A cumulative damage theory for fatigue crack initiation and propagation

A method for evaluating the cumulative damage resulting from the application of cyclic stress (or strain) sequences of varying amplitude is presented. Both the crack initiation and propagation stages of the fatigue failure process are included. The development is based on the concept of plastic strain energy dissipation as a function of cyclic life. The damage accumulated at any stage is evaluated from a knowledge of the fatigue limit in the initiation phase and an ‘apparent’ limit obtained through fracture mechanics for the propagation phase. The proposed damage theory is compared with two-level strain cycle test data of thin-walled specimens, and is found to be in fairly good agreement.     

Cumulative fatigue damage dynamic interference statistical model

After studying in depth the statistical characteristics of cumulative fatigue damage D(t) and its critical value D_c, a new dynamic interference statistical model for fatigue reliability analysis is presented in this paper. Because the non-linearity of fatigue damage accumulation has been taken into account, this model is able to predict the fatigue reliability for random spectrum loading. To verify the predicted results, two fatigue experiments were conducted in which the numbers of specimens were more than 100, using fighter spectrum loading (FALSTAFF spectrum) and constant-amplitude loading respectively. It is shown that the new model is reliable, practicable and better than existing models.     

A stochastic damage accumulation model for crack initiation in high-cycle fatigue

A stochastic damage accumulation model for crack initiation in high-cycle fatigue is proposed. It is assumed that the fatigue damage is accumulated in the form of dislocations under the repeated stress and that the slip band crack is initiated when the strain energy due to a local pile-up of dislocations exceeds a critical value. The size of an initiating crack is the cell size, derived from a probabilistic argument and its depth is determined in relation to the stored dislocation energy. Our theoretical results are compared with the experimental data from a low-carbon steel S20C in order to examine the consistency of our model.     

History influence exponent in cumulative fatigue damage determined using two-step loading experiments

ABSTRACT The only material parameter, which appears in quadratic phenomenological hypothesis of cumulative fatigue damage, is the history influence exponent ϑ reflecting the material sensitivity to loading sequence and loading level interactions. Methods of its determination on the basis of two-step loading experiments are presented. One method is based on the least-squares method using linearizing transformation, other two ones are based on concept of individual fatigue life curves and statistical concept of inexact structural model. Parameter ϑ has been evaluated in 24 cases representing various materials and different test conditions. Possibility of existence of a common ϑ value holding for all materials is discussed. Such a value does not follow from analysed experimental data. However, ϑ = 0.5 is recommended for improving the reliability of engineering fatigue life estimates in case when required experimental material data are not available.     

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.     

The life evaluation by linear cumulative damage rule for cold dwell fatigue of Ti-6Al-4V alloy

Low cycle fatigue (LCF) life at ambient temperature of Ti alloys is well known to decrease with stress dwell. This phenomenon, called cold dwell fatigue (CDF), is influenced by the peak stress, dwell time, and microstructure. For this study, the CDF life was evaluated by the linear cumulative damage rule. The influence of test conditions and microstructure on the linear cumulative damage rule was also verified. By the linear cumulative damage rule, when creep damage is calculated using the time exhaustion rule, theCDF damage was evaluated by the inequality of D_Total = (D_F, D_C) ≤ (0.01, 10^?6). However, the CDF damage can be evaluated in the range of D_Total = 0.6–1.2 when creep damage was calculated using the ductile exhaustion rule. Results indicate that the evaluation was almost independent of the dwell time, peak stress, and microstructure, so it is also a versatile method for evaluating CDF responses.     

A model of cumulative fatigue strengthening effect due to coaxing

In this paper, a fatigue experiment of auto drive shaft smooth specimen is studied in details. Through the analysis of load amplitude and load cycles, which influenced on the residual fatigue strength of structure, we find a mathematical model of strengthening effect due to coaxing. Based on the auto drive shaft work load spectrum, a cumulative fatigue strengthening model is suggested. Then, a new method of lightweight design that can maximise cumulative strengthening effect is proposed. Our model and method can provide a theoretical basis for lightweight design on structural parts of automobiles.     

Fatigue damage discrepancies,the intrinsic fatigue damage map locus and the multiple stages of the similitude concept

The work demonstrates how the theory of the fatigue damage map (FDM) can be used in order to define a closed form locus where fatigue crack growth can be sought. The Intrinsic FDM Locus depending only on readily material properties represents a tool able to accurately predict crack growth of polycrystals. If the Locus is expressed in terms of a surface plot after triangulation of the data, it concludes into visualization of the potential for multiple similitude stages. The stages are defined as a function of the maximum far field stress and ΔK. Multiple similitude stages are found to dominate the short and near threshold area (Stage I growth) and represent direct result of the effect of polycrystalline behaviour to flow resistance. The work concludes that interrogation of the points defining the Intrinsic FDM Locus and related to the three thresholds can provide potential characteristics in the quest for an ideal damage tolerance material.     

