Numerical simulation of fatigue crack propagation under biaxial tensile loadings with phase differences

Fatigue crack propagation under the biaxial tensile loading, which loading directions are normal and parallel to the initial crack position, is highlighted in this study. Most of in-service structures and vessels are subjected to many types of loading. Generally, these loadings have different axial components with different phases. However, the structural integrities of structures and vessels are evaluated according to design codes based on theoretical and experimental investigations under a uniaxial loading condition. Most of these codes are based on the S–N curves approach. An approach that does not use S–N curves has been favored by researchers, with the fracture mechanics approach preferred for evaluating the fatigue life of structures. An advanced fracture mechanics approach was developed based on the Re-tensile Plastic zone Generating (RPG) stress criterion for fatigue crack propagation. In this study, fatigue crack propagation tests under biaxial loading with six different phase and loading conditions are performed and the effect of the phase difference under biaxial loading is evaluated. A numerical simulation method of fatigue crack propagation based on the RPG stress criterion under different biaxial loading phase conditions is presented and compared to measured data.     

Multi-scale modeling of fatigue crack propagation applied to random sequence of clustered loading

Fatigue crack propagation in marine structures is obviously governed by mechanics of the considerably different four levels of multi-scale problems. Problems of structural response to environmental loads have length scale of several hundred meters, whereas possible detectable size of cracks from initial defects in a weld is of the order of millimeters. Once a fatigue crack initiates, crack tip plasticity is of the order of several grain sizes, while the resulting fatigue crack growth in each load cycle is of the order of nanometers. In our previous work, the first author and their associates have developed the so-called CP-System, which can treat the first two multi-level problems as an integrated system. Furthermore, we have incorporated the third level of mechanics by using the stress intensity range corresponding to the repeated tensile plastic deformation ahead of the crack tip. In the present paper, we shall discuss a more rational integral equation-based formulation in order to integrate the third and fourth levels of micro-mechanics to the first two levels of continuum mechanics.The method is then applied to fatigue crack propagation under the effects of random sequence of clustered loading. As an example of the random sequence of clustered load, we shall use the so-called “storm model”. In the crack propagation simulation, we have to take into account of the plastic wake on the crack surfaces, whose thicknesses are influenced by the material parameters involved in the crack growth model. These parameters are first identified by the fatigue tests under combined constant and random loading using a CT specimen. Then, fatigue crack growth is investigated by numerical simulation and fatigue tests for various random sequences of clustered loading. The experimental and numerical results agree quite well with each other, and fatigue crack propagation is found to be considerably retarded under random sequence loading, so that the conventional equivalent stress approach may provide rather conservative results to the real seaway loading.     

考虑残余应力效应的深潜器耐压壳体疲劳研究

本文考虑焊接残余应力的影响,给出包含裂纹萌生和裂纹扩展全过程的载人深潜器耐压球壳疲劳寿命预报方法,分别基于局部应力-应变法和能计及负应力比效应的裂纹扩展单一曲线模型预报了耐压球壳的工艺疲劳寿命和使用疲劳寿命,研究焊接残余应力大小对球壳疲劳寿命的影响。结果表明,忽略拉伸残余应力的影响将导致疲劳寿命预测结果偏于危险;耐压球壳整体受压时,拉伸残余应力使得球壳局部区域承受拉-压循环载荷,计算使用疲劳寿命过程中须考虑其影响;降低拉伸残余应力可有效提高耐压球壳的疲劳寿命。     

基于雨流计数法的高低频复合疲劳试验研究

船体固有频率与遭遇波浪频率及其倍频相接近时,波浪载荷极易引起船体结构产生持续的波激振动现象,对大型船舶结构疲劳损伤的影响达到40 %以上。因此,有必要针对波激振动引起的非线性垂向弯矩载荷特点,开展高低频复合工况下典型切口试件疲劳试验及累计损伤分析研究。基于非线性随机载荷的分析方法,采用闭合雨流计数法提取叠加应力历程中的多级循环载荷,并结合平均应力修正方法和疲劳极限以下SN曲线局部修正法,对叠加应力历程中小载荷的损伤效应展开研究。分析结果表明,高低频载荷叠加产生的附加损伤效应对疲劳寿命的影响显著,在恒定应力比下随平均应力的变化近似成二次函数关系。考虑高频小载荷的叠加应力历程疲劳寿命明显降低,可以通过修正累计损伤临界值或引入应力放大因子,近似的利用线性累积损伤理论预测实际叠加应力历程的寿命范围。     

