A CRITICAL PLANE APPROACH TO MULTIAXIAL FATIGUE DAMAGE INCLUDING OUT-OF-PHASE LOADING

Abstract— A modification to Brown and Miller's critical plane approach is proposed to predict multiaxial fatigue life under both in-phase and out-of-phase loading conditions. The components of this modified parameter consist of the maximum shear strain amplitude and the maximum normal stress on the maximum shear strain amplitude plane. Additional cyclic hardening developed during out-of-phase loading is included in the normal stress term. Also, the mathematical formulation of this new parameter is such that variable amplitude loading can be accommodated. Experimental results from tubular specimens made of 1045 HR steel under in-phase and 90° out-of-phase axial-torsional straining using both sinusoidal and trapezoidal wave forms were correlated within a factor of about two employing this approach. Available Inconel 718 axial-torsional data including mean strain histories were also satisfactorily correlated using the aforementioned parameter.     

形状改变比能密度因子断裂准则

将形状改变比能密度因子S_d用于建立复合型裂纹的断裂准则.该准则表明了裂纹在金属材料里的扩展过程中,起决定作用的是形状改变比能,而不是整个应变能.作为应用举例,它成功地预测了Ⅰ-Ⅱ复合型裂纹的开裂角和临界荷载,其结果与现有公开文献提供的一些理论结果和实验数据取得了较好的一致.     

A MODEL FOR THE FATIGUE LIMIT AND SHORT CRACK BEHAVIOUR RELATED TO SURFACE STRAIN REDISTRIBUTION

A model based on surface strain redistribution and the reduced closure stress of short cracks is shown to successfully predict the fatigue limit and short crack growth behaviour for aluminium alloy 2024-T351. Using this approach, the length of non-propagating cracks can be anticipated. The local stress intensity range may be resolved into two components (first the linear elastic fracture mechanics component and the second is due to surface strain concentration). Consequently, the local stress intensity range of aluminium alloy 2024-T351 is a maximum at a depth of approximately half a grain diameter and a minimum at a depth slightly in excess of three grain diameters. The reduced closure stress for short cracks coupled with the increased applied stress intensity caused by surface strain redistribution accounts for the variation of the effective stress intensity parameter as a function of crack depth. This parameter is a maximum for the smallest possible crack (3 μm) and decreases as crack length increases.     

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.     

THE APPLICATION OF FRACTURE MECHANICS TO FRETTING FATIGUE

Abstract— A fracture mechanics model of fretting fatigue has been developed. This enables the calculation of the critical size of defect which can grow under fretting conditions. The model has been applied to the fretting of aluminium alloy 2014A fatigue specimens in contact with 3.5NiCrMoV steel fretting contact pads. The input parameters to the model include externally applied stresses, contact pressure between pad and specimen and frictional forces between the two contacting surfaces. The latter have been measured using a strain gauge technique. Small fretting defects in the fatigue specimens have been investigated metallographically and fractographically. There is good agreement between their size and critical defect sizes calculated using the fretting model.     

THE LOCAL FRACTURE STRESS AS A FRACTURE TOUGHNESS PARAMETER TO CHARACTERIZE AN HETEROGENEOUS WELD ZONE

Abstract— The toughnesses of specimens of heterogeneous multipass weldments with various ratios of weld metal to base metal can be characterized by a single value of the local fracture stress within a narrow scatter band. Relationships were found between the normalized value of this parameter and the lower bound values of fracture toughness parameters such as the fracture load, the energy absorbed, and the crack opening displacement. These facts indicate that using such a toughness parameter, it is possible to assess a heterogeneous multipass weldment by a single value; within a narrow scatter band. Further experiments indicate that this parameter could be measured on specimens simulating the microstructure of the weakest zone where cleavage cracking is initiated.     

基于塑性应变能的多轴低周疲劳寿命预测模型

在分析多轴疲劳损伤机理的基础上,提出一个新的多轴低周疲劳寿命预测模型。此模型以临界平面上的塑性应变能作为疲劳损伤参量,分析了临界平面的特点并给出了损伤参量的计算过程。利用该模型预测了不同加载路径下的304不锈钢试件的疲劳寿命,并与试验值进行比较。结果表明,该损伤参量具有明确的物理意义,能够适用于多轴比例与非比例等各种复杂的加载情况。     

A MODIFIED FRACTURE MECHANICS APPROACH TO METAL FATIGUE

The fatigue lives, the fatigue limit stress ranges and fatigue notch factors for metallic specimens can be predicted using a modified fracture mechanics model for short cracks based on the combination of solutions for the non-uniform strains at the surface of a metal and the development of crack closure. The resulting local stress intensity factor exceeds that indicated by linear elastic fracture mechanics at short crack lengths. The model predicts a smooth and continuous variation of the fatigue notch factor with notch size between a lower bound of unity and an upper bound equal to the theoretical notch stress concentration factor. The model is verified using experimental data for a 2024-T351 aluminium alloy for smooth and notched specimens tested at various stress ratios.     

