Fatigue Strength Criterion Research Articles

Multiaxial fatigue analysis of additively manufactured hollow specimens from AlSi10Mg

The paper describes experimental results of multiaxial tests on AM AlSi10Mg cavity specimens with the special focus on the phase shift effect. Four typical representatives of multiaxial fatigue strength criteria are assessed to check the correlation of their results with fatigue experiments. The use of the QCP and Liu-Zenner criteria provide overall better results than the Dang Van criterion and the Crosland criterion, but none of the four evaluated criteria fits well to both checked multiaxial loading configurations. The potential reasons for the found discrepancies are commented in the discussion section.

Application of machine learning models for estimating the material parameters for multiaxial fatigue strength calculation

AbstractThis paper deals with a practical task of estimating missing material fatigue strengths required for the evaluation of multiaxial fatigue strength criteria, knowing other static or fatigue material parameters. Instead of searching for various analytical equations describing the dependencies between different material parameters, several machine learning models implemented in the caret R package are used here. The dataset used to train and test these models is based on the FatLim dataset with different material parameters, which has been redesigned for this new purpose. It is demonstrated that substantially more data points, such as were available in this study, are needed to achieve the goal set here. Although the results obtained at the current scale may be improved by the addition of new data points, the best performance of the random forest model rf and the worst performance of the pcr model are evident.

Mode-III fatigue of welded joints in steel maritime structures: Weld notch shear stress distributions and effective notch stress based resistance

The predominant mode-I response of maritime structures can be multiaxial, involving out-of-plane mode-III shear components. Semi-analytical mode-III notch stress distribution formulations have been established for critical details like welded T-joints and cruciform joints, reflecting (non-)symmetry with respect to half the plate thickness. Using a stress distribution formulation based effective notch stress as fatigue strength criterion, the mode-III welded joint mid-cycle fatigue resistance characteristics have been investigated. In comparison to mode-I, the material characteristic length and resistance curve slope estimate suggest the fatigue damage process to be even more an initiation related near-surface phenomenon. Mean shear stress effects seem insignificant.

Automated implementation of the Peak Stress Method for the fatigue assessment of complex welded structures

Dealing with the fatigue design of complex welded structures, the Peak Stress Method (PSM) is a rapid approach to the fatigue strength assessment, which is based on the singular, linear-elastic opening, in-plane and out-of-plane shear peak stresses calculated at the weld toe or weld root adopting coarse FE meshes. By adopting the averaged Strain Energy Density (SED) as a fatigue strength criterion, a design stress, the so-called equivalent peak stress, has been defined as a proper combination of the local peak stresses and adopted in conjunction with a reference design curve to estimate the fatigue lifetime of welded structures. To furtherly enhance the applicability to complex welded structures, the PSM has recently been calibrated by using 10-node tetra elements, which allow to easily discretize complex geometries. Moreover, an interactive analysis tool has been developed within Ansys® Mechanical, in order to automate the application of the PSM to complex both aluminum and steel 3D welded structures subjected to multiaxial fatigue loads. The automated PSM tool has been developed taking advantage of the integrability between Ansys® Mechanical and modern programming languages, enforcing PSM compatibility requirements and automating the implementation tasks and phases of the method. In this perspective, the present work deals with the employment of the PSM tool for the fatigue strength assessment of some complex welded details adopted in modern roller-coaster structures. Due to the geometrical complexity of large-scale structures, private companies usually employ finite element beam models in order to evaluate nominal stresses, that must be compared with appropriate fatigue strength references (FAT classes) in design standards. The assessment procedure proposed in this work aims instead at defining appropriate stress-based FAT classes from the results of automated PSM analyses on the considered joint geometries. Moreover, the proposed approach allows to compensate the limited number of FAT classes and details available in International Standards and Recommendations, when dealing with complex joint geometries.

