Critical Plane Research Articles

Numerical and experimental investigation of the anisotropic tensile behavior of layered rocks in 3D space under Brazilian test conditions

Brazilian disc (BD) testing is a typical method for measuring the indirect tensile strength of rock materials. Both experimental and theoretical studies involving BD testing of anisotropic rocks typically focus on the influence of the 2D bedding effect, where a specimen is parallel to the bedding planes, whereas the influence of the 3D bedding effect combining both the orientation and loading angle has rarely been investigated. Therefore, in this study, BD tests considering the 3D bedding effect were conducted on layered Longmaxi shale, and 3D BD models of layered shale were established using 3D globally embedded cohesive elements with zero thickness. The numerical results were compared to testing results. The 3D BD numerical model was then applied to simulate Asan gneiss and Silurian silty slate to verify the applicability. Finally, the influence of the 3D bedding effect on both the apparent tensile strength (ATS) and failure modes was analyzed. We also considered the influence of the spacing of bedding planes and bedding strength. The results indicated that the numerical results for both the ATS and failure modes were in good agreement with the test results with a maximum error of 17.8% for the ATS. The applicability of the developed 3D BD numerical model to different layered rocks was confirmed by the numerical results for both Asan gneiss and Silurian silty slate. Strong dependencies of the ATS and failure modes on both the orientation (α) and loading (β) angles were observed in the layered Longmaxi shale. The normalized ATS for various orientation and loading angles achieved high values of 3.15 and 2.90, respectively, indicating that the influence of the orientation angle is slightly stronger than that of the loading angle. The Longmaxi shale exhibited a distinct tensile failure mode at α = 0° @ β = 0–15°, α = 0° @ β = 75–90°, and α = 90°, but a more complicated mixed mode of both tensile and shear failure was observed under other conditions. The contribution of shear failure increased significantly at 0° <α < 90° compared to α = 0°. The spacing of the bedding planes had a limited influence on the ATS and failure modes, but the bedding strength had a significant influence. There may be a linear relationship between bedding strength and the spatial distribution parameter of the critical plane approach criterion.

Experimental investigation on the anisotropy of mode-I fracture and tensile failure of layered shale

Mode-I fracture toughness (KIC) and tensile strength (σt) are significant parameters in hydraulic fracturing. Owing to the unique mineral composition and sedimentary environment of shale, the mechanical properties of shale exhibit anisotropy. In this study, the notched semi-circular bend (NSCB) and Brazilian disc (BD) tests were combined with acoustic emission (AE) and digital image correlation (DIC) technology to investigate the anisotropic fracture and tensile behaviors of layered shale. The critical plane approach (CPA) criterion is extended and validated, and the universality of the extended CPA criterion is confirmed for both KIC and σt prediction. In addition, the variation of KIC and σt versus loading angle, the relationship between KIC and σt, the typical failure modes of both NSCB and BD specimens, and the fracture initiation angle of layered shales are discussed comprehensively. The following conclusions were drawn: (1) KIC and σt increased with increasing in the loading angle (β), which indicated significant anisotropy of layered shale, and the AE responses for different loading angles also differed significantly. (2) The variation of anisotropic KIC and σt of different shales could be predicted by adjusting the spatial distribution parameter (Ω0), so that the extended CPA criterion could predict KIC and σt of different shales accurately, which confirmed the universality of the extended CPA criterion for both KIC and σt prediction. (3) There exists an approximately linear or power relationship between KIC and σt, and the power relationship can match both experimental and theoretical results much better. (4) The data from DIC and failure modes confirmed that when β was low, the failure modes were primarily affected by the bedding plane. In contrast, when β was great, the failure modes were primarily affected by the matrix. The NSCB specimens exhibited tensile failure, whereas the BD specimens exhibited more complex failure modes, which were a combination of tensile and shear failure. The results of this study can be used for guiding the design and construction of hydraulic fracturing and rock engineering.

