Critical Plane Approach Research Articles

Influence of multiaxial fatigue loading conditions on white etching crack formation

The rolling contact fatigue phenomenon “White Etching Cracks” (WEC) was investigated in this study. The load conditions in a rolling element bearing causing WEC formation were reproduced with a simplified testing setup, using cylindrical specimens and compression-torsion loads. In-phase and out-of-phase loads were tested. It was found that under the same equivalent stresses, the experimental results varied greatly between the two load cycles. Multiple characterisation techniques were used for comparing crack behaviour and microstructural evolution. It was found that only in-phase loading resulted in WEC-like structures. A critical plane approach was employed to find possible reasons for the differing results.

Early cracking orientation under high stress gradients: The fretting case

Many fretting contacts experience a rapid variation of the magnitude and relative contribution of the stress components away from the surface. This feature of the fretting problem poses an additional difficulty for the modeling of the early cracking orientation. In this work, critical plane approaches associated with a process zone are evaluated by taking into account the fretting crack behavior observed in two different steels. The results show that the conventional approaches may provide inconsistent cracking directions. A new method for early cracking orientation prediction is developed by employing the average values of the normal and shear stresses along a critical direction. This method is simpler to implement and improves the estimates when compared to the other approaches.

Multiaxial fatigue assessment of crankshafts by local stress and critical plane approach

ABSTRACT. For multiaxially-loaded parts several stress-based fatigue assessment concepts are applicable mostly taking uniaxial test results as basis. These approaches work well in case of proportional loading states, but on contrary, for non-proportional stress conditions, implying a change of the principal stress direction, deviations in the fatigue life estimation may occur. The aim of this study is to evaluate the cyclic multiaxial material behavior experimentally and to proof the applicability of stress-based methods to assess the fatigue strength. The investigated base materials incorporate the commonly applied crankshaft steels 50CrMo4 and 34CrNiMo6 without surface-layer post-treatments. Extensive fatigue tests with small-scale specimens are performed to evaluate the material behavior under cyclic loading. The experiments include basic uniaxial characterizations, such as notch stress sensitivity and effect of loading type, including tests under tension, rotating bending, and torsion loading. Additionally, combined loading tests with proportional and non-proportional situations are presented to reveal the fatigue resistance for multiaxial stress states. Significant loading conditions, such as proportional stress under rotating bending and torsion, and further on, non-proportional effects like phase shifts and varying frequency ratios are presented. The local fatigue strength assessment is performed on the basis of the critical plane approach, whereat the normal and shear stresses are transformed in numerous cutting planes. Equivalent stress hypotheses are applied and compared with the experiments showing that the Huber-Mises-Hencky criterion fits well to the test results in case of proportional rotating bending and torsion loading. KEYWORDS. Multiaxial fatigue assessment; Local stress concept; Critical plane approach; Crankshaft.

Comparison between SSF and Critical-Plane models to predict fatigue lives under multiaxial proportional load histories

Materials can be classified as shear or tensile sensitive, depending on the main fatigue microcrack initiation process under multiaxial loadings. The nature of the initiating microcrack can be evaluated from a stress scale factor (SSF), which usually multiplies the hydrostatic or the normal stress term from the adopted multiaxial fatigue damage parameter. Low SSF values are associated with a shear-sensitive material, while a large SSF indicates that a tensile-based multiaxial fatigue damage model should be used instead. For tension-torsion histories, a recent published approach combines the shear and normal stress amplitudes using a SSF polynomial function that depends on the stress amplitude ratio (SAR) between the shear and the normal components. Alternatively, critical-plane models calculate damage on the plane where damage is maximized, adopting a SSF value that is assumed constant for a given material, sometimes varying with the fatigue life (in cycles), but not with the SAR, the stress amplitude level, or the loading path shape. In this work, in-phase proportional tension-torsion tests in 42CrMo4 steel specimens for several values of the SAR are presented. The SSF approach is then compared with critical-plane models, based on their predicted fatigue lives and the observed values for these tension-torsion histories. KEYWORDS. Multiaxial fatigue life prediction; Critical-plane approach; Polynomial stress scale factor approach.

