum alloy joints.

On the basis of the previously suggested multimode two-criterion model of fatigue fracture, a method is proposed for calculating the origin and development of narrow localized damage zones in structural elements for various modes of cyclic loading. Such narrow zones of damage can be considered as quasi-cracks of two types, corresponding to the mechanism of normal opening and shear fracture. We consider an important example of a flight loading cycle (high-cycle fatigue) and high-frequency cyclic loading during torsion-bending vibrations of the blades (very-high-cycle fatigue) of an aircraft gas turbine engine compressor disk. The durability of this element of aircraft structures is assessed. An example of calculating fatigue fracture at high-frequency torsional vibrations of an experimental sample of a certain shape is also considered. For this sample it was possible to reproduce the observed effect of a sharp change in the growth direction and the type of quasi-crack during cyclic loading. [ABSTRACT FROM AUTHOR]

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α). Highlights: Fracture toughness is closely related to the size and configuration of the specimen, which is ultimately attributed to the inconsistent tangential stress distribution at the crack tip. The further improved maximum tangential stress criterion has the best effect on apparent fracture toughness prediction, and higher-order terms of the Williams expansion should be considered in apparent fracture toughness prediction of small-size specimens. The fracture criterion for determining the fracture process zone length should be consistent with the prediction criterion of apparent fracture toughness. The effective establishment of size effect law requires high accuracy tested data, especially for the configuration with large variation of the dimensionless stress intensity factor with normalized crack length. [ABSTRACT FROM AUTHOR]

Central cracking refers to the formation of internal cavities in cross wedge rolling (CWR) products. It occurs in various materials such as aluminium/titanium alloys, steels and plasticine at room or elevated temperatures, driven by different central cracking mechanisms. However, these mechanisms are still elusive, and a unified central cracking predictive model is absent due to the complex stress states within the workpiece, including triaxial stress states, cyclic loading and severe shear effects. In this study, the underlying fracture mechanisms were revealed, and a robust unified damage model with sound physical meanings was developed using a lab-scale CWR physical model and finite element models. The physical model with the plasticine billets was built, allowing the CWR dies with different geometries rapidly 3D printed and the billets with various ductility efficiently manufactured. The central cracking transiting from brittle to ductile fracture was experimentally observed for the first time using specifically designed plasticine/flour composite samples at varying ductility. The corresponding physics-based central cracking predictive model was proposed and validated quantitatively with 60 groups of CWR tests and compared with ten existing damage models/fracture criteria. This study effectively solves the long-lasting central cracking problem in the CWR industry and enhances the scientific understanding of fracture mechanics in complex engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, the deformation law of box-shaped parts drawing was analyzed, and the mathematical expression for calculating the critical fracture blank holder force (BHF) was deduced. In order to determine the fracture parameters of 08Al sheet, notched specimen tensile tests were conducted, the full-field strain of the specimens from deformation to fracture was obtained by the digital image correlation (DIC) technology. The evolution law of the stress triaxiality and Lode parameter with plastic deformation was obtained, and the fracture parameters of the modified Mohr-Coulomb (MMC) fracture criterion were fitted by the least squares method. The finite element (FE) simulation model coupled with MMC ductile fracture criterion was established to simulate the fracture behavior of sheet. The reliability of theoretical calculation was evaluated by FE simulation and experiments under various process conditions. The results demonstrated that the prediction of the critical fracture BHF by theoretical calculation and FE simulation were both partial safety predictions and all fracture earlier than the tests. In the theoretical calculation, when the flange shrinkage rate was 0.19, the critical BHF was the smallest, and the error was 17.5% compared with the tests, the theoretical calculation was closer to the test results. The theoretical calculation and FE simulation coupled with ductile fracture criterion provide a reference value for predicting the critical fracture BHF and intelligent control in actual production. [ABSTRACT FROM AUTHOR]

