Non-proportional Multiaxial Fatigue Research Articles

Fatigue behaviors and life evaluation of AISI304 stainless steel under non-proportional multiaxial random loading

Fatigue tests on AISI304 stainless steel under non-proportional multiaxial random loading conditions were conducted with uniform hollow specimens at room temperature. The results revealed initial hardening and subsequent cyclic softening under uniaxial loadings and additional hardening under non-proportional multiaxial loadings. This shift from softening to additional hardening significantly reduced the failure life. Fractographic analysis and Electron Backscatter Diffraction (EBSD) observations identified planar slip as the dominant deformation mechanism under uniaxial loading. Multiple slip system activations, strong slip interactions, and martensitic transformation were key factors influencing changes in cyclic deformation behavior under non-proportional loadings. A novel life evaluation method based on the Itoh–Sakane (IS) method was established, demonstrating accurate evaluations for both uniaxial and non-proportional multiaxial fatigue life under random loading conditions.

Theoretical and experimental investigations of crack propagation behavior and delamination in GLARE specimens affected by non-proportional fatigue loadings

In actual operation conditions, the structural parts of automotive, aerospace and other significant industrial applications undergo the multi axial fatigue loading with non-proportionality states. Fiber metal laminates (known as FML) are the best options to manufacture these structural parts. The current study examines the effects of a specific condition of multi-axial fatigue loadings (repeated tension with static shear stresses) on the behaviors of crack growth and delamination in GLARE specimens (abbreviated of glass laminates aluminum reinforced epoxy). Analytical model with idea of maximum tangential stress criterion modification has been adopted to represent the non-proportionality state of fatigue loading. Paris equation, equivalent stress intensity factor range, fiber-bridging effects and delamination shape were included in this model. The current idea was compared with a previous idea that depends on the principal stresses in representation of non-proportional multi-axial fatigue loadings. Specimens have coding GLARE_2A 2/1 were fabricated by VARTM technique (vacuum assisted resin transfer molding technique). Special treatments have been done on the aluminum surfaces before specimen fabrication to increasing delamination resistance. Novel fatigue apparatus was manufactured to guarantee apply the under study conditions for multi axial fatigue loading and to introduce experimental investigation of crack and delamination growths in GLARE specimens. The obtained results of the current idea were in a considerable agreement with that of the previous idea of the principal stresses. The maximum deviations between analytically extracted results were less than 1% for crack growth, 5.4% for bridging stress, 4.8% for crack opening and 6.3% for delamination growth. Experimentally, the measured results have been compared with analytical results for the purpose of validation. Acceptable matching between results with maximum difference of 7.65% was the important outcome of this study.

A hierarchical mechanism-informed neural network approach for assessing fretting fatigue of dovetail joints

In the present paper, a hierarchical mechanism-informed neural network (HMNN) life prediction method was proposed. The fretting fatigue was decomposed into different fatigue problems and considered in four neural network layers, which were hierarchically and progressively established for proportional multi-axial fatigue, non-proportional multi-axial fatigue, notch fatigue and fretting fatigue, respectively. Each layer can be used to assess the fatigue life of the previous layer based on the progressive construction of fatigue complexity. The HMNN approach can predict all kinds of fatigue implemented in the method with reasonable accuracy and provides a new approach for complex fatigue assessment.

Glass laminate aluminum reinforced epoxy under non-proportional multiaxial fatigue loading: Experimental testing and new fatigue apparatus development

