Equivalent Stress Intensity Factor Range Research Articles

Numerical prediction of fretting fatigue crack growth in scaled railway axles considering fretting wear evolution

To predict the fretting fatigue crack growth (FFCG) life of railway axles, a series of interrupted fatigue experiments were conducted on scaled railway axles. Subsequently, the evolutions of fretting wear and fatigue cracks in the press-fitted region were analyzed. Based on the test results, finite element models incorporating fretting wear evolution were established, and the FFCG was investigated using the maximum tangential stress criterion, cyclic resistance curve, and the modified NASGRO equation. The analysis revealed that the fretting wear evolution leads to stress redistribution at the press-fitted region, thereby promoting FFCG. When considering fretting wear evolution, the equivalent stress intensity factor (SIF) range of the crack remains above the threshold value throughout the short crack stage. However, neglecting fretting wear evolution results in the SIF range being below the threshold value for cracks shallower than 0.30 mm. This implies that considering fretting wear evolution enables life prediction throughout the short crack stage. As the crack length increases, the influence of fretting wear evolution on crack growth gradually diminishes. By accounting for fretting wear, a more accurate stress distribution in the press-fitted region can be obtained, leading to a more precise and conservative prediction of crack growth life.

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.

Influence of initial crack on fatigue crack propagation with mixed mode in U71Mn rail subsurface

A three-dimensional finite element model of wheel-rail that contains an initial crack in rail subsurface was established, the influences of initial crack angle, depth and size on mixed fatigue crack growth behaviour under actual load were evaluated. The results showed that the initial crack propagated with II + III mixed mode, and the slip propagation of mode II was dominant. Different initial crack angle, depth and size lead to variable proportions of mode II and mode III because of the load mixity at the crack tip, which further affects the equivalent stress intensity factor (SIF) range ΔKeq and residual fatigue lifetime. 45° was the most dangerous angle of initial crack, which leads to the highest ΔKeq and the fastest crack growth initial crack depth increased, the ΔKeq and crack growth rate decreased sharply. With the increase of initial crack size, the ΔKeq increased and crack propagation was accelerated.

Interaction of a fatigue crack and a corrosion dimple in a high-strength steel specimen

Both corrosion and fatigue crack propagation are the most common phenomena degrading metal/steel structures. Therefore, an extensive study is performed on this topic. Namely, results of a numerical analysis made on 2D model of a rectangular specimen containing a corrosion pit near a short edge crack that is arbitrarily oriented towards the cyclic tensile loading. Thus, I+II mixed mode conditions are created and the behavior of the crack is investigated by means of the concept of the equivalent stress intensity factor range. Discussion on effect of various parameters (such as crack length, corrosion pit size, crack inclination angle) on fatigue crack propagation is presented and important conclusions, that can help in further numerical/experimental analyses, are summarized.

Experimental and numerical study on fretting wear and fatigue of full-scale railway axles

This study investigated the fretting wear and fatigue of full-scale railway axles. Fatigue tests were conducted on full-scale railway axles, and the fretting wear and fretting fatigue in the fretted zone of the railway axles were analysed. Three-dimensional finite element models were established based on the experimental results. Then, multi-axial fatigue parameters and a linear elastic fracture mechanics-based approach were used to investigate the fretting fatigue crack initiation and propagation, respectively, in which the role of the fretting wear was taken into account. The experimental and simulated results showed that the fretted zone could be divided into zones I–III according to the surface damage morphologies. Fretting wear alleviated the stress concentration near the wheel seat edge and resulted in a new stress concentration near the worn/unworn boundary in zone II, which greatly promoted the fretting crack initiation at the inner side of the fretted zone. Meanwhile, the stress concentration also increased the equivalent stress intensity factor range ΔKeq below the mating surface, and thus promoted the propagation of fretting fatigue crack. Based on these findings, the effect of the stress redistribution resulting from fretting wear is suggested to be taken into account when evaluating the fretting fatigue in railway axles.

Fatigue Crack Growth under Non-Proportional Mixed Mode Loading in Rail and Wheel Steel Part 2: Sequential Mode I and Mode III Loading

Rolling contact fatigue cracks in rail and wheel undergo non-proportional mixed mode I/II/III loading. Fatigue tests were performed to determine the coplanar and branch crack growth rates on these materials. Sequential and overlapping mode I and III loading cycles were applied to single cracks in round bar specimens. Experiments in which this is done have been rarely performed. The fracture surface observations and the finite element analysis results suggested that the growth of long (does not branch but grown stably and straight) coplanar cracks was driven mainly by mode III loading. The cracks tended to branch when increasing the material strength and/or the degree of overlap between the mode I and III loading cycles. The equivalent stress intensity factor range that can consider the crack face contact and successfully regressed the crack growth rate data is proposed for the branch crack. Based on the results obtained in this study, the mechanism of long coplanar shear-mode crack growth turned out to be the same regardless of whether the main driving force is in-plane shear or out-of-plane shear.