• Extending the fracture criterion for orthotropic materials under mixed mode II/I loading. • A new fracture criterion based on the extension of the Tsai-Hill failure criterion is presented. • Extension of the presented criteria in the case where the crack is aligned or perpendicular to the fibers. • Examining the effects of the non-singular stress component on crack growth. • Extraction of Russian pine wood mechanical and fracture test data. An essential study in the discourse surrounding composite materials is the investigation of their fracture mechanics due to the intricate nature of composite structures, it is necessary to take into account the presence of cracks and faults throughout the design process. In this research, within the context of linear elastic fracture mechanics, the fracture criterion for orthotropic materials under mixed mode II/I loading is presented by expanding the Tsai-Hill failure criterion. According to the crack, it may be aligned or perpendicular to the fibers; the criterion is stated for both cases. Also, the effects of the non-singular stress component on crack growth have been investigated. The mechanical and fracture data of Russian pine wood was extracted through tensile testing and the finite element (FE) method. The validity of the proposed criterion, in comparison with the experimental findings extracted in this research, has been proved. The precision of the previous proposed fracture criteria has been reviewed in comparison with the proposed criterion. The appropriate behavior of the fracture limit curves compared to the experimental data shows the efficacy of the proposed criterion to predict the initiation and propagation of cracks in orthotropic materials. [ABSTRACT FROM AUTHOR]

• Pure shear fracture can occur on notch tips of short beam in compression (SBC) specimens with specific geometries. • An improved fracture criterion was proposed to determine fracture mode and crack initiation angle. • The size effect on shear fracture process zone was observed. • K IIC measured by the SBC method was corrected by adopting the Coulomb friction model. • The SBC geometry was recommended for measuring the K IIC. Mode II fracture toughness is a crucial intrinsic property of rocks, and accurately measuring this parameter is a challenge in rock fracture mechanics. Among the various approaches for measuring the mode II fracture toughness, the short beam in compression (SBC) method is a convenient and effective option. Nevertheless, the validity of measuring the mode II fracture toughness using the SBC method is controversial. This study conducted numerical analyses and experiments on the SBC specimen with different geometries (C / H) to identify the fracture mode and initiation location. In addition, the improved fracture criterion was developed by introducing three components of T -stress to determine the fracture mode at crack tips and the crack initiation angle. The results reveal that the pure shear fracture can occur on notch tips of SBC specimens with C / H =0.1 and 0.2, indicating that the SBC method is valid for measuring the mode II fracture toughness of rocks. The modified fracture criterion can predict the fracture mode and the angle of shear crack initiation observed in the SBC experiment well. Another important finding is that, due to the compressive stress on the notch tip, the measured mode II fracture toughness of rocks using the SBC method should be corrected using the Coulomb friction model. It is also discovered that the length of the fracture process zone and the corrected mode II fracture toughness depend on the value of C / H. A small C / H leads to a significant error between the measured and corrected mode II fracture toughness. [ABSTRACT FROM AUTHOR]

In this study, a modified maximum tangential stress criterion by considering T-stress and uniaxial compression tests have been utilized to theoretically and experimentally reveal the fracture initiation mechanism of a center-symmetric closed crack in compacted clay. The results show that wing cracks occur in the linear elastic phase of the stress-strain curve. In the plastic phase of the stress-strain curve, the wing cracks extend gradually and the shear cracks occur. The crack initiation stress and peak stress of compacted clay first decrease with the rise in pre-crack inclination angle (β = 0°–40°), and then increase with the rise in pre-crack inclination angle (β = 50°–90°). When the pre-crack inclination angle is relatively small or large (β ≤ 10° or β ≥ 70°), the crack type is mainly tension cracks. Secondary shear cracks occur when the pre-crack inclination angle is 10°–80°. When the dimensionless crack length is larger than 0.35, the crack types include wing-type tension cracks and secondary shear cracks. The experimental results were compared with the theoretical values. It was found that the critical size rc of compacted clay under compression-shear loading was 0.75 mm, smaller than the value calculated by the empirical formula (12 mm). The MTS criterion considering T-stress can be used to predict the compression-shear fracture behavior of compacted clay.

