Maximum Tangential Stress Research Articles

Linear crack initiation analysis on rock surface under the combined action of sub-elevated temperature stress and fracture air-vapor pressure

Near the surface of the Sichuan-Tibet line tunnel surrounding rock under construction is in a sub-hot and humid environment, and long-term accumulation will produce damp-heat diseases. The significant temperature difference leads to the thermal stress of the surrounding rock, and the surrounding rock fracture water vaporizes to create fracture air-vapor pressure, which induces crack initiation. The state equation of gases, thermoelastic mechanics, and the theory of linear elastic fracture mechanics are used to study the crack initiation law of rock under the joint action of sub-elevated temperature stress and fracture air-vapor pressure. The stress intensity factor's expression under the two joint actions is derived from the superposition principle. Then the initiation criterion considering both internal influencing factors (rock properties, crack geometry parameters (inclination angle)) and external influencing factors (far-field stress, temperature, humidity factors) is derived. The theory is used to quantitatively analyze the distribution law of tangential stress at the crack tip and the crack initiation form. The effects of each parameter on critical crack initiation angle and crack initiation strength are discussed. The theoretical results are further verified by numerical simulation. The results show that in the sub-elevated temperature range, the thermal stress and the fracture air-vapor pressure jointly affect the crack initiation law, and thermal stress is the dominant factor. With the temperature increase, KI >KII, the critical crack initiation angle increases gradually, the crack initiation form changes from shear to compression-shear, and finally tends to tension. The fracture air-vapor pressure promotes the tension part. The maximum tangential stress increases linearly with temperature. The maximum tangential stress and critical crack initiation angle increase first and then decrease with the rise of crack inclination angle and reach the maximum at 45°. The research results supply a theoretical basis for preventing and treating the rock crack propagation surrounding the tunnel under sub-elevated temperatures and high humidity.

Mixed mode I-III fracture resistance of stainless steel 316L weakened by V-notches with end holes

Notch fracture resistance of stainless steel 316L is investigated under mixed-mode I/III loading. A previously proposed test fixture, utilized in the past for testing low/medium toughness polymeric and metallic materials, is first modified to make it appropriate for testing significantly tough materials like stainless steel 316L. Then, original fracture tests are carried out on a specific sample weakened by V-notches with end holes (VO-notches) and loaded under different combinations of tension and out-of-plane shear, from which the critical loads and the fracture behaviour are extracted. Due to great strain-hardening and significant strain-to-failure for stainless steel 316L, the Fictitious Material Concept (FMC) is first employed to avoid complexities associated with fracture prediction. Then, FMC is combined with the maximum tangential stress (MTS) and mean stress (MS) criteria to predict the notch fracture toughness values determined experimentally. With approximately 87 % and 86 % accuracy in estimation of the mean experimental results, both combined criteria, called FMC-MTS and FMC-MS, are revealed to be successful.

Rock Burst Intensity Classification Prediction Model Based on a Bayesian Hyperparameter Optimization Support Vector Machine

Rock burst disasters occurring in underground high-stress rock mass mining and excavation engineering seriously threaten the safety of workers and hinders the progress of engineering construction. Rock burst classification prediction is the basis of reducing and even eliminating rock burst hazards. Currently, most of mainstream discriminant models for rock burst grade prediction are based on small samples. Comprehensive selection according to many pieces of literature, the maximum tangential stress of surrounding rock and rock uniaxial compressive strength ratio coefficient (stress state parameter), rock uniaxial compressive strength and uniaxial tensile strength ratio (brittleness modulus), and the elastic energy index are used as a grading evaluation index of rock burst based on the collection of different construction engineering instances of rock burst in 114 groups of extensive sample data in different regions of the world, which are used to carry out the training study. The representativeness and accuracy of the index selection were verified by the indicator variance analysis and Spearman correlation coefficient hypothesis test. The Intelligent Rock burst Identification System (IRIS) based on an optimizable SVM model was established using data set samples. After extensive data cross-validation training, the accuracy of the SVM discriminant analysis model can reach 95.6%, which is significantly better than the prediction accuracy of the traditional SVM model of 71.9%. The model is used to classify and predict the rock burst intensity of 10 typical projects at home and abroad. The prediction results are consistent with the actual rock burst intensity, which is better than the discriminant model based on small sample data and other existing prediction models. The application of engineering examples shows that the results of the rock burst intensity classification prediction model based on extensive sample data processing analysis and the SVM discriminant method are in good agreement with the actual rock burst intensity, which can effectively provide a reference for the prediction of rock burst intensity grade in a construction area.

