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This paper presents the results of computer simulations of fracture in three laboratory tests: the three-point bending of a notched beam cut from sandstone, the pull-out test of a self-undercutting anchor fixed in sandstone, and the pull-out test of a bar embedded in concrete. Five material failure criteria were used: Rankine, Coulomb–Mohr, Drucker–Prager, Ottosen–Podgórski, and Hoek–Brown. These criteria were implemented in the Abaqus® FEA system to work with the crack propagation modeling method—extended finite element method (X-FEM). All criteria yielded similar force–displacement relationships and similar crack path shapes. The improved procedure gives significantly better, close-to-real crack propagation paths than can be obtained using the standard subroutines built into the Abaqus® system. [ABSTRACT FROM AUTHOR]

In this research, five fracture criteria (maximum tangential stress (MTS), generalized maximum tangential stress (GMTS), minimum strain energy density (SED), generalized minimum strain energy density (GSED), and modified maximum tangential stress (MMTS)) were evaluated for asphalt concrete using fracture data from tests conducted under various loading modes and conditions. Tests were performed on semi‐circular bend (SCB) specimens of various sizes. Based on the results, the MTS criterion tends to overestimate fractures, while the GMTS criterion exhibits more precise predictions. The SED and GSED criteria inaccurately predict fractures, especially under certain loading conditions. The MMTS criterion shows superior predictive capability for asphalt concrete fractures. Specimen size influences fracture resistance, with larger specimens exhibiting higher fracture values. Overall, the MMTS criterion closely mirrors the crack growth behavior of asphalt concrete, highlighting its precision in predicting fracture results. The errors between the predictions of the fracture criteria MTS, GMTS, SED, GSED, and MMTS, and the experimental results ranged from 0% to 42.8%, 0% to 22.5%, 0% to 52.7%, 0% to 42.4%, and 0% to 14.5%, respectively. Highlights: Fracture tests were conducted on asphalt concrete under various conditions such as temperatures, loading rates, SCB specimen sizes, and loading modes.Five fracture criteria (MTS, GMTS, SED, GSED, MMTS) were assessed for their applicability to asphalt concrete.The MMTS criterion was found to have the best ability to predict fractures in asphalt concrete compared to the other criteria studied.The size of the specimen has an impact on fracture resistance, with larger specimens showing higher fracture values. All the fracture criteria used in the study accurately reflect this trend. [ABSTRACT FROM AUTHOR]

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing. The edge-notched disk bending (ENDB) specimens are employed to measure the entire range of mixed-mode I/III fracture toughness of Longmaxi shale. To theoretically interpret the fracture mechanisms, this research first introduces the detailed derivations of three established fracture criteria. By distinguishing the volumetric and distortional strain energy densities, an improved three-dimensional mean strain energy density (MSED) criterion is proposed. As the critical volumetric to distortional MSED ratio decreases, the transition from tension-dominated fracture to shear-dominated fracture is observed. Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I (i.e., tension) to pure mode III (i.e., torsion or tearing) since mode-III cracking happens in a twisted manner and mode-I cracking occurs in a coplanar manner. The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing. The average ratio of pure mode-III fracture toughness to pure mode-I fracture toughness is 0.68, indicating that the obtained mode-III fracture resistance for a tension-based loading system is apparent rather than true. Compared to the three mainstream fracture criteria, the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-mode I/III fracture toughness of distinct materials and loading methods.

In this study, the interaction force between an in‐plane elliptical inclusion and a crack is evaluated using the Eshelby equivalent inclusion and material configurational force method. The toughening effect of coarse aggregates on concrete is investigated. The fracture criteria for mixed‐mode cracks based on the characteristics of the crack‐tip plastic zone assessed by the principal configurational stress difference are proposed and verified by experimental results in the literature. The fracture probability is then used to improve the fracture criteria, and the dimensionless factor associated with stress intensity factors is introduced to determine the fracture probability. Additionally, the volume fraction of coarse aggregates, the age and fatigue life of concrete are considered in the present fracture criteria. Theoretical studies show that the interaction between a crack and a hard or soft inclusion exhibits mutual repulsion and attraction. The size and shape of the crack‐tip plastic zones assessed by the Mises stress and the principal configurational stress difference are essentially the same. The fracture load envelopes increase with the increase in the volume fraction of coarse aggregates and the age of concrete and shrink with the increase in the life ratio. Highlights: The interaction force between a crack and an elliptical inclusion and toughening effect of coarse aggregates on concrete are evaluated.Fracture criteria based on the characteristics of the crack‐tip plastic zone by the principal configurational stress difference for mixed‐mode cracks are proposed.The fracture probability is introduced to elucidate the fracture mechanism of concrete.The impacts of the volume fraction of coarse aggregates, the age, and fatigue life on concrete fracture are investigated. [ABSTRACT FROM AUTHOR]

This article investigates the effect of friction between crack faces in ASCB (asymmetric semi-circular bend) specimen on fracture parameters of hot mix asphalt concrete. To achieve this, fracture tests were conducted on ASCB specimens containing cracks with different angles (0, 10, 20, 30, and 40°). In addition to the fracture tests, friction tests were also performed by designing a simple fixture. Subsequently, finite element analyses were carried out, and friction coefficients between crack faces were calculated based on the results of fracture and friction tests. Furthermore, two fracture criteria, ASED (average minimum strain energy density) and MTS (maximum tangential stress), were examined under two different scenarios: assuming zero-friction and non-zero friction between crack faces to predict fracture load and fracture strength. The fracture tests showed that with an increase in the crack angle, the fracture load initially decreased up to the crack angle of 20°, and then increased. Furthermore, the friction tests revealed that an increase in the normal load led to an increase in the friction coefficient. As per finite element results, the crack face contact occurred at a crack angle of 13.1°. Hence, crack faces in the ASCB specimens with the crack angles of 20, 30, and 40° had friction, which significantly affected the fracture parameters. The results also indicated that the average error values for the MTS and ASED criteria compared to the experimental results were 22.8 % and 18.8 %, respectively, when the friction` between crack faces is ignored, and 12.4 % and 4.0 % for the scenario that the friction effect is taken into account. The ASED criterion demonstrated higher accuracy than MTS criterion. Additionally, the average error value of fracture strength predicted by the ASED criterion with assuming non-zero friction was 4 %, indicating good predictive accuracy for fracture strength.