Cumulative fatigue damage modeling-crack nucleation and early growth

Prior research into linear and nonlinear fatigue damage accumulation in metals and alloys is briefly reviewed, and general trends are identified. Nonlinear damage rules offer substantially more accurate, and hence less unconservative, fatigue life predictions than the classical linear damage rule (LDR). Increased accuracy does not require excessive cost of analysis or additional databases. The nonlinear damage curve approach and its double linear damage rule (DLDR) equivalent are models that, at most, require only twice the effort of the classic LDR. These models require no increase in complexity of use, nor do they require additional material property or mission loading information to achieve the improved accuracy. Greatest improvements (factors of 5–10 or more in mission lifetime) accrue when missions include considerable high-cycle fatigue with some severe low-cycle fatigue loadings. Criteria are proposed for judging those severe mission loading circumstances when the classical LDR becomes unacceptably nonconservative.     

基于神经网络的材料非稳态疲劳损伤可靠性研究

疲劳累积损伤是一个非稳态能耗过程，可以用遗传算法优化后的3层2—7-1BP神经网络来描述疲劳损伤的非线关系，经仿真验证表明，该神经网络具有较高的精度和泛化能力。通过对材料疲劳损伤临界值和栽荷的分散性的分析研究，建立了疲劳失效动态准则，并运用蒙特卡罗随机抽样法对材料疲劳寿命的可靠性进行了仿真验证；对调质45号钢在随机栽荷和2级栽荷作用下，进行了疲劳寿命可靠性仿真计算，仿真结果与实验结果和理论分析比较吻合。     

A method for assessing critical plane‐based multiaxial fatigue damage models

Fatigue failure is a complex phenomenon. Therefore, development of a fatigue damage model that considers all associated complexities resulting from the application of different cyclic loading types, geometries, materials, and environmental conditions is a challenging task. Nevertheless, fatigue damage models such as critical plane‐based models are popular because of their capability to estimate life mostly within ±2 and ±3 factors of life for smooth specimens. In this study, a method is proposed for assessing the fatigue life estimation capability of different critical plane‐based models. In this method, a subroutine was developed and used to search for best estimated life regardless of critical plane assumption. Therefore, different fatigue damage models were evaluated at all possible planes to search for the best life. Smith‐Watson‐Topper (normal strain‐based), Fatemi‐Socie (shear strain‐based), and Jahed‐Varvani (total strain energy density‐based) models are compared by using the proposed assessment method. The assessment is done on smooth specimen level by using the experimental multiaxial fatigue data of 3 alloys, namely, AZ31B and AZ61A extruded magnesium alloys and S460N structural steel alloy. Using the proposed assessment method, it was found that the examined models may not be able to reproduce the experimental lives even if they were evaluated at all physical planes.     

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.     

Fatigue damage of medium carbon steel under sequential application of axial and torsional loading

Fatigue tests were conducted on S45C steel under fully reversed strain control conditions with axial/torsional ( at ) and torsional/axial ( ta ) loading sequences. The linear damage value (n₁/N₁+n₂/N₂) was found to depend on the sequence of loading mode ( at or ta ), sequence of strain amplitude (low/high or high/low) and life fraction spent in the first loading. In general, at loading yields larger damage values than ta loading and the low–high sequence of equivalent strain leads to larger damage values than the high–low sequence. The material exhibits cyclic softening under axial cyclic strain. Cyclic hardening occurs in the torsion part of ta loading, which elevates the axial stress in the subsequent loading, causing more damage than in pure axial fatigue at the same strain amplitude. Fatigue life is predicted based on the linear damage rule, the double linear damage rule, the damage curve approach and the plastic work model of Morrow. Results show that overly conservative lives are obtained by these models for at loading while overestimation of life is more likely for ta loading. A modified damage curve method is proposed to account for the load sequence effect, for which predicted lives are found to lie in the factor‐2 scatter band from experimental lives.     

