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.     

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.     

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.     

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.     

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。     

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.     

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.     

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.     

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.     

混凝土三轴变幅拉-压疲劳性能试验研究

进行了最小应力水平为0.20fc,最大应力水平为0.20ft~0.55ft,定侧压为0.30fc的变截面混凝土试件三轴拉-压等幅和变幅疲劳试验,分析了混凝土三轴拉-压疲劳最大和最小纵向总应变的三阶段演变规律和级间相似性,给出了疲劳损伤演化规律。进一步验证了Miner线性损伤累积理论的不适用性,提出了非线性损伤累积模型,并进行了疲劳剩余寿命预测,通过与试验结果的比较表明该模型具有较高的精度和适用性。     

应变疲劳循环软化机制的观察,确证及定量估测

通过透射电镜观察和循环应变加时效的试验方法，对淬火回火态地低碳合金钢的循环软件机制进行了研究。     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

定侧压混凝土双轴压疲劳性能研究

利用大型混凝土静、动三轴试验机,完成了3种定侧压混凝土的双轴压疲劳试验.观察了试件破坏形态.将单轴压疲劳试验结果与其他试验者的结果作了比较,验证了结果的有效性.在试验基础上,分析了双轴压混凝土的疲劳特性和变形规律;建立了相应的S-N关系及考虑侧应力影响的统一疲劳方程.研究结果,为受复杂重复荷载作用的混凝土结构设计和分析提供了试验依据.