A notch critical plane approach of multiaxial fatigue life prediction for metallic notched specimens

An approach based on the local stress response is proposed to locate the fatigue critical point for metallic blunt notched specimens under multiaxial fatigue loading. According to the stress analysis, both stress gradient and gradient of loading nonproportionality exist at notch root. The plane in the vicinity of the notch that passes through the fatigue critical point and experiences the maximum shear stress amplitude is defined as the critical plane for notch specimens (CPN). Furthermore, the Susmel's fatigue damage parameter is modified to assess fatigue life of notched components by combining CPN and the theory of critical distance (TCD). The multiaxial fatigue test of the thin‐walled round tube specimens made of Ni‐base alloy GH4169 is carried out to verify the above approaches. In addition, test data of two kinds of materials are collected. The results show that the maximum absolute error of the fatigue critical point is 9.6° and the majority of the predicted life falls within the three‐time scatter band.     

TA17合金薄片材料毫小试样疲劳性能研究

关键工程结构、小尺寸零部件和焊接区的疲劳寿命评估中往往无法采用传统大试样进行疲劳试验,因此本文提出了一种采用毫米级别薄片试样获取材料循环本构关系和低周疲劳寿命的新方法。在Care原位试验机上完成毫米级别薄片漏斗试样的加载工装和低周疲劳试验的基础上,通过变幅对称循环试验和等辐循环试验分别实现了材料循环本构关系和低周疲劳性能的获取。该文提出了一种对不同幂律材料和不同几何尺寸构型均具有良好普适性的材料循环本构关系预测模型,并通过有限元实现了模型准确性的正反向预测验证。将循环本构关系用于有限元计算中,给出了薄片漏斗试样漏斗两侧名义应力、名义应变和漏斗根部真实应力、真实应变的转换方程,进而预测材料的低周疲劳寿命。该文完成了TA17合金等直圆棒试样和1.2 mm厚度薄片漏斗试样的对称变幅循环试验和多级等辐循环试验。由模型预测获得的TA17合金循环本构关系与等直圆棒试样的试验结果比较表明:两种曲线的弹性段和0.009 mm/mm~0.011 mm/mm应变段吻合良好,在弹塑性过渡段（0.004 mm/mm~0.009 mm/mm）模型预测结果最大相对误差小于9%。根据两组应力和应变转换方程获得的漏斗试样材料代表性体积单元疲劳寿命和Manson-Coffin寿命预测模型与等直圆棒试样试验结果均吻合良好。     

Fatigue life evaluation of tension‐compression asymmetric material using local stress–strain method

In this paper, the low‐cycle fatigue characteristics of cold‐drawn steel were investigated under strain‐controlled uniaxial fatigue load. Cyclic softening was observed throughout fatigue life except for the initial relatively short period which exhibited cyclic hardening. Positive mean stress was found under fully reversed strain loading, indicating that there was a significant cyclic asymmetry. A modified local stress–strain method was proposed to estimate fatigue life of notched tension‐compression asymmetric material. In order to verify this method, fatigue experiments on two kinds of notched specimens with different notch radius were carried out under constant and block load spectrum. It was found that the modified local stress–strain method was more accurate than the traditional ones, the maximum relative error between predicted and experimental fatigue life was less than 6%.     

Design methods for reliable fatigue assessment of PM components

The use of PM materials is rapidly expanding with an increasing concentration on highly loaded structural parts such as synchroniser hubs, gears, sprockets or shifting forks. The successful implementation of PM materials for such parts depends on a reliable fatigue design concept. Such a design concept has to consider the local durability, especially in fatigue critical sharply notched areas, depending on the local density of the material and stress gradients. This paper summarises different design methods in order to transfer the fatigue behaviour of specimens to components by considering sharply notched areas. Four different local approaches have been investigated: the highly stressed volume approach, the stress gradient approach, the critical distance method and the stress averaging method according to Neuber. The design methods have been analysed on the basis of fatigue testing results of unnotched and notched fatigue specimens and of synchroniser hubs made from a 4% Ni diffusion‐alloyed steel material (Distaloy AE+0.6%C). The transferability of characteristic fatigue properties from specimens to a sharply notched component, a synchroniser hub, is presented and the practicability of the design methods demonstrated and discussed. These investigations showed that the most reliable concept was the highly stressed volume approach. The accuracy of the approach can be comprehended separating statistical and so called material support effect.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