Predominately, the structures and components in aeronautic, automotive and other important implementations suffer from non-proportional multi-axial fatigue loading. One of the best selected materials to fabricate these structures and components are fiber metal laminates (FML). In this research, fatigue crack-propagation in glass-laminate aluminum reinforced-epoxy (GLARE) specimen under the effect of special case of multi-axial fatigue loading (constant shear with repeated tensile stresses) has been studied analytically, numerically and experimentally. GLARE_2 A 2/1 specimen was fabricated using vacuum assisted resin transfer molding technique after special preparation aluminum surface procedure. New multi-axial fatigue apparatus including mechanical, hydraulic and control systems was manufactured to investigate crack growth experimentally. Analytical model using Paris relation was adopted to predict crack growth through aluminum layers of GLARE specimen. The rate of crack propagation is related to the mixed-mode equivalent stress intensity factor, which is estimated by the superposition for both fiber-bridging and far-field stress intensity factors. The crack opening contour, distribution of fiber-bridging stress, delamination growth and its shape were evaluated in simultaneous manner to find the fiber-bridging stress intensity factor. ABAQUS 2021 software has been used to simulate crack and delamination growth in GLARE specimen with the aforementioned fatigue loading. The extracted results from analytical and numerical models such as crack growth, crack opening, delamination shape and crack angle have been compared with that measured experimentally. The comparison indicates that there is good agreement between the calculated and measured results (with maximum deviation of 8.74% for crack growth).

Investigation of analytical model of crack propagation under multi axial fatigue in fiber metal laminate

Mostly the aerospace and other applications parts during their service life are subjected to the multi axial fatigue with non-proportional loading. In this study, the fatigue crack growth in glass laminate aluminum reinforced epoxy subjected to special case of non-proportional multiaxial fatigue (cyclic tension with constant shear) has been investigated. New prediction analytical model used empirical Paris equation has been adopted. Crack-growth rate was in relation with the equivalent stress-intensity factor for mixed mode at the crack-tip. Bridging stress-intensity factor was superimposed with the far-field stress-intensity factors to evaluate the equivalent stress-intensity factor. Bridging stress distribution, crack opening contour, delamination shape and its growth have been estimated simultaneously to evaluate the bridging stress-intensity factor. The obtained results indicated that there was a considerable enhancement in the crack growth rate (193.8%), number of cycles required to full failure (192%) and other performance characteristic as compared with the monolithic aluminum. Numerical simulation by ABAQUS 2021 software has been implemented to verification of the analytical model. A significant convergence in behavior between the extracted results from both analytical model and numerical simulation with maximum deviation reach to 8.2%.

Effect of hot isostatic pressing on fatigue behavior and fracture mechanism of A319 aluminum alloy under uniaxial and nonproportional multiaxial loading conditions

AbstractThe effect of hot isostatic pressing (HIPing)‐induced porosity difference on the fatigue behavior and fracture mechanism of A319 aluminum alloy under uniaxial and nonproportional multiaxial loading is investigated. Non‐HIPed alloy exhibits weaker nonproportional additional hardening capacity than HIPed alloy, which is ascribed to the nonproportional multiaxial loads that enhance the cyclic softening induced by casting pores. Additional plastic damage caused by nonproportional multiaxial loads is highly susceptible to HIPing. Torsional loads trigger the tension‐compression asymmetry of the axial stress response during nonproportional multiaxial fatigue. Multiaxial fatigue life is more sensitive to HIPing at minor total strain amplitudes. The rapid bridging among adjacent pores serves as the preferred channel for fatigue crack propagation. Nonproportional multiaxial loads improve the probability of encountering pores during fatigue crack initiation and propagation.

Consideration of Fatigue Evaluation of SUS316 and SUS430 Steels under Multiaxial Stresses Combined Internal Pressure and Axial Load using Hollow Cylinder Specimen

This study focuses on discussing fatigue life evaluation method of SUS316 and SUS430 steels under wide ranged proportional multiaxial loading conditions. Fatigue tests under 7 types of loading path which are combined axial stress and inner pressure were carried out using hollow cylinder specimens at room temperature. It has been considered that the proportional loading does not cause additional hardening, however this study shows that the complex loading path causes additional hardening without principal direction change of stress and strain in a cycle. The Itoh-Sakane model which evaluates loading and lives under non-proportional multiaxial fatigue by only considering the maximum and the minimum principal stress or strain and their principal directions. However, this model is also needed to consider middle principal stress because change of the middle principal stress influence fatigue life under current loading paths. Therefore, the Itoh-Sakane model was modified to evaluation fatigue life of SUS316 and SUS430 under combined internal pressure and axial loading conditions.

