Maximum Tangential Stress Criterion Research Articles

Mixed mode I/II fracture behavior of CSTBD sandstone specimen under different loading angles

Cracks are often exposed to mixed mode I/II loading because of the random direction of crack relative to the external load, causing rock failure in rock engineering. However, many mixed mode I/II fracture properties of rock with different loading angles (β) are still poorly understood. To investigate the influence of β on mixed mode I/II fracture behavior, cracked straight through Brazilian disc tests were performed on sandstone under various β at the loading rate of 0.2 kN/s. The results show that the effect of β on the peak load and crack propagation velocity is slight. The mode I stress intensity factor (SIF) decreases from positive to negative with increasing β, while mode II SIF first increases and then decreases as β exceeds approximately 30°. The mixed mode I/II fracture toughness increases linearly with increasing β. When β exceeds 60°, the crack initiation location shifts from the center of the semi-circular notch tip to the surface of preset crack. For non-tip cracking, the crack propagates toward the loading point in a direction approximately perpendicular to the preset crack. The threshold β for it decreases with increasing internal friction coefficient and relative crack length. Moreover, the mixed-mode fracture surface becomes smoother as the mode I component contribution drops. There are remarkable differences in the prediction of fracture initiation angles and SIFs of various rock types applying the generalized maximum tangential stress criterion. The findings of this study could help understand the mixed mode I/II fracture observed in rock engineering.

Multi-fidelity model using GRNN and ANFIS algorithms-based fracture criterion for predicting mixed-mode I-II of sugarcane leaves/epoxy composite

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.

Hygrothermal degradation of MWCNT/epoxy brittle materials under I/II combined mode loading conditions: An experimental, micro structural and theoretical study

The effects of carboxylated multi-walled carbon nanotubes (MWCNTs) are studied experimentally and theoretically on mixed-mode (I/II) fracture behavior of epoxy resin at the presence of hygrothermal aging conditions. In this paper, the mixed-mode fracture of MWCNT/epoxy is experimentally measured using Short Beam Bending (SBB) samples with different crack inclination angles (α) ranging from pure mode I (i.e., α = 0°) to pure mode II (i.e., α = 39°). To examine the effects of hygrothermal aging conditions and water barrier properties of MWCNTs, four groups of samples including a group of neat epoxy specimens, and three groups of MWCNT/epoxy specimens (with 0.1, 0.3, and 0.5 wt% of MWCNTs) were manufactured and immersed into hot deionized water for 15 days at 60 °C temperature and similarly four groups were placed at room temperature conditions (26 °C and 25–35% relative humidity) for 15 days. According to the experimental results, toughening the epoxy resin by incorporating nanotubes with 0.1, 0.3, and 0.5 wt% of MWCNTs improved the fracture toughness at both environmental conditions, but the highest fracture toughness was obtained for composition containing 0.3 wt% nanoparticles. The variations of fracture loads were dependent on the ambient environment, MWCNTs content, and mode mixity. The relationship between the obtained experimental results, microstructure and morphology of fracture in the tested samples was also investigated. In addition, the load-carrying capacity of the SBB samples made of the neat and MWCNTs modified epoxy material was also predicted well using a two-term based fracture model called Generalized Maximum Tangential Stress (GMTS) criterion.

Investigating the effect of raster orientation on fracture behavior of 3D-printed ABS specimens under tension-tear loading