Estimating fatigue damage under variable amplitude multiaxial fatigue loading

The present paper is concerned with the use of the modified Wöhler curve method (MWCM) to estimate both lifetime and high‐cycle fatigue strength of plain engineering materials subjected to complex load histories resulting, at critical locations, in variable amplitude (VA) multiaxial stress states. In more detail, when employed to address the constant amplitude (CA) problem, the MWCM postulates that fatigue damage reaches its maximum value on that material plane (i.e. the so‐called critical plane) experiencing the maximum shear stress amplitude, fatigue strength depending on the ratio between the normal and shear stress components relative to the critical plane itself. To extend the use of the above criterion to those situations involving VA loadings, the MWCM is suggested here as being applied by defining the critical plane through that direction experiencing the maximum variance of the resolved shear stress. Such a direction is used also to perform the cycle counting: because the resolved shear stress is a monodimensional quantity, stress cycles are directly counted by the classical rain‐flow method. The degree of multiaxiality and non‐proportionality of the time‐variable stress state at the assumed critical sites instead is suggested as being measured through a suitable stress ratio which accounts for the mean value and the variance of the stress perpendicular to the critical plane as well as for the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear stress. Accuracy and reliability of the proposed approach was checked by using several experimental results taken from the literature. The performed validation exercise seems to strongly support the idea that the approach formalized in the present paper is a powerful engineering tool suitable for estimating fatigue damage under VA multiaxial fatigue loading, and this holds true not only in the medium‐cycle, but also in the high‐cycle fatigue regime.     

Two methods for predicting the multiaxial fatigue limits of sharp notches

In this paper the problem of the multiaxial fatigue limit estimation of sharply notched components has been addressed using two different methods: a critical distance method and a method involving modified Wöhler curves. These two methods had been previously developed by the authors, but required modification for use in conjunction with finite element stress analysis of sharply notched specimens subjected to multiaxial loadings. Initially, it was demonstrated mathematically that these methods are equivalent in terms of multiaxial stresses near the notch tip. Subsequently, by employing some well‐known uniaxial notch fatigue concepts, some assumptions have been made in order to extend the use of these methods to in‐phase multiaxial notch fatigue situations. Experimental data were obtained from tests conducted on V‐notched specimens subjected to in‐phase mixed Mode I and Mode II loadings. Both methods were successful in giving fatigue limit predictions with an error usually less than 15%. This is interesting because the two methods make quite different assumptions about the nature of fatigue crack growth in the vicinity of the notch.     

多轴载荷下缺口件的疲劳寿命估算方法

提出了一种多轴载荷下缺口件的疲劳寿命估算方法。该方法基于临界平面理论,计算出缺口件各部位的多轴疲劳损伤参数,以损伤参数最大的部位为缺口件的多轴疲劳危险点。根据临界距离思想,提出了热点法和线法的临界距离的计算方法,采用热点法和线法考虑缺口件疲劳危险点附近损伤梯度的影响,以临界距离修正的损伤参数计算多轴载荷下缺口件的疲劳寿命。采用SAE1045钢缺口件的多轴疲劳试验对该文提出的寿命估算方法进行评估和验证,结果表明:该文所建立的寿命预测方法具有较好的预测能力,预测结果大部分分布在试验结果的3倍分散带之内。     

An analytically formulated structural strain method for fatigue evaluation of welded components incorporating nonlinear hardening effects

An analytically formulated structural strain method is presented for performing fatigue evaluation of welded components by incorporating nonlinear material hardening effects by means of a modified Ramberg‐Osgood power law hardening model. The modified Ramberg‐Osgood model enables a consistent partitioning of elastic and plastic strain increments during both loading and unloading. For supporting 2 major forms of welded structures in practice, the new method is applied for computing structural strain defined with respect to a through‐thickness section in plate structures and cross section in piping systems. In both cases, the structural strain is formulated as the linearly deformation gradient on their respective cross sections, consistent with the “plane sections remain plane” assumption in structural mechanics. The structural strain‐based fatigue parameter is proposed and has been shown effective in correlating some well‐known low‐cycle and high‐cycle fatigue test data, ranging from gusset‐to‐plate welded plate connections to pipe girth welds.     

Proposal of an alternating bending technique for evaluating low‐to‐high cycle fatigue of structural steels

This paper proposes an alternating bending technique for evaluating fatigue life in the low‐to‐high cycle fatigue regime. A method was developed for estimating the stress, elastic strain, and plastic strain ranges of a plastically deformed specimen subjected to alternating bending with consideration of stress and strain distributions. To evaluate its effectiveness, fatigue testing was conducted using a specimen made of a steel used for pressure vessels. The stress, elastic strain, and plastic strain ranges could be obtained during cyclic bending. The elastic strain amplitude life and plastic strain amplitude life curves were linear in a log–log plot in the low‐to‐high cycle fatigue regime. Hence, the fatigue life under alternating bending could be evaluated using the proposed strain‐based approach. However, these curves could not be predicted using equations with parameters obtained from tensile testing, such as the universal slope method, due to the strain gradient in the specimen.     