This article presents a study to estimate the possibility of determining the shape and size of a Mannesmann effect crack using the finite element method. Experimental tests were carried out to obtain reference specimens with a crack. A rotational compression test of cylindrical specimens in a channel was used for the experimental studies. Finite element tests were carried out using nine ductile fracture criteria. In the first stage of the study, using the rotational compression test and the finite element method, the limit values of the fracture criteria were determined. In the second stage, the development of a Mannesmann effect crack was simulated using the limit values of the fracture criteria using the finite element method. Based on the analysis, it was found that the greatest agreement in terms of void shape and size obtained in finite element method and experiment was obtained for the Ayada criterion. Analysis of the progression of the shape of the void formed using the Ayada criterion showed that crack initiation occurs as a result of maximum principal stress. The development of the resulting void is the result of the action of the maximum shear stress as well as the maximum principal stress. [ABSTRACT FROM AUTHOR]

In recent years, the issue of aircraft icing has gained widespread recognition. The breaking and detachment of dynamic ice can pose a threat to flight safety. However, the shedding and fracture mechanisms of dynamic ice are unclear and cannot meet the engineering needs of ice-shedding hazard assessment. Therefore, studying the fracture toughness of ice bodies has extremely important practical significance. To address this issue, this article uses a centrally cracked Brazilian disk (CCBD) specimen to measure the pure mode I toughness and pure mode II fracture toughness of freshwater ice at different loading rates. The mixed-mode (I–II) fracture characteristics of ice are discussed, and the experimental results are compared and analyzed with the theoretical values of the generalized maximum tangential stress (GMTS) criterion considering the influence of T-stress. The results indicated that as the loading rate increases, the pure mode I toughness and pure mode II fracture toughness of freshwater ice decrease, and the fracture toughness of freshwater ice is more sensitive to the loading rate. In terms of fracture criteria, the theoretical value of the ratio of pure mode II fracture toughness to pure mode I fracture toughness based on the GMTS criterion is in good agreement with the experimental value, while the theoretical value based on the maximum tangential stress (MTS) criterion deviates significantly from the experimental value, indicating that the GMTS criterion considering the influence of T-stress can better predict the experimental results. [ABSTRACT FROM AUTHOR]

This paper presents the results of computer simulations of fracture in three laboratory tests: the three-point bending of a notched beam cut from sandstone, the pull-out test of a self-undercutting anchor fixed in sandstone, and the pull-out test of a bar embedded in concrete. Five material failure criteria were used: Rankine, Coulomb–Mohr, Drucker–Prager, Ottosen–Podgórski, and Hoek–Brown. These criteria were implemented in the Abaqus® FEA system to work with the crack propagation modeling method—extended finite element method (X-FEM). All criteria yielded similar force–displacement relationships and similar crack path shapes. The improved procedure gives significantly better, close-to-real crack propagation paths than can be obtained using the standard subroutines built into the Abaqus® system.

To choose a rational method for cutting rolled stocks into workpieces made of materials with different mechanical properties, an engineer must have a set of tools that allow them to make such a choice. The results of the conducted research confirm the correctness of the conclusions that synergetic fracture criteria, such as the "crack growth criterion" and "brittleness criterion," are the basic informative features. When any of the remaining complex criteria, such as the "crack initiation criterion" or "scale criterion" are added to them, they form the most informative sets of minimal power, ensuring with a given reliability the classification of materials according to their sensitivity to separation. The boundaries of zones have been established to classify materials that are in a "plastic state," "elastoplastic state," and "brittle state." Recommendations have been developed for selecting a method for cutting rolled stocks into workpieces based on the values of the "crack growth criterion" and "brittleness criterion." The results of the conducted research are well-aligned with experimental data obtained using the methodology for determining the ultimate deformability of rolled stocks applied to separation processes. The ultimate plasticity value is a suitable indicator for ranking metals according to their ability to be separated. The procedure for determining the ultimate plasticity value fully preserves the standardization of the test. Considering the mass production of cutting rolled stocks into workpieces, it is possible to expect an accelerated accumulation of information on the value of the ultimate plasticity for metals with different chemical and structural states, leading to the formation of a corresponding database. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Applied Mechanics is the property of Chinese Journal of Applied Mechanics Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In a two terms approach, the representation of the stress field at the crack-tip consists of the mixed mode stress intensity factors (SIFs) as well as the non-singular term, the so-called T-stress. For the prediction of the crack direction in functionally graded materials, a short beam bend (SBB) containing an inclined pre-crack was considered. The main purpose is to investigate the influence of T-stress on the fracture initial angle under mixed mode conditions. Various specimen combinations were analyzed to generate different opening and shearing modes. Using the displacement field near the crack-tip, the fracture parameters were numerically determined then implemented in a subroutine to evaluate the fracture initial angle by both traditional and generalized maximum circumferential stress criteria. The results showed a difference in the predicted crack initial angle; this difference becomes more noticeable as the mode II becomes dominant which is attributed to the consideration of T-stress. [ABSTRACT FROM AUTHOR]

The forming limit of aluminum alloy (AA) 7075 sheets depending on the deformation mode, the strain-rate, and the temperature was evaluated under the pneumatic stretching technique at elevated temperatures. In order to perform the pneumatic stretching test and to prevent the unfavorable fracture on the edge with the targeted strain-rate, the previously introduced die shape designs were utilized with the pressure-time profile. The two different kinds of strain-rate and temperature-sensitive forming limits were determined, where one is the necking-based forming limit (NFL) and the other is the fracture-based forming limit (FFL). The results show that FFL is highly deviated from NFL at 400 °C than those at 470 °C due to abrupt strain localization, which leads to high dome height at the pneumatic forming during the relatively lower elevated temperature. The microscopical analysis (optical and scanning electron) reveals that higher temperature condition, 470 °C, has early fracture due to the high diffusion of micro-voids and faster coalescence of the voids. The well-known three parameters fracture criteria e.g. Johnson-Cook (J-C), Modified Mohr-Coulomb (MMC3), Lou, and Hu fracture model were multiplicatively extended to strain-rate relationships based on the suggested general equation and independently characterized for each elevated temperature with the error analysis.