Fatigue tests and fatigue-life prediction models for hybrid welded-bolted demountable shear connectors

Four push out tests were conducted to assess the structural performance of a welded demountable shear connector (WDSC) under high-cycle fatigue loading. The primary failure mode observed was stud fracture at the base. The presence of grout inside the tube significantly increased the WDSC's fatigue life by 5.4 times. The study also analysed stiffness degradation and relative slip evolution during fatigue cycles. Two finite element-based approaches were employed for fatigue life prediction: the critical plane method for fatigue crack initiation life and fracture mechanics for crack propagation life. Based on the experimental and numerical results, fatigue life prediction formulas (Wöhler curves) are proposed for WDSCs with and without grout to aid in predicting fatigue failure in fatigue-sensitive structural designs.

Very high cycle fretting fatigue behavior of IN718 reinforced by IN625/20 % WC laser cladding

The objective of this study is to evaluate the very high cycle fretting fatigue (VHCFF) behavior of laser cladding (LC) Inconel 718 (IN718) metal matrix composites reinforced with IN625/20 % WC. Experiments and simulations were conducted to analyze the fretting fatigue behavior of the cladding layer. The wear and fracture morphologies were obtained by using a confocal laser scanning microscope (CLSM) and a scanning electron microscope (SEM). The multiaxial fatigue damage parameters of the FS and SWT models were used to predict fatigue life through the fitting curve, and the critical plane method was adopted to predict the crack initiation and propagation path. Results indicate that the predicted crack corresponds well with the real crack of the specimen. WC particles can improve the anti-fatigue performance of the contact surface, which is proportional to the contact area between the WC and fretting pad.

Physics-constrained Gaussian process for life prediction under in-phase multiaxial cyclic loading with superposed static components

Under multiaxial fatigue loading, the superposed static components are additional factors for life prediction models to be considered. The increased dimension in fatigue data imposes difficulties in pattern recognition using existing functional form models. A framework to build a Gaussian process (GP) model for lifetime prediction under multiaxial loading was developed to solve this problem. Physically consistent constraints were imposed by applying a novel technique on the GP model to control its behavior and to decrease an overfitting risk. The model consistency with the rotationally invariant principle of damage was provided by the application of the critical plane concept. The framework was demonstrated to have excellent prediction capability on S355 steel and 7075-T651 aluminum alloy. Five well-known fatigue models of functional forms were also implemented for comparison. Detailed parametric studies were presented for the training sample effect, GP kernel effect, and model predictability.

Secondary orientation effects on the low cycle fatigue behaviors of rectangular‐sectional Ni‐based single crystal superalloys at medium and high temperatures

AbstractTurbine blades made of Ni‐based single crystal superalloys (NBSXs) have long‐strip shaped cross sections and rectangular‐sectional structures, where the secondary orientation produces potential effects even the primary orientation is fixed at [001]. Low cycle fatigue behaviors between [010] and [110] transversely oriented rectangular‐sectional NBSX specimens were compared. Obvious differences existed under 600°C but disappeared under 850°C, with the deformation mechanism and fracture mode transitions. Secondary orientation effects on stress asymmetry and fatigue life cannot be described by the conventional LCP model and critical plane method but were well explained by dislocation path length‐dependent back‐stress model and A.N. May's random slip model.

Failure Mechanism Research on Bending Fretting Fatigue of 6061-T6 Aluminum Alloy by Experiment and Finite Element Method.

The fatigue failure mechanism of bending fretting for cyclic softening material 6061-T6 aluminum alloy was researched by experiment and finite element method. The influence of cyclic load on bending fretting fatigue was researched and the damage characteristics under different cycles was discussed experimentally though SEM images. In the simulation, a normal load transformation method was employed to obtain a simplified two-dimensional model used for simulating the bending fretting fatigue from a three-dimensional model. An advanced constitutive equation with the Abdel-Ohno rule and isotropic hardening evolution was transplanted into ABAQUS by UMAT subroutine to consider the ratchetting behavior and cyclic softening characteristics. The peak stain distributions under various cyclic loads were discussed. Additionally, the bending fretting fatigue lives and crack initiation locations referring to a critical volume method were estimated using the Smith-Watson-Topper critical plane approach and reasonable results were obtained.

