EVALUATION OF LOW CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

Abstract— A series of low cycle fatigue experiments have been conducted on a 42CrMo steel under tension-torsion loading. Thin-walled tube specimens were used. Low cycle fatigue under various loading paths, including circular and square paths, have been investigated.
The plastic work criterion for low cycle fatigue failure has previously been generally accepted, but it is difficult to calculate stress and strain for complex loading paths, especially for non-proportional loading. This present study suggests a simple method for the calculation of the stable cyclic stress and strain values based on a Modified Endochronic Constitutive Theory (MECT) that redefines an intrinsic time scale. The loading path effect under non-proportional loading is also considered when evaluating fatigue life.
The results show that the plastic work approach using the MECT method in multiaxial fatigue calculations correlates reasonably well the data and is a reflection of loading path dependence.     

EFFECT OF NON-PROPORTIONAL OVERLOADING ON FATIGUE LIFE

Abstract— The effect of non-proportional overloading on both low cycle and high cycle fatigue life has been studied. Low cycle multiaxial fatigue tests were performed on EN 15R (a low alloy steel) using sequential loading blocks which comprised uniaxial "ordinary" cycles and torsion "overload" cycles, and vice versa. In high cycle fatigue, the behaviour of mode I crack growth in a medium carbon steel subjected to mixed (I and II) mode overloading was examined.
Under tension-torsion sequential overloading, crack growth behaviour shows an earlier transition from Stage I to Stage II with a pronounced reduction in accumulated fatigue life. Tensile overloading on torsion cycles was found to be more damaging compared to torsion overloading on repeated tensile cycles. The crack-load interaction in sequential overloading and its influence on crack growth and fatigue life is discussed. In low strain fatigue, Stage II crack growth retardation closely relates to the overload plastic zone size, crack tip blunting and crack surface shielding. Mixed mode overloading is shown to have a significant effect only if the mode I component of overloading is large enough to keep the crack open. Under both low cycle and high cycle fatigue conditions non-proportional overloading is shown to be more damaging than proportional overloading.     

CRITICAL PLANE APPROACHES IN HIGH-CYCLE FATIGUE: ON THE DEFINITION OF THE AMPLITUDE AND MEAN VALUE OF THE SHEAR STRESS ACTING ON THE CRITICAL PLANE

Critical plane approaches are useful methods when designing against long-term fatigue of machine components made from metals. Somewhat surprisingly, the very basic problem of the evaluation of the amplitude and mean value of the shear stress acting on the critical plane is still not resolved satisfactorily for non-proportional cyclic loading conditions. In the present paper, existing proposals for solving this problem are briefly reviewed and their weaknesses highlighted. Then it is shown, through particular examples, that application of these proposals can lead to ambiguous results. Therefore, new definitions of the amplitude and mean value of the shear stress acting on the critical plane are formulated here. These new definitions are free from any ambiguity because they are based on the construction of the unique minimum-circumscribed circle to the path described by the shear stress on the critical plane. The centre of this circle defines the mean shear stress, whereas its radius provides the corresponding shear stress amplitude. The algorithm yielding this minimum-circumscribed circle is presented in some detail.     

DEVELOPMENT OF A CONSTITUTIVE MODEL FOR BIAXIAL LOW-CYCLE FATIGUE

Abstract— A version of the endochronic theory of plasticity for the modelling of nonproportional cyclic loading has been developed. To describe an additional hardening of a material a new engineering method for defining a nonproportionality parameter is proposed for a wide class of cyclic strain paths with a prescribed maximum range of plastic or total strains. This parameter makes it possible to establish an unambiguous linear dependence between the cyclic strain path shape and the stress level in a stabilized state. Conjugation conditions have been formulated to describe complex histories of nonproportional cyclic loading. The results of the modelling are shown to be in fair agreement with the experimental data.     