The cyclic strain evolution and the fatigue prediction in non-proportional multiaxial loadings of NiTi SMAs

NiTi shape memory alloy is a kind of smart material which present unique properties of superelasticity, shape memory and excellent biocompatibility. The applications of such alloys are generally the connectors and fasteners, vibration-dampers, and endovascular stents, etc.. The cyclic deformation and fatigue failure of NiTi SMAs are key issues that need to be investigated since they usually endure complex cyclic loadings during the using process. In this paper, the evolutions of the peak/valley strains in non-proportional multiaxial fatigue loadings of NiTi SMAs are considered, and the fatigue failure mechanism is investigated. The results show that the martensite transformation and martensite re-orientation process greatly influence the transformation ratcheting and fatigue life of NiTi SMAs, and a life-prediction model that considers these deformation mechanisms particular for NiTi SMAs is also proposed to give reasonable predictions.

Lifetime calculation of adhesively bonded joints under proportional and non-proportional multiaxial fatigue loading: a combined critical plane and critical distance approach

ABSTRACT This work presents an approach for lifetime calculation of adhesively bonded joints under proportional and non-proportional multiaxial fatigue loads. In-phase and out-of-phase fatigue data with varying stress ratio (R = 0.1 and −1.0) from several joint geometries (butt, scarf, thick adherend shear test and butt-bonded double pipe joints) was employed. The approach is based on the stress-life concept and the Theory of Critical Distances (TCD) considering point and line methods. Stresses were calculated using 2D-FEA with linear-elastic and elastoplastic adhesive behaviours. Non-proportional stresses were addressed by the Maximum Rectangular Hull method. Three failure criteria were investigated: Drucker-Prager (DPC): an invariant-based equivalent stress criterion; Findley (FC): a critical plane stress-based criterion; (c) Fatemi-Socie (FSC): a critical plane stress-strain-based criterion. The material parameter of each failure criterion was iteratively calibrated using fatigue data. The FSC had the worst prediction performance. The DPC presented good agreement with in-phase data, but less robust as the variation of its material parameter changed considerably the prediction accuracy. For both DPC and FC, the line method and linear-elastic models were capable of providing good predictions. The FC yielded the best predictions considering a normal sensitivity bF > 1.0 for different stress ratios, in-phase and out-of-phase loads.

Low-cycle fatigue behavior and life prediction of CP-Ti under non-proportional and multiaxial loading

Non-proportional multiaxial low-cycle fatigue (MLCF) tests were performed on CP-Ti at different multiaxial strain ratios. The optical microscopy observations and life prediction models verified that the critical plane of CP-Ti was the maximum principal strain plane and that it was effective under non-proportional loading. A non-proportional life coefficient and strain energy density coefficient are proposed. Typical MLCF life prediction models, such as the ESN, FS, KBM, and KBM-P models, are discussed under non-proportional loading. Finally, by associating the newly defined non-proportional life coefficient with the non-proportional hardening factor, two comprehensive non-proportional MLCF life prediction models are established, which have higher accuracies than those of previous models.

Polar damage sum concept for constant amplitude proportional and nonproportional multiaxial fatigue analysis

This paper proposes a new concept for the evaluation of fatigue damage parameters. It is suggested that evaluation of fatigue damage may not necessarily be confined to a single plane, i.e., a critical plane. Rather, it is suggested here that the culmination of fatigue crack on a particular plane(s) is due to the contributions of damage on all planes. Mathematically, the polar damage sum concept is calculated as the area enclosed by the polar curve of the damage parameter. The proposed concept is examined using multiaxial experimental data for six different alloys. A total of 241 samples are included in this study. Using the proposed concept, fatigue life estimations are improved compared to those obtained from the original critical plane based on Fatemi-Socie and Smith-Watson-Topper models.