Prediction of Mode I Fracture Toughness of Shale Specimens by Different Fracture Theories Considering Size Effect

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α).

Investigation of the deleterious effects of low-temperature and hygrothermal aging conditions on the mixed-mode fracture resistance of epoxy resin using a short-beam bend specimen

The effect of different environmental aging conditions on the mixed-mode fracture behavior of epoxy resins was investigated using a sub-size specimen. The short-beam bend (SBB) specimens with different crack inclination angles were manufactured and subjected to low-temperature (-71 °C), hygrothermal (immersion in deionized water at 60 °C) and room-temperature conditions. The deleterious effect of low-temperature and hygrothermal aging conditions on the mode-I, mode-II and mixed-mode I/II fracture responses of the epoxy resin was studied by testing the aged and unaged SBB specimens under three-point bend loading. The experimental results indicated that the hygrothermal aging condition, with a reduction of 49% in the effective fracture toughness, imposed a more severe deleterious effect on the fracture response of the specimens in comparison with the low-temperature condition with a decrease of 35% in the effective fracture toughness. The generalized maximum tangential stress criterion was used to predict the fracture loads of the aged and unaged specimens. Moreover, optical microscopy and scanning electron microscopy techniques were employed to assess the fracture surfaces of the specimens aged under different conditions.

Mixed-mode load bearing estimation of the cracked additively manufactured materials using stress/strain-based models

PurposeThe main aim of this study is to investigate the mixed-mode I/II failure and the cracking manner of three-dimensional (3D)-printed components made by the fused deposition modeling technique in an experimental and theoretical manner.Design/methodology/approachAcrylonitrile butadiene styrene (ABS) material and a modified printing method (that increases the adhesion and integrity between the layers and strands) are used for manufacturing the semicircular bending (SCB) test samples. In addition to precracking, the effect of additional stress concentration on the stress field is studied by introducing three small holes to the SCB fracture samples. The critical mixed-mode I/II failure loads obtained from the experiments are predicted using different stress/strain-based fracture theories, including maximum tangential stress (MTS), maximum tangential strain (MTSN), generalized form of MTS and MTSN and combination of them with equivalent material concept (EMC). The effects of plastic deformation, as well as the structural stress concentration, are considered for a more realistic prediction of mixed-mode fracture load.FindingsThe stress-based criteria are more suitable than the strain-based theories. Among the investigated fracture models, the EMC–generalized maximum tangential stress theory provided the best agreement with the experimental results obtained from 3D-printed SCB tests.Originality/valueThe influences of stress risers and applicability of different failure theories in cracked layered 3D-printed parts are studied on the fracture behavior of tested specimens under mixed-mode I/II.

An energy-based criterion for mixed-mode I/II/III fracture considering effective critical distances

Traditionally, fracture criteria have been established based on a crack-tip material length scale which famously is called the critical distance. This parameter is considered to be independent of the mode mixity and measured under pure mode I loading conditions as a material parameter. However, recent studies show this parameter may considerably change between the fracture modes depending on the mode mixity. The mode-dependent critical distance, called the effective critical distance, is found to be a reasonable approach when implemented into a strain-based framework. In this paper, the concept of effective critical distance (ECD) is combined with the maximum tangential strain energy density criterion (MTSED), and a novel mixed-mode I/II/III brittle fracture criterion, called ECD-MTSED, is suggested. The new criterion is used to predict the experimental data reported in the literature for the mixed-mode I/II/III fracture toughness and fracture angles along with four other criteria – namely, maximum tangential stress (MTS), maximum principal stress (MPS), strain energy density (SED), and maximum principal strain using an effective critical distance (ECD-SN). The results not only showed the superiority of the suggested criterion but also accentuated the necessity of employing effective critical distance in the three-dimensional brittle fracture theories.