The study of salt rocks deformation and fracture processes is an essential part of mining parameters justification for mineral salt deposits. The results of uniaxial compression tests on large salt rock specimens are presented as a loading curve and diagrams of the transverse-longitudinal displacements at various distances from the side faces. Based on an isotropic elastoplastic model, a multivariant numerical simulation was performed. Its purpose was to select fracture criteria that accurately describe the loading diagram of specimen and its transverse-longitudinal deformations. The following fracture criteria are considered: Tresca with the associated plastic flow rule, the associated and non-associated Mohr-Coulomb, the parabolic analogue of Mohr-Coulomb criterion and the volumetric fracture criterion. Numerical simulation was carried out by the displacement-based finite element method. Three-dimensional hexahedral eight-node isoparametric elements were used for discretization of the solution domain. It has been established that within the elastoplastic model of media the process of uniaxial compression of a large cubic salt rock specimen is adequately described by the linear Mohr-Coulomb fracture criterion with the non-associated plastic flow, as well as by the associated volumetric parabolic yield criterion with the linear isotropic hardening

A novel analytical model to predict fracture resistance of a quasi-brittle material, like wood, is presented. The model is based on a scaling parameter introduced into the non-local fracture theory to take into account the specimen size effect on the development of the damage zone. An expression for length of the critical process zone, which can be used in damage tolerant design of wooden structures is derived from this theory. The model is validated with mixedmode bending tests. A numerical analysis using cohesive elements is performed to understand the role of specimen size in the development of the damage zone. The analytical predictions of the fracture resistance and the critical process zone length for wood are compared with numerical results and experimental data available in the literature. [ABSTRACT FROM AUTHOR]

Today, artificial intelligence plays a huge role in the mechanical engineering field for solving many complex problems and the problem with fracture mechanics is one of them. In fracture mechanics, artificial intelligence is used to predict crack behavior under various conditions such as mixed-mode loading. Many parameters are used for explaining the crack behavior under various conditions, but those parameters are obtained from destructive testing, in which usually, only one data point is obtained from each test. An artificial problem method requires a large amount of data to train the model to be able to learn crack behavior, which is a disadvantage of applying this method to fracture mechanics. To eliminate the disadvantage of the large amount of experiment data required for modeling, in this study, the small data obtained from the experiment along with data obtained from fracture criteria that were used for elementary prediction of mixed mode fracture toughness were used to create an artificial intelligence model. Data from the experiment was combined with fracture criteria data using the multi-fidelity surrogate model that is described in this study. The mixed mode I/II fracture toughness of the PMMA material was tested in order to primarily propose the data combination technique. After the modeling process, the prediction results indicated that the performance of a model in which the actual test data was combined with the data from the fracture criteria (multi-fidelity surrogate model) was more predictively effective compared to only actual data-based modeling. [ABSTRACT FROM AUTHOR]

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Peridynamics is a recent nonlocal theory of continuum mechanics that is suitable to describe fracture problems in solid mechanics. In this paper, a new failure criterion based on the stress field is developed by adopting the damage correspondence model in the ordinary state-based peridynamic theory. The proposed stress tensor-based failure criterion is capable of predicting more accurately crack propagation in the mixed mode I-II fracture problems different from other failure criteria in peridynamics. The effectiveness of the proposed model is demonstrated by performing several examples of mixed-mode dynamic fracture in brittle materials.

The influence of temperature and strain rate on the deformation behavior of twin-roll casting AZ31 alloy has been examined as a function of stress state using notched and un-notched tensile specimens. Failure behavior during the physical tension was carried out using FEM simulations with different fracture criteria. Using a combined experimental-FEM investigation, the applicability of each fracture criterion was verified to serve the prediction for the crack initiation under multiaxial stress state. Results show that the critical fracture strain presents a clear exponential relationship with stress triaxiality and strain rate, and a linear relationship with temperature. Through the quantitative analysis of the relationship, a mathematical model can be well established. After comparison and verification, the fracture model can accurately predict the forming limit during the plastic deformation of twin-roll casted AZ31 magnesium alloy under complex stress state, and the classical Cockcroft & Latham criterion is the most suitable criterion for predicting the related crack initiation.

• The apparent fracture toughness of sandstone is significantly influenced by the cracked specimen configurations and loading types. • The difference of T-stress for various cracked specimens is the primary factor causing the disparity in apparent fracture toughness. • Positive T-stress can improve the K IC , while negative T-stress will decrease the K IC. The dependence of K IIC on the T-stress is exactly opposite to that of K IC. In order to investigate the impact of cracked specimen configurations on the apparent fracture toughness of the green sandstone, a series of fracture experiments were conducted utilizing four distinct types of specimens. The experimental results show that the cracked straight-through Brazilian disk (CSTBD) specimens observed the minimum mode I fracture toughness K IC and the maximum mode II fracture toughness K IIC. The K IC measured by notched semi-circular bending (NSCB) specimens is nearly twice that of CSTBD specimens, while the K IIC is only 77% of CSTBD specimens. It indicates that both the specimen configurations and loading conditions are significant factors influencing the apparent fracture toughness, which may be attributed to the different T-stress for different specimens. Furthermore, several fracture criteria were employed to evaluate the experimental results. Simultaneously, a theoretical framework based on the generalized maximum tangential strain (GMTSN) criterion was proposed to investigate the impact of T-stress on apparent fracture toughness. The results indicate that positive T-stress can improve the K IC , while negative T-stress can decrease the K IC. In addition, we also found that the dependence of K IIC on T-stress is exactly opposite to that of K IC. The study provides theoretical references for systematically evaluating experimental results and selecting specimens reasonably. [ABSTRACT FROM AUTHOR]

• A statistical treatment is applied to the same 19 specimens originally used for the verification of EN1993-1-10. • A new way to incorporate uncertainty in fracture toughness into the Master Curve is introduced. • Future developments of EN 1993-1-10 can be based on this new statistical treatment. EN 1993-1-10 contains tables for selection of steel quality class with respect to avoidance of brittle fracture. The conservatism of the method has not previously been examined statistically. The original verification of the method has been established basically on a deterministic assessment of 19 double edge cracked specimen tests. This verification has not accounted for e.g. constraint effects and the treatment of nominal data versus measured data is not fully satisfactory. Therefore, here the confidence of the procedure is examined statistically using more up to date information regarding the Charpy-V vs fracture toughness correlation and a quantitative assessment of the constraint effect. The study has two main purposes. First, to present a method by which consistent statistically defined criteria for a standard like EN 1993-1-10 can be developed and second, to obtain an approximate estimate of the conservatism contained in the present methodology. The statistical treatment is applied to the same 19 specimens originally used for the verification of the method. [ABSTRACT FROM AUTHOR]