The paper studies the adhesive strength of aluminum alloy specimens bonded with the use of an epoxy adhesive, under the tensile-shear stress state, depending on the testing temperature. Tension of modified Arcan specimens with load angles of 0, 22.5, 45, 67.5, and 90� with respect to the plane of adhesion is chosen as the experimental method. Experiments were performed at temperatures of -50, +23, and +50 �?. The analysis of the obtained results yields a linear fracture criterion and a fracture locus for the adhesive failure strain energy density, which takes into account the ratio of the elastic properties of the adhesive to those of the substrate. The region bounded by the fracture loci of adhesive strength and ultimate strain energy density determines the conditions for the safe loading of the bonded assembly in terms of the energy and force criteria of adhesive failure. The proposed fracture loci can be used, preferably simultaneously, to estimate the in-service strength and reliability of adhesively bonded assemblies.

Traditional hydraulic fracturing theory believes that as the initial pore pressure increases, the breakdown pressure of the rock will decrease. Previous experimental studies have shown that the breakdown pressure of rock hydraulic fracturing may increase with the increase of initial pore pressure (gradient), which cannot be explained by traditional theory. The current understanding of the effect of pore pressure and its gradient during hydraulic fracturing is still unclear. In this study, the pore pressure effect of rock hydraulic fracturing is analyzed based on a large number of macroscopic and microscopic phenomena of rock hydraulic fracturing in the previous study. Then, a new fracture criterion of rock fracturing is built considering the pressure-gradient effect. This new fracture criterion can reflect the main influence factors, including the rock particle size, porosity, pumping flow, inner diameter of open hole section, length of main fracture, height of main fracture (or length of open hole section), fluid viscosity, pore pressure, minimum initial in situ stress and rock tensile strength. The new fracture criterion is examined by the rock fracturing experiment which considering the pressure-gradient effect. The results show that the proposed fracture criterion considering the pore pressure effect can well predict the breakdown pressure of rock, and the prediction trend is consistent with the experimental results. The average error is less than 1% when adopting the present fracture criterion. The parameter sensitivity of the fracture criterion is analyzed. Results show that the fracture pressure increases with the rock porosity and this trend becomes more apparent with a larger initial pore pressure. It shows that the fracture pressure increases with the pumped flow rate. Besides, it shows that the fracture pressure decreases when increasing the particle size of the rock, but the decreasing trend gradually slows down. The research results can provide a theoretical basis for the mechanism of rock hydraulic fracturing and the structural modification effect of fluids in rock engineering.

Considering T‐stress components under compression, the crack initiation characteristics of HT200 and PMMA under uniaxial compression have been investigated by theoretical analysis and experimental study for central cracked plate (CCP) and compact tension shear (CTS) specimens with I‐II mixed mode crack. Crack initiation angles of CCP and CTS specimens under compressive load were theoretical predicted according to modified maximum tangential stress (MMTS) criterion and modified maximum shear stress (MMSS) criterion. The influence of material parameters and specimen geometrical configurations on crack initiation characteristics was illustrated through experiments. It demonstrates that the modified fracture criterion considering T‐stress components is more consistent with experiments. Crack initiation angle is related to material properties. Limit load PL is controlled by KII under compression for CCP specimen, and PL of PMMA is less than that of HT200. The closure effect on CTS specimens is less significant than that on CCP specimens. Highlights: Crack initiation angle of closed crack is related to material properties.Limit load PL is controlled by KII under compression for CCP specimens.The closure effect on CTS specimens is less significant than that on CCP specimens. [ABSTRACT FROM AUTHOR]

In order to deeply investigate the tensile properties and fracture behaviors that are obtained by tensile tests of welded joints, constitutive and damage models are imperative for analyzing the tensile behaviors. In this work, the tensile tests are conducted on the T-welded joint specimens of aluminum alloy 6061-T6, which were cut from the T-welded joints of thin-walled parts under different welding currents of Tungsten Inert Gas Welding (TIGW). A modified Johnson-Cook (J-C) model based on the original J-C equation, Swift model, Voce model, and Hockett-Sherby (H-S) model, their linear combination model, and fracture failure model are constructed and applied to simulate tensile behaviors, combined with tensile test data. What is more, the finite element (FE) simulation of tension tests is executed with the VUMAT and VUSDFLD subroutines. Compared to those results simulated with different fracture criteria and tensile experiments, the tensile strength and yield strength of T-welded joint thin-walled parts under different welding currents were achieved, and their best mean errors were only about 1%. Furthermore, the accuracy of different fracture criteria is also evaluated by the correlation coefficient and mean squared error. The results show that the combination model can accurately predict the tensile properties and fracture behaviors of T-welded joints better than the single model, especially the results simulated with the Swift-H-S model and H-S-Voce model, which are in good agreement with tensile test results, which will provide an analysis foundation for enhancing the welding assembly quality and preventing fracture failure for complex thin-walled antenna structures.