Investigation of low cycle fatigue crack propagation behavior of 316H steel at 550℃ based on cyclic response and damage accumulation: experiment and modelling

In the framework of the unified elastic-plastic constitutive theory, the cyclic response and damage evolution of 316H steel in the low cycle fatigue (LCF) regime was analyzed and modeled. A unified damage-coupled elastic-plastic constitutive model was established based on the results of uniaxial strain-controlled LCF tests, which includes a novel strain-based continuum damage model in the framework of the critical plane theory, an accumulative plastic strain and fatigue damage-related kinematic hardening model, and an isotropic hardening model. The comparison between the simulated and the experimental results indicated that the proposed model is efficient to precisely characterize the cyclic response throughout the whole fatigue process. The model was also used to simulate the fatigue crack growth behavior under different maximum loads and load ratios via finite element (FE) simulation. The effects of the load conditions on the crack growth rate and crack tip parameters were analyzed systematically.

Estimation of fretting fatigue lifetime in heterogeneous material based on microstructure characterization and multi-scale homogenization

Fretting fatigue is a complex phenomenon that is affected by multiaxial stress and contact problems. In the contact surface, due to the cyclic load, a relatively small displacement is generated, and the stress concentration is established as well. To assess the fretting fatigue endurance complimentary to experimental efforts, the Finite Element Method (FEM) has become a useful tool combined with theoretical approaches. Meanwhile, most (if not all) of commercially available structural materials can be regarded as heterogeneous materials due to the existence of secondary phases and some fabrication defects and porosity. Therefore, to further understand the mechanism of fretting fatigue, knowledge of the material’s microstructure is important. In this study, several microstructure characterization techniques are applied to characterize precipitates and micro-voids in aluminium alloy AA2024-T3. These techniques are Transmission Electron Microscopy (TEM) and Energy Dispersive Spectroscopy (EDS). To account for the precipitates, the homogenization method is adopted in this study. Additionally, a 3D structure non-destructive reconstruction technique is applied to obtain accurate information on micro-voids. The fretting fatigue lifetime is estimated by using the critical plane approach combined with the theory of critical distance. The numerical results are compared with experimental data showing a good agreement. The influence of micro-voids on the fretting fatigue endurance is studied and discussed as well.

Numerical simulation of damage evolution of bolted connectors considering fretting fatigue effect

ABSTRACT In engineering, the failure of bolted connector is mainly caused by multi-axis non-proportional fretting fatigue damage. A three-dimensional finite element model of bolted connector is established in this paper, and a damage constitutive model suitable for multi-axial fatigue analysis is established based on the critical plane SWT (Smith Watson-Topper) method and continuous damage mechanics theory. A material subroutine UMAT is developed to describe the damage model and realizes the visualization of the damage evolution process caused by the fretting fatigue effect. Based on the test, the validity of the program is verified, the fretting fatigue characteristics and damage evolution characteristics of the bolted connector are analyzed. The results show that (i) the damage evolution analysis method can make up for the deficiency that the critical plane SWT method is only used for simple components and can be applied to the damage evolution analysis and fatigue life evaluation of three-dimensional complex structures. (ii) The crack initiation position of the connecting plate does not change with the magnitude of the tensile load and pre tightening force. In the process of losing the bolt preload from 1 to 0.8 times, the connected parts will be damaged faster as the preload 20 decreases.

Bearing life prediction based on critical interface method under multiaxial random loading

The bearing was a key component of the mining machine tire unloader machine and was subjected to random multiaxial stress during operation. Therefore, the life prediction of bearing was of safety guidance. In this paper, a bearing life prediction method based on the critical plane method under multiaxial random loading was proposed. Firstly, a virtual prototype model was built based on the actual working conditions of the tire unloader machine to obtain the time load history of the bearing. Transient dynamic analysis of the bearing was carried out to obtain the triaxial stress-strain time histories at the hazardous locations of the bearing. A new coordinate system was established using the hazard node as the coordinate origin, and the location of the critical plane was searched for based on the critical plane multiaxial fatigue theory, combined with the maximum shear strain amplitude on the critical plane for multi-axial rain flow cycle counting to obtain the damage amount in each direction. At the same time, the life calculated from the maximum damage amount was used as the final life, resulting in a cycle count of the bearing of 268,303 cycles and a duration of 1490.58h. The results of this study could be used as a guide to predict the service life of the bearing in large machinery subjected to multiaxial random stress conditions.