A reliability approach to fatigue crack propagation analysis of ship structures in polar regions

Fatigue is a common failure mode in ship structures. For structures with an initial crack, the fatigue crack propagation behavior needs to be considered. The purpose of this study is to establish a procedure for analysis of fatigue crack propagation of ship structures in combination with reliability methods. The stress intensity factor (SIF) and geometry correction factor are calculated by means of finite element analysis. Validation for the SIF calculation is achieved by comparing the computed results with those based on related solutions. Since fatigue damage usually occurs in weld areas, the effect of such components on the fatigue crack propagation behavior was also considered in this work. The Paris law in combination with the Monte Carlo technique are employed for the fatigue crack propagation analysis in this study. Reliability updating based on inspection for cracks is also carried out. A computer program was developed for the purpose of fatigue crack propagation analysis within the framework of reliability methods. An application example of fatigue crack propagation in relation to the hull of the icebreaker Xuelong 2 is presented. The sensitivity of the procedure to key analysis parameters (sample size, initial crack size) is also considered. Finally, the effect of low temperatures on the computed results is also analyzed.     

具初始裂纹钢桥梁焊接构件疲劳裂纹扩展和疲劳寿命计算

钢桥梁构件因焊接缺陷或者在疲劳应力交互作用下萌生裂纹,钢桥梁构件因存在初始裂纹大大地降低焊接构件的疲劳性能.文中考虑到焊接构件往往会存在初始缺陷,研究了含初始缺陷的桥梁焊接构件的疲劳分析方法.在已有的大量含裂纹构件的疲劳实验工作基础上,结合课题组所做的焊接构件疲劳实验资料,假设初始裂纹焊接构件在疲劳裂纹扩展过程中裂纹形状保持为半椭圆形状;针对桥梁构件实际受力特征,由钢桥梁构件的高周疲劳损伤演化方程入手,考虑初始裂纹条件下裂纹前缘的损伤区的存在及其对裂纹扩展的影响,采用虚拟裂纹扩张方法推导了适用于钢桥梁构件的疲劳裂纹扩展分析的疲劳裂纹扩展率公式,建议了裂纹扩展和疲劳寿命数值计算方法.采用文中的计算方法,研究了已有的钢桥梁结构焊接构件疲劳实验的裂纹扩展过程和疲劳寿命的计算.计算结果表明:裂纹的扩展过程中裂纹的深度和表面半长度之比a/c是一个变化的数值,且在一定的a0/t0条件下,随着a0/c0的增加,循环次数逐渐增大.     

基于断裂力学的散货船外底纵骨疲劳寿命评估

基于断裂力学的疲劳裂纹扩展理论,按《散货船共同结构规范》确定疲劳载荷及计算工况,通过有限元应力分析对某散货船外底纵骨与横舱壁或横框架连接节点处进行疲劳寿命分析,并探讨了裂纹形状比对疲劳寿命的影响。研究结果表明,外底纵骨上远离横舱壁或横框架一侧的软趾端处的疲劳寿命比靠近横舱壁或横框架一侧的通焊孔焊缝趾端处的疲劳寿命要短,并且疲劳寿命随着裂纹形状比的增大而增大。     

基于累积递增塑性变形的船体裂纹板断裂韧性研究

裂纹尖端张开位移（CTOD）是评估结构材料韧性以及分析低周疲劳破坏引起的裂纹扩展的重要参量。文章结合Dugdale模型,以裂纹尖端累积塑性应变为控制参量,提出了一个循环载荷下含裂纹船体板的CTOD计算模型;利用有限元法模拟了裂纹尖端累积塑性应变、平均应力、裂纹长度等相关因素影响;结合最小二乘法拟合出了基于累积塑性应变、平均应力比以及裂纹长度的两阶多项式。文中基于累积塑性应变的CTOD计算模型为正确评估循环载荷下船体板的累积塑性破坏提供了一种新途径。     