The study of salt rocks deformation and fracture processes is an essential part of mining parameters justification for mineral salt deposits. The results of uniaxial compression tests on large salt rock specimens are presented as a loading curve and diagrams of the transverse-longitudinal displacements at various distances from the side faces. Based on an isotropic elastoplastic model, a multivariant numerical simulation was performed. Its purpose was to select fracture criteria that accurately describe the loading diagram of specimen and its transverse-longitudinal deformations. The following fracture criteria are considered: Tresca with the associated plastic flow rule, the associated and non-associated Mohr-Coulomb, the parabolic analogue of Mohr-Coulomb criterion and the volumetric fracture criterion. Numerical simulation was carried out by the displacement-based finite element method. Three-dimensional hexahedral eight-node isoparametric elements were used for discretization of the solution domain. It has been established that within the elastoplastic model of media the process of uniaxial compression of a large cubic salt rock specimen is adequately described by the linear Mohr-Coulomb fracture criterion with the non-associated plastic flow, as well as by the associated volumetric parabolic yield criterion with the linear isotropic hardening. [ABSTRACT FROM AUTHOR]

The existing behaviour models of the structures under constant load (creep) have a fairly wide forecast horizon and low accuracy. As a rule, they consider the transition from an undestroyed state of an element to a destroyed one, in one stage. The purpose of this study is to substantiate and develop a new approach to predicting long-term strength based on kinetic equations, which, in turn, should consider the multistage nature of the process of gradual destruction of structure elements. To achieve this purpose, the study solves the tasks of creating a multistage kinetic transition of individual structure elements from an initially elastic state to a viscoelastic state, and then to a fractured state. When describing this process, the authors employed the methods of formal kinetics and the theory of continuum damage mechanics, including the method of basic diagrams. Wood-based composites were used as the materials under study. Based on the results of the conducted full-scale and computational experiments, the study discovers that a mathematical model based on kinetic equations adequately describes the behaviour of the materials under study for long-term strength; the proposed two-stage model determines the forecast horizon much more accurately than the available one-stage models. The kinetic parameters that determine the rate of transition of a structural element from an elastic state to a viscoelastic state, and then to a destroyed state, were determined based on experimental base chart. The time to fracture was determined at three-point bending at a load equal to 70% of the flexural strength at temperatures of 20°C and 60°C, constant humidity RH 65% and moisture content MC 8%. When building control charts, the load increased by another 15%. The method allows narrowing the forecast horizon and determining the moment of transition of a structure from a stationary state to a blow-up regime with a higher accuracy

The study of salt rocks deformation and fracture processes is an essential part of mining parameters justification for mineral salt deposits. The results of uniaxial compression tests on large salt rock specimens are presented as a loading curve and diagrams of the transverse-longitudinal displacements at various distances from the side faces. Based on an isotropic elastoplastic model, a multivariant numerical simulation was performed. Its purpose was to select of fracture criteria that accurately describe the loading diagram of specimen and its transverse-longitudinal deformations. The following fracture criteria are considered: Tresca with the associated plastic flow rule, the associated and non-associated Mohr-Coulomb, the parabolic analogue of Mohr-Coulomb criterion and the volumetric fracture criterion. Numerical simulation was carried out by the displacement-based finite element method. Three-dimensional hexahedral eight-node isoparametric elements were used for discretization of the solution domain. It has been established that within the elastoplastic model of media the process of uniaxial compression of a large cubic salt rock specimen is adequately described by the linear Mohr-Coulomb fracture criterion with the non-associated plastic flow, as well as by the associated volumetric parabolic yield criterion with the linear isotropic hardening.

This paper provides a brief overview of the issues concerning the stress field singularity in a solid with a Griffith crack. A new model of the crack is proposed which takes into account the effect of the plastic deformation zone around the crack on the stress field in the solid. The stress field singularity arises as a special case when the curvature radius at the crack tip and the size of the plastic deformation zone around the crack reduce to zero. The model allows analyzing the influence of plastic strain gradients on the concentration and distribution of stresses at the crack tip. It is shown that the plastic strain gradient at the free surface of the crack is crucial for stress and strain calculations for a solid with a crack. An energy analysis is carried out for the fracture parameters of ductile materials with cracks. The derived equations can be used to evaluate the crack resistance of sufficiently ductile materials. [ABSTRACT FROM AUTHOR]

In a process of sheet drawing technology developing, the probability of workpiece buckling during deformation and the necessity of blank holder using to prevent corrugation, is estimated in accordance with the recommendations of the reference book. However, reference literature does not have clear recommendations, or it gives contradictory recommendations for blank holder use cases for some deformation conditions. In these cases, problem solving requires additional experimental research. Possibility and efficiency establishing of computer simulation using DEFORM environment of axisymmetric drawing processes to forecast the buckling of a thin-sheet workpiece during deformation. Technological processes of sheet drawing with a high probability of workpiece buckling were investigated by means of finite element computer simulation in DEFORM 3D. Research has established that simulation of thin-sheet workpiece drawing process in DEFORM 3D, allows to visualize the process of corrugation, and predict workpiece buckling with high probability, provided that the deformation occurs relatively simple geometry of the workpiece and deforming tool. In more complex deformation conditions, the experiments results, and computer simulation may differ (simulations may not indicate corrugation). This somewhat complicates corrugation prediction, but the problem is solved by an extended analysis of the stress-strain state and workpiece behavior in the deformation zone. The emergence of areas in the workpiece with an unpredictable and uncontrolled contact loss of the workpiece material with the deforming tool, or appearance of areas with significant irregular velocity of workpiece points movement, clearly indicates problem areas with high probability of corrugation in the real sheet drawing process. Obtained results allow to increase the efficiency of expecting places of corrugation appearance prediction by means of computer simulation of sheet drawing process in the DEFORM 3D environment. [ABSTRACT FROM AUTHOR]

Fracture Forming Limit Diagram (FFLD) is gaining special attention for high strength materials like Inconel 718 alloy where the substantial necking tendency rarely seen. The present study mainly aims at accurate evolution of forming limits for Inconel 718 alloy with an improved Marciniak–Kuczynski (M–K) model coupled and various ductile fracture criteria. Firstly, uniaxial test has been performed for analyzing material properties and anisotropic parameters. The stretch forming tests have been conducted to evaluate the limiting forming limits of Inconel 718 alloy. Subsequently, an improved M–K model coupled with ductile fracture criteria has been developed for the theoretical prediction of the fracture strains. The different ductile fracture criteria, namely; Clift, Cockcroft and Latham, Oyane and Brozzo, have been implemented in the improved M–K model. A Newton–Raphson method has been used to solve improved M–K model. The improved M–K model coupled with Oyane's fracture criterion has shown good predictability of the fracture loci with the least average absolute errors and root-mean-square deviation (Δavg = 0.075 and RMSD = 0.105).