A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

非比例载荷下缺口件疲劳寿命预测

针对Mod.9Cr-1Mo铁素体钢缺口件进行了一系列非比例载荷低周疲劳试验,采用直流电位差法测量裂纹萌生寿命,比较了缺口半径和应变路径对疲劳裂纹萌生寿命的影响。结果表明,缺口件裂纹萌生寿命占总寿命的比例与材料类型、应变路径相关,更与缺口半径尺寸直接相关。同一路径下,随着缺口半径增加,裂纹萌生寿命所占比例增大。采用Neuber律进行缺口局部应力-应变损伤的计算,结合Smith-Watson-Topper (SWT)模型和Kandil-Brown-Miller (KBM)模型进行疲劳寿命预测。结果表明,除单轴路径和比例路径外,SWT模型得到的预测结果偏于不安全;KBM模型除对单轴预测偏于保守外,其他预测值较好,总体预测结果位于2倍分散带内。     

疲劳加载下纤维复合材料的剩余强度

回顾了纤维复合材料在疲劳加载下的剩余强度的描述方法和试验结果, 并按照纤维复合 材料中疲劳损伤发展的行为, 提出了一个描述纤维复合材料的剩余强度的模型, 该模型考虑了疲 劳损伤在纤维复合材料中产生和扩展的特征, 试验结果与理论描述吻合较好。      

在多轴载荷下45钢的循环特性

通过多轴疲劳试验，研究了在多轴加载条件下45钢的循环特性变化规律，分析了非比例附加强化、多轴循环软化/硬化特性及疲劳寿命对加载路径参数的依赖性，结果表明，相位角主要影响非比例附加强化程度，幅值比主要影响多轴循环软化/硬化特性，二者都影响多轴疲劳寿命。     

钢纤维混凝土等幅弯曲疲劳加载下的疲劳应变和疲劳模量以及损伤研究

利用已有试验数据,对最大疲劳应变和疲劳残余应变进行拟合,得到疲劳应变演化方程,其相关系数均在0.97以上。考虑到等幅弯曲疲劳加载条件下,疲劳模量与疲劳应变成反比关系,利用对称性,由疲劳应变演化方程得到疲劳模量演化方程,通过拟合试验结果,发现由疲劳模量演化方程表达的拟合曲线与试验曲线吻合很好,其相关系数均在0.99以上。最后,利用疲劳应变与疲劳模量定义损伤变量,得到损伤变量演化曲线,经对比发现,由最大疲劳应变和疲劳残余应变定义的损伤变量演化曲线基本一致,且相差很小;而由疲劳模量定义的损伤变量演化曲线明显大于由疲劳应变定义的损伤变量演化曲线。     

混凝土双轴拉压、三轴拉压压变幅疲劳性能研究

利用大型多轴疲劳试验机,进行了拉压双轴和拉压压三轴荷载作用下混凝土两级、三级变幅疲劳试验研究,重点分析了残余应变的变化规律。试验结果表明：混凝土在拉压和拉压压加载工况下的残余应变主要与相对疲劳次数和侧压应力比有关,基本不受加载历程因素的影响。定义相对残余应变为损伤变量,建立了损伤演变方程,并进行了疲劳损伤分析和剩余疲劳寿命预测,为混凝土在多轴变幅疲劳试验研究及疲劳损伤评价提供参考。     

非对称荷载下疲劳强度临界值的统一公式

本文对非对称荷载下的疲劳强度临界值预测公式和疲劳寿命预测公式进行了系统深 入的研究,分析了着名的Goodman公式,Soderberg公式和Gerber公式的适用条件,建立了 一种新的疲劳强度临界值预测公式和疲劳寿命预测公式。新公式的最大优点是,对实际破坏 面的形状不做任何限制,并可使用任意疲劳寿命实验数据进行拟合。     

随机荷载下疲劳裂纹扩展寿命的统计模型

根据断裂力学和随机过程理论,提出了一个随机荷载作用下疲劳裂纹扩展的统计模型。在基于应变能密度因子变程的确定性疲劳裂纹扩展速率公式中引入材料内在的分散性和外部荷载的随机性,将疲劳裂纹扩展近似为连续型马尔可夫过程。应用随机平均法导出了裂纹扩展过程转移概率满足的向后Fokker-Planck方程,并得出相应的边界条件。采用本征函数法进行求解,以收敛的无穷级数表示出疲劳裂纹扩展寿命的分布函数。作为一个算例,具体计算出疲劳裂纹扩展寿命的分布密度曲线。     

A FATIGUE LIFE PREDICTION METHOD BASED ON A MESOSCOPIC APPROACH IN CONSTANT AMPLITUDE MULTIAXIAL LOADING

The aim of this paper is to present a high cycle multiaxial fatigue life prediction method for metallic materials based on Papadopoulos' previous works and limited to constant amplitude loading. The initiation process of a crack is treated as a mesoscopic phenomenon taking place on a scale of the order of a grain or a few grains. The damage variable chosen is the accumulated plastic strain at this mesoscopic scale. Its estimation requires a macro-meso passage and the location of the plane subjected to maximum damage. Initiation is achieved as soon as a critical value of the accumulated plastic mesostrain is reached in these grains, so-orientated that their easy glide directions coincide with a particular direction of the critical plane. The detrimental effect of out-of-phase loading on damage accumulation is taken into account through a newly defined coefficient estimated from mechanical loading parameters; no adjustable parameter is required. A good agreement has been found between the predicted and experimental results for in-phase and out-of-phase sinusoidal constant amplitude loadings by examining a large amount of experimental data.     