Strength Characteristic of SUS316 and STPT410 Steels under Cyclic Overloading with Pre-Cracked in Non-Proportional Multiaxial Fatigue

Strength Characteristic of SUS316 and STPT410 Steels under Cyclic Overloading with Pre-Cracked in Non-Proportional Multiaxial Fatigue

Design optimization of composite wind turbine blades considering tortuous lightning strike and non-proportional multi-axial fatigue damage

This article presents a design optimization framework which integrates realistic lightning strike electrostatic and fatigue analyses for designing reliable and economical composite wind turbine blades. The novel aspects of this work include: a parametric tortuous lightning stepped leader model that reflects one of the true natural characteristics of the lightning phenomenon; and characterization of both the lightning strike dielectric breakdown failure and multi-axial fatigue failure mechanisms for structural design of composite wind turbine blades. A case study of the structural design optimization of a 5 MW composite wind turbine blade is tested using the framework with two optimization solvers: sequential quadratic programming (SQP) and Bayesian optimization (BO). SQP produces a superior optimal design to BO. In the optimum blade design based on the SQP algorithm, the lightning safety ratio increased by 32% and the expected fatigue life increased more than 15 times compared with the initial blade design.

On the phase angle role in the shear response of ZK60 Mg alloys under multiaxial fatigue

Proportional and non-proportional multiaxial fatigue tests are conducted on the closed-die forged ZK60 extrusion. The shear strain amplitude was kept constant at 0.5% for all the tests, while two different axial strain amplitudes of 0.4% and 0.7% were considered. At the higher strain amplitude (0.7%) significant difference was observed between the torque amplitudes of proportional and non-proportional tests, whereas the axial load amplitude responses remained the same regardless of the phase angle shifts. It is likely that as the phase angle changes from 0-90, the twin volume fraction at the peak shear strain decreases resulting in higher torque responses. On the other hand, at the lower strain amplitude, i.e. 0.4%, where twinning is not active, phase angle does not show any effect on the shear response. An energy-based fatigue model is employed that effectively explains the different damage contributions by the axial and torsional loadings at different strain amplitudes, and accurately predicts the proportional and non-proportional multiaxial fatigue lives.

A universal, damage-criterion-independent cycle counting method for multiaxial and variable amplitude fatigue

None of the procedures for cycle-counting defined in the ASTM document with designation E1049-85 (Reapproved 2017) [1] are generally applicable to non-proportional, multi-axial Fatigue. In addition, as the concepts of amplitude and mean stress are defined per cycle, their values are dependent (or co-define) the cycle counting method. This poses an obvious problem to the analysis of non-proportional, multi-axial fatigue damage, as lifetime is, not in all but in many cases, an amplitude and mean stress dependent material property. Most of the newer cycle counting methods developed till date are at least inspired by the works of Wang & Brown [2] and of Bannantine & Socie [3], both of which are themselves still frequently used. Being built inspired by counting methods developed for uniaxial cycling, all of the approaches to date known to this author are limited in a way that is very well phrased by Anes et al [4], whom, on page 79 of their article, write that (quote): The damage criterion is the base stone to set up random fatigue. The damage parameter must capture the fatigue damage behavior to allow set up a cycle counting method and an accumulation model. Challenging this statement, a new cycle counting procedure is presented that is completely independent of the damage criterion, and universally works from the simplest uniaxial experiment, to the most complex, variable amplitude and frequency, non-proportional multiaxial fatigue loading. The definition of this new cycle counting concept is surprisingly simple. Despite of its simplicity, the new cycle counting procedure has different advantages when compared to the procedures known to date. Its standalone definition, allows it to be combined with any damage criterion. It does not require periodicity of the loading cycle, and can therefore be straightforwardly used to analyze variable frequency and amplitude, multiaxial fatigue loading.

