Critical Plane Method Research Articles

Increasing fatigue crack initiation life in butt-welded UIC60 rail by optimization of welding process parameters

In this work, to reduce the fracture in butt-welded rail under service loads, a numerical study is carried out to estimate the crack initiation life. For this purpose, the J-S model in terms of the critical plane method is used. To increase the fatigue life of the welded joint, considering the amount of fractured butt welded joints in the railway of the Iranian network, the important variables of the flash-butt welding process are optimized. To this end, the welding process modeling in Abaqus is converted to Python code, and by using a coupled procedure utilizing Matlab, the optimization process is performed by the imperialist competitive algorithm (ICA). The capability of each governing variable on increasing crack initiation life is discussed.

Low-cycle fatigue life prediction of I-shaped steel brace components and braced frames

Four methods (seven models) are extended and applied to the low-cycle fatigue life prediction of steel brace, including the ductile damage method, the equivalent strain method, the critical plane method, and the representative strain method. Using these models, the fatigue life of 53 steel brace components and 5 bracing members in single diagonal braced frames is predicted and compared with the measured life in experiments. Thus, some useful information on the accuracy and reliability of different methods is provided. Based on a parametric sensitivity analysis, the ductile damage model can represent the fracture process of the brace and has a good application on fatigue life prediction, especially when the fatigue life is less than 60. The equivalent strain method overestimates the fatigue life while the critical plane method underestimates the fatigue life. The fatigue parameters of steel Q235B in these two life prediction methods are obtained. The proposed representative strain method compensates for the fact that the fiber model cannot consider the effect of local buckling on the fatigue life of the bracing member. This method has good accuracy and computational efficiency on fatigue life prediction.

Сопоставление различных методов сведения сложного напряженного состояния к простому при непропорциональном нагружении

Object and purpose of research. This paper discusses ship structures. Its purpose is to compare the most common methods for transition from complex strained state to the simple one in calculations of fatigue strength under non-proportional loading. Materials and methods. This paper describes the method of absolute maximum principal stresses, the method of signed von Mises stresses, Sins method and critical-plane method. Main results. Analysis of time histories for design stresses obtained as per above-mentioned methods for the simplest examples of non-proportional loading. The comparison of these results was illustrated by a case study (loading of an icebreaker propulsion shaft). Conclusion. It is shown that, of all the methods discussed in this paper, only critical-plane method can fully take the loading process into account. None of the other methods can take into account the changes in orientation of principal stresses, so their results could be both somewhat too high and too low.

Summary of fatigue durability analysis of whole vehicle

Technical characteristics and development trend of the fatigue durability analysis of the whole vehicle were reviewed in the directions. These existing research results were systematically summarized from the research status, signal acquisition, finite element analysis, load spectrum extraction and fatigue life. Wherein, the strengths and weaknesses of the virtual iteration technology was explained in detail, in which the result evaluation standard was mainly composed of relative damage value; and also the characteristics of fatigue damage theory and analysis method were summarized detailedly; additionally, the practical critical plane method possessed the advantages of the measurable component damage values, but this method still needed to be solved the problems of crack propagation direction. Moreover, according to the existing technology and achievements, reducing model errors and road conditions selection will become the development trends of vehicle fatigue durability technology in the future.

Multiaxial fatigue life prediction method of notched specimens considering stress gradient effect

AbstractThis paper investigates the effect of stress gradient on the fatigue life of U‐notched specimens under multiaxial proportional loading by studying the shear stress gradient and normal stress gradient on the crack initiation plane separately. First, based on the energy method and critical plane method, an energy‐critical plane method for determining the direction of crack initiation is proposed. Second, with the help of the concept of stress field intensity, the shear stress gradient and normal stress gradient on the critical plane are studied. Finally, a multiaxial fatigue life prediction model is established by combining the equivalent stress field intensity, composed of the shear stress field intensity and normal stress field intensity, with the Manson–Coffin equation. Theoretical analysis is verified by the experiments of Q345 steel notched specimens, and the results show that the predicted accuracy of the proposed method is not conservative and is superior to the local stress–strain method.

Прямой расчет усталостного ресурса гребных валов на основе современных методов

This study is an alternative FEM-based fatigue strength calculation for propulsion shafts as per RS Rules. Direct numerical simulation yielded the fields of stresses and strains. Lifetime assessment was based on S-N fatigue model: critical stresses for this model were obtained as per critical-plane method taking into account non-proportional loading of propulsion shafts. It compares two shaft designs: in compliance with RS Rules and with deviation from them.

