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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]

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 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 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]

• 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.

[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]

This paper presents for the first time an approach to the problem of electromechanical fracture and crack propagation in piezoelectric solids with peridynamics. Fracture in piezoelectric ceramics is an important problem in engineering due to its complexity. The majority of the computational models available on the literature rely on sharp crack representations, which have difficulties dealing with complex crack patterns, or rely on diffusive crack models, such as the phase-field fracture model, that can predict complex patterns but does not represent cracks in a discrete way. On the other hand, peridynamics has been designed to solve this problems and is able to simulate discrete cracks as well as complex crack phenomena like fragmentation and branching. We present a novel approach to the implementation of different electric crack face boundary conditions in a peridynamic way, by a field selective bond breaking approach. Moreover, it is also presented the first electromechanical failure criterion for fracture in piezoelectric ceramics. We develop an energy based failure criterion due to its generality and wide range of applications. These approaches are presented in a way such that they are valid for any type of peridynamic formulation. The used numerical model is implemented using correspondence-based peridynamics with the linear piezoelectricity constitutive setting, using a meshfree discretization and solved quasi-statically with an implicit incremental-iterative scheme. Numerical examples are presented to demonstrate the capabilities of these new approaches and assess the performance of the model against experimental results. The model is capable of numerically predicting complicated fracture behaviour and crack propagation in an intrinsic/autonomous way, as demonstrated by the results. [ABSTRACT FROM AUTHOR]

[Display omitted] • The artificial intelligence prediction model from the different modeling techniques of mixed mode I-II fracture toughness of sugarcane leaves/epoxy was investigated. • When determining whether a material will break or not, the GMTS fracture criteria are a very reliable indicator. • The single-fidelity AI model, which was modeled solely from experiment data, produced a prediction that was rather inaccuracy. • The multi-fidelity AI model, which was modeled using a technique that combined experimental data and GMTS criteria data, exhibits high prediction performance and is suitable in cases where there is a small amount of experimental data. Artificial intelligence plays a huge role in solving engineering problems. In the fracture mechanics field, artificial intelligence is used to predict fracture behavior or parameters, based on testing data, which is a destructive type of testing, so it is difficult to get a large amount of data for the learning modeling process. Therefore, this study presents artificial intelligence modeling to predict the fracture toughness by reducing the use of the actual testing fracture toughness data, while replacing the data with a sufficient quantity of data by fracture toughness prediction from the fracture criterion, for which artificial intelligence was modeled by the concept called the "multi-fidelity model". The concept of the modeling begins with calculating and predicting the difference between the actual data set and the criterion data set, then combining the data sets, which is the data from the criterion performed mathematically with the data from the above difference prediction to the actual data set to create a model based on the increased data volume of combining the two data sets. In this study, the mixed-mode I-II fracture toughness of sugarcane leaves/epoxy composite with different mixing conditions was performed on an inclined crack specimen via the three-point bending test configuration used as the actual data set, while the generalized maximum tangential stress criterion (GMTS), which is preliminary fracture toughness, was used as criterion data. The multi-fidelity model is proposed via different artificial intelligence algorithms, namely the general regression neural network (GRNN) and the adaptive neuro-fuzzy inference system (ANFIS). Once the modeling process was complete, the performance metrics showed a clear increase in the efficiency of multi-fidelity models compared to the original artificial intelligence models. [ABSTRACT FROM AUTHOR]