Most of the engineering components are servicing under complex loading conditions or have complex geometries that lead to a multiaxial stress state in the component. Thus, the fracture behavior of parts under mixed-mode loading conditions should be investigated. The Fused Deposition Modeling (FDM) is a subcategory of the Additive Manufacturing (AM) techniques that has some important manufacturing parameters. The raster orientation (or raster angle) is one of fabricating parameters that significantly affect the mechanical behavior of fabricated parts. Therefore, this study aims to investigate the fracture behavior of FDM specimens made of Acrylonitrile Butadiene Styrene (ABS) under mixed-mode I/III loading conditions. To this goal, four different raster configurations of ψR = 0/90°, 15/-75°, 30/-60°, and 45/-45° were selected for FDM fabrication of edge cracked rectangular specimens, and five loading angles of β = 0° (mode I), 40°, 65°, 72°, and 90° (mode III) were used for performing mixed-mode I/III fracture experiments on the pre-cracked specimens. Besides, some tensile experiments were performed on dog-bone specimens fabricated with the mentioned raster configurations. In order to theoretically predict the failure loads in the tested cracked specimens, a theoretical model named Equivalent Material Concept (EMC) was utilized for equating the ductile behavior of FDM-ABS material with a brittle one. The mentioned concept was coupled with J-integral (EMC-J) and Maximum Tangential Stress (EMC-MTS) criteria to predict the failure loads under mixed-mode loading conditions. The results showed that both EMC-J and EMC-MTS criteria could predict the experimental failure loads well. Additionally, Scanning Electron Microscopy (SEM) was performed on the fracture surfaces to analyze the failure mechanisms of the tested specimens. SEM analysis confirmed the presence of three failure features namely air gaps, filament pullouts, and hackle regions that were discussed comprehensively.

Effect of T‐Stress on Crack‐Tip Stress Field and Crack Propagation of Concrete

In order to predict the fracture toughness and propagation of the mixed mode fracture of concrete, the modified MTS (maximum tangential stress) criterion combined with T‐stress was presented. The modified MTS criterion uses a two‐parameter model (stress intensity factor K and T‐stress) to describe the concrete’s fracture. Through calculation, it is found that T‐stress can affect the maximum tangential stress, especially when T‐stress is negative. T‐stress is not taken into account in the traditional MTS criterion, which will lead to errors in calculating the maximum circumferential stress. The result of the specimen is not consistent with the predicted result of the traditional MTS. The modified criterion can provide accurate predictions for the experimental results. This provides a basis for the simulation of concrete’s fracture.

Numerical & experimental assessment of mixed-modes (I/II) fracture of PMMA/hydroxyapatite nanocomposite

Nowadays, polymer-based nanocomposites widely used in biocompatible restorative materials and medical equipment and polymer-based nanocomposites are the most important of them. One of the most useful biocompatible polymers in this field is polymethyl methacrylate (PMMA). In this research, the experimental and numerical analysis of the fracture behaviors of PMMA nanocomposites that are reinforced with hydroxyapatite (HA) nanoparticles are investigated under pure mode I, pure mode II and mixed-mode (I/II) loading. For this purpose, notched semi-circular bend (SCB) specimens containing various Wt. % of HA nanoparticles and different notch angles were fabricated. Then, the mechanical properties of the specimens and the fracture toughness of the notched specimens were investigated. To evaluate the accuracy of nanomaterial distribution, scanning electron microscopy (SEM) images are analyzed and it was observed that at Wt. % of more than 1.5%, specimens with more cumulative masses of hydroxyapatite nanoparticles have more strength reduction. Also, to investigate the fracture behaviors of the produced specimens, the failure criteria of maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS) were evaluated and it was observed that the GMTS criterion is more in line with the experimental results. In addition, the results showed that by increasing the Wt. % of HA nanoparticles from zero to 1% mass, the KIC value increased compared to the pure PMMA, whereas, by increasing this value to 1.5% mass, the fracture toughness decreased. Finally, the fracture initiation and propagation are evaluated using FEM and XFEM numerical methods and the values of stress intensity factors and crack growth path are predicted and compared with experimental values. The obtained numerical results are in good agreement with the experimental results.

Effect of heat-treatment on the pure- and mixed-mode fracture properties of a homogeneous sandstone