Effects of centring error and angular misalignment on crack initiation life in herringbone gears

The effects of centring error and angular misalignment on crack initiation life in herringbone gears are investigated in this work. Herringbone gears with centring error or angular misalignment are modelled for contact analysis. A crack initiation life model of standard and error gears is proposed in accordance with tooth stress history and a critical plane method for nonproportional loading. Then, the effects of centring error and angular misalignment on crack initiation life in herringbone gears are investigated. Results show that centring error and angular misalignment sharply reduce crack initiation life, but a moderate tip relief can eliminate stress concentration and extend crack initiation life. Furthermore, angular adjustment balances the load distribution of the left and right teeth in herringbone gears with centring error, improving tooth crack initiation life.

Assessing variable amplitude multiaxial fatigue lifetime of notched components based on the notch critical plane approach

In the present paper, the notch critical plane method proposed by the authors is extended from 2D- to 3D-cases. The plane passing through the assumed critical point and experiencing the maximum variance of the resolved shear stress is defined as the the notch critical plane. The linear-elastic stress fields around the notch root are fitted via polynomial functions. The relationship between critical distance, l, and fatigue damage, Db, under variable amplitude loading blocks is proposed. Susmel’s parameter and a specific multiaxial cycle counting method are incorporrated into this approach to estimate multiaxial variable amplitude fatigue life. Numerous fatigue data generated by testing five different notched metallic materials were collected from the literature to check the accuracy of the proposed approach. This validation exercise allowed us to demonstrate that this method is highly accurate, with the majority of the predicted experimental results falling within an error band of 2.

Adaptive finite element simulation of fretting wear and fatigue in a taper junction of modular hip prosthesis

Modular taper junctions are commonly used in total hip arthroplasty to offer a wide range of intraoperative choices to surgeons. The damage at the taper surfaces can lead to the implant failure either by material removal (wear) or by cracks nucleation (fatigue). This paper presents a methodology based on the finite element approach to study both fretting wear and fatigue, taking into account their interaction in the modular taper. The modified Archard's law was employed to compute wear depth and the corresponding volume loss while the fatigue life was predicted using two critical plane fatigue parameters (Smith-Watson-Topper and Fatemi-Socie). An adaptive meshing technique was implemented to take into account the geometry changes and the material removal effect on fatigue life. The methodology developed was discussed and validated against available experimental data from the literature. In this case considered, a transition from a partial slip regime to a large slip one, which is mainly controlled by the contact slip amplitude, was found to reduce the fatigue life and a critical slip value was identified. This provides an efficient tool for an in-depth understanding of fretting in taper junctions and for future design.

Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design

AbstractThis article proposes a heuristic model to predict the fatigue life of rubber parts. The developed model is mainly based on the Cracking Energy Density (CED), originally developed by Mars, for the study of rubber parts fatigue. The main contribution consists in the integration of the theoretical framework of the critical plane analysis proposed by Mars with Saintier's experimental research carried out in tension and torsion modes. The CED parameter, derived from the Strain Energy Density (SED), can predict the occurrence of the first crack and its possible orientation depending on the type of loading path. In this context, an analytical analysis of this parameter is carried out for typical loading cases. Furthermore, the variation of CED by SED ratio (WC/W), as a function of the probable crack angle θ and the principal stretch λ1 is investigated. A finite element (FE) model is, then, developed to measure the performance and efficiency for some basic criteria used to investigate rubber fatigue life in literature. The pertinence of such criteria is evaluated in terms of a determination coefficient. The CED parameter can be considered as the most effective criterion for describing the multiaxial fatigue life of rubbers.

An improved critical plane and cycle counting method to assess damage under variable amplitude multiaxial fatigue loading

AbstractThe plane with the maximum variance of the resolved shear stress is taken as the critical plane. Two algorithms are used along with the maximum variance method (MVM) to determine the orientation of the critical plane. The maximum variance of the normal stress on the potential critical planes is calculated to determine the one experiencing the maximum extent of fatigue damage. A new multiaxial cycle counting method is proposed to count cycles on the critical plane. The modified Wöhler curve method is used to assess fatigue damage. About 200 experimental results were collected from the technical literature to validate the approaches being proposed. The results show that the improved design technique being proposed is successful in assessing fatigue damage under variable amplitude multiaxial cyclic loading.

Mechanism of fine granular area and white etching crack formation in AISI 52100 bearing steel

Fine Granular Area (FGA) and White Etching Cracks (WEC) are two types of fatigue damage phenomena which are characterised by the development of cracks accompanied by a local microstructural transformation. The resulting microstructures share many properties, chiefly a strong reduction in grain size. In this study, the thickness of the transformed zones along the crack formed during FGA and WEC experiments is investigated. It is shown that in WEC, similar to earlier results on the FGA, the size of the transformed zones increases with increasing crack length. For further analysis of the more complex WEC case, an approach is presented that uses the results of a critical plane analysis for the calculation of key figures in fracture mechanics. The results are shown to be very similar to those of the FGA. Drawing on these and earlier results, it is proposed that a common mechanism of WEC and FGA formation exists. In addition, some important differences of the two phenomena are explained within the framework of the common mechanism.

