Critical Plane Approach Research Articles

Using physics-informed neural networks to predict the lifetime of laser powder bed fusion processed 316L stainless steel under multiaxial low-cycle fatigue loading

Axial-torsional Low-Cycle Fatigue (LCF) tests were conducted under strain control on Additively Manufactured (AM) 316L stainless steel using laser powder bed fusion. The tests covered various strain amplitudes under tension-compression, proportional, and pure shear loading paths. The AM 316L stainless steel exhibited cyclic softening and transgranular cracking under all the investigated loading conditions. The presence of deposition defects, predominantly the lack of fusion type, was identified as the main factor influencing the crack initiation and propagation, as well as the scatter in the fatigue lifetime. Therefore, to account for the damaging effects of these deposition related defects on fatigue lifetime, a novel physics-informed neural network was proposed. Subsequently, this neural network was combined with the critical plane approach, based on the tensile mode of failure, in order to predict the lifetime of AM 316L stainless steel. The predicted data exhibited a good correlation with the experimental results.

Nonlocal multiaxial fatigue model based on artificial neural networks for predicting fretting fatigue life of dovetail joints

Fretting fatigue of dovetail joints is of paramount importance for ensuring equipment safety, where the swift and precise estimation of their fatigue life is crucial. In this study, we present a nonlocal multiaxial fatigue model based on artificial neural networks (ANN) to tackle these challenges. Initially, the damage parameters were calculated using critical plane approaches (CPA) and theory of critical distance (TCD) analysis, and the fretting fatigue stress was computed. Subsequently, these parameters were integrated as input features in the ANN model to predict the fretting fatigue life of dovetail joints. The predicted results demonstrate that this proposed model can accurately predict the fretting fatigue life of dovetail samples within a 1.5× limit band. Furthermore, a comparative analysis with other ANN models inspired by previous researchers also supports this viewpoint. This capability stems from its integration of ANN representation capabilities with physics and domain knowledge, such as CPA/TCD methods and fretting fatigue stress analysis. This approach not only establishes a theoretical foundation for predicting the fretting fatigue life of dovetail samples but also showcases promising practical applications.

Evaluation of the accuracy and efficiency of the modified maximum variance method for multiaxial fatigue analysis under constant amplitude loading

An optimized version of the Maximum Variance Method (MVM) is employed to determine maximum shear stress amplitudes in high-cycle multiaxial fatigue analysis using the critical plane approach, increasing accuracy and reducing computational burden. This refined approach posits that the MVM assumes that the critical plane is the one subjected to the maximum variance of the shear stress history. Comprehensive statistical analyses, including Analysis of Variance (ANOVA) and multiple comparison techniques such as Tukey’s HSD and Bonferroni correction, were conducted to systematically investigate the impact of critical factors on fatigue resistance, such as mean stress, phase, synchrony, failure criteria, and the strategy for calculating maximum shear stress amplitude. These analyses highlighted significant effects of mean stress and phase on the accuracy of fatigue strength predictions, underscoring the effectiveness of the enhanced MVM in managing complex loading scenarios. The results demonstrate that the proposed methodology performs equal to or better than conventional methods, with significantly lower computational costs.

Dealing with multiaxial non-proportional fatigue with varying mean stress: Invariant and critical plane approaches for component-like structural adhesive joints

A comparative investigation between an invariant-based approach using the signed Beltrami-stress and critical-plane approach using the Findley-stress is carried out for the fatigue lifetime prediction of an epoxy structural adhesive under multiaxial non-proportional loading with varying mean stress. Fatigue experiments with uniaxial and multiaxial loading (proportional and non-proportional) are done at stress ratios of −1 and 0.1. Two adhesive joints are evaluated: a hollow-cylinder butt-joint (HCBJ, sample with homogeneous stresses distribution), and a flange-rod-joint (FRJ, component-like specimen with complex stress state). For both geometries, multiaxial loading and an increasing mean stress lead to fatigue strength reduction, whereas the phase-shift effect is less pronounced. A systematic procedure for parameter determination is implemented for both approaches. For predictions of the HCBJ-sample, stresses are analytically obtained. For validation with the FRJ-sample, FEA-based stress calculation is used. For both joints, the critical plane approach results in more accurate predictions than the invariant-based approach. In comparative terms, the invariant-based approach is experimentally more complex, by requiring a mean stress correction, but its numerically simpler with lower calculation time. The critical-plane approach requires fewer experiments for parameter determination and provides more accurate results for non-proportional loading. However, it is more numerically demanding with larger computing time.

Study on the behavior of small cracks in PA38-T6 (6060-T6) aluminum alloy under multiaxial fatigue loadings

This study investigated the effects of multiaxial cyclic loading on the initiation and propagation of fatigue cracks in an industrial-grade aluminum alloy. Four different loading cases, including 90° out-of-phase and asynchronous loading, were used under the control of strain. The study used cellulose acetate film replication and SEM fractography techniques to increase the understanding of the evolution of fatigue damage on specimen surfaces. The material exhibited a shear damage mechanism with a significant amount of small cracks coalescence. It was explained why, despite a high agreement with the assumptions of the critical plane approach, the predicted fatigue life was overestimated at high loading levels. A correlation between the crack initiation period and overall fatigue life, regardless of loading case, was presented, which has a potential for practical applications.