Multiaxial fatigue life prediction method based on path‐dependent cycle counting under tension/torsion random loading

A path‐dependent cycle counting method is proposed by applying the distance formula between two points on the tension‐shear equivalent strain plane for the identified half‐cycles first. The Shang–Wang multiaxial fatigue damage model for an identified half‐cycle and Miner's linear accumulation damage rule are used to calculate cumulative fatigue damage. Therefore, a multiaxial fatigue life prediction procedure is presented to predict conveniently fatigue life under a given tension and torsion random loading time history. The proposed method is evaluated by experimental data from tests on cylindrical thin‐walled tubes specimens of En15R steel subjected to combined tension/torsion random loading, and the prediction results of the proposed method are compared with those of the Wang–Brown method. The results showed that both methods provided satisfactory prediction.     

A stress-based method to predict lifetime under multiaxial fatigue loadings

This paper extends to low/medium‐cycle fatigue a stress‐based method recently proposed by the same authors for high‐cycle multiaxial fatigue assessments. By considering the plane of maximum shear stress amplitude coincident with the microcrack initiation plane, the method requires the calculation both of the maximum shear stress amplitude and the maximum normal stress relative to the same plane. Multiaxial fatigue life estimates are made by means of bi‐parametric modified Wöhler curves, which take into account the mean stress effect, the influence of the out‐of‐phase angle and the presence of notches by using a generalization to multiaxial fatigue of the fatigue strength reduction factor K_f. Approximately 700 experimental data taken from the literature are used to demonstrate that the method is a useful tool to summarize fatigue strength data of both smooth and notched components, subjected to either in‐phase or out‐of‐phase loads. Finally, a simple practical rule for the calculation of the multiaxial fatigue strength reduction factor is proposed.     

Total Fatigue Life Estimation of Notched Structural Components Using Low‐Cycle Fatigue Properties

Abstract: In this investigation, an efficient fatigue life computation method under variable amplitude loading of structural components has been proposed. Attention in this study is focused on total fatigue life estimation of aircraft structural components. Flat specimens with central hole made of quenched and tempered steel 13H11N2V2MF were tested as representatives of different structural components. Total fatigue life of these specimens, defined as sum of fatigue crack initiation and crack growth life, was experimentally determined. Specimens were tested by blocks of positive variable amplitude loading. Crack initiation life was computed using theory of low‐cycle fatigue (LCF) properties. Cyclic stress–strain curve, Masing’s curve and approximate Sonsino’s curve were used for determining stress–strain response at critical point of considered specimens. Computation of crack initiation life was realised using Palmgren–Miner’s linear rule of damage accumulation, applied on Morrow’s curves of LCF properties. Crack growth life was predicted using strain energy density method. In this method, the same LCF properties were used for crack initiation life and for crack growth life computations also. Computation results are compared with own experimentally obtained results.     

The linear‐elastic Theory of Critical Distances to estimate high‐cycle fatigue strength of notched metallic materials at elevated temperatures

This paper investigates the accuracy of the linear‐elastic Theory of Critical Distances (TCD) in estimating high‐cycle fatigue strength of notched metallic materials experiencing elevated temperatures during in‐service operations. The TCD postulates that the fatigue damage extent can be estimated by directly post‐processing the entire linear‐elastic stress field acting on the material in the vicinity of the crack initiation locations. The key feature of this theory is that the high‐cycle fatigue assessment is based on a scale length parameter that is assumed to be a material property. The accuracy of this design method was checked against a number of experimental results generated, under axial loading, by testing, at 250 °C, notched specimens of carbon steel C45. To further investigate the reliability of the TCD, its accuracy was also checked via several data taken from the literature, these experimental results being generated by testing notched samples of Inconel 718 at 500 °C as well as notched specimens of directionally solidified superalloy DZ125 at 850 °C. This validation exercise allowed us to prove that the linear‐elastic TCD is successful in estimating high‐cycle fatigue strength of notched metallic materials exposed to elevated temperature, resulting in estimates falling within an error interval of ±20%. Such a high level of accuracy suggests that, in situations of practical interest, reliable high‐cycle fatigue assessment can be performed without the need for taking into account those non‐linearities characterising the mechanical behaviour of metallic materials at high temperature, the used critical distance being still a material property whose value does not depend on the sharpness of the notch being designed.     