Fracture-mechanical properties of the sedimentary rocks at elevated temperature strongly control hydraulic fracturing in rocks, geothermal energy extraction, deep tunnelling, and spent fuel disposal in geological medium. This paper investigates the relationship between the strength properties (e.g. tensile strength, brittleness index and Young’s modulus) and the pure-mode and mixed-mode fracture toughness of Dholpur sandstone at temperatures ranging from room temperature to 500 °C. A suitable brittleness index definition was identified to quantify the deformational changes. Additionally, evolution of the stress–strain behaviour, change in the degradation degree (DD), peak strain, and evolution in porosity values were closely studied to comment on the potential brittle–ductile transition of the rock. The fracture toughness remained unchanged between 25–150 °C, sharply increased 3%–28% between 150–200 °C, and followed by a 75%–80% decrease from 200–500 °C. All the pure- and mixed-mode fracture toughness were found to maintain an exponential relationship with the Young’s modulus, tensile strength, and brittleness index of the heat-treated rocks across all the temperatures. A potential brittle to quasi-brittle/semi-ductile transition temperature of 225 °C was identified for Dholpur sandstone. Additionally, mixed mode fracture behaviour of the heat-treated rock was investigated using generalized maximum tangential stress (GMTS) criterion. It was noticed that GMTS is far better at predicting the KII/KI ratio of mode-II fractures than the conventional maximum tangential stress (MTS) criterion. Statistical analysis of the test data indicate that a 3-parameter Weibull function can be successfully employed to predict the mode-II fracture toughness of heat-treated sandstone in terms of the mode-I data.

Heat treatment effects on fracture resistance of additively manufactured PLA specimens under mode I loading

AbstractThe current paper deals with the influence of heat treatment on the tensile, flexural, and fracture strength of polylactic acid (PLA) specimens made by the fused deposition modeling (FDM) technique. Three different temperatures of 80°C, 100°C, and 120°C were used to anneal the dog bone and enlarged compact tension (ECT) specimens to examine the mechanical and fracture performance of the FDM‐PLA parts, respectively. The fracture behavior was assessed using the equivalent material concept (EMC) combined with the J‐integral, average strain energy density (ASED), and maximum tangential stress (MTS) criteria, and the theoretical estimates were compared with the experimental results. Finally, the effectiveness of these criteria was discussed comprehensively, and the failure mechanisms in the broken tensile and flexural specimens were investigated using scanning electron microscopy (SEM). Overall, applying heat treatment to the FDM specimens could improve their structural integrity by around 57% from the fracture resistance point of view.

Mixed Mode Fracture Investigation of Rock Specimens Containing Sharp V-Notches.

This work aims to assess both experimentally and analytically the fracture behavior of rock specimens containing sharp V-notches (SV-notches) subjected to mixed mode I/II loading. To this end, firstly, several mixed mode fracture tests were conducted on Brazilian disk specimens weakened by an SV-notch (SVNBD sample), performed in their corresponding center and with various notch opening angles. Secondly, the fracture resistance of the tested samples was predicted using a criterion named MTS-FEM. This approach is based on the maximum tangential stress (MTS) criterion, in which the tangential stress is determined from the finite element method (FEM). Additionally, in the present research, the required critical distance is calculated directly from finite element analyses performed on cracked samples. Comparing the experimental results and the analytical predictions, it is shown that the fracture curves obtained from the MTS-FEM criterion are in agreement with the experimental results. These results are achieved without the need for the calculation of stress series expansion coefficients, as an additional advantage of the proposed approach.

Study on the Accuracy of Fracture Criteria in Predicting Fracture Characteristics of Granite with Different Occurrence Depths

The fracture network of a deep geothermal reservoir forms the place for heat exchange between injected fluid and rock mass with high temperature. The fracture resistance ability of reservoir rocks will affect the formation of fracture-network structure, heat exchange and transmission characteristics, and reservoir mechanical stability. However, there are few reports on the fracture toughness and trajectory prediction of geothermal reservoirs with different depths. In this paper, the modified maximum tangential stress criterion (MMTS) is analyzed. The results show that the experimental data are significantly different from the theoretical estimate of MMTS under the influence of different occurrence depths. It is found that the fracture process zone (FPZ) seriously affects the accuracy of predicting fracture initiation angle and mixed-mode (I+II) fracture toughness by MMTS. The FPZ value, considering the influence of different occurrence depths, is modified, and the accuracy of MMTS in predicting the fracture mechanical characteristics of granite is improved. In addition, the mechanical test results show that the Brazilian splitting strength (σt) of granite fluctuates increase with the increase in temperature. With the increase in deviatoric stress, the Brazilian splitting strength and the Brazilian splitting modulus of rock show a trend of first increasing, then decreasing, and then increasing.