A new multiaxial fatigue life prediction model considering additional hardening effect

The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

Leading edge erosion of wind turbine blades: Multiaxial critical plane fatigue model of coating degradation under random liquid impacts

AbstractA computational model of rain erosion of wind turbine blades is presented. The model is based on the transient fluid–solid coupled finite element (FE) analysis of rain droplet/coating interaction and fatigue degradation analysis. The fatigue analysis of the surface degradation is based on multiaxial fatigue model and critical plane theory. The random rain fields are constructed computationally, and the estimated droplet sizes are included in FE model to acquire a library of load histories. Subsequently, the resulted nonproportional multiaxial high cycle fatigue problem is solved to assess the damage and lifetimes of the coatings. The approach can be used to design new coating systems withstanding longer service times.

Numerical study on the influence of artificial internal stress relief groove on fretting fatigue in a shrink-fitted assembly

Fretting fatigue failure occurs in shrink-fitted assemblies due to the combination of high stresses and relative displacements near the contact edge. Due to these high stresses, fatigue crack initiates followed by crack propagation until final rupture. Additive manufacturing (AM) is a game changing technology, which enables new component capabilities that cannot be manufactured with conventional techniques. This research work analyses numerically the influence of an artificial internal stress relief toroidal groove inside a shrink-fitted shaft, which could be manufactured using AM technology. Due to the toroidal void, the stress/strain fields are redistributed improving the fretting fatigue crack initiation and propagation lifetimes. To do so, 2D finite element models are created in Abaqus software with and without the internal groove. To estimate the fretting fatigue initiation and propagation lifetime and crack propagation direction, critical plane methods are used. In terms of the crack propagation, eXtended Finite Element Method (XFEM) is used to simulate mixed mode crack advancing in a single mesh structure. Finally, the obtained results with and without void were compared concluding with significant improvements in terms of total fatigue lifetime.

A topologized resolved shear stress method for the life prediction of nickel-base single crystal superalloys

Fifteen multiaxial critical-plane fatigue damage parameters of isotropic metal materials are applied to the life evaluation of nickel-base single crystal superalloys. These parameters are classified into stress-, strain- and strain-energy parameters, and their predictive abilities are evaluated by 12 groups of single crystal fatigue data obtained from mainly an intermediate temperature range (500–760 °C) where the slip deformation is the main damage mode. The results show that the strain energy group exhibits the best fitting characteristics with correlation coefficients. A topologized resolved shear stress method (TRSS) considering the interaction of main slip systems is further proposed. The dispersion degree of resolved shear stress among the main slip systems is quantified by a dispersion factor, and the real driving capacity of resolved shear stress is amended according to the topology of driving force. The obtained results show that the proposed method has achieved an improvement of correlation ability.

Extremely-Low-Cycle Fatigue Damage for Beam-to-Column Welded Joints Using Structural Details.

The multiaxial fatigue critical plane method can be used to evaluate the extremely-low-cycle fatigue (ELCF) damage of beam-to-column welded joints in steel frameworks subjected to strong seismic activity. In this paper, fatigue damage models using structural detail parameters are studied. Firstly, the fatigue properties obtained from experiments are adopted to assess ELCF life for steel frameworks. In these experiments, two types of welded specimens, namely, plate butt weld (PB) and cruciform load-carrying groove weld (CLG), are designed according to the structural details of steel beam and box column joints, in which both structural details and welded factors are taken into account. Secondly, experiments are performed on three full-scale steel welded beam-to-column joints to determine the contribution of stress and/or strain to damage parameters. Finally, we introduce a modification of the most popular fatigue damage model of Fatemi and Socie (FS), modified by us in a previous study, for damage evaluation, and compare this with Shang and Wang (SW) in order to examine the applicability of the fatigue properties of PB and CLG. This study shows that the modified FS model using the fatigue properties of CLG can predict the crack initiation life and evaluate the damage of beam-to-column welded joints, and can be subsequently used for further investigation of the damage evolution law.