• Applicability of generalized fracture criteria on thermally treated rocks. • Rock fracture behaviour in granite and mudstone under thermal effect. • The effect of thermal treatment on fracture process zone (FPZ). • The effect of thermal treatment and loading mode on brittle-ductile transition of fractured rocks. Temperature and thermal damage have a major impact on the behaviour of fractures in the earth's crust. For deep earth engineering such as underground coal gasification, geothermal energy extraction, and nuclear waste repositories, developing fracture criteria governing the propagation of fractures under thermal effect is crucial. As a result, the ability of stress, energy, and strain-based fracture criteria to predict rock fracture behavior both before and after thermal treatment is assessed in this paper considering two rock types; granite, and mudstone, which are very different from one another in terms of their mineralogical composition and mechanical properties. The overall findings showed that the energy-based criterion was more effective in predicting fracture parameters both before and after thermal treatment than the stress and strain-based criteria. Specifically, after thermal treatment at 500 °C for the granite, and at any temperature for the mudstone, the strain-based criterion was no longer valid. It was found that the temperature and loading mode have a significant impact on the granite's transition from brittle to ductile, where this transition can occur at an approximated temperature of 460 °C. Meanwhile, an increase in brittleness with rising temperature was noted in mudstone. Moreover, the Fracture Process Zone (FPZ) size was predicted by the energy-based criterion to be greater than that predicted by stress and strain-based criteria. It was found that the FPZ size is proportional to the brittleness degree of the two rock types, which is considerably impacted by thermal treatment. In addition, this study discusses several critical areas in rock fracture mechanics in the presence of thermal effects including fracture envelopes under mixed mode loading I/II, fracture stress, and initial crack extension angle. All of these are of high importance in assessing the safety and stability of rock structures in the presence of thermal effects. [ABSTRACT FROM AUTHOR]

To select a rational method for cutting of rolled stocks made from materials with different physical and mechanical properties, an engineer must have the tools to make such a choice. In order to find the most informative system of fracture criteria allowing to classify materials authentically by their fracture sensitivity, the software was developed. It allows to solve the clustering problem in a multidimensional space of parameters and present the obtained information in a visual form using self-organizing Kohonen maps. The cluster analysis of the material fracture criteria was carried out. The most informative criterion among the ones characterizing the mechanical properties of steels is the «offset yield strength», among the synergistic ones – «scale criterion». At the same time, among the traditional mechanical features of steels, a set allowing to classify materials with a given integrity by their cutting sensitivity has not been found. It was established that the fracture criteria: «crack growth criterion» and «brittleness criterion» are basic informative features. When adding any of the remaining complex criteria («crack nucleation criterion» or «scale criterion»), they form the most informative sets of minimal power, providing the classification of materials by their cutting sensitivity with a given integrity. In order to obtain high-quality workpieces at a minimum conversion cost, recommendations were developed for choice of the method for cutting of rolled stocks in magnitude of criteria values: «crack growth criterion» and «brittleness criterion». To cut materials «in plastic state», the cutting by shear should be used, specifically—a closed cutoff scheme or an incompletely closed cutoff scheme with an active transverse clamp or a cutoff scheme with a differentiated clamp of rolled stocks. If increased requirements are imposed on the geometric accuracy of the workpieces, it is recommended to use complex blanking and cutting processes. For cutting materials «in elastoplastic state» there are good reasons to use the cutting by shear, and in particular—an incompletely closed cutoff scheme with an active and passive transverse clamp. Closer to the class interval, it is possible to apply breaking by bending with the application of an effective stress concentrator. Breaking by bending should be used to cut «brittle» materials. The carried out experiments confirmed the adequacy of theoretical conclusions and recommendations on the choice of a rational method for cutting of the rolled stocks to obtain high-quality workpieces. [ABSTRACT FROM AUTHOR]

Peridynamics is a recent nonlocal theory of continuum mechanics that is suitable to describe fracture problems in solid mechanics. In this paper, a new failure criterion based on the stress field is developed by adopting the damage correspondence model in the ordinary state-based peridynamic theory. The proposed stress tensor-based failure criterion is capable of predicting more accurately crack propagation in the mixed mode I-II fracture problems different from other failure criteria in peridynamics. The effectiveness of the proposed model is demonstrated by performing several examples of mixed-mode dynamic fracture in brittle materials. [ABSTRACT FROM AUTHOR]

Today, artificial intelligence plays a huge role in the mechanical engineering field for solving many complex problems and the problem with fracture mechanics is one of them. In fracture mechanics, artificial intelligence is used to predict crack behavior under various conditions such as mixed-mode loading. Many parameters are used for explaining the crack behavior under various conditions, but those parameters are obtained from destructive testing, in which usually, only one data point is obtained from each test. An artificial problem method requires a large amount of data to train the model to be able to learn crack behavior, which is a disadvantage of applying this method to fracture mechanics. To eliminate the disadvantage of the large amount of experiment data required for modeling, in this study, the small data obtained from the experiment along with data obtained from fracture criteria that were used for elementary prediction of mixed mode fracture toughness were used to create an artificial intelligence model. Data from the experiment was combined with fracture criteria data using the multi-fidelity surrogate model that is described in this study. The mixed mode I/II fracture toughness of the PMMA material was tested in order to primarily propose the data combination technique. After the modeling process, the prediction results indicated that the performance of a model in which the actual test data was combined with the data from the fracture criteria (multi-fidelity surrogate model) was more predictively effective compared to only actual data-based modeling.