Multiaxial fatigue life prediction model for notched specimen based on modified energy gradient and critical plane method

The distribution of energy field on the crack initiation plane directly affects the crack initiation behavior. Therefore, studying the energy gradient is of crucial help for accurate evaluation of the fatigue performance for the notched specimen. Firstly, the energy distribution on the critical plane is characterized by the sixth-order polynomial. Meanwhile, the relative energy gradient is adopted to calculate the critical distance. Secondly, considering the influence of energy gradient, size effect and non-proportional additional strengthening, a general procedure is explored. Finally, the experimental data of Al7050, En8 and C40 is utilized for model validation and the comparison results show that prediction results of the proposed model in this paper is superior to other models.

An Improved Multiaxial Low-Cycle Fatigue Life Prediction Model Based on Equivalent Strain Approach

The fatigue life of the materials is significantly reduced under non-proportional loading. In this study, the factors affecting additional hardening are explored, and a hardening function is proposed. Firstly, the stress and strain states of the specimen under multiaxial loading are analyzed, and the deficiencies of the equivalent strain models are discussed. Secondly, the factors affecting the additional hardening are analyzed from both stress and strain perspectives, and the effect of phase differences on fatigue life is investigated. The stress on the critical plane is considered to reflect its effect on crack initiation and growth. An improved multiaxial low-cycle fatigue life prediction model is developed based on the equivalent strain approach. Finally, experimental data from five metals are used to verify the established model and are compared with existing classical models. The results show that the proposed model has good accuracy.

Investigation into rolling contact fatigue performance of aerospace bearing steels

In this investigation common aerospace-quality bearing steels was evaluated in rolling contact fatigue both experimentally and analytically. Three aerospace-quality bearing steels was procured and evaluated. First, the bearing steels were evaluated using a 3 ball-on-rod rolling contact fatigue test rig. Next, the same bearing steels were evaluated using a torsion fatigue test rig in order to quantify these materials’ performance against the damage causing stress in RCF – shear reversal. The torsion S-N data provided the foundation for the determination of material constants that were used in a continuum damage mechanics finite element model (CDM-FE model), which considered the Fatemi-Socie critical plane approach as the failure criteria. These material constants captured the material cleanliness effect between the various materials investigated. Additionally, the CDM-FE model utilized Voronoi tessellations to capture the material topological effect. RCF simulations were performed at the same operating conditions as in the 3 ball-on-rod test apparatus. Torsional fatigue results from this investigation indicated which material possessed the largest ultimate shear strength, and which material performed best in low cycle and high cycle fatigue. The three ball-on-rod results established experimentally which material performed superior in RCF. It was observed that good corroboration existed between the analytical simulation life predictions and the 3 ball-on-rod experimental results.

Data-Driven, Physics-Based, or Both: Fatigue Prediction of Structural Adhesive Joints by Artificial Intelligence

Here, a comparative investigation of data-driven, physics-based, and hybrid models for the fatigue lifetime prediction of structural adhesive joints in terms of complexity of implementation, sensitivity to data size, and prediction accuracy is presented. Four data-driven models (DDM) are constructed using extremely randomized trees (ERT), eXtreme gradient boosting (XGB), LightGBM (LGBM) and histogram-based gradient boosting (HGB). The physics-based model (PBM) relies on the Findley’s critical plane approach. Two hybrid models (HM) were developed by combining data-driven and physics-based approaches obtained from invariant stresses (HM-I) and Findley’s stress (HM-F). A fatigue dataset of 979 data points of four structural adhesives is employed. To assess the sensitivity to data size, the dataset is split into three train/test ratios, namely 70%/30%, 50%/50%, and 30%/70%. Results revealed that DDMs are more accurate, but more sensitive to dataset size compared to the PBM. Among different regressors, the LGBM presented the best performance in terms of accuracy and generalization power. HMs increased the accuracy of predictions, whilst reducing the sensitivity to data size. The HM-I demonstrated that datasets from different sources can be utilized to improve predictions (especially with small datasets). Finally, the HM-I showed the highest accuracy with an improved sensitivity to data size.