The Peak Stress Method applied to fatigue lifetime estimation of welded steel joints under variable amplitude multiaxial local stresses

Fatigue actions of most engineering welded structures involve variable amplitude (VA) loading cycles. The fatigue design of welded joints in such structures is based on the use of a fatigue strength criterion for constant amplitude (CA) loading in conjunction with a cumulative damage rule. In the present work, the Peak Stress Method (PSM), has been reformulated to estimate the lifetime of welded joints subjected to VA loadings. The PSM is an engineering finite element (FE)-oriented technique to rapidly estimate the mode I, II, and III notch stress intensity factors (NSIFs) at the weld toe or at the weld root, by taking advantage of the singular linear elastic, opening, sliding, and tearing peak stresses, respectively. Such stresses are computed at the V-notch tip by means of 2D or 3D FE models discretized using coarse meshes, provided that some conditions of applicability of the method are satisfied. The fatigue strength under CA loading is then evaluated by combining the simplicity and rapidity of the PSM in evaluating the NSIFs with a robust and validated fatigue strength criterion such as the one based on the averaged Strain Energy Density (SED), which can be written as a function of the relevant NSIFs. To preserve the simplicity of the method, its extension to VA loading conditions has been achieved by assuming the Miner’s Linear Damage Rule (LDR) as a cumulative damage rule. The proposed method has been validated against new experimental results generated by testing non-load-carrying (nlc) fillet-welded joints with double inclined attachment and made of structural steel under pure axial loading.

Procedure for Estimating Bending and Torsional Fatigue Strength of Smooth Specimens on Criteria of Axial-Load Fatigue Strength Diagrams

The equivalent cyclic stress ratio REQ followed by elastic-completely plastic yield zone partition type cross-section dimension dependence magnification factor, which is modified to fatigue strength criterion specification, is applied to estimation of plane bending fatigue strength of a smooth bar with rectangular, circular and rhombic cross-section, and rotating bending and torsion fatigue strength of a round smooth bar from an axial load fatigue strength diagram of a smooth specimen. This approach is expected to be effective in elucidating the size effect and its material dependence.

The lifetime forecasting of machine elements by fatigue strength criterion

The lifetime forecasting of machine elements by fatigue strength criterion

Application of the Gaussian process for fatigue life prediction under multiaxial loading

Fatigue life prediction with failure probability estimation for materials subjected to multiaxial loading is an important task in engineering design because it reduces the financial cost by eliminating expensive experimental tests. Owing to the complex deterioration mechanisms of fatigue failure, existing fatigue life prediction models are of the empirical or semi-empirical type, and their applicability is limited to validating the loading condition and material. Improper selection of the fatigue model could result in non-conservative life prediction with high financial and catastrophic consequences. To solve this problem, an innovative approach based on the Gaussian process for fatigue life prediction under multiaxial loading is presented. The inherent features of the Gaussian process predispose its application to fatigue life prediction under multiaxial loading as an efficient and practical approach to avoid the problem in selecting adequate semi-empirical parametric fatigue models. The model was validated on two sets of experimental data obtained by fatigue testing of S355N steel and 2124 T851 aluminum alloy under uniaxial and multiaxial loadings. In the model training process, only data obtained under uniaxial and pure torsion cyclic loadings were applied. Owing to the implemented physics-based input data, which are related to the stress components acting on the critical plane of crack initiation, the model accurately predicted the fatigue lives of the two tested materials by implementing the squared exponential covariance function. In addition, the fatigue lives were also computed using four parametric fatigue strength criteria (Crossland, Matake, Carpinteri et al., and Papuga–Růžička models). The best results obtained by the parametric models exhibited a lower fatigue prediction performance than the results using the Gaussian process-based model.

Issues encountered in the application of multiaxial fatigue strength methods to experiments with various stress distributions

This paper attempts to describe the effect of a non-constant stress distribution on the fatigue strength of unnotched hollow specimens of various sizes and loaded by different load combinations. The chosen solution evaluates the critical volume, which decides the level of fatigue damage. It relates dimensions of these critical entities to component fatigue strengths, which replace the material parameters in multiaxial fatigue strength criteria. The output shows that the proposed critical volume method is a promising solution. The PCRN and MMP multiaxial fatigue strength methods result in the best prediction outputs from the seven methods assessed here.