A comparative study of several life prediction models based on the critical plane approach for fretting fatigue crack initiation

AbstractTo reasonably forecast the crack initiation characteristics of fretting fatigue, this study evaluates the accuracy of several damage models. The existing experimental and simulation investigations are compared, noting the similarities and differences in the crack initiation location, crack orientation angle, and crack initiation life predicted by various damage models. It is crucial to employ a reasonable and reasonable damage prediction model of fretting crack initiation life, as fretting fatigue, a phenomenon of mechanically fastened connecting parts, can considerably reduce the fretting fatigue life of the components. This paper compares the fatigue damage prediction models of fretting fatigue specimens under partial slip conditions, and it will help researchers understand the benefits and drawbacks of various damage models and give them the knowledge and foundation to select the more reasonable fretting fatigue damage model.

Propeller blade structural reliability analysis considering mixed-mode fatigue crack growth

Legacy propeller blades made of aluminum alloy are susceptible to fatigue cracking. Once the crack nucleated, it propagates rapidly because of the high rotational speed of the blade. This study uses mixed-mode fatigue crack analysis to understand the out-of-plane interaction of intergranular crack (IGC) and fatigue crack revealed in a U.S. Marine Corp. C-130 crash in 2017. The cracking mechanism is sequential: IGC followed by fatigue cracking, which eventually causes the liberation of the blade. A finite-element-method-based stress analysis elucidates the transition from IGC to fatigue crack. The result showed that the IGC provided enough driving force for the fatigue crack nucleation. A Monte-Carlo-simulation-based risk analysis is performed using the stress and crack growth analyses. The critical plane approach is utilized to determine the equivalent stress intensity factor for the crack growth analysis. The risk analysis results support the rapid liberation of the blade with consideration of large variation in initial crack size. The results also clearly show the necessity of structural risk analysis for planning inspection and maintenance.

A simplified fracture mechanics method for fatigue life analysis of weld roots

Volvo CE currently uses the effective notch stress method for assessing fatigue life in welded structures. For large structures such as frames, a sub modelling technique with a very fine mesh is necessary using millions of DOF. Stress tensors from unit load cases, estimated with FEA, are combined with time history loading from Multi Body Simulations of the complete machine operating on customer representative digitized test tracks. A critical plane approach (the Modified Wöhler Curve Method) is used to estimate the fatigue life. The usage of the effective notch method implies a very time-consuming design process. An LEFM approach for weld roots would be even more time-consuming but would be a more natural approach since the weld root consists of crack like defects. To overcome the drawbacks with the current design process that involves usage of the effective notch method, a hybrid method is defined using pre-calculated geometry factors for different crack sizes and weld geometries. The geometry factors as a function of crack size, and the weld geometry, are stored in a database. From the unit load cases the structural stress using a coarse mesh in the weld is extracted. Together with the geometry factors, the stress intensity factors may be estimated and used with Paris law to calculate the fatigue life of welds. A comparison between the effective notch method, LEFM and the new hybrid method is carried out for typical fillet welds is presented in this paper.

Numerical study on effects of microstructure randomness on fatigue fracture of non-oriented electrical steel

Advances in battery technology and electrical drive systems has allowed for more versatility in mobile applications found in automotive, logistics and aerospace engineering. Rotor cores used for electrical motors are often made from thin sheet metals with a maximum thickness of 0.5 mm. During operation, this material is subjected to variable dynamic loading conditions. As a consequence, fatigue testing is required for a more complete material characterisation. However, experiments on thin metals are generally more challenging as they require finer testing equipment that can apply low loads with high precision. Therefore, a micro-fatigue machine can be implemented to identify the high cycle fatigue behaviour of thin electrical steel sheets. Further, the manufacturing process of electrical steels often results in non-oriented grain structures. In other words, the material properties can vary between adjacent grains at the surface, thereby influencing the fatigue crack initiation mechanism. To investigate this effect, a finite element analysis is performed that includes a randomly generated set of grains with different elastic material behaviour. Using a critical plane approach the impact on the fatigue life prediction is assessed.