Simulation-based fatigue crack management of ship structural details applied to longitudinal and transverse connections

It is of continuing importance for ship structural design to establish a system to compute the growth behavior of fatigue cracks propagating in structural details. In the present paper, a simulation program is developed for multiple fatigue cracks propagating in a three-dimensional stiffened panel structure, where it can predict fatigue crack lives and paths by taking into account the interaction of multiple cracks, load shedding during crack propagation and welding residual stress. Various fatigue crack propagations in longitudinal stiffeners of ship structures are investigated by both the present simulation method and experiments. From these results, it is found that the crack propagation may considerably change, depending on the loading conditions, structural details and residual stress distributions. This means that one could possibly manage to avoid fatal damage of the skin-plate by properly designing the structural details. Furthermore, these results may imply a possibility to realize a rational fatigue crack management if one can estimate the fatigue crack-propagation behavior during the ship lifecycle. The present simulation program may offer a useful numerical tool for this purpose.     

Corrosion fatigue load frequency sensitivity analysis

This paper presents experimental assessment of crack growth rates of S355J2+N steel in a corrosion fatigue environment similar to what is experienced on offshore wind farm monopile structures under various cyclic load frequencies in order to assess the effect of cyclic frequency of the applied loading within a frequency range pertinent to the structure. Fatigue crack propagation behaviour in this test programme is evaluated through fatigue tests on six compact tension test specimens in air and in laboratory simulated seawater under free corrosion condition. Fatigue crack lengths were monitored by back face strain (BFS), DCPD and ACPD. A regression model was derived through the BFS method to express strain values as a function of crack length to width ratio. The effectiveness of BFS method is particularly demonstrated in the simulated marine environment. Within the range of test frequencies, crack growth rates in simulated seawater when compared to the equivalent air test revealed environmental reduction factors of 2 and 4 at lower and higher values of stress intensity factors respectively. Significant difference in the results of the seawater test frequencies is discussed.     

基于损伤力学和XFEM的舰船蒸汽轮机叶片裂纹扩展研究

叶片作为舰船汽轮机的核心零部件,其在复杂工况下的低周疲劳寿命一直是备受关注的问题。传统的寿命预测方法大多是基于经验公式进行求解,没有考虑损伤累积对材料固有属性的影响,也没有对裂纹萌生和扩展过程进行全面的分析。文章以损伤力学的基本理论为基础,考虑叶片实际非对称循环的工作状态,引入平均应力的概念,推导叶片低周疲劳寿命的计算公式以及损伤随循环次数变化关系的表达式。同时基于有限元分析软件ABAQUS,使用XFEM方法模拟叶片裂纹扩展并进行低周疲劳寿命分析,并与所给出的理论计算结果进行对比。结果表明,所建立的基于损伤力学的低周疲劳寿命计算结果与基于扩展有限元的裂纹扩展模拟结果吻合较好,其对于舰船汽轮机叶片等工程结构的寿命预测具有一定价值。     

循环载荷下考虑累积塑性影响的船体板CTOD理论及数值模拟研究

裂纹尖端张开位移(CTOD)是研究大范围屈服的低周疲劳破坏的重要参数之一,其值可反映结构材料抵抗低周疲劳裂纹形成和扩展的能力,是评估结构材料韧性的重要参量以及分析低周疲劳破坏引起裂纹扩展的主要控制参量。文章基于弹塑性断裂力学理论,从循环J积分着手,以裂纹尖端累积塑性应变为重要参量,建立循环载荷下船体板CTOD理论模型,并在有限元模拟中分析了应力比、应力幅等相关因素影响。将本模型结果与有限元计算结果进行了比较,发现结果吻合良好。结果表明：在考虑累积塑性影响下,该模型能较好地反映在循环载荷下船体板CTOD的变化规律,同时也为正确评估循环载荷下船体板低周疲劳破坏与累积塑性破坏两种破坏模式耦合作用的总体断裂破坏提供了途径。     