大面积生长金刚石相关物理参量的空间分布

研究了在热丝化学气相生长金刚石的过程中,衬底温度,衬底表面附近的气体温度以及气流的质量流密度分布对金刚石膜的形核和生长的影响模拟计算结果表明,这三个参量是空间位置的函数,在某些区域,这三个参量均匀分布当热丝阵列面与衬底间距离超过7mm之后,这三个参量在衬底上有一个较大的均匀区域,在该区域的两侧,各参量值显著变化在衬底中心的均匀区域,金刚石膜晶形清楚而致密;偏离该区域,这三个参量数值明显下降,形核密度和生长速度较低,三个参量值均匀的区域可作为金刚石大面积均匀的形核和生长的位置.     

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.     

PSEUDO STRESS AND PSEUDO STRAIN BASED APPROACHES TO MULTIAXIAL NOTCH ANALYSIS

Abstract The analysis of notch stresses and strains is one of the key parts of fatigue life prediction of components and structures, In this paper two related approaches are introduced, covering the whole field from uniaxial to multiaxial non-proportional loading. The pseudo stress at the notch root computed by theory of elasticity is introduced as the governing variable for elastic-plastic notch analysis. Although the pseudo stress is just a specially defined nominal stress, it eases notch analysis in comparison to using arbitrarily definable nominal stresses, especially for non-proportional multiaxial loading. Additionally a pseudo strain based approach is introduced and compared to the stress approach. Both proportional and non-proportional loading are discussed, and compared with the approaches of other workers.     

A SIMPLE THEORY FOR LOW CYCLE MULTIAXIAL FATIGUE

Abstract— A theoretical development based on a simple physical model is proposed to help the designer predict high strain multi-axial fatigue behaviour. This approach hypothesises that the maximum shear strain γ*, on planes driving the crack through the thickness, controls the fatigue crack propagation rate and hence the life. The direct strain δ*_n acting normal to the plane of γ* can exert a secondary modifying influence. Experimental results from several research laboratories have been analysed in this manner with some success.     

基于应变能的预应力平面实体结构拓扑优化设计

研究了预应力平面实体钢结构拓扑优化设计问题。建立了以索力值和结构拓扑为设计变量,以结构储存应变能为约束条件,以结构重量最小为目标函数的数学优化模型。在求解方法上,首先以结构储存应变能最小(刚度最大)确定施加在结构上的索力值,然后采用渐进结构优化法(ESO方法)删除低应变能的单元实现结构的拓扑优化并减轻结构重量。算例结果与相应体系受力性能的结论相吻合,表明本文所提出的优化方法是可行的。     

不同超弹性本构模型和多维应力下开裂能密度的计算方法

橡胶隔振器的疲劳失效多属于大变形(有限变形)下的多轴疲劳问题。在多轴疲劳载荷下,有效用来驱动裂纹扩展的那部分应变能密度称为开裂能密度。基于开裂能密度和橡胶材料的裂纹扩展特性预测橡胶部件的疲劳寿命时,须计算在外载荷下橡胶部件的开裂能密度。为了由有限元软件ABAQUS默认输出的应变计算在有限变形下的开裂能密度,该文推导了不同超弹性本构模型下开裂能密度在主坐标系下的计算式和所需的积分方法。基于该文开裂能密度的计算方法,采用3次Ogden本构来描述大变形下橡胶材料的本构行为,计算分析了不同应变状态下开裂能密度的分布特点。通过分析计算得到的开裂能密度与应变能密度的关系,说明该文开裂能密度计算方法的准确性。最后将上述计算方法应用到橡胶隔振器的多轴疲劳寿命预测中。     

A FRACTURE MODEL TO STUDY THE EFFECT OF SPECIMEN SIZE ON DYNAMIC ENERGY RELEASE RATES

The aim of this research was to simulate the ability of a material to transfer energy to the tip of a rapidly propagating crack when varying the specimen geometry and other factors. For this study, a distributed mass spring model was used which could be hosted on a Personal Computer (PC) of the type now available in most fracture laboratories to capture and process experimental data. The distributed mass spring model was chosen because it was easy to reconfigure for different studies. Also, it could produce the required data in the same format as more powerful FE models and at a quality not dramatically less than FE models. A most useful feature of the model was the good visibility of the fracture processes it was able to represent.     