Validating the Methods to Process the Stress Path in Multiaxial High-Cycle Fatigue Criteria.

The paper discusses one of the key features in the multiaxial fatigue strength evaluation—the procedure in which the stress path is analyzed to provide relevant measures of parameters required by multiaxial criteria. The selection of this procedure affects the complete equivalent stress derived for any multiaxial load combinations. Three major concepts—the minimum circumscribed circle, minimum circumscribed ellipse, and moment of inertia methods—are described. Analytical solutions of their evaluation for multiaxial stress state with components described by harmonic functions are provided. The concepts are validated on available experimental data when included into six different multiaxial fatigue strength criteria. The results show that the moment of inertia results in too conservative results. Differences between both methods of circumscribed entities are much smaller. There are indications however that the minimum circumscribed ellipse solution works better for critical plane criteria and for the criteria based on stress tensor transformation into the Ilyushin deviatoric space. On the other hand, the minimum circumscribed ellipse solution tends to shift integral criteria to the conservative side.

Validation of Multiaxial Fatigue Strength Criteria on Specimens from Structural Steel in the High-Cycle Fatigue Region.

The paper describes results of fatigue strength estimates by selected multiaxial fatigue strength criteria in the region of high-cycle fatigue, and compares them with own experimental results obtained on hollow specimens made from ČSN 41 1523 structural steel. The specimens were loaded by various combinations of load channels comprising push–pull, torsion, bending and inner and outer pressures. The prediction methods were validated on fatigue strengths at seven different numbers of cycles spanning from 100,000 to 10,000,000 cycles. No substantial deviation of results based on the selected lifetime was observed. The PCRN method and the QCP method provide best results compared with other assessed methods. The results of the MMP criterion that allows users to evaluate the multiaxial fatigue loading quickly are also of interest because the method provides results only slightly worse than the two best performing solutions.

Gear Ratio Distribution of Electric Vehicle Reducer

Based on the contact fatigue strength criterion of tooth surface, the mathematical model of gear ratio distribution of the electric vehicle is established. In the process, there are two objective functions. One is the minimum diameter of electric vehicle reducer, the other is the minimum mass of electric vehicle reducer. Through examples, relevant program is compiled with matlab software. It is obtained that there is a distribution method for gear ratio of the electric vehicle reducer.

Mid- and High-Cycle Fatigue of Welded Joints in Steel Marine Structures: Effective Notch Stress and Total Stress Concept Evaluations

The characteristic far field response spectrum of welded joints – the governing fatigue sensitive locations in steel marine structures – is predominantly linear elastic, meaning mid- and high-cycle fatigue (MCF and HCF) is most important for design. Using the effective notch stress- and the total stress concept, involving respectively Se and ST as intact- and cracked geometry fatigue strength criterion, one MCF-HCF resistance curve has been obtained for all welded joints. A generalised random fatigue limit model explicitly incorporating the MCF life time and HCF strength limit scatter provides statistically the most accurate fatigue strength and fatigue life time estimates. Similar MCF performance is obtained for Se and ST. Although crack growth dominates the MCF damage process, the results for an initiation related criterion like Se and natural crack growth related criterion like ST are similar. Adopting Se rather than ST as fatigue strength criterion naturally related to the crack initiation dominated HCF region showing the largest data scatter may explain the better effective notch stress concept HCF performance. Since the HCF resistance scatter is relatively large, the MCF-HCF generalised random fatigue limit model design curves show approximately 1-slope behaviour. meaning that for design purposes a linear Basquin model approximation rather than a piecewise continuous bi-linear MCF-HCF formulation according to guidelines, standards and classification notes should be adopted.