Application of the Moment Of Inertia method to the Critical-Plane Approach

The Moment-Of-Inertia (MOI) method has been proposed by the authors to solve some of the shortcomings of convex-enclosure methods, when they are used to calculate path-equivalent ranges and mean components of complex non-proportional (NP) multiaxial load histories. In the proposed 2D version for use with critical-plane models, the MOI method considers the non-proportionality of the projected shear-shear history on each candidate plane through the shape of the load path, providing good results even for challenging non-convex paths. The MOI-calculated path-equivalent shear stress (or strain) ranges from each counted load event can then be used in any shear-based critical-plane multiaxial fatigue damage model, such as Findley’s or Fatemi-Socie’s. An efficient computer code with the shear-shear version of the MOI algorithm is also provided in this work. KEYWORDS. Multiaxial fatigue; Non-proportional loadings; Equivalent ranges; Critical-Plane Approach.

An evaluation of total fatigue life prediction of a notched shaft subjected to cyclic bending load

This article deals with the fatigue life prediction of a notched shaft in a bend loading state. The life prediction models applied include both initiation and propagation phases, without a prior definition of an initial crack length. Two criteria based on the critical plane approach were carried out to predict initiation fatigue life. The model proposed by Socie is applied to predict initial crack size in the propagation phase, and total fatigue life includes a combination of both initiation and propagation phases. In order to validate the estimated lives, results from experimental tests carried out on notched shafts were compared with predicted lives.

Multiaxial fatigue assessment of friction stir welded tubular joints of Al 6082-T6

The present paper addresses the problem of designing aluminium friction stir (FS) welded joints against multiaxial fatigue. After developing a bespoke FS welding technology suitable for joining aluminium tubes, some one hundred welded tubular specimens of Al 6082-T6 were tested under pure axial, pure torsional and biaxial tension-torsion loading. The influence was explored of two independent variables, namely the proportional or non-proportional nature of the biaxial loading and the effect of axial and torsional non-zero mean stresses. The experimental results were re-analysed using the Modified Wöhler Curve Method (MWCM), with this bi-parametrical critical plane approach being applied in terms of nominal stresses, notch stresses, and also the Point Method. The validation exercise carried out using these experimental data demonstrated that the MWCM is applicable to prediction of the fatigue lives for these FS welded joints, with its use resulting in life estimates that fall within the uniaxial and torsional calibration scatter bands. The approach proposed in the present paper offers, for the first time, a complete solution to the problem of designing tubular FS welded joints against multiaxial fatigue loading.

Multiaxial high-cycle fatigue life prediction model based on the critical plane approach considering mean stress effects

The aim of this paper is to propose a modified multiaxial high-cycle fatigue criterion based on the critical plane approach. The proposed criterion contains three parameters, that is, shear stress amplitude, normal stress amplitude and mean normal stress. In order to take into account the mean shear stress effects, the critical plane is determined by the maximum shear stress. In the proposed multiaxial fatigue criterion, the influence of mean normal stress on fatigue damage is also considered. Based on the proposed criterion, the multiaxial fatigue life is predicted, and the results showed a good agreement with experimental data obtained from some literatures.

Thermo-mechanical fatigue approach to predict tooling life in high temperature metal forming processes

In high temperature metal forming processes, strong mechanical and thermal cyclic loads coexist in the formed material and in the tooling. Such a phenomenon has a negative influence in the tool life cycle. The thermal and mechanical ranges lead to the appearance of cracks on the tool surface because of thermo-mechanical fatigue damage (TMF). The objective of this paper is to present a simplified cumulative thermo-mechanical fatigue model which has been developed in order to study the most critical areas in the forming tools according to the predicted number of cycles up to crack appearance considering multi-axial fatigue and oxidation. This model is based on assumptions of a general cumulative TMF model proposed by Neu and Sehitoglu; and critical plane approaches by Smith, Watson and Topper, and Fatemi and Socie. In general, cumulative TMF approaches three agents are considered: multiaxial-fatigue, oxidation and creep. The developed model has been applied to a specific manufacturing process of seamless steel pipes which includes three basic forming steps: backward extrusion, perforation and Pilger rolling mill. This process transforms a blank, or ingot, into a final seamless steel pipe with specific dimensions and characteristics depending on market requirements. These studies have been carried out in order to improve the tool life. To this end, the forming process has been reproduced by means of coupled thermo-mechanical FE simulations using the ABAQUS/Explicit solver. Moreover, a post-processing subroutine has been incorporated which enables to predict the number of cycles until crack appearance (tool life) according to both the general model of Neu and Sehitoglu, and the specific model developed. Good correlations between predicted and actually observed damage areas have been reached in both cases. The advantage of the hereafter proposed TMF model is that, it takes the most convenient features of general TMF models and it is particularized to a reduced input TMF model in order to analyze high temperature metal forming processes.