Mixed mode fracture is a widely studied topic, while the coupling effects of mixed mode cracking are unclear. In this paper, elastic fracture behaviors and the coupling effects of the mixed mode cracks are studied in detail based on the finite element method, experimental study and linear elastic fracture mechanics. Results show that there always exist II-III coupling effects at the crack tips of mixed mode cracks, which have many effects on the crack tip field and crack propagation behavior. It is found that a mode II component at the tip of a mixed mode crack is the main reason for crack deflection, while the mode III components show no effect. For any mixed mode crack, mode II components at the crack tip can be divided as that by mode II loading which causes plane crack propagation, and by the coupling effect which causes spatial crack propagation. On this basis, a new fracture criterion suitable for any mixed mode crack is proposed, combined with the coupling effect and the linear elastic superposition principle. The research in this paper provides a solution to the problem of an II-III coupling effect in mixed mode fracture research and further promotes the development of fracture mechanics.

The interfacial fracture of rock joints is an important although easily ignored issue in jointed rock engineering. To conduct this study, an interface crack model of rock joints was proposed. By analyzing the ratio of stress intensity factor to fracture toughness, the fracture mode of the interface crack was studied. Based on the Mohr-Coulomb criterion, an interface fracture criterion considering T-stress was established. To verify the proposed fracture criterion, laboratory and numerical tests were conducted. Finally, the effect of relative critical size α, internal friction angle φ and cohesion c on the initiation of an interface crack was comprehensively discussed. It is concluded that the proposed fracture criterion can predit the initiation of the interface cracks properly. With an increase in cohesion c, mode II fracture toughness KIIC also clearly increases. When the absolute value of KI is small, the effect of α is much larger than that of φ. In addition, with an increase in the absolute value of the mode I stress intensity factor, the φ of the joint plays a more important role in the initiation of the interface crack. [ABSTRACT FROM AUTHOR]

• The constitutive equation and fracture criterion of Nd-Fe-B permanent magnet materials were determined. • The Nd-Fe-B magnetic ring produced by combined extrusion outperforms that produced by backward extrusion. • The back pressure tool located at half of the magnetic ring significantly suppresses the occurrence of cracks. The hot deformation behavior of hot-pressed Nd-Fe-B material was investigated using a Gleeble-3500 thermal simulation machine, with deformation of 50 %, temperatures ranging from 700 to 850 °C, and strain rates ranging from 0.01 to 1 s−1. A hyperbolic sine model was employed to establish a constitutive equation suitable for this material. In addition, the chosen fracture criterion and damage threshold in the simulations were validated against the experimental results. Then, a three-dimensional thermo-mechanical coupled model was developed to simulate the damage evolution of the material during the extrusion process. The effects of different extrusion processes and positions of the back pressure tool on the magnetic performance and forming quality of the material were investigated. The simulation results indicate that both the combined extrusion process and the back pressure tool located at the half of the workpiece will contribute to improve the uniformity of the magnetic properties, and effectively ensuring the regularity of the forming process at the top of the magnetic ring and suppressing the occurrence of cracks. The results of this paper will help to a better understanding of the deformation mechanism of Nd-Fe-B permanent magnet and provide a valuable theoretical guidance for the preparation of high-performance Nd-Fe-B magnetic rings. [ABSTRACT FROM AUTHOR]

