Multiaxial Criterion Research Articles

Micromechanical analysis of spherulitic polymers in multiaxial and non-proportional fatigue crack nucleation

This study focused on understanding the fatigue response of anisotropic spherulitic polymers by employing a multiscale microscopic modeling approach. The crystal plasticity model together with the Arruda-Boyce model were used to describe the mechanical response of crystalline phase and amorphous. The fatigue behaviors and crack initiation were captured by Fatemi-Socie multiaxial criterion and continuous damage theory under multiaxial and non-proportional loading conditions. The sheaf-like structure of spherulitic polymers was considered to shed light on the anisotropic nature of fatigue failure. The results highlight the role of features of sheaf structure, e.g., initiation orientation, on the fatigue performance of spherulitic polymers, which have not been reported. The localized degradation of mechanical properties and the accumulation of fatigue damage were systematically discussed with various loading patterns. This study provided an in-depth understanding of potential fatigue mechanisms, offering robust support for fatigue resistance design in engineering applications.

Study on Structure Optimization and Vibration Fatigue Analysis of Aluminum and Composite Brake Control Boxes

ABSTRACTThe brake control box beneath an EMU is exposed to dynamic and fluctuating load cases, increasing its susceptibility to vibration fatigue failure. A novel lightweight design approach was implemented to integrate structural and material optimizations. Static and fatigue tests of the T700/5429 CFRP were carried out to augment the stress analysis and predictions of the vibration fatigue life. The local stresses perpendicular and parallel to the welds were obtained to calculate the stress ratio, stress range, and allowable stress value corresponding to the stress component. The fatigue strength of the aluminum box was estimated on the basis of multiaxial criteria, and the fatigue life of the two boxes was predicted with Dirlik's theory. These computational findings unequivocally indicated a noteworthy reduction in damage to the composite box subsequent to lightweight modification, thereby successfully satisfying both the stiffness and strength criteria essential for the safety and reliability of the EMU.

Multiaxial fatigue on cableway installations components: use of the Dang Van criterion based on detail categories of EN 1993-1-9 standard.

In order to predict fatigue lifetime of cableway installations components, EN 1993-1-9 standard (Eurocode 3) is commonly used. However, EN 1993-1-9 is based on a major hypothesis : stress state has to be uniaxial. But for some components, this uniaxial hypothesis is not verified (for example : fixed grip of chairlift submitted to horizontal tightening stress and vertical load stress, or chairlift structure stressed by gravity and lateral shake when passing a tower). It then appears important to use a fatigue criterion taking into account multiaxial stress state. Our research work proposes to apply for fatigue study the Dang Van criterion, which takes into account multiaxial stress state. Results are then compared to Eurocode SN curves, representing a huge experimental database on unixaxial fatigue, that we propose to use in multiaxial fatigue thanks to an appropriate recalibration. The scientific originality of this work lies in the justification of that Dang Van criterion's recalibration. Therefore, a theorical study ensures that our use of Dang Van's multiaxial criterion is still consistant with the Eurocode SN curve even if these SN curves are experimentally performed under uniaxial stress state. Finally, that hitherto unpublished use of the Dang Van criterion makes it possible to consider the entire database of detail categories defined in NF EN 1993-1-9, by generalising their use for components under multiaxial fatigue.

Algorithm for Designing a Removable Complete Denture (RCD) Based on the FEM Analysis of Its Service Life.

(1) Background: The paper addresses the computer simulation and prediction of the service life of the base of removable complete dentures (RCDs) under typical loads caused by biting and chewing food. For this purpose, the finite element method (FEM) was used. It is assumed that various blocks of teeth, such as incisors, canines, premolars and molars, are subjected to cyclic impacts during a human life. (2) Methods: Both symmetric and asymmetric mastication (two- and one-sided loads, respectively) cases were considered. The load level was assumed to be 100 N, which corresponds to the average muscular compression force of typical human jaws. (3) Results: The FEM analysis of the stress–strain state evolution for RCDs under cyclic loads was carried out. Maps of equivalent lines were drawn for the denture base in terms of its durability. A multi-axial criterion was implemented to determine the number of cycles prior to failure by the mechanism of a normal opening mode crack. The FEM-based assessment of the service life of RCDs enabled us to establish the critical stress concentration areas, thereby allowing for further planning for the correction of an occlusal scheme or teeth inclinations. As a result, the service life of RCDs under cyclic loading can be improved. (4) Conclusions: An algorithm for designing RCDs in the case of edentulism based on the FEM simulation using commercial software as part of the procedure is proposed.