Crack path and life prediction under mixed mode cyclic variable amplitude loading through XFEM

In the present paper, a mesh independent computational algorithm is developed and incorporated into a commercial finite element software (Abaqus) for automated fatigue crack growth analysis under mixed mode variable amplitude loading conditions. The algorithm calculates the stress intensity factor (SIF) at predetermined small crack growth increments in the finite element software by using Extended Finite Element Method (XFEM) and predict the fatigue crack growth (FCG) path through local symmetry (KII=0) criterion. The aforementioned algorithm also computes the FCG life by means of cycle-by-cycle integration method through Nasgro equation based on the equivalent SIF range. Load history effects are also taken into account by using appropriate retardation models according to nature of the loading. For verification purpose, experimental crack path trajectories and fatigue life data available in the open literature are compared with computational results. Quite good agreements are obtained between the computed and the experimental results.

Fatigue life prediction under mixed-mode loading using equivalent stress intensity factor models

Damage tolerance principles are widely used to assess the structural integrity and failure of engineering components. The advances in numerical simulation techniques facilitate the prediction of fatigue life of engineering component, which is essential in damage tolerance design. For the components under mixed mode (I/II) loading, the fatigue crack growth and life is predicted by using a modified form of Paris' law along with the equivalent stress intensity factor (ΔKeq). Numerous ΔKeqmodels are available for correlating the equivalent stress intensity factor range and the fatigue crack growth rate. The knowledge of proper ΔKeqmodel is essential for the accurate fatigue life estimation. In this work, the authors numerically assess the performance of ΔKeqmodels in mixed mode fatigue life prediction with the help of published experimental mixed mode data.

Spectral-based fatigue crack propagation prediction for very large floating structures

This paper provides a fatigue assessment for a very large floating structure using a spectral-based fracture mechanics approach that combines hydrodynamic response analysis, spectral stress intensity factor calculation, load spectrum, and fatigue crack propagation model. To predict fatigue crack growth in the critical welded joints, this paper summarizes formulas associating equivalent stress intensity factor range with equivalent stress range of a given hot spot. Both are performed using spectral analysis in stochastic sea conditions. The unique curve model is introduced for crack propagation prediction. Thus, this paper provides a reasonable way to convert complex wave loads into crack growth, and can be widely applied to other marine structures.

A path-dependent fatigue crack propagation model under non-proportional modes I and III loading conditions

It has been well established that fatigue damage process is load-path dependent under non-proportional multi-axial loading conditions. Most of studies to date have been focusing on interpretation of S-N based test data by constructing a path-dependent fatigue damage model. This paper presents a two-parameter mixed-mode fatigue crack growth model which takes into account of crack growth dependency on both load path traversed and a maximum effective stress intensity attained in a stress intensity factor plane (e.g.,KI-KIII plane). By taking advantage of a path-dependent maximum range (PDMR) cycle definition (Dong et al., 2010; Wei and Dong, 2010), the two parameters are formulated by introducing a moment of load path (MLP) based equivalent stress intensity factor range (ΔKNP) and a maximum effective stress intensity parameter KMax incorporating an interaction term KI·KIII. To examine the effectiveness of the proposed model, two sets of crack growth rate test data are considered. The first set is obtained as a part of this study using 304 stainless steel disk specimens subjected to three combined non-proportional modes I and III loading conditions (i.e., with a phase angle of 0°, 90°, and 180°). The second set was obtained by Feng et al. (2007) using 1070 steel disk specimens subjected to similar types of non-proportional mixed-mode conditions. Once the proposed two-parameter non-proportional mixed-mode crack growth model is used, it is shown that a good correlation can be achieved for both sets of the crack growth rate test data.

Crack growth and splitting failure of silicon nitride ceramic balls under cyclic pressure loads

In order to examine the splitting failures of silicon nitride balls under cyclic pressure loads, fatigue tests of pre-cracked balls were carried out. The cracks of initial length ranging from 0.260 to 0.290mm were observed under different stress ratio conditions and the effects of stress ratio and residual stress on the fatigue strength were investigated. Furthermore, the initial threshold limit of the equivalent stress intensity factor range (ΔKeqth) was measured.