循环载荷下考虑累积塑性影响的含中心穿透裂纹板CTOD研究

裂纹尖端张开位移(CTOD)是评估结构材料韧性以及分析低周疲劳破坏引起的裂纹扩展的重要参量。结合Dugdale模型,以裂纹尖端累积塑性应变为控制参量,提出了一个循环载荷下含裂纹船体板的CTOD计算模型;利用有限元法模拟了裂纹尖端累积塑性应变、平均应力、裂纹长度等相关因素影响;结合最小二乘法拟合出了基于累积塑性塑性应变、平均应力比以及裂纹长度的两阶多项式。研究表明,基于累积塑性应变的CTOD计算模型为正确评估循环载荷下船体板的累积塑性破坏提供了一种新途径。     

随机海况下的船体结构疲劳裂纹扩展

传统的疲劳问题一般都是采用S—N曲线及Miner累计损伤理论进行的,文章在基于断裂力学的基础上,通过权函数法来计算应力沿裂纹面的非线性效应力强度因子,鉴于船舶在海洋环境中受到载荷的随机性,充分考虑加载次序、过载峰和应力比等对裂纹扩展的影响,给出了船舶结构疲劳裂纹在随机载荷下的扩展寿命的计算过程。     

Numerical simulations of fatigue crack initiation and propagation based on re-tensile plastic zone generating load criterion for in-plane gusset welded joints

Many accidents are caused by fatigue in welded built-up steel structures, and so it is important to estimate the fatigue lives of such structures quantitatively for safety reasons. By assuming that fatigue cracks cannot grow without an accumulation of alternating tensile/compressional plastic strain, one of the authors identified an improved effective stress intensity factor range ΔK _RPG based on the re-tensile plastic zone generating (RPG) load, which represents the driving force for fatigue cracks, and suggested that ΔK _RPG should be used as the parameter to describe fatigue crack growth behavior. The “FLARP” numerical simulation code in which ΔK _RPG is implemented as the fatigue crack growth parameter, was developed in order to predict fatigue crack initiation and propagation behavior. In this paper, it is demonstrated that FLARP gives accurate estimates for fatigue life by comparing the estimated fatigue crack growth curves and S–N curves with the experimental results for in-plane gusset welded joints, which are used in many welded steel structures. Moreover, the effect of induced bending moment due to the linear misalignment in the out of plane direction on the fatigue strength of in-plane gusset welded joints is investigated through numerical simulations.     

A computational approach for fatigue crack propagation in ship structures under random sequence of clustered loading

The authors have developed a simulation program, CP-System, for multiple cracks propagating in a three-dimensional stiffened panel structure, where through-the-thickness crack propagation is formulated as a two-dimensional in-plane problem, and the crack propagation behavior is simulated by step-by-step finite element analyses. In order to evaluate the fatigue lives of marine structures accurately, it is necessary to take into account the load histories induced by sea waves, which may be composed of a random sequence of certain clustered loads with variable stress range. In the proposed crack growth model, the crack opening and closure behavior is simulated by using the modified strip yielding model, and the effective tensile plastic stress intensity range, ΔK _RP, is calculated by considering the contact of plastic wake along the crack surfaces. The adequacy of the proposed crack growth model is examined by comparison with fatigue tests under non-constant-amplitude loading. The usefulness of the developed method is demonstrated for a ship structural detail under certain simulated load sequences. It is shown that the fatigue crack growth of a ship structure is significantly retarded due to the load interaction effects, so that the conventional method for fatigue life assessment may predict a relatively conservative fatigue life of a structure.     