Three-dimensional fatigue crack growth prediction method based on consistency retention

To reduce the influence of uncertain factors, a three-dimensional fatigue crack growth prediction method based on consistency maintenance is proposed. Firstly, the crack growth update under complex loads is realized based on XFEM. Subsequently, the life correction method based on the improved particle filter and the path correction method based on the improved maximum tangential stress criterion are proposed. Taking real crack data as input, the accuracy of prediction results is improved from two dimensions of life and path. Finally, five cases are used to verify the proposed framework, which proves that it can realize dynamic tracking of crack growth.

Crack initiation characteristics of brittle materials with I‐II mixed mode crack under uniaxial compression

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

A stress-based approach for considering the size effect on the mixed mode fracture behavior of rock

It is aimed in this research that a new approach is represented for justifying the influence of specimen size on the mixed mode I/II fracture behavior of rock. The new approach, namely, the MTS-FEM criterion, is an extension of the maximum tangential stress (MTS) criterion in which the finite element method (FEM) is employed for characterizing the tangential stress at the critical distance. Also, two points exist in the MTS-FEM approach for the critical distance. First one is that the critical distance is obtained directly from finite element analysis corresponding to results of mode I fracture test. The second point is that the critical distance from the crack tip is considered as a function of specimen size. The experimental results carried out in the previous studies on cracked Brazilian disks (CBD) with four different radii and under mixed mode loading are utilized with the aim to evaluate the new size effect criterion. It is illustrated that the MTS-FEM criterion is able to predict the mixed mode fracture resistance of rock considering the size effect well without calculating any parameters related to the stress or strain series expansion.

Crack initiation considering the possible stress acting on the crack surface under uniaxial tension or compression

In the classical fracture mechanics theory, it is generally believed that the crack surface is open under tension and closed under compression. However, under uniaxial tension at a small angle with the crack surface, especially when parallel, the stress field at the crack tip calculated by traditional theory is small. Although many scholars have proved that the stress field at the crack tip needs to consider T-stress, it is just a non-singular term. This is because under small angle uniaxial tension, the crack surface may also be closed. Similarly, it may be open under uniaxial compression. Therefore, aiming at the shortcomings of the existing theories, both the far-field stress and the possible stress acting on the crack surface are considered in this paper. Based on the stress boundary conditions of the far-field and the crack surface, the stress function of the infinite plate with a single crack under complex load is deduced and the stress field at the crack tip is obtained, that is, the stress intensity factors KI, KII and T-stress. Based on the generalized maximum tangential stress (GMTS) criterion, the crack initiation angles of open or closed cracks under uniaxial tension or compression are studied respectively, the relationships between crack initiation angle θ0 and β (β: angle between the tensile/compressive direction and crack surface) are obtained. A parameter η is introduced to judge whether the crack surface is open or closed under different loading angles. Compared the above research results with the methods proposed by predecessors and experimental data, it is found that they are in good agreement. The results show that the stress intensity factors KI, KII and T-stress are related to not only the far-field stress, but also the possible stress acting on the crack surface; The stress on the crack surface changes with far-field stress; The crack surface under small angle tension regarded as closed while under compression as open is reasonable.

Fatigue crack propagation simulation method using XFEM with variable-node element

The extended finite element method (XFEM) with the local refinement technique using the variable-node element (VNE) is proposed to simulate the fatigue crack propagation under the cyclic loadings, in which the initially generated coarse mesh around the crack tip is refined after the crack propagation and the VNE is used to connect the refined elements and the adjacent elements. The local refine elements are used to improve the accuracy of stress near the crack tip and it is unnecessary to conform the discretization to the crack surfaces. The maximum tangential stress criterion is used to determine the crack propagation angle θc and the fatigue life is estimated by the Paris law. With this method, the condition number of the global stiffness matrix is alleviated by using the only discontinuous branch enrichment function and the crack increment size can be set flexibly and small enough to reproduce true crack path. Because only the refined mesh around crack tip is updated at each increment step during crack propagation, the simulation cost is much less than that of the method in which global fine mesh is required. Numerical examples of the crack propagation under the monotonic and cyclic loadings are given out and it is demonstrated that the proposed method can calculate the stress intensity factors (SIFs) and predict the crack paths more accurately with the local refine elements near the each crack tip. The proposed method is also suitable to simulate the crack propagation of the functional graded materials under the thermal loadings in the future works, in which the material non-homogeneity near the crack tip requires accurate modeling.