Separating plasticity-induced closure and residual stress contributions to fatigue crack retardation following an overload

The introduction of an overload or underload within a constant amplitude loading fatigue test leads to a retardation or acceleration of the Fatigue Crack Growth Rate (FCGR). The understanding of the causes of these effects is essential in the context of variable amplitude fatigue loading, since in principle any loading history can be represented as a sequence of overloads and underloads. In the case of overload, along with some other minor causes, the residual stress changes at the crack tip and crack closure behind the tip can be thought of as the main factors that affect the fatigue crack growth rate. Whilst this has been recognised and accepted for many decades, controversy persists regarding the relative significance and presence of these two effects, and consensus is yet to emerge. The effect of crack closure, when the baseline loading ratio is high enough, can be inhibited so that the main cause of retardation becomes doubtless the residual stress present ahead the crack tip.In the present paper we report our attempt to deconvolve the contributions of crack closure and residual stress on crack retardation following an overload. To accomplish this task we analyse the results of fatigue tests run at two baseline load ratios, namely R=0.1 and R=0.7. At the load ratio of R=0.7 the crack closure effect is not operative, as confirmed by Digital Image Correlation analysis of the crack flanks close to the tip, and post mortem fractographic analysis of crack surfaces. Therefore, for R=0.7 the compressive residual stress region created by the overload ahead of the crack tip is the sole mechanism causing crack retardation. Therefore, for R=0.7 the focus must be placed entirely on the strain field around the crack tip. To this end, line profiles along the crack bisector of elastic strain in the crack opening direction were collected at several stages of crack propagation past the overload using in situ Synchrotron X-ray Powder Diffraction (SXRPD) technique.By performing comparison between the two loading conditions (R=0.7 and R=0.1), information was extracted regarding the role of residual stress alone, and then, by subtracting this effect for the R=0.1 sample, for crack closure alone. To enable this analysis, we propose a introducing the concept of equivalent effective stress intensity factor range, ∆Keq,eff proposed by Walker. Afterwards, the SIF range reduction ratio, β, which represents the “knock down” factor with respect to the steady state growth was assessed. It is in terms of these newly introduced parameters that the magnitude and extent of the overload-induced crack growth rate retardation can be plotted, fitted and decomposed into closure and residual stress effects, respectively. It is concluded that although the residual stress effect is present at all values of the load ratio R, its effect is relatively short-lived, whilst the closure effect that is dominant at low values of R causes longer range retardation.

Fatigue strength evaluation of self-piercing riveted Al-5052 joints under different specimen configurations

In this study, static and fatigue tests were conducted using coach-peel, cross-tension and tensile–shear specimens with Al-5052 plates for evaluation of the fatigue strength of the SPR joints. For the coach-peel, cross-tension and tensile–shear geometries, the ratios of the fatigue endurance limit to static strength were 11%, 14% and 34%, respectively, assuming fatigue cycles of 106 for an infinite lifetime. The equivalent stress intensity factor range can properly predict the current experimental fatigue lifetime. Fatigue crack initiation occurred due to fretting damage between the upper and lower sheets and between the rivet and these sheets.

혼합모드 하중조건에서의 철도 차륜재의 피로균열 실험에 관한 연구

Fatigue crack growth tests were conducted on urban railway wheel steel under mode I and mixed-mode conditions. Fatigue crack growth rates were evaluated in terms of equivalent stress intensity factor ranges, using both the extended and projected crack lengths. The equivalent stress intensity factor range with the growth rate results obtained under mode I loading conditions can be used to predict the crack growth rate under mixed-mode loading conditions. Extended crack length rather than projected crack length is appropriate for the prediction of the crack growth rate under the mixed-mode loading conditions.

Mixed-mode fatigue crack growth behavior of fully lower bainite steel

Fatigue tests were conducted on fully lower bainite steel, which is applicable to vehicle components due to its good resistance against crack propagation. The crack growth rates of this steel under mode-I and mixed-mode conditions were evaluated in terms of equivalent stress intensity factor range. The equivalent stress intensity factor range with growth rate results obtained under mode-I loading conditions can be used to predict the crack growth rate under mixed-mode loading conditions. Extended crack length rather than projected crack length is appropriate for the prediction of the crack growth rate under the mixed-mode loading conditions.

판재 Al 2024-T3 합금재료의 두께효과를 나타내는 형상인자 및 하중인자에 의한 피로관계식

Aluminum alloys have been used with various thicknesses suitable for light weight of structure. It is known that the thickness effect of material is an important factor affecting fatigue crack propagation under constant fatigue stress condition. In this work, we presented the behavior of fatigue crack propagation in thin plate compared to thick plate Al 2024-T3 alloy with referred thickness effect in a correlative equation determined by the shape factor and the loading factor. We chose two factors that are used in the correlative equation with considering that the experiments were carried out under a constant fatigue stress condition. The thickness ratio of thin plate compared to thick plate and the equivalent effective stress intensity factor ratio depending on thickness were chosen as shape and loading factors. A correlative equation is utilized to determine the equivalent effective stress intensity factor range of thin plate and identify the degree of increasing phenomenon of fatigue life in thin plate compared to thick plate.