Professor Ewald Macha’s contribution to the development of methods for multiaxial fatigue life estimation

Multiaxial fatigue of machine elements and construction is still a remarkable problem in everyday life. Many accidents were consequences of inaccurate estimation of stresses and fatigue life. Despite many years of work and research on the subject, fatigue life estimation is still very important to be examined. Professor Ewald Macha was a researcher involved in the development issues of fatigue life estimation and, in particular, was interested in multiaxial fatigue failure criteria based on the critical plane approach, where he formulated the stress, strain and strain energy density criteria. Particularly noteworthy are the methods for determination of the critical plane position. In this field, Professor Macha proposed a weight function method, and then a variance method. These methods have been verified experimentally. Professor Macha also proposed a method for determination of the energy fatigue characteristics, especially for cyclically unstable materials. This paper describes the scientific achievements of Professor Macha.

Numerical Modelling of AISI 316L Cardiovascular Stent Behaviour under Blood Pressure and Restenosis Loadings

In the present study, ABAQUS finite element modelling was used to explore the durability of cardiovascular stent made of AISI 316L. It was found that the blood pressure loading never causes the fracture of the stent. This result was confirmed by the application of two critical plane approaches and one mean stress criterion. However, when subjected to restenosis compressive loading the stent was found to experience an in-service failure. The last proved to be dependent on the stent diameter reduction, rate and location of restenosis. Since restenosis forms gradually and randomly within the artery, two distributions were considered and investigated. The eccentric restenosis turned out to be more deleterious than the concentric one.

Numerical procedure for fatigue life prediction for railway turnout crossings using explicit finite element approach

In this paper a numerical procedure for analysis of rolling contact fatigue crack initiation and fatigue life prediction for the railway turnout crossing is presented. To analyse wheel–rail interaction, a three-dimensional explicit finite element (FE) model of a wheelset passing a turnout crossing is developed to obtain the dynamic responses such as the contact forces, displacements and accelerations as well as the stresses and strain in the crossing nose. The material model accounting for elastic–plastic isotropic and kinematic hardening effects in rails is adopted. The fatigue life of the rails is defined as the time to rolling contact fatigue crack initiation. In predicting the fatigue life Jiang and Sehitoglu model is used, which is based on the critical plane approach. Using the FE simulation results the ten critical locations on the crossing nose susceptible to crack initiation are determined first. Then, using the fatigue model the critical planes in these locations are obtained and the number of cycles to fatigue crack initiation is calculated for each location, based on which the most decisive location and the crossing life is determined. The results of the numerical simulations are presented and discussed.

Fatigue life and early cracking predictions of extruded AZ31B magnesium alloy using critical plane approaches

The Smith–Watson–Topper (SWT) criterion, the Fatemi–Socie criterion, and the Jiang criterion were evaluated based on the experimentally observed cracking behavior and fatigue life of an extruded AZ31B magnesium alloy. The fatigue experiments were performed on thin-walled tubular specimens subjected to tension–compression, torsion, and combined axial–torsion loading. The SWT criterion fails to correlate the tension–compression and torsion baseline experiments. The Fatemi–Socie criterion predicts well the fatigue lives for all experiments, but the criterion yields a less satisfactory prediction of the cracking behavior for most of the tests. The difficulty of the SWT and Fatemi–Socie criteria in correlating the observed cracking orientations is attributed to the mixed cracking behavior of the material. The Jiang criterion provides a reasonable description of the cracking behavior and fatigue life predictions. A discussion on the current capability of the critical plane approaches to predict the fatigue behavior of wrought magnesium alloys is presented, and further studies are recommended.

Assessment of Bending Fatigue Strength of Crankshaft Sections with Consideration of Quenching Residual Stress

High-cycle bending fatigue is the primary failure mode of crankshafts in engines. Compressive residual stresses are often introduced by induction quenching to improve the fatigue strength of crankshafts. The residual stresses, which are commonly obtained by numerical methods, such as the finite element method (FEM), should be included in fatigue failure analysis to predict the fatigue strength of crankshafts accurately. In this study, the simulation method and theory of quenching process are presented and applied to investigate the residual stresses of a diesel engine crankshaft. The coupling calculation of temperature, microstructure, and stress fields of the crankshaft section is conducted by FEM. Then, the fatigue strength of the crankshaft section is analytically assessed by Susmel and Lazzarin’s criterion based on the critical plane approach that superimposes the residual stresses onto the bending stresses. The resonant bending fatigue tests of the crankshaft sections are conducted, and the tests and analytical assessments yield consistent results.