Combining Gleeble hot compression and tensile tests with finite‐element (FE) simulations, this study delivers a robust assessment of the elevated temperature damage and cracking of AISI 410 martensitic stainless steel. The effects of hot deformation parameters on the macroscopic flow and deformation behaviors as well as microscopic damage and fracture characteristics are discussed, determining the critical damage values with the aid of FE calculations. Furthermore, a novel critical damage value model is proposed using the Zener–Hollomon parameter to establish the normalized Oyane fracture criterion coupling hot deformation parameters. The results reveal that the flow stress and tensile load both increase, as the strain rate increases and the temperature decreases and vice versa. The occurrence of localized necking and internal damage cracking causes the tensile load to decline drastically. The hot deformation parameters manipulate not only the plat and dimple fractures, each caused by intergranular and transgranular fractures, but also the internal damage cracking before the final fracture. The established criterion predicts outcomes in good agreement with experimental results. This work provides essential information and a model for the cracking prediction of AISI 410 steel at elevated temperatures, helping to derive a rational hot forming design to prevent cracking. [ABSTRACT FROM AUTHOR]

[Display omitted] • The basalt fiber and gelling effects on mode I/III fracture of mortar were assessed. • The fracture performance is enhanced mainly due to the fiber crack-bridging effect. • The 3D-MTSN criterion is suitable for forecasting mode I/III fracture toughness. The study of the crack resistance of modified cement-based materials can provide a valuable guidance for pavement structural design. In this work, the plain mortars with 3 different water/cement ratios (0.35, 0.45 and 0.55) and the basalt fiber (BF) reinforced mortars with 3 different amounts of basalt fibers (0 %, 0.3 % and 0.8 % by mass) were prepared to investigate mixed mode I/III fracture performance. In the BF reinforced groups, we take the water/cement ratio of 0.45 as a reference. Then, the fracture experiments were conducted using the Edge Notch Disc Bend (ENDB) testing, and the pore structure measurements of each sample were performed using the nuclear magnetic resonance (NMR) testing system. The results show that an appropriate reduction in water/cement ratio and an increase proportion of basalt fibers are both beneficial to improving the fracture performance of the cement mixtures. However, a superior fracture performance was achieved for BF reinforced mortar composites over the mortar with gelling enhancement. For instance, the enhancement rate of applied load, fracture energy, and effective fracture toughness for BF reinforced mortar under mode III are 3.27, 2.35, and 1.34 times the values of those for gelling-enhanced mortar under mode III, respectively. We also find that the three dimensional maximum tangential strain (3D-MTSN) criterion is applicable for predicting mixed mode I/III stress intensity factor (SIFs) of mortar composites. The reduction in water/cement ratio significantly increases the amount of micropores inside the mortar specimen. By contrast, the addition of basalt fibers to the cement mixture deteriorates its pore structure by raising the proportion of macropores to total pores from 3 % to 10 %. However, the basalt fiber crack-bridging effect on improving the fracture toughness of the cement mixtures is also revealed. [ABSTRACT FROM AUTHOR]

• The mode-I fracture toughness of Longmaxi shale for different testing methods is evaluated. • The fracture criteria are employed to interpret and predict the variation in mode-I fracture resistance. • The acoustic emission technique is applied to identify the fracture mechanisms of distinct mode-I test specimens. Abundant shale gas in shale reservoirs can be successfully extracted by the fracking technique. The formation of hydraulic fractures is related to the mode-I fracture toughness that represents the resistance to cracking propagation. Two typical Longmaxi shale samples with horizontal and vertical bedding planes are selected in this work. To adequately measure the mode-I fracture resistance of shale, this research adopts four mode-I test specimens with different geometries (cuboid, cylinder, disk, and semi-disk). The experimental results demonstrate that there is an acceptable linear correlation between mode-I fracture resistance and critical T -stress. Further, the discrepancies in mode-I fracture resistance are due to distinct T -stresses that exist in the mode-I test specimens. Consequently, the mode-I fracture toughness K Ic for the shale with horizontal bedding is 1.57 MPa·m0.5, while that for the shale with vertical bedding is 1.36 MPa·m0.5. Considering the influences of singular and non-singular stress terms, the GMTSN (generalized maximum tangential strain) and GMTSEDF (generalized maximum tangential strain energy density factor) fracture criteria can provide theoretical explanations for the variation of mode-I fracture resistance measurements. Based on the AE (acoustic emission) technique, the classical RA - AF method can identify the fracture mechanisms of distinct mode-I test specimens. However, the differences in the high-density zones of the RA - AF distribution are conspicuous for distinct mode-I testing methods. [ABSTRACT FROM AUTHOR]

I-II mixed mode fracture is a common fracture pattern of asphalt pavement under the coupled tension and shearing loads. To address the roles of reclaimed asphalt pavement (RAP) and loading effect, this study proposed a novel test method to characterize the I-II mixed fracture toughness of two types of asphalt mixture. Within the novel tensile test, direct tension load could be applied on the bottom of the notched semi-circular specimens at −10 °C. I-II mixed fracture could be generated by varying the notch angle. Fracture parameters, including the stress intensity factors of mode I and mode II fracture (K I C and K I I C) and the T stress were obtained for specimens with five notch angles, including 0 ∘ , 15 ∘ , 30 ∘ , 45 ∘ and 60 ∘ , respectively. Results indicated that from 0 ∘ to 30 ∘ , pure mode I to pure mode II fracture could be generated. Under the same loading rate, compared to mixture A, mixture B presented superior fracture toughness in terms of mode I and mode II stress intensity factors (K I and K I I), which was attributed to the fact that the inclusion of RAP in mixture A deteriorated the fracture resistance. Loading rate played positive effect on the fracture toughness. From 1 mm/min to 5 mm/min, the improvements of K I C were 52% and 33% for mixture A and B, respectively. For K I I C , the increase of loading rate enhanced the pure mode II fracture resistance by 30% and 20% for mixture A and B, respectively. Several fracture criteria were adopted for the fracture prediction. Comparison was performed between the test data and the predictions. It was found that compared to MTS criterion, the inclusion of T stress in GMTS criterion made the prediction closer to the test data. Compared to GMTS and GEMTS criteria, GEMTS criterion could provide better estimates for I-II mixed mode, indicating considering the effect of fracture mode on the critical distance (r c) could make the prediction with a higher reliability. • A novel test method was proposed to measure the I-II mixed mode fracture performance. • Effects of loading rate and RAP on fracture behaviors of asphalt mixture were investigated. • Predictions based on MTS, GMTS and GEMTS criteria were carried out. [ABSTRACT FROM AUTHOR]