Automated fatigue strength assessment of arc-welded structures according to the Peak Stress Method

The Peak Stress Method (PSM) is an approximate, FE-oriented application of the notch stress intensity factor (NSIF) approach to fatigue design of welded joints. This approach is based on the singular linear elastic peak stresses calculated from coarse FE models. The PSM was calibrated by using 2D, four-node plane quadrilateral elements; 3D, eight-node brick elements and 3D, four-node or ten-node tetra elements. By adopting the averaged Strain Energy Density (SED) as a fatigue strength criterion, a design stress, the so-called equivalent peak stress, has been defined and adopted in conjunction with a reference design fatigue curve to estimate the fatigue life of welded structures. The equivalent peak stress has successfully been adopted to assess the fatigue strength of arc-welded joints made of either structural steels or aluminum alloys and subjected to axial, torsion or multiaxial fatigue loadings. In the present work, a subroutine, named ANSYS-PSM, has been developed in the post-processing environment of ANSYS® FE code to automate the PSM for 2D or 3D FE models. After having briefly recalled the theoretical background of the PSM and the procedure to apply it step by step, the paper presents the adopted programming languages and the workflow of the developed subroutine.

Formulation of the fatigue fracture criterion of composite materials

According to numerous studies of different types of composite materials was found that the main processes of fatigue fracture in these materials are caused by the accumulation of damage. The measure of damage is determined by various degradation processes of the material: the fibers fracture, delamination, destruction of the matrix, the joint destruction of the matrix and fibers, separation on the interface, re-inclusion. The sequence of these damages can be various up to full fracture of a material. Unlike metals, for which the formation and development of cracks are the main mechanisms that determine the durability of the material, for composite materials, these mechanisms are determined by the kinetics of the development of the damaged state until the final fracture. The cumulative damage accumulation curve is an increasing function of the time (number of loading cycles) until the moment of macro-fracture. In the general formulation of the kinetic equation for the damage parameter was considered in the works of Howard and Bokshitsky. According to these works, the damage of the system, in accordance with the conception of statistical physics, proceeds at a rate that depends on some external factors (mechanical, physical, chemical, etc.), as well as the value of the accumulated damage. Since that the real materials have a random structure, therefore, the continuity or damage parameter is a statistical index. This index can defined using a kinetic equation, the right part of which is given in the form of a power dependence on the value of the effective stress. The given conception was used in the works of Kachanov-Rabotnov and on its basis, the criterion of brittle fracture under hightemperature creep was formulated. In this paper, the damage conception is used to describe the damage processes of composite materials and the formulation of the fatigue strength criterion. The relative changes of the elasticity modulus in the process of cyclic loadings is considered as a continuity (damage) parameter. The critical value of damages is accepted as a fracture condition and on this basis the criterion of fatigue strength is formulated. The coefficients of the criterion are concretized and damage accumulation curves and fatigue curves are plotted. A good agreement between the theoretical damage and fatigue curves with the results of the corresponding experiments on the fatigue of carbon fiber plastics is observed.

Fatigue fracture criterion of composite materials

The first investigations on the fatigue strength of composite materials were carried out on cyclic tension of plastics reinforced by fiberglass. Since that time, intensive studies of fatigue strength of composite materials were begin. The experimental data obtained for different types of composite materials shown, that the fatigue fracture processes are governed by the accumulation of defects of different nature. The main mechanisms that determine the durability of composites is the kinetics of the damaged state development until the final fracture. At the same time, according to the experimental results, the damage accumulation curve of the total damage is defined by increased function of the time (number of loading cycles) until to the moment of macro fracture. In this paper, based on these studies and the conception of scattered damage and fracture, fatigue strength criterion is formulated. Fatigue criterion coefficients are concretized and damage accumulation curves are plotted, which depends on the number cycles and stress level. The comparison with experimental results on fatigue of glass-reinforced plastics and carbon fiber reinforced plastics is given.