Stochastic fatigue damage assessment of metro switch blade

Stochastic fatigue damage of a metro switch blade is studied with a combination of explicit finite element model (FEM), multiaxial fatigue criterion, and statistical analysis. The explicit FEM is used to reproduce dynamic procedure and to provide detailed stress/strain state variation. A multiaxial fatigue criterion proposed recently is extended to 3D conditions for fatigue prediction. The influence of stochastic impact position is considered by statistical analysis. After analysis, the formation of the serious unstable crack (continuous bites) on the switch blade can be revealed. From the perspective of service life, increasing traction coefficient and decreasing friction coefficient between wheel flange and switch blade gauge surface are beneficial but not significant. However, a speed increase from 36 to 54 km/h can lead to 40% reduction in service life. This work enhances the cognition of damage mechanism on switch blade and provides theoretical foundation for service life design and maintenance operation.     

Two-stage fatigue damage cumulative rule

This paper studies the loading sequence effect on fatigue damage accumulation and puts forward the kneepoint coordinate formulae and two-stage fatigue damage cumulative rules (KDR) under L-H loading and H-L loading by analysing extensive fatigue damage test data and theoretical research. KDR can be used more widely for various complex loadings than Manson's double linear damage rule. The damage line in the paper is closer to experimental data than Miner's straight line. Experimental verification of two- and three-level stresses with different loading sequences has shown that the average error of residual life estimated by KDR is 12.2% and is much less than that of 50.1% estimated by Miner's rule.     

锻锤基础的冲击疲劳损伤分析

用损伤力学的概念提出了一种研究由锻锤锻打引起锻锤基础系统的疲劳损伤增长和疲劳寿命估计的方法。该方法通过定义,引入锻锤基础系统中减振垫与基础块的损伤状态寿命因子,能够估计出锻锤基础系统的减振垫和基础块的损伤疲劳寿命上、下限。通过分析发现,长期的重复冲击载荷会引起锻锤基础系统发生疲劳微损伤积累,疲劳损伤积累的宏观损伤又引起锻锤基础的动力响应随宏观损伤发展而增大,动力响应的增大又加剧基础系统的损伤发展。因此,为减少周围环境的振动以及保护周围环境免受锻锤冲击损伤,在锻锤基础系统设计中需考虑吸振和损伤控制。     

Optimal stopping in a cumulative damage model

Summary We consider the problem of optimal stopping in a cumulative damage model in which a prescribed level may be surpassed only with small probability, but should be approached as precise as possible. Questions of this kind occur, e.g., in the determination of tolerance levels of medical treatments and in coping with metal fatigue. A control limit policy is proved to be optimal.     

Stochastic modelling of low-cycle fatigue damage in 316L stainless steel under variable multiaxial loading

In the present study, a stochastic model is developed for the low-cycle fatigue life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. In the proposed model, fatigue phenomenon is considered as a Markov process, and damage vector and reliability are defined on every plane. Any low-cycle fatigue damage evaluating method can be included in the proposed model. The model enables calculation of statistical reliability and crack initiation direction under variable multiaxial loading, which are generally not available. In the present study, a critical plane method proposed by Kandil et al . ( Metals Soc., London 280, 203–210, 1982) maximum tensile strain range, and von Mises equivalent strain range are used to calculate fatigue damage. When the critical plane method is chosen, the effect of multiple critical planes is also included in the proposed model. Maximum tensile strain and von Mises strain methods are used for the demonstration of the generality of the proposed model. The material properties and the stochastic model parameters are obtained from uniaxial tests only. The stochastic model made of the parameters obtained from the uniaxial tests is applied to the life prediction and reliability assessment of 316L stainless steel under variable multiaxial loading. The predicted results show good aggreement with experimental results.     

A cumulative model of fatigue crack growth

A model of fatigue crack growth based on an analysis of elastic/plastic stress and strain at the crack tip is presented. It is shown that the fatigue crack growth rate can be calculated by means of the local stress/strain at the crack tip. The local stress and strain calculations are based on the general solutions given by Hutchinson, Rice and Rosengren. It is assumed that a small highly strained area existing at the crack tip is responsible for the fatigue crack growth. It is also assumed that the fatigue crack growth rate depends mainly on the width, x¹, of the highly strained zone and on the strain range, $\text{Δ?}{}^1$, within the zone. A relationship between stress intensity factor K and the local strain and stress has been developed. It is possible to calculate the local strain for a variety of crack problems. Then, the number of cycles N¹ required for material failure inside the highly strained zone is calculated. The fatigue crack growth rate is calculated as the ratio $\text{x}{}^1\text{N}{}^1$.The calculated fatigue crack growth rates were compared to the experimental ones. Two alloys steels and two aluminium alloys were analyzed. Good agreement between experimental and theoretical results is obtained.