Multiaxial high-cycle fatigue failure and life prediction based on critical plane method

Multiaxial high-cycle fatigue failure criterion and life prediction is important for structural components under complex low stress. A new multiaxial high-cycle fatigue damage parameter based on the plane of maximum shear stress is proposed, which includes the maximum shear stress amplitude, normal stress amplitude and maximum equivalent normal stress. The maximum equivalent normal stress is defined in the form of SWT stress function considering the influence of mean stress. The feasibility of the proposed failure criterion and life prediction model is verified by test data of different materials. The predicted results show that the life prediction error of the proposed fatigue model is basically within three times by comparing with McDiarmid, Matake, Crossland and Papadopoulos fatigue models.

Influence of induction hardening residual stresses on rolling contact fatigue lifetime

Rolling contact fatigue is a unique mode of fatigue that components under cyclic contact loading experience. In this work, the impact of induction hardening residual stresses in rolling contact fatigue lifetime is investigated experimentally and numerically using the Dang Van multiaxial criterion. Various residual stress fields from induction hardening are simulated using the finite element method and are mapped into a classical mono-contact finite element model. The impact of induction hardened residual stresses on the lifetime of a component has been investigated, and the importance of incorporating the residual stress profile into fatigue life assessments is affirmed.

Adapted multiaxial fatigue models based on the critical plane approach to consider the presence of small defects in steel

Non-metallic inclusions can often be seen in the fatigue crack initiation site in high-strength steels. These inclusions are known to be detrimental to the fatigue strength, as they behave as stress concentration elements. The same is valid for small defects such as notches, holes and scratches. The goal of this research is to investigate not only the effect of non-metallic inclusions but also of small artificial defects on the fatigue strength of the AISI 4140 steel under multiaxial loading conditions. In order to do so, two critical plane based multiaxial fatigue models are coupled with the √area parameter. This is an empirical parameter, which is used to estimate the uniaxial fatigue strength of metals containing small defects or inclusions. One of the major merits of √area parameter is the fact that the material fatigue limits (under push-pull or torsion) can be estimated by considering only the material hardness and the geometry (area) of the small defect, i.e no costly and lengthy fatigue tests are required. To validate the analysis, experiments under pure and combined push-pull and torsional loading in and out-of-phase have been conducted in smooth and also in specimens containing an artificially produced micro hole. Comparison between the estimates provided by the coupled critical plane-√area parameter multiaxial criterion and data provided very good results, with errors around 20%.

The crack path prediction and fatigue durability estimation based on the damage function approach

In the process of the material degradation under cyclic loading is usually distinguishing several stages such as crack initiation, crack growth and final fracture. The local stress stage is changing with the degradation process and especially during the crack growth stage. The convenient approach to predict the total fatigue life is usually based on two different problems: (1) use of a multiaxial criterion to estimate duration of the crack initiation; (2) used of Paris law to estimate the stable crack growth duration. However, during the evaluation of stress state a different crack opening modes can act. This change is clearly observed in the case of pure torsion loading. The propagated torsion crack combines normal and shear crack opening stages. The convenient approaches are not suitable to predict such fatigue behavior of structural elements. This paper is introducing a new approach to estimate the total fatigue life, including the crack initiation and propagation stages, with regards to crack opening mechanisms. The proposed approach is based on the modern model of the full SN curve, damage theory and takes into an account the normal and shear mechanisms of fatigue damage accumulation. The paper contains the result of numerical simulation for VHCF torsion tests prediction.

Multiaxial plain and notch fatigue strength of thick-walled ductile cast iron EN-GJS-600-3: Combining multiaxial fatigue criteria, theory of critical distances, and defect sensitivity

Multiaxial fatigue tests were carried out on plain and notched specimens extracted from EN-GJS-600-3 pearlitic DCI heavy-section castings. Two notches of different severities were combined for the determination of mode I and mode III critical distances, along with the related intrinsic fatigue strengths. SEM and CT clearly showed that fatigue cracks initiated from graphite nodules and shrinkage pores in notched and plain specimens, respectively. Different multiaxial criteria were compared, and best predictions were obtained with the Carpinteri et al. criterion with four parameters: axial and torsional intrinsic fatigue strengths, combined with the two different related critical distances.

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.