• The combined-mode I + III fracturing characteristics of shale is investigated. • The 3D-MSED criterion is developed. • The developed 3D-MSED criterion can predict the combined mode I + III fracture toughness envelope. The combined mode I + III fracture toughness of shale plays a significant role in the exploitation of shale gas. To investigate the combined mode I + III fracture characteristics of shale, the ENDB (edge-notched disk bending) fracture experiments with AE (acoustic emission) monitoring are implemented to accomplish the full range of fractures from pure mode I (tension) to pure mode III (tearing). By considering the contribution of the mean strain energy to the onset of fracturing, this work develops the 3D-MSED (mean strain energy density) criterion. The measured results indicate that the fracturing energy of the ENDB shale increases linearly with the move from pure tension to pure tearing, while the effective fracture toughness for the ENDB shale decreases linearly. In comparison with the published 3D fracture criteria, the developed 3D-MSED criterion can predict an excellent combined mode I + III fracture toughness envelope for the ENDB shale. Interestingly, the Gaussian function can adequately describe the distribution of AE amplitudes, and the distribution discrepancy in AE amplitudes is insignificant for the ENDB shale specimens under different loading types. However, the percentage of the AE high dominant frequency for the tearing-dominated loading case is relatively greater than that of the tension-dominated loading case, and the tearing-dominated fracturing response is characterized by the nonplanar shear deformation. [ABSTRACT FROM AUTHOR]

• The fracture toughness (K Ic , K I + II , and K IIc) for the CCBD bedded shale are investigated using the AE technique. • The fracture criteria (MTS, MTSN, and MTSEDF) are applied to predict the fracture toughness. • The proposed k-means clustering method succeeds in identifying the specific fracture modes for the CCBD bedded shale. To investigate the fracture toughness including pure mode I, combined mode I + II, and pure mode II, the CCBD (centrally cracked Brazilian disk) fracture experiments with acoustic emission (AE) detecting are conducted on the shale specimens with distinct bedded inclination angles (0°, 30°, 60°, and 90°), and this research first introduces the detailed derivations on the three dominating fracture criteria. The investigated results demonstrate that the fracture resistances for the tested CCBD shale are insensitive to the bedded direction and the anisotropy of the fracture toughness is regarded as relatively weak, which is reflected in the smoother and more regular rupturing paths. The improved criteria (GMTS, GMTSN, and GMTSEDF) can provide a reasonable agreement with the measured data by considering the variable damaged radius of microcracking zone. The proposed k-means clustering method succeeds in identifying the specific fracture modes for the tested CCBD bedded shale in conjunction with the KDE (kernel density estimation) method, whereas the conventional AE parameter (RA and AF) method fails to analyze the fracture mechanisms. [ABSTRACT FROM AUTHOR]

• Mixed mode I-II fracture criteria in LEFM and their applications are systematically reviewed and discussed. • Suggestions are given to select appropriate criteria according to crack types and failure characteristics. • T -stresses greatly affect the crack propagation behavior and they should be introduced into the fracture criteria. Fracture criteria play a very important role in predicting crack propagation behavior and life evaluation of cracked bodies. In this paper, mixed mode I-II fracture criteria in the framework of linear elastic fracture mechanics and their applications in brittle or quasi-brittle fracture analysis are systematically reviewed. Meanwhile, the advantages and shortcomings of these criteria are briefly discussed. Furthermore, the effects of T -stresses on brittle fracture characteristics are also studied and some suggestions are given to select appropriate fracture criteria. The results show that different types of fracture criteria differ greatly in predicting the crack propagation behavior, and a suitable criterion can be chosen according to the crack types, loading modes and failure characteristics. Tension-based fracture criteria are applicable for the opening cracks under tensile-based failure, but not for the closed cracks under shear-based failure. T -stresses around the crack tip have significant effects on crack initiation angle, fracture resistance and crack tip plastic zone, which should be introduced into the classical fracture criteria only determined by singular terms for providing more accurate predictions. Moreover, the variable fracture process zone radius can be further considered in these modified criteria considering stress intensity factors and T -stresses, which are not only suitable for brittle materials, but also for plastic materials under small scale yielding. This review will contribute to the development of mixed mode fracture criteria. [ABSTRACT FROM AUTHOR]

