Critical Plane Parameter Research Articles

Fatigue assessment of structural components through the Effective Critical Plane factor

The integrity assessment of structural components under complex loading conditions relies on the evaluation of the fatigue damage typically arising from stress concentrations, such as geometric irregularities, notches, weld beads, grooves etc.. Various methodologies, including the Notch Stress Approach (NSA), the Theory of Critical Distances (TCD), the Strain Energy Density (SED), and the Critical Plane (CP) concept, have been pivotal in assessing fatigue strength for notched and welded components. Recent works combine some of the above mentioned methodologies, while other works propose to vary the embedded parameters accounting for the loading type or the fatigue lives, trying to improve the accuracy of the fatigue assessment process. This paper introduces a novel approach, the Effective Critical Plane (ECP), which is founded on the critical plane concept. The CP factor is, however, calculated starting from an averaged, over a small volume, stress–strain field. The size of the averaging volume is assumed to be a material parameter and is determined by a best fitting procedure over different experimental data sets. The novel approach is illustrated by means of the Fatemi-Socie and the Smith-Watson-Topper CP damage factors. Its potential application to other CP formulations is straightforward, as well. Literature experimental data for low carbon steel specimens possessing different notches and loading conditions are used to validate the method’s capability in accurately determining the fatigue life and to set the radius of the averaging volume for the given material and CP parameter. A spherical volume or circular area are used in case of fully 3D or 2D numerical models, respectively. Results are compared to those of some of already existing methods, namely SED, TCD and the Modified Wöhler Curve Method.

On the transition from shear to tensile failure mode in multiaxial fatigue

Depending on several factors, the failure mechanism can change with life for a particular material, from shear in Low Cycle Fatigue (LCF) to tensile in High Cycle Fatigue (HCF). Critical plane-based approaches to multiaxial fatigue have the capability of reflecting the damage mechanisms of the material and can, therefore, not only provide fatigue life estimation under different stress states, but also predict the highest damage (i.e., critical) plane orientation. While Fatemi-Socie critical plane parameter has been used extensively in the literature for many materials with shear failure mechanism, a modified form of the parameter recently proposed by Gates and Fatemi is shown to also be able to capture the failure mechanism transition from shear in LCF to tensile in HCF. The mechanisms by which this parameter accounts for the transition from shear to tensile is discussed in this work. A wide range of materials from the literature with failure mechanism change from shear in LCF to tensile in HCF are evaluated based on this parameter.

The effect of porosity size and oxidation on the HCF property of nickel-based single crystal superalloy at 980 ℃

The high-cycle fatigue (HCF) lives and fatigue limits of nickel-based single crystal superalloys (NBSX) with different porosity sizes were investigated at 980 °C. The test results show that the failure cracks prone to initiate from large internal pores, and the HCF properties are mainly controlled by the critical pore size. However, when the stress is close to the fatigue limit, the secondary cracks will initiate from the oxide layer obviously, which will further weaken the HCF properties. Therefore, a life prediction model based on the critical plane parameter and oxidation kinetic equation was proposed to evaluate the effect of porosity size and oxidation on the HCF life of NBSX. Then, combing the life prediction model and Murakami model, a fatigue limit evaluation model was presented. Compared with test results, the life prediction model and fatigue limit evaluation model are accurate and effective. Finally, the defect-tolerance analysis was carried out by the Kitagawa-Takahashi diagram, which could be a visual guide for the anti-fatigue design of NBSX.

Four actuators fretting fatigue rig and tests with cyclic normal load for Ti-6Al-4V

In the present paper, a new four actuators fretting fatigue rig is presented. This machine is capable of performing tests at high or room temperature. Further, it is possible to independently control all the loads involved in the fretting tests (bulk, normal and tangential loads) in a static and cyclic way. In order to evaluate the influence of cyclic normal load on the fretting case, a new set of fretting fatigue and coefficient of friction tests were carried out for the Ti-6Al-4V alloy. Also, a finite element model (considering and neglecting wear) was used in conjunction with a critical plane parameter (SWT) and a non-local stress averaging approach to estimate fretting life. The experimental results have shown that cyclic normal load has a beneficial effect on fretting life compared with those under constant normal load. Further, no significant difference was noticed for the coefficient of friction measured under static and cyclic normal load conditions. Concerning the life estimate approaches considered in this work, for the constant normal load case, both implemented methodologies, whether accounting or neglecting wear, provided satisfactory results, with the former being slightly more accurate. However, life estimates were more accurate for the cyclic normal load case when disregarding wear.