Fatigue crack growth behaviour of A5083 series aluminium alloys and their welded joints

We investigated the difference in fatigue behaviour between the aluminium alloys A5083-O and A5083-H321, which are used as structural components in ships and high speed craft. We obtained S–N curves for the base materials and the welded joints made of A5083-O. The relationships between the fatigue crack propagation rates and the stress intensity factor ranges ΔK, ΔK _eff and ΔK _RPG (Toyosada et al. in Int J Fatigue 26(9):983–992, 2004) were determined. Additionally, the evolution of fatigue crack growth for the base materials and the welded joints made of A5083-O was measured. We also carried out numerical simulations of fatigue crack growth for both base metals and their welded joints made of A5083-O. The difference in fatigue crack growth behaviour for each alloy and the validity of the numerical simulations of fatigue crack growth based on the RPG stress criterion (Toyosada et al. 2004) in the base materials and their welded joints was investigated.     

基于累积塑性破坏的船体板低周疲劳裂纹扩展寿命研究

船体板的总体断裂破坏往往是低周疲劳破坏与累积塑性破坏两种破坏模式耦合作用的结果,故在船体板低周疲劳裂纹扩展寿命评估中,其基于累积塑性应变的船体板低周疲劳裂纹扩展寿命分析能够更为符合实际地评估船体板的总体断裂承载能力。船体板低周疲劳裂纹扩展寿命由宏观可检测裂纹扩展到临界裂纹而发生破坏这段区间的寿命。船体在实际航行中受到多次波浪外载作用而使其进入塑性变形不断累积或不断反复的破坏过程,并最终导致低周疲劳裂纹的萌生及扩展而使结构破坏,其破坏形式分别对应于增量塑性变形破坏（或棘轮效应）或交变塑性变形破坏（或低周疲劳）。局部塑性变形的累积会加剧低周疲劳裂纹不断扩展,因而基于累积塑性破坏研究船体板低周疲劳扩展寿命更为合理。文中以船体板单次循环载荷后塑性应变大小为基础,依据累积递增塑性破坏过程及弹塑性理论,计算经过N次变幅循环载荷后船体板累积塑性应变值,结合循环应力—应变曲线获得相应的稳定的迟滞回线,确定裂纹尖端应力应变曲线及确定相关塑性参量并依据选取的断裂判据判定裂纹扩展。建立循环载荷下基于累积递增塑性破坏的船体板低周疲劳裂纹扩展寿命的计算模型考虑应力比对此裂纹扩展寿命计算模型的影响。由该方法计算出的疲劳裂纹扩展寿命将对正确预估船舶结构的低周疲劳强度从而提高船舶安全性有重要意义。     

变幅载荷作用下焊接接头疲劳寿命预测方法

船舶与海洋结构物在其服役过程中受到波浪等载荷的交变作用而引起结构的疲劳损伤.检测结果表明船舶及海洋结构的疲劳热点部位大多数是在构件相互连接的焊缝焊趾处.因此,研究典型接头表面裂纹应力强度因子统一计算方法以及变幅载荷作用下表面裂纹扩展规律对船舶与海洋结构物的寿命预测是十分重要的.本文讨论了裂纹闭合及开口比的计算,在Newman有效应力强度因子计算方法的基础上,提出了考虑因素更全面的有效应力强度因子幅计算式以及变幅载荷作用下船舶与海洋结构物典型焊接接头疲劳裂纹扩展寿命预测模型.     

基于奇异强度理论的疲劳特性评估方法

疲劳是海洋结构物破坏的重要因素,为简化舰船结构疲劳评估方法,基于线弹性断裂力学和切口应力强度理论,针对典型薄板结构研究拐角节点处的应力强度,分析结构形式,利用ANSYS有限元模拟和MathCAD函数拟合,分别给出计算应力强度因子的＂奇异权函数法＂和＂奇异等效裂纹法＂的研究方法,同时给出简便算法和经验公式。进而应用Paris裂纹扩展法则进行结构奇异强度疲劳特性评估,并结合S-N曲线分析拐角节点处的应力集中,得到与结构尺寸相关的＂奇异应力集中系数＂函数。最后,针对切口应力,提出有限元分析所需要的＂奇异应力等效取值点＂的参考位置。希望能将奇异强度理论纳入船舶结构疲劳强度校核规范中做参考。