• A new test configuration consisting of SECC specimen and J-fixture is proposed for conducting mixed mode (I/III) fracture experiments. • Setup can be used under static and fatigue loads, and both the metallic and non-metallic specimens can be used. • Experimental results agree well with the predictions made by the mixed mode (I/III) fracture criteria. • Finite element analyses and experimental results show that the testing setup is suitable for mixed mode (I/III) fracture studies. • Mixed mode (I/III) fatigue experiments with the proposed setup have also been presented. In the present work, mixed mode (I/III) fracture studies have been investigated using a new specimen and an out-of-plane loading fixture that can be used with the conventional uniaxial universal testing machines. The proposed specimen is a single edge cracked circular (SECC) specimen which can be employed on both metallic and non-metallic materials under static and fatigue loads. A large number of three-dimensional finite element analyses have been performed on the proposed specimen setup to demonstrate the efficacy of the proposed setup. Experimental fracture studies have also been performed under mixed mode (I/III) loading conditions. The present experimental results are in very good agreement with the available mixed mode (I/III) fracture criteria. Experimental results indicate that the pure mode III fracture toughness is nearly 1.46 times greater than that of the mode I. This has been found due to an increase in the inelastic region around the crack tip in pure mode III and is in accordance with the published results. Detailed analyses of the fractured surfaces have also been carried out. It has been demonstrated that the fractured surfaces become more rough as the mode III component increases. Preliminary results of mixed mode (I/III) fatigue crack growth studies on Al 7075-T6 using the metallic SECC specimen have also been presented. The results of the present study confirm that the proposed specimen setup can be used to study the mixed mode fracture behavior of linear elastic materials under static and fatigue loading. [Display omitted] [ABSTRACT FROM AUTHOR]

• Mixed-mode I/II fracture properties were investigated for SLS Polyamide using SCB specimen. • The fracture toughness value was decreased by increasing the contribution of mode II component. • The crack path for the 3D-printed SCB specimens are numerically and experimentally obtained. • Interlayer-to-intralayer fracture transition is observed in Laser-Sintered Polyamide specimens. • Brittle Gmax and ESIF failure criteria can predict 3D-printed specimen's fracture properties. Additive manufacturing (AM) is a topical field today and has received the attention of many researchers. However, further research is needed to overcome the many challenges facing AM, especially in the mixed-mode fracture. The results presented in this paper are framing the experimental data obtained for mixed-mode I/II fracture properties of laser sintered polyamide. The experiment was carried out on Semi-Circular Bend (SCB) specimens manufactured from polyamide PA2200 using EOS Formiga P100 laser sintering machine. To achieve the full range of fracture toughness values, from pure mode I to pure mode II, five crack orientations of the SCB specimens (0, 15, 30, 45 and 54°) were considered. Further, crack initiation angle and crack paths of SCB specimens have been assessed in order to identify the fracture phenomena (interlayer and/or intralayer fracture). The main fracture properties (fracture toughness, crack initiation angles and crack paths) were compared with the theoretical predictions of three mixed-mode fracture criteria (Maximum Tensile Stress-MTS, Maximum Energy Release Rate-Gmax and Equivalent Stress Intensity Factor-ESIF). The results underline differences between theoretical approaches and experimental data, especially due to the interlayer fracture phenomenon. However, it was obtained that the Gmax and ESIF criteria show the best match with the experimental data. [ABSTRACT FROM AUTHOR]

Phase field approaches have been developed to analyze the failure behavior of ductile materials. In the previous phase field models, a constant critical energy or strain threshold is commonly introduced to the formulation of the driving force, aiming to avoid damage initiation at a low level of elastic and plastic deformations. However, it may not suffice to describe complex ductile fracture behavior of materials subject to various stress states. In this study, a new phase field approach is proposed to consider the effects of stress triaxiality and Lode angle, by incorporating phenomenological ductile fracture criteria. The proposed models are formulated using variational principles and implemented numerically in the finite element framework. Analytical homogeneous solutions for uniaxial tension, simple shear, and equibiaxial tension loads are derived to demonstrate the effectiveness of the proposed models. Three groups of numerical examples, covering a wide range of stress states, are utilized to further examine the proposed models. The results show that the models can reproduce the experimental response of the specimen in terms of force versus displacement curve, crack initiation, and crack propagation under various loading conditions. The proposed models are able to capture the stress-state dependence of fracture behavior of ductile materials. • A new phase field model is proposed to predict ductile fracture behavior. • Stress state dependent damage thresholds are introduced via the MMC criterion. • Analytical solutions demonstrate the effectiveness of the proposed models. • Crack initiation and propagation can be reproduced in various benchmark examples. • The proposed models can capture the stress-state dependence of ductile fracture. [ABSTRACT FROM AUTHOR]