A Fatigue-Fracture Criterion for Composite Materials

The fatigue strength of composite materials was first investigated under cyclic tension of plastics reinforced by fiberglass. Since that time, intense investigations of the fatigue strength of composite materials have begun. The experimental data obtained for different types of composite materials show that the fatigue-fracture processes are induced by the accumulation of defects of various nature. The main mechanisms for determining the durability of composites are the kinetics of development of the damaged state until final fracture. At the same time, according to the experimental results, the total-damage-accumulation curve is an increased function of time (the number of loading cycles) until the moment of macrofracture. In this study, on the basis of these investigations and the concept of scattered damage and fracture, the fatigue strength criterion is formulated. The fatigue criterion coefficients are specified, and the damage-accumulation curves are plotted in dependence on the number of cycles and the stress level. A comparison with the experimental results on the fatigue of glass-reinforced plastics and carbon-filled plastics is given.

Design of Jack-Up Platform for 6 MW Wind Turbine: Parametric Analysis Based Dimensioning of Platform Legs

Abstract The article presents the results of the research conducted within the framework of the project entitled WIND-TU-PLA (ERA-NET, MARTEC II), the general aim of which was to design and analyse supporting structures for wind turbines intended for operation on the South Baltic area. The research part described in the article aimed at developing a preliminary design for a jack-up platform which can operate on water areas with depth of 40 m. The main task was to determine optimal dimensions of platform legs and the radius of their spacing. Two jack-up platform concepts differing by spacing radius and hull dimensions were designed with the intention to be used as a supporting structure for a 6-MW offshore wind turbine. For each concept, the parametric analysis was performed to determine optimal dimensions of platform legs (diameter Dleg and plating thickness tleg). Relevant calculations were performed to assess the movements of the platform with parameters given in Table 1 in conditions simulating the action of the most violent storm in recent 50 years. The obtained results, having the form of amplitudes of selected physical quantities, are shown in comprehensive charts in Fig. 6 and 7. Based on the critical stress values (corresponding to the yield stress), the area was defined in which the impact strength conditions are satisfied (Fig. 14). Then, the fatigue strength analysis was performed for two selected critical leg nodes (Fig. 12). Its results were used for defining the acceptable area with respect to structure’s fatigue (Fig. 14). Geometric parameters were determined which meet the adopted criteria, Table 6. The decisive criterion turned out to be the fatigue strength criterion, while the yield point criterion appeared to be an inactive constraint.

The peak stress method applied to the fatigue assessment of tube-tube steel joints with weld ends under multiaxial loadings

The Peak Stress Method (PSM) is an approximate, FE-oriented application of the notch stress intensity factor (NSIF) approach to fatigue design of welded joints, which is based on the singular linear elastic peak stresses calculated from FE analyses performed by using coarse mesh patterns. By adopting the averaged strain energy density (SED) as a fatigue strength criterion, a design stress (the equivalent peak stress) can be defined; in conjunction with a reference design curve previously defined, the fatigue strength assessment of welded joints subjected to multiaxial fatigue loadings can be performed. In the present contribution, the PSM has been applied to the fatigue assessment of tube-tube steel joints with weld ends, which have been fatigue tested in a previous contribution under combined loadings: namely pure axial, pure torsion and in-phase as well as out-of-phase axial-torsion loadings, all of which with two load ratios, i.e. R = 0 and R = -1. The experimental fatigue results have been re-converted in terms of equivalent peak stress by adopting a 3D FE model including an idealised weld end geometry. The equivalent peak stress has proved to assess the fatigue crack initiation location in agreement with experimental observations, moreover a quite good agreement has been obtained between the experimental results and the PSM-based design scatter band.

Evaluation of fatigue strength criteria for thick-walled nodular cast iron components from EN-GJS-400 under multiaxial load

This paper discusses the quality of common methods for estimating the fatigue strength of EN-GJS-400-18-LT specimens under multiaxial stress. This is particularly important for the lightweight design of wind turbines. Experimental fatigue tests with axial, torsional and combined loads with a load ratio of R = -1 were performed. The results of these fatigue tests are used to validate commonly used multi-axial stress hypotheses. The investigated methods are the von Mises hypothesis, the Findley-criterion, the modified Gough-Pollard method and the critical plane nominal stress hypothesis.