New test-based detail categories for fatigue design of crane runway beams

Top-running overhead bridge cranes are frequently supported by welded crane runway beams whose wheel loaded constructional details, such as the welded flange-to-web connections and the continuous double fillet welds to fasten the crane rail, are subject to multiaxial fatigue. The fatigue stressing is composed by normal and shear stresses due to the local wheel load introduction and global bending. As the fatigue stressing exhibits a phase shift of the stress components, it is referred to as nonproportional. The currently applicable detail category of welded flange-to-web connections according to EN 1993-1-9 (2005) is theoretically derived and does not appropriately address the specifics of these connections. A classification of rail welds including a detail-related nominal stress formula is missing. A design proposal for both constructional details is presented that is based on fatigue tests on girders with travelling and stationarily pulsating wheel loads to simulate the nonproportional fatigue stressing. To derive new detail categories from the test results, a fatigue failure hypothesis is formulated modifying Findley’s critical plane approach for the evaluation of welded constructional details with partial penetration and weld root failure on the basis of notch stresses.

Multiaxial fatigue life predictions of additively manufactured metals using a hybrid of linear elastic fracture mechanics and a critical plane approach

This paper introduces a hybrid approach which leverages Fatemi-Socie critical plane analysis to determine an equivalent-damage uniaxial stress amplitude for various multiaxial loading conditions including uniaxial, torsion, and axial-torsion. Then, mode I crack growth constants along with initial defect information are used to make life predictions for multiaxial loadings as a function of their equivalent-damage uniaxial stress amplitudes. Two different Laser-Powder Bed Fusion metals, Ti-6Al-4V and 17-4 PH stainless steel, in a total of nine different surface and heat treatment conditions are analyzed and life predictions based on initial defect size and mode I crack growth properties from the literature are made using the Hartman-Schijve crack growth equation.

Rolling contact fatigue performance of M50 steel: A combined experimental and analytical approach to determine life

This article presents an experimental and analytical investigation into the rolling contact fatigue (RCF) performance of AISI M50 bearing steel across a range of Hertzian contact pressures (Ph=2.6GPa to 3.4GPa). RCF experiments were conducted using a ball-on-rod test rig at three contact pressures to experimentally establish the relationship between contact pressure (contact stress) and the RCF life of M50. Simultaneously, a previously developed continuum damage mechanics finite element (CDM-FE) model, employing the Fatemi-Socie critical plane approach as the failure criteria, was utilized to provide analytical predictions of RCF life. The CDM-FE model’s damage rate equation was calibrated using open literature AISI M50 bearing steel torsion stress life (SN) data. The CDM-FE model incorporated Voronoi tessellations to represent the material microstructure and capture the material topological effect on fatigue scatter. RCF simulations were conducted at seven contact pressures ranging from 1.0 GPa to 3.4 GPa in 0.4 GPa increments. Similar to the experimental results, the analytical RCF life data set yielded a relationship between contact pressure and simulation life for M50. Good corroboration is observed between the contact pressure – life relationships from the experimental and analytical RCF life data sets. This is significant as it supports the use of a hybrid approach combining experimental tools (e.g. torsion fatigue and ball-on-rod) and a CDM-FE computational model to efficiently assess the RCF performance of bearing materials.

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.

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.

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.

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.

MFLP-PINN: A physics-informed neural network for multiaxial fatigue life prediction

In this study, a physics-informed neural network (MFLP-PINN), combining multiaxial fatigue critical plane model and the neural network, is proposed for life prediction. First, a multiaxial fatigue life prediction model based on the critical plane approach is proposed, which takes the equivalent strain amplitude on the critical plane as the main damage parameter, and considers the normal strain energy on the critical plane. Then, a total of four prediction models including the new critical plane model are integrated into the loss function of a neural network to build the MFLP-PINN. The accuracy of the proposed critical plane criterion and the MFLP-PINN are respectively verified using multiaxial fatigue test data of three materials. Finally, the results show that the prediction model integrated into the loss function has a significant impact on the neural network prediction. For a specific material, integrating a life prediction model with good prediction ability to this material as the loss function into a neural network model is helpful to improve prediction accuracy. Conversely, integrating a life prediction model with poor prediction ability to this material as the loss function into a neural network model will reduce the prediction accuracy.

Component Tests and Numerical Investigations to Determine the Lifetime and Failure Behavior of End Stage Blades

Abstract The paper focuses on experimental and numerical fatigue assessment procedures to evaluate the influence of multi-axial stress state caused by high centrifugal forces superimposed with bending loads due to blade vibrations on the lifetime of end stage blades from steam turbines. The experimental investigations on original-sized end stage blades were carried out on a test rig specially developed for high forces and multicomponent force application. This was based on detailed numerical simulations by the MPA University of Stuttgart. During the fractographic postexaminations of the tested blades using magnetic particle inspection, light and scanning electron microscopes, two competing damage mechanisms were identified that occurred at different locations. Numerical investigations by means of elastic–plastic finite element analyses were carried out to estimate the local stress conditions acting in the blade root. The local stresses and strains were postprocessed using the critical plane approach and advanced multi-axial fatigue damage parameters. Due to the high stress gradients at the edge of contact, over-conservative predictions may result if their effects are not taken into account. Based on the critical plane method in conjunction with fatigue damage parameters, an approach taking the stress gradient into consideration was developed to predict the fatigue life of the end stage blades. The approach is verified by the component tests on original-sized blades.