• Synchrotron radiation experiments were used to characterize the void evolution with strain. • Voids develop along the grain boundaries of Cu layer in the interface layer. • A newly developed damage model was constructed based on the GTN-Thomason and M-K models considering size effect individually. • The developed model takes into account the combined effects of interfacial void evolution and surface roughening affected by size effect. • The developed model can predict the variation of FLCs affected by size effect and was validated by experiments. Lack of systematic researches on mesoscaled deformation and damage criteria would obstruct the development of optimal microforming of clad foils. In this paper, a newly developed damage model, inspired by fracture mechanism, was developed to determine the forming limit of Cu/Ni clad foils via considering size effect and its influences on deformation and fracture behavior. The newly developed model integrates the interface separation model based on GTN-Thomason model and the Marciniak-Kuczynski (M-K) model to represent the two stages of ultimate strain before instability in the fracture process of Cu/Ni clad foils. In addition, the former model describes the first-stage strain of the interface separation dominated by void evolution; while the latter one models the second-stage strain of the localized instability of clad foils at interface separation locations via introducing the effects of surface roughness and interface separation on thickness. The results of the synchrotron radiation experiments indicate that void nucleation, growth and coalescence occurring in the interface layer are mainly located in the Cu layer grain boundary region. The localized high density of the nucleated voids is the direct cause of the localized instability. The results of surface roughness experiments demonstrate that surface roughness increases rapidly with strain and saturates at a low strain condition. The surface roughening becomes severe with the increase of grain size. The experimental results of the forming limit show that forming limit curves (FLCs) shift down and strain concentration occurs prematurely with the increasing grain size. The FLCs of Cu/Ni clad foils influenced by grain size are predicted by the newly developed model successfully. This study reveals the interfacial void evolution and surface roughening behavior and their influences on the forming limit of clad foils, in such a way to provide a theoretical basis for microforming of clad foils. [ABSTRACT FROM AUTHOR]

[Display omitted] This paper investigates the effect of loading rate on the mixed-mode I/II fracture behavior of PolymethylMethacrylate (PMMA). Experimental studies are performed using a novel fracture test specimen which has recently been developed, called short bend beam (SBB), in different loading rates of 1 mm/min, 20 mm/min, and 200 mm/min. Fracture test data are presented for pure mode I, pure mode II, and mixed-mode I/II conditions, thanks to the geometrical configuration offered by the specimen covering a full spectrum of mode mixities. Two fracture criteria including maximum tangential stress (MTS), and generalized maximum tangential stress (GMTS) are employed to predict the onset of fracture and the fracture initiation angle in different loading rates. The MTS criterion only considers the singular crack tip terms associated with the stress intensity factors (SIFs) in the solution while the GMTS includes the T -stress effect as well as the SIF-related terms. While enhanced predictions provided by the GMTS criterion, as compared to MTS results, reveals the significance of including the T -stress term in the theoretical calculations, the critical distance (r c) is also found as another major parameter playing an important role in the fracture behavior. It is shown that the size of r c decreases by increasing the loading rate. Therefore, for the first time, a variable and loading rate dependent r c value is utilized for employment of the GMTS criterion and it is demonstrated that considering variable critical distance can provide acceptable theoretical predictions for different loading rates. [ABSTRACT FROM AUTHOR]