Fatigue life assessment of welded joints under sequences of bending and torsion loading blocks of different lengths

AbstractIn this work, the nominal stress concept, the notch stress approach and two critical plane approaches are used to analyse the fatigue endurance of a pipe‐to‐plate welded joint subjected to complex loading histories. Both the pipe and the plate were made of S355JR steel. Starting from already known fatigue endurance curves obtained for the same specimens under pure bending and pure torsion, a first series of tests was conducted, in which specimens were loaded in bending for a given fraction of the estimated life and then in torsion until failure. A similar series of tests was then carried out by changing the loading order: specimens were firstly loaded in torsion for a given fraction of the estimated endurance and then in bending until failure. The whole test campaign was repeated for two different fractions of the estimated life, that is, 0.3 and 0.45, respectively. After that, additional three series of tests were carried out, in which the specimens were subjected to consecutive sequences of bending and torsion blocks of different lengths (short, medium and long, respectively); the relative length of the bending and torsion block in each series was determined in order to produce the same damage. The experimental results, in terms of total damage at failure, were analysed using the Palmgren–Miner hypothesis. For all the assessment methods, the characteristic endurance curves were firstly calibrated on the basis of finite element (FE) analyses and of the experimental results obtained under pure bending and pure torsion loadings. The observed damage at failure resulted always greater than 0.5 for all the employed methods and greater than 1 for most of the tests. The different methods gave similar results, with the critical plane methods giving a slightly more stable damage at failure and a correct determination of the failure location. For all the methods, the damage at failure slightly reduces as the block length shortens.

Incremental, Critical Plane Analysis of Standing Wave Development, Self-Heating, and Fatigue during Regulatory High-Speed Tire Testing Protocols

ABSTRACT Tire speed ratings derive from regulatory testing in which tire structural integrity is validated over a series of steps with successively increasing speed. For the FMVSS 139 high-speed standard, there are four half-hour duration speed steps at 80, 140, 150, and 160 kph. Speed ratings from Q through Y may be attained through the UN ECE R30 regulation high-speed testing. For either protocol, a tire must demonstrate the ability to operate without crack development at high speed for a specified period. After the test, “there shall be no evidence of tread, sidewall, ply, cord, inner liner, belt or bead separation, chunking, broken cords, cracking, or open splices.” A workflow for simulating regulatory high-speed durability performance has been developed based upon (1) recent improvements to the Abaqus steady-state transport formulation that now permit converged solutions to be obtained at high speed (including after the development of standing waves in the tire) and (2) Endurica DT self-heating and incremental fatigue simulations that account for thermal effects and for damage accumulation occurring due to a schedule of load cases. The self-heating calculation features the Kraus model and accurately captures viscoelastic loss modulus dependence on strain amplitude and temperature. For each step of the high-speed procedure, steady-state structural and thermal solutions are first computed. The deformation history in the presence of standing waves is shown to require rainflow counting due to the occurrence of multiple load cycles per tire revolution. Crack growth is finally integrated for each potential critical plane through each step of the test until failure is indicated. Standing waves at high speed induce significant self-heating and damage, rapidly limiting high-speed performance. The temperature dependence of self-heating and strength properties also plays a major role in limiting high-speed durability. The simulations were executed on both a flat surface and on the regulation specified 1.7 m diameter road wheel. As expected, durability testing on the road wheel is more severe, and the beneficial effect of a nylon overwrap is predicted.

Finite Element Modeling and Critical Plane Analysis of a Cut-and-Chip Experiment for Rubber

ABSTRACT Rubber surfaces exposed to concentrated, sliding impacts carry large normal and shearing stresses that can cause damage and the eventual removal of material from the surface. Understanding this cut-and-chip (CC) effect in rubber is key to developing improved tread compounds for tires used in off-road or poor road conditions. To better understand the mechanics involved in the CC process, an analysis was performed of an experiment conducted on a recently introduced device, the Instrumented Chip and Cut Analyzer (ICCA), which repetitively impacts a rigid indenter against a rotating solid rubber wheel. The impact process is carefully controlled and measured on this lab instrument, so that the contact time, normal force, and shear force are all known. The numerical evaluation includes Abaqus finite element analysis (FEA) to determine the stress and strain fields during impact. The FEA results are combined with rubber fracture mechanics characteristics of the material as inputs to the Endurica CL elastomer fatigue solver, which employs critical plane analysis to determine the fatigue response of the specimen surface. The modeling inputs are experimentally determined hyperelastic stress-strain parameters, crack growth rate laws, and crack precursor sizes for carbon black–filled compounds wherein the type of elastomer is varied in order to compare natural rubber (NR), butadiene rubber (BR), and styrene-butadiene rubber (SBR). At the lower impact force, the simulation results were consistent with the relative CC resistances of NR, BR, and SBR measured using the ICCA, which followed the order BR > NR > SBR. Impact-induced temperature increases need to be considered in the fatigue analysis of the higher impact force to provide lifetime predictions that match the experimental CC resistance ranking of NR > SBR > BR.