Effect of wear debris on fretting fatigue crack initiation

Both wear and fatigue occur in fretting condition, and they interact with one another during the whole process. Fretting fatigue is commonly analysed without considering the effect of wear in partial slip regime, although wear affects the lifetime of crack initiation. This paper investigates, for the first time, the effect of wear debris on fretting fatigue crack initiation. To investigate the effect of debris, first fretting wear characteristics in partial slip regime are analysed for loading conditions. Then, the effect of wear on fretting fatigue crack initiation is investigated using Ruiz parameters and critical plane methods without considering the debris effect. Through the results, we can see that loading conditions affect the wear profiles in different ways. Moreover, wear has a significant effect on the fatigue in partial slip regime without considering debris especially on the crack initiation location. Finally, considering wear debris in the analysis, its effect on critical plane parameters is investigated. It is found that by considering the wear debris effect, the fretting fatigue crack initiation location is shifted towards the trailing edge. The predictions of both crack initiation location and lifetime show a good agreement with the experimental data.

Rolling effect in fretting fatigue test at the crack initiation stage

The aim of this work is to perform a detailed analysis of the cracks paths obtained in fretting fatigue tests with cylindrical contact but taking into account the presence of an unavoidable (due to the fretting device’s stiffness) small oscillatory rolling. In order to obtain the crack paths crack surfaces were measured with a confocal microscope after the tests. Besides, the contact area and the surface crack initiation location were obtained by means of an optical microscope. The measurements indicate that the contact area is substantially larger than the theoretical one according to Hertz´s theory, contrary to tests done with only static normal load, in which both theoretical and experimental areas match perfectly. This observation means, that, due to the surface contact pad’s geometry (cylindrical) and the stiffness of the test setup, rolling is occurring during tests when tangential loading is developed. To reproduce this phenomenon, a 2D FEM model is developed. Stress/strain fields along the fretting cycle are analysed, noticing a substantial change of the contact surface hot-spot point and surface contact stress distribution, when compared with the non-rolling case. To predict the initial crack path, a previously developed model, based on a critical plane parameter, is applied using FEM stress/strain results. The results obtained show a better prediction of the surface hot-spot point and initial crack orientation estimation, when compared with the non-rolling case, and considering as a reference the experimental crack paths measured via confocal microscope.

Numerical analysis of crack propagation in fretting fatigue specimen repaired by stop hole method

Fretting fatigue is a common structural failure phenomenon. It can greatly reduce the fatigue life of a structure, and because of the complexity of its load condition, it is a challenging research topic. This paper applies, for the first time, the widely used stop hole repair technology to a fretting fatigue specimen in crack propagation stage in order to extend its lifetime. LEFM approach is adopted for the crack propagation phase using Paris’ law to predict the fatigue life. The critical plane parameter and variable length critical distance method are used together to predict the second crack initiation lifetime. This prediction method is validated by the central crack tensile fatigue experiment, which considers the stop hole. It is shown that the stop hole changes the propagation path and leads to a secondary crack initiation from the lower edge of hole. The increase of crack propagation life mainly comes from the secondary crack initiation. It is also found that the larger the radius of the stop hole, the greater the fatigue life is.

Experimental and numerical fretting fatigue using a new test fixture

A unique dovetail-based test fixture for fretting fatigue was designed and is demonstrated with a combined experimental and numerical campaign. Fretting fatigue damage is analysed and correlated with numerical analyses using a modern Ruiz formulation and Findley critical plane parameter with the Theory of Critical Distances. Initial test results show that a simple critical plane model correlates life and cracking directions with experiments; however, the Ruiz parameter only serves as a hot-spot indicator. The fixture is designed to permit testing in submerged conditions and to allow additional loads to the specimens by using a multi-axial fatigue machine.