A radioanatomical study of 3rd segment terminal branches of the maxillary artery in the pterygopalatine fossa

This study describes the clinical anatomical topography and relationship of the terminal branches of the maxillary artery to the bony wall of the maxillary sinus in the pterygopalatine fossa (PPF) to estimate the bleeding risk during surgical interventions. Using contrasted computer tomography records, (i) the route of the maxillary artery in the infratemporal fossa, (ii) the number of the arteries in the critical PPF surgery plane, (iii) the diameter of the largest artery in the area and (iv) its relation to the posterior wall of the maxillary sinus were examined. Furthermore, measurements were extended with (v) the minerality of the bony posterior wall of the maxillary sinus on bone-window images. For statistical analyses Student’s t- and Fisher-test were applied. 50 patients (n = 50, 100 cases including both sides) were examined in this study. The maxillary artery reached the pterygomaxillary fissure on the lateral side of the lateral pterygoid muscle in 56% of the cases (n = 32), in 37% (n = 23) on its medial side and in 7% (n = 4) on both sides. The number of arteries at the level of the Vidian canal in the PPF varied between 1 and 4 with a median of 2. The diameter of the biggest branch was 1.2–4.7 mm, the median diameter was 1.90 mm. In 41% (n = 30) of the cases the biggest artery directly contacted the posterior wall of the maxillary sinus, and the mineral density of the posterior wall was decreased in 14.3% (n = 12) of all investigated cases. The present description and statistical analysis of the vasculature of the PPF optimizes operative planning—like clip size or the type and direction of the surgical approach—in this hidden and deep head/neck region.

Comparison of critical plane models based on multiaxial low-cycle fatigue tests of 316L steel

An endurance against multiaxial fatigue of 316L steel is studied. A fatigue life curve of torsional mode is substantially shifted to longer fatigue lives while tension/compression mode causes fracture the earliest. Fatigue life curves of both multiaxial modes are close to axial mode. Fourteen critical plane models for fatigue life predictions were applied and compared. Modified Smith-Watson-Topper models proved to be the most accurate. Criteria proposed by Fatemi and Socie, Li et al., Zhu et al. and by Wang and Brown provided satisfactory results as well. Smith-Watson-Topper model led to the most precise predictions of fatigue crack orientation.

Multiaxial fatigue life estimation based on weight-averaged maximum damage plane under variable amplitude loading

An innovative critical plane determination approach with weight-averaged largest fatigue damage is proposed, in which the material failure modes can be considered. If material exhibits shear cracking behavior, a strain-based critical plane model with shear failure mode is selected to evaluate the weight function. Otherwise, other one with tensile failure mode is adopted. According to the proposed critical plane, a multiaxial fatigue lifetime estimation methodology is established for evaluating fatigue life. And, six kinds of materials are employed to validate the validity of presented methodology. The validation results reveal the presented methodology can estimate the orientation angles of failure plane accurately and supply satisfactory fatigue lifetime estimations for both shear and tensile failure mode materials. Furthermore, the proposed critical plane framework can be extended to be utilized with stress-based fatigue criteria, and prediction results show a good agreement with experimental data by another two materials.

Energy-based critical plane fatigue methods applied to additively manufactured 18Ni300 steel

In this work, the uniaxial and biaxial fatigue behaviour of maraging steel (18Ni300) obtained by additive manufacturing was studied. The material was evaluated using several biaxial load paths and different load levels. The predictive capacity of the fatigue life and crack initiation angle of the critical plane methods of Liu (I and II), and Chu, Conle, and Bonnen (CCB) were evaluated. The results obtained showed that normal stresses had a strong effect on the fatigue life. In general, the best estimates of the useful life and initial crack angle prediction were obtained with the CCB method.

Comparing fatigue life prediction capability of critical plane models using multiaxial test database on 17 materials

AbstractThe present study validates recent as well as extensively used critical plane (CP)‐based fatigue life assessment models for 10 ferrous and 7 non‐ferrous materials. Fourteen CP models, including recently reported in‐house developed model, have been analyzed. These models use resolved stresses, strains, strain energy density, and combinations of stresses and strains to identify critical plane and quantify fatigue damage. The loading conditions cover various proportional and non‐proportional axial‐torsion strain paths with different phase shift angles with (or without) mean stress/strain component(s), loading waveforms, and asynchronous axial‐torsion stain paths. The comparative study brought out the goodness of various models by quantifying the extent of scatter and computational time.Some of the strain energy density‐based models (including in‐house model) have been shortlisted, which produced accurate fatigue life assessments. Among the shortlisted models, in‐house model is free from the calculation subjectivities of resultant shear and performs faster fatigue damage calculations.