Simulation of fatigue life of constructional steels within the mixed modes I and III loading

The authors analysed influence of a component of the torsional moment M as under the complex loading state, that is under bending with torsion, on fatigue life during initiation and propagation of fatigue cracks. Simulation of specimen life was performed according to the relationships describing the crack propagation rate and including the equivalent stress intensity factor range K eq . Under complex loading, increase of amplitude of the torsional moment M as for a given initial value of the resultant moment M aw0 caused a higher fatigue life of specimens made of 10HNAP and 18G2A steels. This fatigue life increase was described by a nonlinear equation, the parameters of which had been determined from the experimental results. The fatigue lives estimated according to the assumed models were compared with those obtained from tests.

Short fatigue crack growth behavior under mixed-mode loading

Mixed-mode loading represents the true loading condition in many practical situations. In addition, most of the fatigue life of many components is often spent in the short crack growth stage. The study of short crack growth behavior under mixed-mode loading has, therefore, much practical significance. This work investigated short crack growth behavior under mixed-mode loading using a common medium carbon steel. The effects of load mixity, crack closure, and load ratio on short crack growth behavior were evaluated by conducting experiments using four-point bending specimens with several initial KII/KI mixed-mode ratios and two load ratios. Cracks were observed to grow along the paths with very small KII/KI ratios (i.e. mode I). The maximum tangential stress criterion was used to predict the crack growth paths and the predictions were found to be close to the experimental observations. Several parameters including equivalent stress intensity factor range and effective stress intensity factor range were used to correlate short crack growth rates under mixed-mode loading. Threshold values for short cracks were found to be lower than those for long cracks for all the mixed-mode loading conditions. Crack closure was observed for the entire crack length regime with all load mixity conditions at R ≈ 0.05 and for short crack regime under high load mixity condition at R = 0.5. Several models were used to describe mean stress effects and to correlate crack growth rate data.

A unique crack growth rate curve method for fatigue life prediction of steel structures

In this paper, a unique crack growth rate curve method, which is based on the equivalent stress intensity factor range (ESIFR) as the driving force, has been proposed and examined with crack growth rate data of base metals and as welded joints of some structural steels under constant amplitude external loading. By expressing the crack growth rate data with ESIFR instead of stress intensity factor range (SIFR) make it possible to establish a concise model for crack growth data under different R-ratios to the curve corresponding to R=0 both for base metals and welded joints. The most commonly tested crack growth rate constants under R=0 ∼0.1 are sufficient in fatigue crack growth life prediction of components subjected to tensile-tensile, tensile-compressive loading. Only two equations, one for Mean curve, and the other for Mean + 2SD curve replace the recommended crack growth rate curves in BS7910 for most structural steels. The phenomena that crack growth rates of as-welded joints under different applied loading ratios behaves independent of the applied loading ratio can be explained and the crack growth rate in residual stress field can be predicted well by the present model. The unique crack growth rate curve method does not only allow us to estimate the fatigue life of specimens of base metal and weld joints, but also the fatigue life of structural components under complex loading conditions.

Optimization of a crankshaft rolling process for durability

A crankshaft is often designed with a small fillet radius. The crankshaft fillet rolling process is one of the commonly adopted methods in engineering to improve fatigue life of the crankshaft. Compressive residual stresses on and below the fillet radius surface are induced through the fillet rolling operation. Consequently, fatigue life of the crankshaft is improved. An analytical technique is used to optimize the crankshaft rolling process to comply with a crankshaft design criterion for durability. A nonlinear finite element analysis is implemented to approximate the stress distributions induced by the crankshaft rolling process, and a crack modeling technique is developed to calculate the equivalent stress intensity factor ranges based on the combined residual and operational stress distributions along various crack growth planes. The threshold equivalent stress intensity factor range is obtained from previous staircase testing on crankshaft sections. The durability design criterion is met if the threshold equivalent stress intensity factor range exceeds the largest calculated equivalent stress intensity factor range. Due to the complexity of the modeling techniques in simulating the rolling process and calculating the equivalent stress intensity factors, a meta-model is generated based on the uniform design method for the choice of sample points and the quadratic polynomial fitting technique for a response surface generation. In the meta-model optimization process, rolling force, rolling angle, and fillet radius are the control factors, while the variations of the threshold equivalent stress intensity factor range, rolling force, rolling angle, and fillet radius are considered as the noise factors. By using the Hooke–Jeeves direct pattern search method and the Monte Carlo simulation technique, the optimal design is obtained for the highest reliability and the smallest coefficient of variation (COV).