When studying mechanical behavior of structures made of laminated polymer composite materials, issues related to their relatively high susceptibility to damage, such as delamination, fiber breakage and matrix failure, play significant role. Key aspects are also related to accurate description of the internal structures and heterogeneity of the material. This work is aimed at a numerical study of the processes of damage accumulation in plies as well as development of delamination in laminated polymer composite L-shaped specimen taking into account microstructural parameters. The influence of contact conditions between the plies on the model�s behavior has been studied. It was established that the delamination processes inside the specimen can initiate at the early stages of deformation, which is reflected in the difference of the results obtained using models with various numbers of separated plies. Comparison of the results of modelled elastic behavior of the specimen and models with the developed delamination leads to conclusions about influence of a number of model parameters on the results obtained before and after propagation of delamination. In particular, such factors as the geometry and mechanical properties of models, the number and conditions for specifying contact pairs in the model were analyzed.

This paper reports the results of acoustic parameter measurements in a deformed material with simultaneous recording of autowave patterns of localized plastic deformation for steels of various compositions. It discusses the possibility of using an autowave model for the derivation of structural strength criteria of materials. It was shown that the time and place of future fracture in steel specimens can be predicted from the kinetic dependences of localized deformation sites at the prefracture stage long before visible necking. It was found that the ultrasonic velocity vs. strain curve has a kink in the elastic–plastic transition in low-carbon steels. This kink may serve as an acoustic criterion for the onset of irreversible deformation in metal forming and non-destructive testing of components and structures. [ABSTRACT FROM AUTHOR]

A micropolar peridynamic model is presented for characterizing crack propagation in isotropic and orthotropic brittle materials. The analytical formulation of the two-dimensional model is based on the definition of a micropotential energy function that accounts for the four independent elastic constants that define orthotropy and that in the limit can be reduced to isotropy. A distinctive feature of the model is that the bonds' elastic parameters are continuous functions of orientation with respect to principal material axes. By defining three deformation parameters that quantify bond stretch, bond shear deformation and particles relative rotation, the first continuum bond-based peridynamic model is obtained for two-dimensional Cauchy orthotropic materials characterized by four independent material moduli that is suitable for describing fracture as well as homogeneous and non-homogeneous deformations. The accuracy of the computational model as applied to crack-tip analyses is assessed by comparing the displacement and stress fields within the boundary layer that develops in the immediate vicinity of a crack with the analytical asymptotic results for an orthotropic continuum. The extension of such cracks when they are subjected to mixed-mode loading is simulated under the assumption of illustrative crack extension criteria, and the predictions are compared to those of the maximum hoop stress intensity factor criterion (HSIF-criterion) and the maximum energy release rate criterion (G-criterion). [ABSTRACT FROM AUTHOR]

It is shown that a multiparameter system of strength, resource, survivability, and safety assessment applies to measuring parameters such as the static, dynamic, and cyclical strength, cracking resistance, cold resistance, and corrosion resistance. The laws of straining and fracture are used, and the general statement and solutions of basic and applied strength, resource, survivability, and safety problems are considered in building structures of the defining equations and their parameters for design models and actual engineering systems, taking into account standard, emergency, and catastrophic situations as well as the accumulated process and operational failure rate. The fundamental elements of ensuring safe operation of engineering and process facilities loaded in complex modes are the equations of state, fracture criteria, and the criterial base of the science of structural materials. Taken together, these elements form a multiparameter system of strength, resource, survivability, and safety assessment. [ABSTRACT FROM AUTHOR]

This work is devoted to research and development of models for the processes of nucleation and growth of delamination in laminated composite materials. Possibilities of fracture mechanics approaches using virtual crack closure technique as well as progressive failure analysis based on the failure criteria are demonstrated. Influence of the initial delamination size on the rate of growth of the defect is studied. A comparative analysis of the applicability of fracture criteria to modeling of samples with delamination were performed, including implementation of element deletion algorithm. The numerical results obtained with the studied methods were compared.

We study the effects realistic fracture criteria have on crack morphology obtained in numerical simulations with a stochastic discrete element method. Results are obtained with two criteria which are consistent with the theory of elasticity and compared with previous results using the original criterion, chosen when the method was first published. The conventional choice has been to consider the combined loading as an interaction between bending and tensile forces only, leaving out shear forces altogether. Moreover the combination of bending and tension used in the old criterion is correct only for plastic deformations. Our results show that the inclusion of shear forces have a profound effect on crack morphology. We consider two types of external loading, torsion applied to a circular cylinder and tension applied to a cube. In the tensile case, the exponent which characterizes scaling of crack roughness with system size is found to be very close to the experimental value ζ ~ 0.5 when realistic fracture criteria are used. In the present calculations we obtain ζ = 0.52, a value which remains constant for all disorders. It is proposed that the small-scale exponent ζ = 0.8 appears as a consequence of cleavage between crystal planes and consequently requires a different fracture criterion than that which is used on larger scales.

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does, however, not always agree with the established failure criteria of fracture mechanics. In this work different variational formulations for linear and finite elastic materials are discussed and ad-hoc driving forces are presented which are motivated by general fracture mechanical considerations. The superiority of the generalized approach is demonstrated by a series of numerical examples. • Discussion of various variational formulations in linear and finite elasticity. • Introduction of failure criteria based on physically motivated driving forces. • Investigation on the influences of the various parameters through parametric studies. • Numerical simulations of real-world problems by applying different failure criteria. • Demonstration of the superiority of the driving forces derived from fracture mechanics. [ABSTRACT FROM AUTHOR]

When studying mechanical behavior of structures made of laminated polymer composite materials, issues related to their relatively high susceptibility to damage, such as delamination, fiber breakage and matrix failure, play significant role. Key aspects are also related to accurate description of the internal structures and heterogeneity of the material. This work is aimed at a numerical study of the processes of damage accumulation in plies as well as development of delamination in laminated polymer composite L-shaped specimen taking into account microstructural parameters. The influence of contact conditions between the plies on the model's behavior has been studied. It was established that the delamination processes inside the specimen can initiate at the early stages of deformation, which is reflected in the difference of the results obtained using models with various numbers of separated plies. Comparison of the results of modelled elastic behavior of the specimen and models with the developed delamination leads to conclusions about influence of a number of model parameters on the results obtained before and after propagation of delamination. In particular, such factors as the geometry and mechanical properties of models, the number and conditions for specifying contact pairs in the model were analyzed. [ABSTRACT FROM AUTHOR]