Description of Inherent and Induced Anisotropy in Granular Media with Particles of High Sphericity

ABSTRACTThe primary objective of this study was to demonstrate that a significant degree of anisotropy may occur in particulate materials that have nearly spherical aggregates (i.e., are typically considered as isotropic) provided there is a bias in the distribution of pore space as a result of the initial densification process. The study included both an experimental and a theoretical component. An experimental program was conducted on dynamically compacted samples of Ottawa standard sand (C109) and incorporated a series of tests performed at different orientations of the specimens. Following the experimental part, a plasticity formulation based on the critical-plane approach was presented. A systematic procedure for identification of material parameters was outlined, and some numerical simulations of a series of triaxial tests were conducted. The last part of this work dealt with a much weaker load-induced anisotropy. Here, the mathematical framework was enhanced by an evolution law for the material fab...

Research of Fatigue Crack Growth Based on Critical Plane Method

To precisely simulate the path of crack growth, a simulation of crack growth progress has been presented by using the redevelopment function of ANSYS APDL and introducing the random criterion of crack propagate directions with critical plane approach. Based on the C(T) specimen test, extract the stress fields of crack tips, and set reasonable simulation parameters to verify the simulation method. The result shows that the initiation site and propagation path of crack are basically anastomoses to the results of test, which make a guiding function for preventing the accidents of crack growth and making anti crack plan.

Spectral fatigue life estimation for non-proportional multiaxial random loading

A frequency-domain High-Cycle Fatigue (HCF) criterion based on the critical plane approach is here proposed to estimate fatigue life of smooth metallic structural components under multiaxial random loading. The procedure consists of the following three steps: (a) definition of the critical plane; (b) PSD evaluation of an equivalent normal stress; and (c) computation of the fatigue life. A new formulation to define the critical plane is adopted in order to improve the lifetime estimation. The criterion is validated through comparison of the obtained numerical results with experimental fatigue data available in the literature for structural steel specimens subjected to a combination of random non-proportional bending and torsion.

Multiaxial fatigue modeling for Nitinol shape memory alloys under in-phase loading

The realistic loading condition for many components is multiaxial arising from multidirectional loading or geometry complexities. In this study, some multiaxial stress-based classical and critical plane fatigue models are briefly reviewed and their application for martensitic Nitinol under torsion and in-phase axial-torsion loading is evaluated. These models include von Mises equivalent stress, Tresca, Findley, McDiarmid, and a proposed stress-based Fatemi–Socie-type model. As the fatigue cracks appear to be on the maximum shear plane for the martensitic Nitinol, all the models examined here consider the shear stress as the primary damage parameter. Among all the models considered in this study, the proposed Fatemi–Socie-type model provides a better prediction for fatigue lives when compared to torsion and in-phase multiaxial fatigue experimental data from literature. Analyses indicate that critical plane approaches are more appropriate for multiaxial fatigue prediction of Nitinol alloys, at least in martensitic phase. Finally, recommendations are made to calibrate more reliable multiaxial fatigue models for Nitinol.

Multiaxial fatigue assessment of welded joints using the notch stress approach

This paper presents an evaluation of the safety involved when performing fatigue assessment of multiaxially loaded welded joints. The notch stress approach according to the IIW is used together with 8 different multiaxial criteria, including equivalent stress-, interaction equation- and critical plane approaches. The investigation is carried out by testing the criteria on a large amount of fatigue test results collected from the literature (351 specimens total). Subsequently, the probability of achieving a non-conservative fatigue assessment is calculated in order to evaluate the different criteria quantitatively. Large variation in safety is observed, especially for non-proportional loading.

A correction in the algorithm of fatigue life calculation based on the critical plane approach

The paper presents the algorithm for calculating the fatigue life taking into account the variability of coefficients occurring in the multiaxial fatigue criterion depending on the number of cycles to failure. The algorithm has been analysed under uniaxial cyclic loads and a combination of bending and torsion for four structural materials. Significant increase of convergence of calculated and experimental fatigue life using the new algorithm as compared to the classical approach for five selected multiaxial fatigue criteria based on a critical plane has been demonstrated.