The Effect of Surface Pit Treatment on Fretting Fatigue Crack Initiation

This paper analyses the effect of surface treatment on fretting fatigue specimen by numerical simulations using Finite Element Analysis. The processed specimen refers to artificially adding a cylindrical pit to its contact surface. Then, the contact radius between the pad and the specimen is controlled by adjusting the radius of the pit. The stress distribution and slip amplitude of the contact surface under different contact geometries are compared. The critical plane approach is used to predict the crack initiation life and to evaluate the effect of processed specimen on its fretting fatigue performance. Both crack initiation life and angle can be predicted by the critical plane approach. Ruiz parameter is used to consider the effect of contact slip. It is shown that the crack initial position is dependent on the tensile stress. For same type of model, three kinds of critical plane parameters and Ruiz method provide very similar position of crack initiation. Moreover, the improved sample is much safer than the flat-specimen.

Multiaxial fatigue of quenched and tempered U2 steel: Testing and fatigue life prediction

AbstractTension‐compression, tension‐tension, torsional, and 90° out‐of‐phase axial‐torsional fatigue tests were performed on a quenched and tempered U2 steel. All tests were conducted under force/torque control because macroscopic plastic strains were insignificant in the life range of interest (from 104 to 2 × 106 loading cycles). Stress‐based versions of the Fatemi‐Socie critical plane parameter and of the Smith‐Watson‐Topper parameter with a critical plane interpretation were evaluated using the experimental data. The Smith‐Watson‐Topper parameter was not able to correlate the test data. The Fatemi‐Socie method correlated most of the test data within factor‐of‐three boundaries. A modified Crossland invariant‐based parameter made of two interaction rules between the shear stress amplitude and the maximum hydrostatic stress, and of a definition of shear stress amplitude based on the maximum prismatic hull method, yielded fatigue life estimates in reasonable agreement with the experimental observations.

Significance of hot isostatic pressing (HIP) on multiaxial deformation and fatigue behaviors of additive manufactured Ti-6Al-4V including build orientation and surface roughness effects

Additive manufacturing (AM) technology has gained significant attention in recent years due to several important advantages. However, design of critical load carrying parts using this technique is still at its infancy, partly due to the inferior performance and lack of sufficient understanding of cyclic deformation and fatigue behaviors of AM metals as compared to their wrought counterparts. Similar to most other components in different industries, AM parts typically undergo cyclic loadings through their service life; therefore, fatigue performance is a key performance criterion. In addition, due to common presence of multiaxial stress states at fatigue critical locations, multiaxial fatigue is of special interest. In this study, thin-walled tubular specimens made of Ti-6Al-4V alloy fabricated with powder bed fusion (PBF) process were used to investigate their cyclic deformation and fatigue behaviors. The main focus of this study was on the effect of hot isostatic pressing (HIP) on fatigue performance under uniaxial, torsion, combined in-phase, and 90° out-of-phase axial-torsion loads. To study build orientation effect, both vertically built and diagonally built (at 45°) specimens were included. However, no substantial difference on the fatigue behavior of vertical and 45° built specimens was observed. Although the majority of specimens had a machined surface, some torsional tests with as-built surface were also included to evaluate surface roughness effect. It was found that even after HIP treatment, the rough surface is the dominant factor in shortening the fatigue life. In addition, to evaluate the effectiveness of the HIP treatment, torsion fatigue performance of the HIPed specimens were compared to torsion fatigue performance of annealed AM specimens, as well as to the multiaxial fatigue behavior of the conventional wrought material. Fatigue failure mechanism of the HIPed material was shear, similar to the wrought material, and fatigue performance was found to be similar to the wrought alloy. Fatigue test results were correlated well using a shear-based critical plane parameter approach, also similar to the wrought material. Comparison of multiaxial fatigue data in this study and a similar previous study by the authors indicates that fabrication machine-to-machine and the associated build parameter differences can result in substantial differences in the observed defect size and population, resulting in different failure mechanisms and subsequently different fatigue performance.

Generalized probabilistic model allowing for various fatigue damage variables

This paper proposes a generalization of the Castillo and Fernández-Canteli probabilistic fatigue model and shows how most fatigue models can be obtained as particular cases. Models that include mean-stress effects and multiaxial loading conditions are considered as examples of this general framework. Several fatigue damage parameters such as the Smith-Watson-Topper, the Walker-like strain, energy-based parameter in uniaxial and multiaxial loading conditions, and multiaxial critical plane parameters are proposed as reference parameters for the probabilistic model. It is shown that the Castillo & Fernández-Canteli probabilistic approach can be successfully extended to these advanced fatigue models.