Abstract The deformation and fracture behaviors of as-cast AZ31B Mg alloy were studied by uniaxial compression experiments and finite element simulations with wide ranges of temperature and strain rate. The strain-rate and temperature sensitivities of flow stress, fracture morphology, critical strain to fracture, fracture criteria and related mechanism were discussed. Results show that the observed sharp in stress caused by micro-cracks initiation and propagation can be readily produced at relatively low temperatures and high strain rates. Shear deformation bands are easily formed along the shear direction under uniaxial compression, which are the main reasons for approximately 45° shear cracking during the compression, and the presence of spheroidal precipitates makes a great contribution to the formation of crossed shear cracks. There exists a strong correlation between the fracture mode and power dissipation efficiency, i.e., the crossed and parallel shear cracking can significantly reduce the efficiency. Freudenthal fracture criterion is applicable to hot forming of AZ31B alloy due to its accurate prediction of the cracking initiation and fracture position under uniaxial compression. The critical cracking strain and further the critical damage value of Freudenthal criterion can be successfully achieved by combining the high-speed photography and numerical simulation. The present mathematical analysis indicates that a linear relationship exists not only between the critical cracking strain and Ln(Zener-Hollomon parameter, Z) but also between the critical damage and Ln Z. In response to high strain-rate and temperature sensitivities of AZ31B alloy, the Freudenthal fracture criterion should be optimized. Highlights • Strain-rate and temperature sensitivities of flow stress, fracture modes and related mechanism were revealed. • Surface cracking process was successfully tracked using high speed photography. • Critical cracking state in high-speed compression was achieved. • A fracture criterion applicable to the prediction of cracking in AZ31B was defined. [ABSTRACT FROM AUTHOR]

From experimental and theoretical investigations it is known that cracks are sensitive to geometry, e.g., to the inclination angle to the load. A small deviation of a crack from the normal direction to a tensile load causes mixed mode conditions near the crack tip which lead to deviation of the crack from its initial propagation direction. Besides, the presence of other cracks, inhomogeneities, surfaces and their interaction causes additional deformations and stresses which also have influence on the initiation of the crack propagation and on the direction of this propagation. The aim of this paper is to show the effects of the interaction of edge cracks on further crack formation. The main fracture characteristics, such as, stress intensity factors, fracture angles and critical loads are provided in this study. A series of illustrative examples is presented for different geometries of arbitrarily inclined edge cracks.

In this study, experimental and numerical results of compact tension shear (CTS) specimen and a new specimen type under in-plane mixed mode (Mode-I/II) loading conditions are compared with existing inplane mixed mode fracture criteria to investigate and understand the nature of fracture behavior properly. The material used in numerical and experimental analyses is Al 7075-T651 aluminum machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction). In Part 1 of the study, results from numerical and experimental analyses are given. Having computed the mixed mode stress intensity factors from the numerical analyses, fracture loads are predicted and compared with different mixed mode-I/II fracture criteria. The experimental and numerical results show that many criteria are in good agreement with each other for predominately mode I to moderate mixed mode conditions. However, existing criteria increasingly differ from the experimental measurements for highly mode-II conditions. Using the computational and experimental results obtained, improved empirical mixed mode I/II fracture criteria for fracture condition and angle are also proposed.

In age-hardened high-strength aluminum alloys, the area with and around a joint has a large impact on the load-bearing capacity of a welded structure. Therefore, in this study the fracture behavior of welded EN AW 6082 T6 plates is investigated experimentally and numerically. From butt joints, smooth and notched tensile specimens as well as shear specimens have been manufactured and tested for the base material (BM), heat-affected zone (HAZ) and fusion zone (FZ). With numerical simulations of these tests, the dependency of the fracture strain on the stress triaxiality is determined, and two phenomenological fracture criteria are calibrated. Whereas the one-parameter Rice–Tracey/Cockcroft–Latham (RTCL) criterion describes the behavior of the tension specimens as accurately as the two-parameter Bao–Wierzbicki (BW) criterion, the BW criterion is more accurate for shear tests. Subsequently, the material model is validated on axial compression tests of welded X-profiles. The experiments comprise tests with different plate thicknesses (8 mm, 10 mm and 12 mm) and varying strain rates (up to 1/s locally), showing the same behavior for all specimens. After crack initiation within the FZ, coalescence of cracks leads to crack growth in axial direction and a subsequent reduction of the load-bearing capacity. This behavior is reproduced well by the numerical simulations with the BW criterion, whereas simulations with the RTCL criterion predict fracture initiation at too high displacements. Overall, the results show the strong influence of the ductility of the FZ on the crushing behavior of welded X-profiles.

Fracture toughness of anisotropic rocks can vary with many factors such as geological anisotropy, geometrical properties of specimens used in the laboratory (e.g., pre-existing crack properties), and loading conditions. This fact has been widely acknowledged. Yet the variation in fracture toughness remains enigmatic, as there is still lack of a comprehensive study on how those influential factors affect fracture toughness behavior of anisotropic rocks. The present paper shows a broad-spectrum mixed-mode fracture toughness of an anisotropic sandstone from a numerical scheme, which is based on the Discrete Element Method (DEM). In this study, a total of 340 semi-circular bend (SCB) specimens with various geological and geometrical conditions were numerically prepared by systemically varying the orientations of planar anisotropy (i.e. incipient bedding plane), as well as the magnitudes of the ISRM-suggested geometrical parameters of the SCB specimens (i.e. crack length, crack angle, and span length). The numerical model used in the study was calibrated against a series of laboratory experiments to select proper micro-parameters to reproduce the mechanical characteristics of anisotropic Midgley Grit sandstone (MGS). Additionally, four different fracture criteria, which are based on stress and strain analysis, and the analysis of energy density, were used to predict the mixed-mode fracture behaviour of MGS. Numerical findings from this study were compared with experimental observations (qualitatively) and theoretical predictions (quantitatively). A broad agreement was observed in the comparison study. [ABSTRACT FROM AUTHOR]