Failure analysis of cemented carbide roller for cold rolling: Material characterisation, numerical analysis, and material modelling

Cemented carbides, also known as hard metals (HM), are composite materials that are widely used in many technological applications requiring favourable mechanical properties, specifically a high wear resistance. In the steelmaking industry, these materials have been effectively used to produce rollers for both hot and cold rolling operations.In this study, failure analysis of a roller used for cold rolling was performed, starting from a detailed material investigation to a fracture surface characterisation using scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM + EDXS). A finite element (FE) analysis of the roller was performed to determine the Hertzian-type stress distribution in the contact area. To identify the most critical zone, the Crossland multiaxial criterion was applied, and the results were then compared with measurements obtained from a component failure analysis. An additional investigation of the possible causes of failure was performed by adopting a material model (the Murakami–Endo equation) to distinguish the actual causes of failure more clearly, mainly at the crack nucleation site.The failure analysis results showed that the roller failed primarily because of rolling fatigue, which started from an internal pore acting as a source of local stress concentration. The component reached the fatigue limit of the material in proximity to the pore, which behaved as a crack nucleation site.

Multiaxial fatigue assessment of steels with non-metallic inclusions by means of adapted critical plane criteria

The goal of this research is to investigate the detrimental effect of non-metallic inclusions on the fatigue strength of the AISI 4140 steel under multiaxial loading conditions. In order to do so, two multiaxial fatigue models based on the critical plane approach are coupled with Murakami’s √area parameter. The proposed adapted multiaxial criteria are proved simple to calibrate. Experiments under combined push-pull and torsional loading in and out-of-phase are conducted and compared with the estimates provided by the proposed adapted models. The adaptation is conservative with errors around 20%. An analysis of the fracture surfaces is carried out to compare the estimated crack initiation planes with the observed ones.

The performance of selected multiaxial criteria under tension/torsion loading conditions

Dependencies σa = f(Nf) and τa = f(Nf) were experimentally obtained for two steels with different material properties. Specimens of these materials were exposed to multiple tensile and torsional proportional stress combinations. In the present paper, the experimentally obtained fatigue lifetime values are compared with fatigue lifetime estimations calculated by means of selected criteria, namely those of Findley, McDiarmid, Dang Van, Carpinteri-Spagnoli, and Margetin-Ďurka-Chmelko. The results for steel with a high ratio of Rm/Re are different from the results of the second material. The analysis of the results shows the need to take into account the failure mode in the multiaxial fatigue criteria.

Influences of up-milling and down-milling on surface integrity and fatigue strength of X160CrMoV12 steel

This paper aims to compare the influences of the two peripheral milling modes, up-milling and down-milling, on surface integrity and fatigue strength of X160CrMoV12 high-alloy steel. The experimental investigations showed an important difference between integrity of both milled surfaces. The down-milled surface is lowly work-hardened and well finished (lower roughness), but subjected to tensile residual stresses and severely damaged by folds of metal and short micro-cracks. The up-milled surface is highly work-hardened and subjected to compressive residual stresses, but poorly finished (higher roughness) and damaged by a density of micro-cavities due to carbide extraction. The results of 3-point bending fatigue tests revealed that the fatigue limit at 2 × 106 cycles of the up-milled state is largely higher of about 26% in comparison with the down-milled state. The effects of surface integrity induced by each milling mode on fatigue strength were evaluated using a HCF behaviour predictive approach based on Dang Van’s multiaxial criterion. The predictive results estimated that the pre-existing micro-cracks play a dominant role in the fatigue strength degradation of the down-milled surface while the other surface effects seem to be lower. On the contrary, the fatigue strength of the up-milled surface is less affected by the pre-existing micro-cavities. The detrimental roughness effect (stress concentration effect) is significantly reduced by the beneficial effects of superficial hardening and compressive residual stresses. So, this study revealed that up-milling is the more appropriate mode for a better surface integrity towards fatigue strength of X160CrMoV12 steel than the down-milling mode.

A stochastic prediction of roughness evolution in dynamic contact modelling applied to gear mild wear and contact fatigue

Abstract This study proposes a statistical formulation to depict the evolution of asperity shape induced by wear and plastic deformations under mixed lubrication. The paper develops an asperity strain-hardening model. The complete procedure includes a contact crack initiation prognosis combining multiaxial criteria with a damage accumulation procedure incorporating the load history. The degradation prediction is coupled with a dynamic gear model. A comparison with experimental measurements shows that the roughness prediction of 1.27 μm after 2295 × 103 cycles agrees with the measurement of 1.3 μm. The crack initiation results suggest that micro-pitting and pitting are simultaneous fatigue processes; while micro-pitting originates from the surface, pitting emanates from positions slightly below the surface when surface micro-cracks coalesce with already-weakened sites.