Multiaxial Fatigue Life Prediction of Metallic Materials Based on Critical Plane Method under Non-Proportional Loading

The critical plane method is widely discussed because of its effectiveness for predicting the multiaxial fatigue life prediction of metallic materials under the non-proportional loading conditions. The aim of the present paper is to give a comparison of the applicability of the critical plane methods on multiaxial fatigue life prediction. A total of 205 multiaxial fatigue test data of nine kinds of metallic materials under various strain paths are adopted for the experimental verification. Results shows that the von Mises effective strain parameter and KBM critical plane parameter can give well predicted fatigue lives for multiaxial proportional loading conditions, but give poor prediction lives evaluation for multiaxial non-proportional loading conditions. However, FS parameter shows better accuracy than the KBM parameter for multiaxial fatigue prediction for both proportional and non-proportional loading conditions.

Application of the critical plane approach to the torsional fatigue assessment of welds considering the effect of residual stresses

This study aims to investigate how the welding residual stresses affect the fatigue life of steel tubular joints. A single pass weld with filler material is created on the tubular specimens made of structural steel S355J2H. At first, welding residual stresses are calculated numerically by means of FE simulations. The validity of the results is verified experimentally by means of diffraction measurement techniques. Then, an uncoupled damage model based on the critical plane approach is utilized in order to calculate the fatigue life and the initial crack orientation. The as-welded specimens were subjected to cyclic torsional loading with constant stress amplitudes. The Fatemi-Socie (FS) damage parameter is used which is interpreted as the cyclic shear strain damage modified by the normal stress to include the crack closure effect. The stable portion of welding residual stresses is accounted for by the normal stress term of the model. It was observed that despite the common understandings about the critical weld notches, the crack initiation sites under torsional loading have been shifted from the weld toe and from the surface to the heat affected zone and beneath the surface where high tensile residual stresses exist. Then the initial cracks propagated toward the surface whose orientations were influenced by the presence of compressive residual stresses on the surface.It was generally found that the Fatemi-Socie parameter is capable of torsional fatigue damage assessment of welded tubular specimens which contain residual stresses since this critical plane parameter is based on the maximum shear strain plane.

Multiaxial Cycle Deformation and Low-Cycle Fatigue Behavior of Mild Carbon Steel and Related Welded-Metal Specimen

The low-cycle fatigue experiments of mild carbon Q235B steel and its related welded-metal specimens are performed under uniaxial, in-phase, and 90° out-of-phase loading conditions. Significant additional cyclic hardening for 90° out-of-phase loading conditions is observed for both base metal and its related weldment. Besides, welding process produces extra additional hardening under the same loading conditions compared with the base metal. Multiaxial low-cycle fatigue strength under 90° out-of-phase loading conditions is significantly reduced for both base-metal and welded-metal specimens. The weldment has lower fatigue life than the base metal under the given loading conditions, and the fatigue life reduction of weldment increases with the increasing strain amplitude. The KBM, FS, and MKBM critical plane parameters are evaluated for the fatigue data obtained. The FS and MKBM parameters are found to show better correlation with fatigue lives for both base-metal and welded-metal specimens.

Mean Stress in Algorithms Estimating Fatigue Life of Selected Structural Materials

The paper presents comparison of the mathematical models for fatigue life calculations including influence of the mean load value. Several model based on stress analysis on the critical plane and energy density parameter were investigated. In this paper three types of materials were tested and subjected to bending, torsion and combination of bending with torsion loading with the participation of mean value of the load. It was found, that the best fatigue life estimations obtained by models taking into account changes of the material behavior under fatigue loading related to the specified numbers of cycles of the load.