LIMITATIONS ON THE USE OF THE STRESS INTENSITY FACTOR, K, AS A FRACTURE PARAMETER IN THE FATIGUE PROPAGATION OF SHORT CRACKS

Abstract— It is well known that for very short cracks the stress intensity factor K is not a suitable parameter to estimate the stress level over the small but finite Stage II process zone activation region of size r_s near the crack tip, within which crack growth events take place. A critical appreciation of the reasons for the limitations on the applicability of ΔK as a fatigue crack propagation (FCP) parameter, when the crack length a is of the same order of magnitude or smaller than the size of the ‘fatigue-fracture activation region’, r_s is presented. As an alternative to ΔK the range Δσ_s of the cyclic normal stress at a point situated at the fixed distance s=r_s/2, ahead of the crack tip, inside the fatigue-fracture activation region, is proposed. It is observed that the limitation on the use of ΔK when the crack is short, is mathematical (and not physical) but this inconvenience is easily circumvented if the stress Δσ_s at the prescribed distance is used instead of ΔK since nowadays Δσ_s can be obtained numerically by using finite element methods (FEM). It follows that the parameter Δσ_s is not restricted by the mathematical limitations on ΔK and so it would seem that there is, a priori, no reason why the validity of the parameter Δσ_s cannot be extended to short cracks. It is shown that if the Paris law is expressed in terms of Δσ_s (πrr_s)^½ instead of ΔK the validity of the modified Paris law can be extended to short cracks. A coherent estimate of the value of the fatigue-fracture activation region r_s is derived in terms of the fatigue limit Δσ_FL obtained from S-N tests and of the threshold value ΔK_th obtained from tests on long cracks where both relate to Stage II crack growth that ends in failure, namely, r_s= (ΔK_th/Δσ_FL)²/π. An overall, threshold diagram is presented based on the simple criterion that, for sustained Stage II FCP, Δσ_s must be greater than Δσ_FL. The study is based on a simple continuum mechanics approach and its purpose is the investigation of the suitability of both ΔK and Δσ_s to characterise the crack driving force that activates complex fracture processes at the microstructure's scale. The investigation pertains to conditions that lead to the ultimate failure of the component at values of Δσ_s > Δσ_FL.     

一种考虑应力梯度效应的剪切疲劳损伤参量

该文研究了剪应力梯度对疲劳寿命的影响。首先,基于缺口件疲劳寿命研究中常用的应力场强法,针对纯扭载荷作用的圆管试件,推导出一种新的剪切疲劳损伤参量。该参量依据疲劳破坏区内各点的相对剪应力梯度,得到区域内的加权平均应力,从而全面描述材料在剪应力作用下的疲劳损伤水平。然后,使用30CrMnSiA合金钢进行了拉压、扭转疲劳试验。通过对比分析试验结果可以证明：当危险点应力水平相同时,剪应力梯度的存在可以使材料疲劳寿命增加;而该文提出的剪切损伤参量可以很好地描述这种影响。     

A GENERAL CRITERION FOR HIGH CYCLE MULTIAXIAL FATIGUE FAILURE

Abstract— A new simple general criterion of failure for high cycle multiaxial fatigue, τ_a/ t _A.B+σ_{n. max}/2σ_T= 1 presented. The failure criterion is based on a critical plane approach where fatigue strength is a function of the shear stress amplitude and the maximum normal stress on the critical plane of maximum shear stress amplitude. The criterion takes account of whether case A cracks, growing along the surface, or case B cracks, growing into the surface, occur. It requires knowledge of the material properties, tensile strength, σ_T, and reversed shear fatigue strength for case A, t _A, or case B, t _B, cracking, whichever is relevant. t _A is the reversed torsion fatigue strength and t _B is found from a case B cracking test case. The criterion is applicable in the region, 0.5 t ≤ t _a≤ t , and 0 ≤σ_n.max≤σ_T.     

应变疲劳寿命的概率特性

依据试验数据,采用统计研究方法对钛合金进行了应变疲劳寿命的概率特性分析,发现了分布规律,提出了考虑置信度的可靠性寿命许用值的计算方法。为进一步可靠性分析和评定提供了理论基础。