Theoretical and Experimental Study considering the Influence of T-Stress on the Fracture Behavior of Compression-Shear Crack

The influence of the nonsingular stress term (T-stress), existing in the Williams expansion of the crack tip stress field, on the fracture behavior of the compressive-shear crack is comprehensively considered in this paper. According to the stress boundary conditions on the crack surfaces, the theoretical solution of the stress field around the closed crack tip is established using the complex potential theory, which includes not only the singular term containing the stress intensity factor KII but also three nonsingular terms (T-stress: Tx, Ty, and Txy) without KII. Then, the differences between tangential stresses and shear stresses at the crack tip obtained in the cases with and without T-stress are compared, respectively. Outcome indicates that there are tangential tensile stress and compressive stress zones at the crack tip when considering T-stress, while only the former exists when ignoring T-stress. In the case of considering T-stress, an improved crack initiation criterion is proposed, where the maximum tangential tensile stress and maximum shear stress are utilized simultaneously to predict the crack initiation and failure mode under the multiaxial compression stress state. Besides, the triaxial compression tests were carried out on the prismatic rock-like material samples with a central crack, and the effectiveness and validity of the proposed criterion are verified by comparing the experimental results and theoretical predictions. It reveals that the proposed criterion can reliably predict the crack initiation angles and failure modes with higher accuracy than traditional fracture criterion.

Translaminar notch fracture toughness expressions for composite laminates

First, two different test specimens, namely the rectangular tension (RT) and semi-circular bend (SCB) specimens, weakened by U-notches of various notch tip radii and made of E-glass/epoxy composite laminates of different lay-up configurations, are considered for measuring experimentally the translaminar notch fracture toughness (TLNFT) of the composite material under pure mode I loading conditions. Then, two new closed-form expressions are proposed for the TLNFT, by taking advantages of the maximum tangential stress (MTS) and the mean stress (MS) criteria, as well as the recently proposed virtual isotropic material concept (VIMC), with the goal to estimate the experimental results. It is found that both criteria can well estimate the test results that locate always between the predictions of MTS and MS criteria. Taking into account that MTS criterion is more conservative and simpler than MS criterion, it is preferred in mechanical design of notched E-glass/epoxy composite structures.

Investigation of dynamic fracture in VASCT samples under the effect of different loading modes

In order to clearly reveal the dynamic failure mechanism of cracked rock mass with mixed-mode I/II cracks under impact loads, a variable angle single cleavage triangle (VASCT) sample was proposed. A series of impact tests were implemented using a drop weight impact (DWI) apparatus, dynamic crack initiation time and crack speeds were measured using two strain gauges in the experimental process. AUTODYN code was applied to simulate crack propagation trajectories, and the simulation results of sample failure pattern and crack initiation time were in good agreement with experimental results. The maximum tangential stress around the crack tip was calculated and crack fracture mechanism was also discussed in numerical simulation. Dynamic initiation toughness of mixed-mode I/II crack was calculated using the experimental–numerical method. The results of this study revealed that dynamic crack initiation time becomes earlier with the increase of crack inclination angle α, but the crack speeds decrease with the crack inclination angle α; When crack inclination angle α changes from 0° to 10°, i.e., the failure modes of the pre-crack change from pure mode I fracture to mixed-mode I/II fracture, and the maximum tangential stress, crack initiation time and dynamic fracture toughness change sharply; With the increasing of crack inclination angle α, the variation of mode II dynamic fracture toughness is little, and the crack gradually transforms from opening to closing mode.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

Analytical and experimental investigation on the effect of loading rate on the fracture toughness and fracture envelope in brittle rocks