A fatigue model developed by modification of Gough’s theory, for random non-proportional loading conditions and three-dimensional stress fields

As a first stage, fatigue damage models proposed by some well-known references and the corresponding assumptions are discussed and some enhancements are proposed. Generally, these models are suitable for bending–torsion fatigue problems with zero mean stress and are restricted to cases where the numbers of cycles of the stress components are identical. In the present paper, a general fatigue model for the HCF regime is proposed. This model overcomes most of the shortcomings of the previous theories and is suitable for life assessment in three-dimensional stress fields. Furthermore, a different critical plane concept is introduced and a different life assessment algorithm is presented. Since results of the previous fatigue theories are generally validated by experiments done on simple components with simple loading time histories, the discrepancies exist among the various theories have not been invoked appropriately. In the current paper, validity of these theories as well as the modified versions proposed in the current paper and the new criterion is examined for more general cases with non-proportional random loadings and complicated geometries. Finally, results of the various theories are compared with the experimental results. Experimental results are prepared for both proportional and non-proportional cases. Significant enhancements are observed due to employing the proposed modifications, especially for three-dimensional stress fields and random loadings.     

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。     

ON THE USE OF THE STRIP-YIELD MODEL TO PREDICT FATIGUE CRACK GROWTH UNDER IRREGULAR LOADING

Abstract— In this paper, the behaviour of the LEFM strip-yield model proposed by Newman and implemented in the FASTRAN II computer program is analyzed. The capabilities of the model to predict crack growth life under variable amplitude loading is considered. Special attention is paid to the effect of the constraint factors used to consider the stress condition (plane stress to plane strain), the effect of the finite length loading sequence and the effect of overloads into an irregular loading history. The results of simulation for 30 different loading histories obtained from the same stationary random process are analyzed and compared with the experimental results obtained for 2024-T351 aluminium alloy. The simulated lives present a fairly good fit with the experimental results, with a strong influence of the constraint factor selected and of the maximum peak in the loading history. Although predictions are usually good, it has been found that for any constraint factor producing good life predictions (with respect to the mean value of the Life obtained with the 30 loading histories) the results of each particular simulation may be over- or under-conservative depending on the maximum peak in the loading history used.     

FATIGUE CRACK GROWTH UNDER ULTRASONIC FATIGUE LOADING

Abstract— In this paper, a stress and modal analysis of an ultrasonic vibration system consisting of a notched specimen and one or two amplifying horns have been performed by using 3D finite element calculations. The stress intensity factors in ultrasonic fatigue crack propagation are evaluated by means of displacement and energy approaches. The particular advantages as well as limitations of the two approaches are briefly discussed. Two types of ultrasonic fatigue loading, with a different stress ratio, are exerted on the specimen. From a comparison of the results a conclusion is formed that the energy approach is more accurate; it also has a wide range of practicality in engineering industries.     

DISLOCATION STRUCTURE AND NON-PROPORTIONAL HARDENING OF TYPE 304 STAINLESS STEEL

Abstract— This paper describes the microstructure of Type 304 stainless steel after cyclic loading at room temperature under tension-torsion non-proportional strain paths. The degree of cyclic non-proportional hardening is correlated with changes in the dislocation substructure. Dislocation cells, dislocation bundles, twins and stacking faults are all observed. The type of microstructure formed and resultant stress response is dependent on the degree of non-proportional loading and strain range. Cyclic stress range was uniquely correlated with mean cell size.     

混凝土的P-D-ε曲线及其累积损伤特性分析

本文在大量试验的基础上建立了描述混凝土在疲劳载荷作用下损伤与应变的概率关系的 曲线。使用该曲线可以十分方便地研究在不同存活率下混凝土的损伤阈值应变、破坏极限应变与损伤量的关系，判断混凝土结构在任意应变状态下所处的损伤状态或剩余强度。提供了一种依据实测应变量及应变变化评估混凝土结构可靠度和寿命的有效途径。