Mixed-mode fracture of compacted tailing soils. I: Fracture toughness

Mine tailings are man-made soils and leftovers from the mineral processing that share the similar geotechnical properties with natural soils. In areas with abundant mineral reserves and developed mining industries, tailings could be utilized as an alternative of natural soils for subgrade materials of pavement and adobes for building and construction constructions. The tailing soils are also the based materials for tailing dams. The compacted tailing soils might thus be subject to combined opening or shearing deformations that were unexplored in the current academic society. In this paper, a test configuration called asymmetric semi-circular bending (ASCB) was adopted to investigate the mixed I/II mode fracture properties of the compacted tailing soils. First, the load–displacement relationships of the SCB specimens for different notch depths and span ratios were presented. The mode I and II fracture toughness components were then calculated by referring to the theoretical solutions derived from classical fracture mechanics. The fracture envelope from mode I and II fracture toughness components were presented. Meanwhile, the mixity parameter was introduced to evaluate the mode mixity of the ASCB specimens. Finally, the crack initiation angles of the SCB specimens were measured through experimental tests and compared to the theoretical results obtained from generalized maximum tangential stress criterion (GMTS). Results show that the mode I fracture toughness component of the compacted tailing soils increased with the span ratio, while the mode II fracture toughness component increased with the decrease of span ratio. The mode mixity and crack initiation angles of the SCB specimens under mixed mode loading conditions increased with the decrease of span ratio.

Two-level simulation of injection-induced fracture slip and wing-crack propagation in poroelastic media

In fractured poroelastic media under high differential stress, the shearing of pre-existing fractures and faults and propagation of wing cracks can be induced by fluid injection. This paper presents a two-dimensional mathematical model and a numerical solution approach for coupling fluid flow with fracture shearing and propagation under hydraulic stimulation by fluid injection. Numerical challenges are related to the strong coupling between hydraulic and mechanical processes, the material discontinuity the fractures represent in the medium, and the strong effect that fracture deformation and propagation have on the physical processes. The solution approach is based on a two-level strategy that is classified into the coarse and fine levels. In the coarse level, flow in and poroelastic deformation of the matrix are coupled with the flow in the fractures and fracture contact mechanics, allowing fractures to frictionally slide. Fracture propagation is handled at the fine level, where the maximum tangential stress criterion triggers the propagation of fractures, and Paris' law governs the fracture growth processes. Simulations show how the shearing of a fracture due to fluid injection is linked to fracture propagation, including cases with hydraulically and mechanically interacting fractures. • Wing-crack propagation caused by injection-induced slip of fractures and faults. • Modeling of fracture slip, deformation and propagation in poroelastic media. • Two-scale solution strategy with local adaptive remeshing on fine-level and coarse-level grids. • Open-source 2D implementation combining finite volume and finite element methods. • Simulation results on hydromechanical coupling in fracture slip and propagation.

A comprehensive study on ring shape specimens under compressive and tensile loadings for covering the full range of I+II fracture modes of gypsum material

Using ring-shape specimens containing two aligned cracks on the internal surface of the ring, two test configurations subjected to tensile or compressive loads namely (i) diametrically compressed ring (DCR) and (ii) diametrically tensile ring (DTR) specimens were suggested to investigate the full mixed-mode I/II fracture problem. The fracture parameters, including modes I and II stress intensity factors and T-stress, were determined numerically for these two test specimens with different crack lengths and crack angles. Also, the ability of the specimens was examined by conducting experimental fracture tests on gypsum material. In addition, the direction of fracture kinking was investigated both experimentally and theoretically. The experimental results were then compared and predicted using the mixed mode fracture criteria such as maximum tangential stress (MTS) and generalized maximum tangential stress (GMTS). The normalized fracture toughness (KIIc/KIc) ratios of the tested DCR and DTR specimens were about 0.72 and 0.95, respectively. Such difference was related to the considerable effect of T-stress values and it was shown that the GMTS criterion provides more accurate predictions for the test results of both DCR and DCT samples compared to the MTS criterion.