This paper aims to propose a novel fracture criterion to predict complex propagation behaviors of a bimaterial interface crack, either delaminating along the interface or kinking out of the interface into one of the adjoining materials. A strength-based criterion is used to predict the crack deflection, and an energy-based criterion is adopted to assess delamination along the interface. To determine the competition between these two cracking modes, a competing strategy is developed by comparing the strength-based and energy-based criteria. This coupled strength-energy fracture criterion eliminates the disadvantages arising from a criterion based solely on strength or energy, and is convenient to be calculated and embedded into numerical models. As practice, we embed the criterion into a homemade extended finite element model to simulate bimaterial interface crack propagation. Several numerical examples are performed to verify the effectiveness and accuracy of the developed model. Finally, this model is applied to simulate an interface crack propagation in a sandwich structure that has a specially designed peel-stopper. Parametric studies reveal that the material and interface toughness as well as geometrical dimensions of the structure have significant effects on the propagation mode of the interface crack. The results provide practical suggestions on the optimal design of peel-stopper in sandwich structures. • A novel strength-energy fracture criterion is proposed for crack propagation. • The developed XFEM model embedded with fracture criterion is established. • The developed model correctly captures the crack propagation behavior. [ABSTRACT FROM AUTHOR]

• Experimental results of fracture test under biaxial loading tension with torsion (proportional mixed-mode I + III) on PMMA notched specimens. • Distinguishing critical load values, places and angles of crack initiation depending on the type of load being tested (mode I, mode III and mixed-mode I + III). • Nonlinear numerical analyses – FEM. • The stress–strain fracture criterion was formulated, which was then positively verified. This paper presents the results of experimental fracture test of flat PMMA specimens under biaxial loading condition tension with torsion (proportional). The specimens were made in two thicknesses: 5 and 15 mm and were weakened with V-type edge notches with different root radii: 0.5; 2 and 10 mm. Thanks to the ARAMIS 3D 4 M non-contact vision system, measurement of the elongation and twist angle were recorded. During experimental part all of the deformation processes were observed using PHANTOM cameras. Obtained records made it possible to precisely indicate the moment of crack initiation (tensile force and torsional moment values). Using the microscopic observations the location of crack initiations were determined. Results obtained for biaxial loading were compared with those obtained for uniaxial tension and torsion. Based on experimental data the numerical calculation with FEM were carried out. The principal stress and plastic strain distribution under critical load, were obtained. The points of occurrence of stress maxima and plastic strain were indicated, which were taken as potential crack initiation sites. On the basis of the stress and plastic strain values measured at the critical points, a stress–strain fracture criterion was formulated, which was then positively verified. Additionally, new form of stress–strain fracture criterion was proposed. The bilinear form of the fracture criterion can be successfully used to predict fracture in PMMA flat specimens, regardless of the notch root radius, type of load or element thickness. [ABSTRACT FROM AUTHOR]

The low yield point (LYP) steel components for energy dissipation generally experiences substantial plastic deformation at triaxial stress states before fracture failure. This paper presents experimental and theoretical studies on the ultra-low cyclic fatigue performance of LYP at triaxial stress states. The monotonic mechanical properties of LYP steel under triaxial stress states are established through 14 tensile tests on four types of specimens with different initial geometries. Subsequently, 10 ultra-low cyclic tests are conducted to investigate the ultra-low cycle fatigue behavior of LYP steel at various triaxial stress states. An optimization-based technique is employed to calibrate the constitutive model for LYP steel, incorporating both isotropic and kinematic hardening performances. A phase-field framework is established and used for fracture prediction of LYP steel loading at triaxial stress states. In this proposed framework, the critical fracture density representing the fracture toughness in phase-field theory is taken as a variable related to equivalent plastic strain and stress states rather than a constant to describe the variation of fracture ductility of material under cyclic loading. The calibrated constitutive model and proposed fracture prediction framework are both implemented in finite element model and validated by simulating experimental results. • Monotonic and cyclic tests on specimens with various geometries were conducted. • A combination hardening constitutive model of LYP225 was established by an optimization algorithm. • A phase-field framework for fracture failure prediction of LYP225 was established. [ABSTRACT FROM AUTHOR]

Biaxial (axial and torsional loading) static tests were performed for the first time on EN‐GJS‐600–3 ductile cast iron tubular specimens obtained reproducing the solidification conditions typical of thick‐walled castings. The experimental results were elaborated to determine the yield and fracture loci of the material, which exhibited significant deviations from those predicted by the von Mises and Mohr–Coulomb criteria usually adopted for steels and gray cast iron, respectively. For this purpose, several alternative criteria proposed in the technical literature, some of them specifically devised for composite materials, have been calibrated and compared to account for the peculiar mechanical properties of this natural composite material. [ABSTRACT FROM AUTHOR]