Taking into account the non-proportional loading effect on high cycle fatigue life predictions obtained by invariant-based approaches

Industrial structures are often subjected to multiaxial fatigue loadings. If the multiple stress signals are not synced the loading is said to be non-proportional. Most of the multiaxial fatigue criteria give highly inaccurate lifetime predictions when used in the case of such loadings. The scalar equivalent stress defined by the criteria does not take into account the non-proportional nature of the multiaxial loading and leads to non-conservative predictions. Moreover a multiaxial fatigue criterion can only be applied on a stress cycle which has no clear definition when multiple unsynced signals are to be considered. This study addresses these issues by proposing a correction of an invariant based multiaxial fatigue criterion through the definition of a non-proportional degree indicator. A definition of multiaxial cycle is also given based on the Wang-Brown method. Finally a complete chain of invariant based lifetime prediction for non-proportional multiaxial fatigue is validated.

Evaluation of Non-proportional Multiaxial Fatigue Strength of Lead-free Solder with Elements Addition

The effect of element addition on creep and fatigue properties of Sn1.0Ag0.7Cu solder with addition of nickel, germanium and bismuth are reviewed. Element additions imporove creep properties although those deteriorate fatigue properties. From above results, necessity of non-proportional multiaxial fatigue tests are discussed. The load cell with high sensitivity was designed by making to detect small load during fatigue test was developed by making the strain detection part hollow circular. The inner diameter and the outer diameter of the load cell satisfying the condition that excessive strain does not occur regardless of high sensitivity was determined by strength calculation.

A simple energy‐based model for nonproportional low‐cycle multiaxial fatigue life prediction under constant‐amplitude loading

AbstractFrom the literature concerning the traditional nonproportional (NP) multiaxial cyclic fatigue prediction, special attentions are usually paid to multiaxial constitutive relations to quantify fatigue damage accumulation. As a result, estimation of NP hardening effect decided by the entire history path is always proposed, which is a challenging and complex task. To simplify the procedure of multiaxial fatigue life prediction of engineering components, in this paper, a novel effective energy parameter based on simple material properties is proposed. The parameter combines uniaxial cyclic plastic work and NP hardening effects. The fatigue life has been assessed based on traditional multiaxial fatigue criterion and the proposed parameter, which has been validated by experimental results of 316 L stainless steel under different low‐cycle loading paths.

Proportionally and non-proportionally perturbed fatigue of stainless steel

Computational fluid dynamics and finite element based simulation of the cyclic thermal shock loading caused by turbulent mixing of water of different temperatures in the primary cooling system of a nuclear power plant, suggest a specific kind of non-proportional multi-axial fatigue loading exists on the inner surface cooling structures. Stress controlled experiments mimicking these loading conditions were designed and run on an axial-torsional fatigue testing system. The cyclic loading observed in the finite element simulations consists of the superposition of proportional loading and a second, non-proportionality inducing component, the latter with a substantially lower amplitude and running at a higher cycling frequency. The amplitude of the non-proportionality inducing loading component is of a magnitude so small that the fatigue loading criteria, typically used in engineering standards for nuclear power plant safety, do not recognize the difference with the reference loading without this component. However, first experimental results show that the endurance limit of stainless steel of grade 316L is reduced by this additional loading, which we name non-proportional fatigue noise. The fact that the endurance limit is unexpectedly lowered is a non-conservative safety issue that challenges the currently existing criteria used to estimate the fatigue damage for this type of loading.

Pit to crack transition behavior in proportional and non-proportional multiaxial corrosion fatigue of 304 stainless steel

Multiaxial corrosion fatigue tests with interruption were carried out on 304 stainless steel in 6wt.% FeCl3 solution at room temperature. Pit initiation, growth and pit to crack transition behavior under proportional and non-proportional loading were investigated. Under proportional loading, significant sharper pits, higher initial pit density and growth rate were observed in comparison with non-proportional loading. The pit depth growth rate under proportional loading was larger than those under non-proportional loading and without loading. Pit to crack transition mechanism was mainly controlled by mechanical assisted local dissolution under proportional loading while additional hardening under non-proportional loading.