Fracture toughness of brittle rocks is an essential factor for analyzing and designing many problems in rock mechanics such as crack initiation and propagation in rock masses, hydraulic fracturing, geothermal energy, etc. This parameter is closely related to the strain rate to which the rock mass is subjected. Therefore, the effect of strain rate on the fracture toughness under three loading modes (pure mode I, mixed mode loading I/II and pure mode II) by taking into account crack propagation speed was investigated in this work. Experiments were conducted on rectangular specimens of hornfels rock and two fracture criteria that include maximum tangential stress criterion (ϭ-criterion) and minimum strain energy density criterion (S-criterion) were adopted to verify their ability to predict the fracture envelope as a function of the strain rate. Results indicated that by increasing the strain rate from 6 × 10−4 to 6 × 10−2 S−1, fracture toughness under pure mode I, mixed mode loading I/II and pure mode II increased by 1.6, 1.8 and 1.9 orders of magnitudes, respectively. The fracture toughness under pure mode I and mixed mode loading I/II almost has the same increment rate versus strain rate (∼21). While the increment rate of the fracture toughness under pure mode II (∼37) is larger than that under pure mode I and mixed mode loading I/II. S-criterion indicated that by increasing the crack propagation speed, fracture envelope moves up and the fracture resistance for growth under mixed mode loading I/II increases. While for ϭ-criterion, two cases can be distinguished, for crack propagation speed less than 80% the Rayleigh wave speed, fracture envelope moves down by increasing the crack propagation speed, and the vice is versa for crack propagation speed greater than 80% of the Ryleigh wave speed. S-criterion is better than ϭ-criterion to characterize the fracture envelope under low strain rate, and for high strain rates, S-criterion should be developed to better characterize the fracture envelope.

Crack Deflection Under Mixed-Mode Loading Conditions in Fine-Grained Composites Based on Water Glass-Activated Slag

This paper is devoted to an analysis of the crack deflection angle in a semi-circular disc made of a fine-grained composite based on water glass-activated slag. Three-point bending together with an inclined crack ensures the crack propagation in I + II mixed mode. Generally, concrete material exhibits quasi-brittle fracture behavior, which is difficult to understand. Multi-parameter fracture mechanics (MPFMs) concept shall help us to describe the crack propagation and the influence of choice of a suitable distance for application of generalized fracture criteria is investigated. In this work, the well-known maximum tangential stress (MTS) criterion as well as strain energy density (SED) criterion are applied in their multi-parameter (MP) form to find the initial kink angle. Williams power expansion is used to approximate the crack-tip stress field. Its coefficients need to be calculated numerically via combination of the finite-element (FE) solution and over-deterministic method. Results are discussed and recommendations are stated regarding the critical length parameter as well as the number of the Williams expansion (WE) coefficients.

A coupled wear and crack initiation-propagation methodology for fretting fatigue life assessment in press-fitted axles

A methodology that coupled the fretting wear, crack initiation, and propagation was firstly proposed for the total fatigue life assessment of press-fitted axles. The Smith–Watson–Topper (SWT) fatigue indicator parameter (FIP), the theory of critical distance (TCD), and the Miner damage rule were adopted to estimate the crack initiation. The contour integral method and the Paris’s law were used to predict the crack propagation. Furthermore, fretting wear was simulated using the energy wear approach. The simulation results showed that TCD used in this methodology could mitigate high-stress gradient effects, and define the critical crack length for crack initiation and propagation prediction. The crack initiation prediction provided accurate information about the initial crack angle and site for the propagation estimation. The Maximum Tangential Stress criterion considering the wear effect could reasonably predict the crack propagation path of press-fitted axles. As compared with the total fatigue life predicted by the SWT FIP alone, the proposed methodology provided a better prediction result.

Elastoplastic fracture analysis of thin notched AA7075‐AA2024 dissimilar friction‐stir‐welded plates under mixed mode I/II loading

AbstractIn this research, fracture of friction‐stir welding (FSW) of AA2024‐T3 and AA7075‐T6 aluminum alloys weakened by notches is studied. In the experimental part, a rectangular specimen, called U‐notched diagonally loaded square plate (UNDLSP) and made of welded AA2024‐T3 and AA7075‐T6 aluminum alloys, is used for fracture tests under pure mode I and mixed mode I/II loading conditions. For fracture tests, different notch tip radii and different ratios of loading mode combinations are considered. In the theoretical part, due to ductility of the material under test, combination of the equivalent material concept (EMC) with two brittle fracture criteria (maximum tangential stress and mean stress criteria) is used to predict the load‐bearing capacity (LBC) of the samples. By comparing the experimental and theoretical results, it is revealed that both criteria in combination with EMC are able to predict the LBC of the U‐notched samples well and with high accuracy.