Notched fatigue behavior and stress analysis under multiaxial states of stress

The effect of notches on multiaxial fatigue behavior was studied using thin-walled tubular 2024-T3 aluminum specimens with a circular transverse hole. Constant amplitude fully reversed axial, torsion, and in-phase and 90° out-of-phase axial–torsion tests were performed in load control. Stress analysis was performed using both Neuber’s rule and FEA to study local stress distributions. Neuber’s rule was found to be in reasonable agreement with FEA results for all loading conditions considered. Fatigue crack initiation for all loading cases examined was experimentally observed to occur on planes of maximum shear. For the same equivalent nominal stress, experimental lives in pure torsion were longer than those for pure axial loading. In-phase fatigue lives were also longer than out-of-phase lives at the same equivalent stress. The nominal stress–life approach, applied by considering the fatigue notch factor along with both maximum principal stress and von Mises equivalent (or effective) stress, produced mostly non-conservative fatigue life predictions that varied by as much as a factor of 10 from experimental results. The local stress and strain–life approaches, based on von Mises effective stress or strain, resulted in reasonable correlation of test data at shorter fatigue lives, but became increasingly less accurate in the mid to high cycle fatigue regime, where predictions were in error by more than a factor of 10. The Fatemi–Socie critical plane parameter correlated all test data reasonably well (typically within a factor of 3) and is consistent with the experimentally observed damage mechanism for the tested material.

Microstructure-sensitive weighted probability approach for modeling surface to bulk transition of high cycle fatigue failures dominated by primary inclusions

A simulation-based probabilistic strategy is developed to characterize the surface to bulk transition of high cycle fatigue failures dominated by primary inclusions. The probability of fatigue crack initiation in the surface region is calculated by computing the expected number of critical fatigue hot spots in this region. This is done by considering the probability of inclusion-matrix debonding and the fatigue crack initiation potency of partially-debonded inclusions for a given load ratio and stress amplitude.A case study is presented whereby the surface initiation probability is studied in uniaxial strain-controlled cyclic loading simulations of round smooth specimens of the fine grained powder metallurgy (PM) processed Ni-base superalloy IN100. The fatigue crack initiation potency of partially-debonded nonmetallic inclusions is assessed by calculating the Fatemi–Socie (FS) critical plane parameter from generalized plain strain crystal plasticity finite element simulations. Idealized spherical ceramic inclusions with homogeneous linear elastic isotropic material properties are considered to isolate the FS parameter sensitivity to inclusions’ size, stress amplitude, and polycrystalline microstructure realization around the inclusion.

Notched fatigue behavior including load sequence effects under axial and torsional loadings

Notch effects on axial and torsion fatigue behaviors of low carbon steel were investigated. Fully-reversed tests were conducted on thin-walled tubular specimens with or without a transverse circular hole. A shear failure mechanism was observed for both smooth and notched specimens and under both axial and torsion loadings. The notch effect was more pronounced under axial loading, in spite of higher stress concentration factor in torsion. The commonly used nominal S–N approach with fatigue notch factor in conjunction with von Mises effective stress resulted in overly conservative life predictions of both smooth and notched torsion fatigue lives. Neuber’s rule yielded notch root stress and strain amplitudes close to the FEA results for both axial and torsion loadings. The local strain approach based on effective strain obtained from Neuber’s rule or FEA resulted in poor correlation of the fatigue life data of smooth and notched specimens. The Fatemi–Socie critical plane parameter represented the observed failure mechanism and resulted in very good correlations of smooth and notched specimens fatigue data under both axial and torsion loadings. In block loading tests with equal number of alternating axial and torsion cycles at the same stress level, beneficial effect of axial loading was observed. Possible potential reasons for this unexpected behavior are discussed.

A computer simulation of four-point bending fatigue of a rear axle assembly

The bending fatigue test of a rear axle assembly is simulated by using a FE-integrated fatigue analysis methodology. The presented technique is based on local stress–strain approach in conjunction with two critical plane damage parameters. The stress–strain response at a material point is computed with a cyclic plasticity model coupled with a notch stress–strain approximation scheme. Linear elastic FE stress analyses are used in the calculation of local fatigue loading. All computational modules are implemented into the software tool and used in the four-point bending fatigue test simulation of rear axles made of a high-strength alloy steel. In fatigue models, proportional loadings with a static preload are considered, and the effects of residual stresses are neglected. The fatigue test cycles and crack initiation locations are predicted using Smith–Watson–Topper and Fatemi–Socie fatigue damage parameters. Both damage parameters provided conservative test cycle estimates for the test conditions simulated. It is also observed that von Mises stress distributions cannot be used to predict fatigue crack initiation locations while Smith–Watson–Topper critical plane parameter estimated the cracking location suitably. Comparisons with the prototype tests showed the applicability of the proposed approach.