Investigation on the mixed mode fracture toughness of freshwater ice using the semi-circular bend method

The fracture toughness of ice is of great importance to understand the fracture behaviour of ice impact and blasting. In this study, the mixed mode (I + II) fracture toughness and mode II fracture toughness of granular freshwater ice were first investigated using the semi-circular bend method. A series of fracture tests were carried out to investigate the effects of the grain size (0.8 mm to 4.5 mm) and notch inclination angle (0° to 75°) on the fracture toughness under mixed mode loading conditions. The experimental results indicate that the mode II and mixed mode fracture toughness values slowly decrease in general as the grain size increases. The fracture initiation angles and critical stress intensity factors of the SCB ice specimens were predicted using the generalized maximum tangential stress (GMTS) criteria and conventional maximum tangential Stress (MTS). The GMTS criterion provides a better understanding for mixed mode fracture toughness of ice specimens with various grain sizes, particularly for mode II dominated loading conditions. The grain size of ice directly affects the size of the fracture process zone, which in turn affects the variation law of mixed mode fracture toughness. The strain field and displacement field were initially analysed based on digital image correlation. The results indicate that the variation in the mixed mode crack was complex, eventually exhibiting an asymmetrical distribution of the displacement field.

Investigation of Fatigue Crack Growth in TA2 Cruciform Specimen with an Inclined Crack, Considering Stress Ratio and Biaxial Load Ratio

The biaxial fatigue crack growth behavior of commercial pure titanium TA2 of cruciform specimens with different crack inclination angles (β = 90°, 60°, 45°) under various biaxial load ratios (λ = 0, 0.5, 1) and different stress ratios (R = 0, 0.1, 0.3) is studied by an IPBF-5000 biaxial testing machine. The test results prove that the maximum tangential stress criterion is suitable for predicting the initiation angle of uniaxial and biaxial mixed-mode I–II fatigue cracks. The fatigue crack growth rate of a cruciform specimen with mode I and mixed-mode I–II cracks decreases with the increase of biaxial load ratio and increases with the stress ratio. The Walker model and Kujawski model have better compression effects on fatigue crack growth data than the Paris model.

Coupled multiphysics 3-D generalized finite element method simulations of hydraulic fracture propagation experiments

Intentional creation and propagation of fractures driven by fluid under high pressure have several applications in oil and gas exploration, geological mining, disposal of toxic waste, flow of molten magma within crevices/fissures, etc. Due to the need to design hydraulic fractures, especially in the oil and gas industry, and the limitation of their full scale/field testing, the use of laboratory experiments and/or numerical simulations remain viable alternatives. While several computational methods for this class of problems exist in the literature, their reliability and robustness hinge on their ability to replicate experimental results with acceptable confidence. This paper presents the application of a coupled multiphysics 3-D generalized finite element method (GFEM) for the simulation of hydraulic fracture experiments based on a regularized Irwin criterion and adaptive mesh refinement. Built with an automatic time step search, the algorithm computes the time step size that ensures the satisfaction of the propagation criterion. Modes I, II, and III stress intensity factors are computed using the displacement correlation method, while the fracture propagation direction is determined using the Schöllmann’s criterion, which is a generalization of the maximum tangential stress criterion for 3-D stress state. The GFEM is validated against a hydraulic fracture experiment on PMMA specimen, on one hand, and against four different cases of experimental fractures within concrete (a granite-like) material which serves as the pioneer application of the algorithm to verify hydraulic fracture simulation in non-PMMA materials. The influence of the initial shear stresses along the fracture plane (assuming unnotched condition) on the resulting propagation paths in the latter benchmarked problem is also assessed and found to have good agreement with experimental observations.

Mixed-mode fracture prediction of acrylonitrile butadiene styrene material fabricated via fused deposition modeling

Fused deposition modeling is one of the additive manufacturing techniques that is used for rapid manufacturing and prototyping, in various industries. Due to the layer-wise fabrication routine in the fused deposition modeling process, the final fabricated products often show anisotropic behavior. As a result, to investigate the mechanical performance of the three-dimensional-printed parts, complex and time-consuming analyses are required. The main purpose of the current research paper is to determine whether the isotropic assumption of material using maximum tangential stress and mean stress criteria is capable of predicting the mixed-mode fracture resistance of the three-dimensional -printed parts. Here, three different building conditions are considered for fabricating tensile and fracture specimens, and various mechanical and fracture characteristics are evaluated. Finite element simulations of the test specimens are executed and the stress results are used as input for fracture prediction of the fused deposition modeling parts. Two different cases are considered for isotropic assumptions wherein the first case (case A), each fracture specimen is modeled by using its own direct mechanical properties. While in the second case (case B), the average mechanical properties are used for modeling the cracked specimens. The results showed that both maximum tangential stress and mean stress criteria can predict the fracture loads of the fused deposition modeling parts, without the need for complex and time-consuming analyses associated with fully anisotropic materials. In addition, an improvement of the predictions was observed while using case A compared to case B.