Theoretical and numerical investigation of stress mode shapes in multi-axial random fatigue

Abstract Random fatigue is inherently multi-axial due to the complex stress state in real vibrating structures. This paper investigates the role of Stress Modal Analysis (SMA) in multi-axial random fatigue. Predicting hotspots of multi-axial random fatigue by Stress Mode Shapes (SMSs) was theoretically demonstrated. An improved approach was proposed to exploit SMSs in random fatigue with a multi-axial criterion. First, SMA is conducted to locate the multi-axial fatigue hotspots in a vibrating structure. Second, the frequency-domain approach for random fatigue is performed at the identified hotspots. The capability of SMSs in locating multi-axial fatigue hotspots was verified by numerical investigation. The finite element (FE) model of an L-shaped thin-walled structure containing geometry changes was constructed for case study. Local regions were identified as hotspots by SMSs information. Then, random response and multi-axial fatigue damage of the whole structure were evaluated for verification. Damage map indicates that the critical positions predicted by SMSs have good accuracy. Results show the improved approach with SMA can ensure both accuracy and efficiency for multi-axial random fatigue.

Fatigue Life Analysis Method for Freight Carbody Based on Multi-axial Criteria

Fatigue Life Analysis Method for Freight Carbody Based on Multi-axial Criteria

ОЦЕНКА УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ И ОПРЕДЕЛЕНИЕ КРИТИЧЕСКОЙ ПЛОСКОСТИ ПРИ МНОГООСНОМ ЦИКЛИЧЕСКОМ НАГРУЖЕНИИ С ПРОИЗВОЛЬНЫМ СДВИГОМ ФАЗ

The real experience of different structural elements shows that cyclic loading conditions and stress strain state are often quite different from laboratory test conditions such as axial tension-compression, bending or pure torsion. As a rule, the structural elements are subjected to complex (multiaxial) loading conditions during service, that is why multiaxial fatigue criteria should be used for durability estimation of such elements. A present multiaxial criterion allows us to estimate the number of cycles to fracture for specimens or structural element (fatigue life) with an influence of the orientation of the so-call critical plane of fatigue damage accumulation. Analytical solutions were obtained for the present fatigue criterion to determine the orientation of the critical plane of the fatigue damage development under cyclic loading for multiaxial stress states. Cyclic loading with arbitrary shifts of phases for the classical fatigue range (low-cycle and high-cycle fatigue) was considered. Several common cases of the three dimensional cyclic loading, i.e. tension-compression and bending-torsion, are studied. It is shown that at certain values of phase shifts the fatigue durability can be very low even under stress amplitudes that do not lead to fracture in the case of sine phase loading. The comparison with the experimental data and numerical calculations based on the other criterion is made. A disc of a low-pressure stage of a gas-turbine engine subjected to cyclic loading due to centrifugal forces was considered. By using a simplified stress distribution, as well as a stress distribution calculated by the finite element method, the areas of stress concentration and orientation of the critical plane in these zones are determine and the durability of the disk operating was estimated.

General Procedure for Formulation of Multiaxial Fatigue Failure Criteria in Frequency Domain

Fatigue life assessment under multiaxial loading conditions needs the use of multiaxial fatigue failure criteria. There are many formulations of such criteria which are usually divided in the groups of critical plane criteria and invariants based criteria. Other classifications refer to the parameter that determines fatigue, and these are stress, strain and energy criteria. Recently, the development of computational techniques for fatigue analysis in the frequency domain have been noticed. Analyzing the literature, it can be noted that these criteria are mainly created by the new formulation of them in the new domain. There is therefore a need to develop a general approach to the problem of formulating criteria in the frequency domain on the basis of existing proposals for the time domain. The paper presents the manner in which the values appearing in the criteria in the frequency domain can be determined. In particular, the process of formulating criteria of multiaxial random fatigue, using the critical plane approach proposed by Macha was presented. During the formation the linearity of such criteria was successfully used. Situations that indicate the correctness of transformations are also presented.

An efficient procedure to speed up critical plane search in multiaxial fatigue: Application to the Carpinteri-Spagnoli spectral criterion

A more efficient procedure is proposed to speed up the Carpinteri-Spagnoli (CS) algorithm in numerical computations. The goal is accomplished by deriving the exact solution for the spectral moments and expected maximum peak of normal/shear stress in any rotated plane orientation. The algorithm then avoid the use of “for/end” loops to identify the five rotations that locate the critical plane in CS method. The procedure is especially advantageous if applied to three-dimensional finite element analysis, in which the stress spectra in thousands of nodes need to be processed iteratively. The procedure is based on theoretical results that have, however, a more general validity, being applicable to any multiaxial criterion that makes use of angular rotations to identify the critical plane.