Prediction methods of fatigue critical point for notched components under multiaxial fatigue loading

Two methods based on local stress responses are proposed to locate fatigue critical point of metallic notched components under non‐proportional loading. The points on the notch edge maintain a state of uniaxial stress even when the far‐field fatigue loading is multiaxial. The point bearing the maximum stress amplitude is recognized as fatigue critical point under the condition of non‐mean stress; otherwise, the Goodman's empirical formula is adopted to amend mean stress effect prior to the determination of fatigue critical point. Furthermore, the uniaxial stress state can be treated as a special multiaxial stress state. The Susmel's fatigue damage parameter is employed to evaluate the fatigue damage of these points on the notch edge. Multiaxial fatigue tests on thin‐walled round tube notched specimens made of GH4169 nickel‐base alloy and 2297 aluminium‐lithium alloy are carried out to verify the two methods. The prediction results show that both the stress amplitude method and the Susmel's parameter method can accurately locate the fatigue critical point of metallic notched components under multiaxial fatigue loading.     

A fatigue damage accumulation model for reliability analysis of engine components under combined cycle loadings

Rotor components of an aircraft engine in service are usually subjected to combined high and low cycle fatigue (CCF) loadings. In this work, combining with the load spectrum of CCF, a modified damage accumulation model for CCF life prediction of turbine blades is first put forward to take into account the effects of load consequence and load interaction caused by high‐cycle fatigue (HCF) loads and low‐cycle fatigue (LCF) loads under CCF loading conditions. The predicted results demonstrate that the proposed model presents a higher prediction accuracy than Miner, Manson‐Halford model does. Moreover, to evaluate the fatigue reliability of rotor components, reliability model with the failure mode of CCF is proposed on the basis of the stress‐strength interference method when considering the strength degeneration, and its results show that the reliability model with CCF is more suitable for aero‐engine components than that with the failure mode of single fatigue.     

Low cycle fatigue life prediction in shot‐peened components of different geometries – part II: life prediction

This study investigates the effects of shot peening on the low‐cycle fatigue performance of a low‐pressure steam turbine blade material. The finite element model incorporating shot‐peening effects, which has been introduced in part I, has been used to predict the stabilised stress/strain state in shot‐peened samples during fatigue loading. The application of this model has been extended to different notched geometries in this study. Based on the modelling results, both the Smith–Watson–Topper and Fatemi–Socie critical plane fatigue criteria have been used to predict the fatigue life of shot‐peened samples (treated with two different peening intensities) with varying notched geometries. A good agreement between experiments and predictions was obtained. The application of a critical distance method considering the stress and strain hardening gradients near the shot‐peened surface has been found to improve the life prediction results. The effects of surface defects on the accuracy of life predictions using the proposed method were also discussed.     

Comparison of HCF life prediction methods based on different critical planes under multiaxial variable amplitude loading

High‐cycle fatigue life prediction methods based on different critical planes, including the maximum shear stress (MSS) plane, the weighted average shear stress plane and the Maximum Variance shear stress plane, are compared by two multiaxial cycle counting methods, i.e. the main and auxiliary channels (MAC) counting and the relative equivalent stress counting. A modified damage model is used to calculate the multiaxial fatigue damage. Compared with the experimental lives for 7075‐T651 aluminium alloy, the predicted results show that the MSS method together with MAC counting is suitable for the multiaxial fatigue life prediction.     

Cumulative fatigue damage of stress below the fatigue limit in weldment steel under block loading

To investigate the cumulative fatigue damage below the fatigue limit of multipass weldment martensitic stainless steel, and to clarify the effect of cycle ratios and high‐stress level in the statement, fatigue tests were conducted under constant and combined high‐ and low‐stress amplitude relative to stress above and below the fatigue limit. The outcomes indicate that neither modified Miner's nor Haibach's approach provided accurate evaluation under repeated two‐step amplitude loading. Moreover, effect of cycle ratios has been determined. Additionally, the cumulative fatigue damage saturated model is established and validated. Cumulative fatigue damage contributed by low‐stress below the fatigue limit in high stress of 700 MPa is higher than that with 650 MPa at identical conditions (fatigue limit 575 MPa). Thus, high stress affects fatigue damage behaviour below the fatigue limit. A new predicted approach has been proposed based on Corten‐Dolan law, whose accuracy and applicability have been proven.     

Determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading

A weight function method for the determination of the critical plane is here proposed for the case of specimens under combined bending and torsion in the high cycle fatigue regime. The critical plane is assumed to be coincident with the mean maximum absolute shear stress plane, which is calculated by averaging the instantaneous angle between the specimen axis and the normal to the maximum absolute shear stress plane. Two kinds of weight functions are proposed to determine such a plane. The proposed method to determine the critical plane is verified by employing fatigue data available in the literature in terms of experimental fracture planes, and the multiaxial fatigue life is also predicted by a reformulation of the criterion proposed by Carpinteri et al. to verify the determined critical plane. The results show that the proposed method can be applied to determine the critical plane under both constant and variable amplitude loading.