Experimental and theoretical assessment of crack kinking in marble stones in the presence of a V-notch under mode I loading

Marble has been used extensively in the historical monuments as a building material. Notches and sharp corners in these buildings are potential locations for crack formation, crack extension and in some cases their eventual failure. In this study, some fracture tests are accomplished on a number of V-notched marble specimens under mode I loading condition. The specimens are in the configurations of double cantilever beam (DCB) and compact tension (CT) each embedding two various notch opening angles. It is substantiated that although both the loading conditions and geometry were symmetric, the crack initiation angle is not necessarily along the notch bisector line. It is also shown that the classical fracture criteria are not able to predict crack kinking in the tested marble specimens. Thus, the conventional strain energy density and maximum tangential stress criteria used for V-notches, V-SED and V-MTS respectively, are generalized by introducing the first non-singular term of notch stress field into the calculations. Finally, it is demonstrated that the generalized criteria, V-GSED and V-GMTS, can predict the fracture strength and the crack initiation angle of the tested marble specimens well.

Mixed-mode dynamic fracture behavior of a rubber toughened epoxy adhesive under stress wave loading

This work seeks to measure mixed-mode fracture parameters for a dynamically growing crack in a core shell rubber toughened epoxy adhesive (EPONTM 828 with PARALOID™ EXL-2691J particles). Digital image correlation technique coupled with ultrahigh-speed photography and a hybrid finite element-based post-processing approach are used to extract fracture parameters. The dynamic loading is accomplished by using a striker to induce stress waves in an incident bar in contact with a free-standing semi-circular specimen. A companion finite element analysis is performed for investigating suitable experimental parameters and configurations for implementing the approach and determining specific experimental parameters (crack length, crack angle, and impact velocity) necessary to achieve the desired experimental conditions (mode mixity at crack initiation and strain rate). The critical fracture parameters are used to generate mixed mode fracture envelope and fracture toughness-mode mixity relationship for the material. Further investigation is carried out to evaluate various fracture criteria for predicting initial crack kink angles. The measured dynamic fracture quantities are also compared with the quasi-static counterparts to assess strain rate-dependence of the adhesive. The results reveal a decrease in critical stress intensity factors of approximately 10 % and 30 % for the mode I and mode II states, respectively, with increasing strain rate. Post-initiation, the dynamic crack propagates at a near-constant mode I stress intensity factor of ∼1.4 MPa-√m. Under dynamic conditions, the critical, effective stress intensity factors are relatively constant with respect to mode mixity. This is in contrast to quasi-static results where the effective values increased with respect to mode mixity. Experimentally measured crack kink angles agree well with those predicted by the maximum energy release rate criteria and the maximum tangential stress criteria, particularly under mode I dominant conditions.

Evaluating MTS criterion in predicting mixed‐mode crack extension under different loading conditions

AbstractThe maximum tangential stress (MTS) criterion is one of the most widely used criteria for predicting the direction of crack extension. The suitability of this criterion is examined under different loading conditions using the extended finite element method (XFEM). Experimental and numerical results reported in the literature are considered to evaluate the validity and accuracy of the criterion. The results demonstrate that the MTS criterion evaluated by stress intensity factors (SIFs) can accurately predict the direction of crack propagation in specimens under direct tensile loading. This criterion overestimates the angle of crack initiation in the specimen under indirect tensile loading but underestimates the angle in the specimen subjected to 3‐point bending. It is concluded that the MTS criterion based on SIFs could not accurately predict the direction of the crack initiation, which could, however, be determined properly based on the stress distribution around the crack tip obtained by the XFEM numerical models.