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.     

Numerical study on fatigue crack growth at a web-stiffener of ship structural details by an objected-oriented approach in conjunction with ABAQUS

It is necessary to manage the fatigue crack growth (FCG) once those cracks are detected during in-service inspections. This is particular critical as high strength steels are being used increasingly in ship and offshore structures. In this paper, a simulation program (FCG-System) is developed utilizing the commercial software ABAQUS with its object-oriented programming interface to simulate the fatigue crack path and to compute the corresponding fatigue life. In order to apply FCG-System in large-scale marine structures, the substructure modeling technique is integrated in the system under the consideration of structural details and load shedding during crack growth. Based on the nodal forces and nodal displacements obtained from finite element analysis, a formula for shell elements to compute stress intensity factors is proposed in the view of virtual crack closure technique. Neither special singular elements nor the collapsed element technique is used at the crack tip. The established FCG-System cannot only treat problems with a single crack, but also handle problems with multiple cracks in case of simultaneous but uneven growth. The accuracy and the robustness of FCG-System are demonstrated by two illustrative examples. No stability and convergence difficulties have been encountered in these cases and meanwhile, insensitivity to the mesh size is confirmed. Therefore, the FCG-System developed by authors could be an efficient tool to perform fatigue crack growth analysis on marine structures.     

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.     

450MPa级船体钢焊缝疲劳试验研究

通过对450MPa级船体用钢母体试件、焊缝试件在波浪随机载荷和均方根等效载荷下的疲劳裂纹扩展规律的试验和模拟计算，结果表明用均方根等效载荷替代波浪随机载荷下的疲劳裂纹扩展规律是一种安全有效的方法，并且焊缝金属在抵御疲劳裂纹扩展方面优于母材金属。     

Numerical simulation of fatigue crack propagation under superimposed stress histories containing different frequency components with several mean stress conditions

Fatigue crack propagation behavior under superimposed stress histories containing different frequency components with several mean stress conditions was investigated. Numerical simulation of fatigue crack propagation based on an advanced fracture mechanics approach using the RPG (Re-tensile Plastic zone Generating) stress criterion for fatigue crack propagation was improved to extract the effective part from the applied stress history for fatigue crack propagation. The parameter, which is based on the plastic hysteresis energy consumed in the vicinity of a crack tip, was applied and implemented into the numerical simulation code of fatigue crack propagation. Fatigue crack propagation tests under various superimposed stress conditions with several mean stress conditions were performed and compared with the fatigue crack propagation histories obtained from the improved numerical simulations. These comparisons show the validity of the proposed procedure for extracting the effective stress history from the superimposed stress histories with different frequency components and mean stresses. Additionally, practical fatigue strength evaluations based on the linear cumulative fatigue damage parameter were conducted to investigate the tendency of the fatigue damage value under these stress conditions.     

Fatigue crack propagation and computational remaining life assessment of ship structures

The fitness for serviceability of structural members of marine structures in which fatigue cracks might be found during in-service inspection is investigated in order to prevent instantaneous failures of ships, as well as a loss of serviceability such as the oil- and/or watertightness of critical compartments. The essential features of fatigue crack propagation and the remaining life assessment are discussed in the first part of the paper, where the effects of weldment, complicated stress distributions including stress biaxialities at three-dimensional structural joints, structural redundancy, and crack curving are found to be of primary importance. The second part of the paper contains a discussion of an advanced numerical simulation method for the remaining life assessment, in which the above-mentioned effects of fatigue crack propagation are taken into account. The simulated crack paths and the fatigue crack propagation lives are found to be in fairly good agreement with the experimental results.     

肘板趾端表面裂纹在随机波浪载荷作用下的疲劳扩展预报

肘板趾端是船舶与海洋结构的疲劳热点。文章用三维有限元分析了趾端表面裂纹应力强度因子修正系数的变化规律,并与BS7910推荐的典型节点表面裂纹应力强度因子公式计算结果作了对比,结果表明趾端表面裂纹应力强度因子沿深度方向的放大系数和T型节点相差很小,而表面端点应力强度因子修正系数则当裂纹长度在肘板厚度范围内时和T型节点相差很小,超出后则相差较大。以某客滚船上肘板趾端应力范围长期分布服从Weibull分布,产生系列均值为零的应力幅,应力强度因子分别采用有限元结果和BS7910中T型接头公式进行计算,采用单一曲线模型计算该趾端表面裂纹的裂纹扩展。计算等效应力强度因子幅时,考虑焊接残余应力的影响。计算结果表明以T型接头的公式计算趾端表面裂纹应力强度因子和有限元结果相差很小。建议将T型节点表面裂纹应力强度因子计算公式用于趾端表面裂纹应力强度因子的计算,并采用单一曲线模型对随机波浪载荷下作用下船舶典型节点疲劳裂纹的扩展寿命进行了预报。     

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.     

一种复杂载荷作用下船舶结构疲劳裂纹扩展预报方法

风暴模型是Tomita等提出的用来评估船舶结构疲劳强度的一种随机波浪载荷简化模型,它能表达波浪载荷是与时间相关的随机过程。文中介绍了风暴模型及波浪诱导应力短期分布的基本特征。将风暴模型和裂纹扩展率单一曲线模型及焊趾表面裂纹应力强度因子的计算方法结合起来,探讨了复杂载荷作用下船舶结构疲劳裂纹扩展预报方法。并用权函数法计算了给定残余应力分布的表面裂纹应力强度因子。预报了对接焊接接头焊趾处表面裂纹在风暴波浪载荷作用下的疲劳裂纹扩展行为,结果表明风暴的大小、顺序,初始裂纹尺寸及残余应力对裂纹扩展行为影响明显。合理的风暴模型参数及初始裂纹尺寸的确定对船舶结构的疲劳寿命预报是非常重要的。     

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.     

Residual stresses at a longitudinal stiffener — Web frame intersection and their effects on crack growth

Stress coining at geometrical discontinuities may introduce compressive residual stresses which will lower the propagation of surface cracks and thus increase the fatigue life. In a non-linear finite element analysis, the residual stresses after welding of a transverse web-frame to a ship hull plating is first estimated. Stress coining of one corner of a longitudinal cut-out in a transverse web-frame is then simulated in detail. The calculated residual compressive tangential stresses in the corner of the cut-out is seen to lower the propagation of edge cracks. Experiments performed on web-frames taken from a shipyard after manufacturing show indeed that large tensile residual stresses exist in the web-frame after welding. Stress coining is therefore believed to have a beneficial effect on the fatigue life.     

耐压船体结构典型接点疲劳寿命评估

潜艇在潜浮过程中,由于静水外压引起的工作应力与焊接残余应力叠加,形成拉压循环应力,导致耐压船体的局部结构可能出现低周疲劳裂纹.一般情况下,高强度钢在抗拉强度提高的同时往往伴随着材料塑性储备和断裂韧性的下降,因此分析高强度钢潜艇结构的低周疲劳寿命非常重要.本文基于断裂力学和Paris公式建立了潜艇耐压结构低周疲劳寿命的工程估算方法,根据裂纹无损检测的概率统计和含裂纹圆柱壳极限应力分析,给出了初始裂纹和裂纹临界状态的建议值.应用本文的简化方法分析了某潜艇结构和锥柱结合壳模型的低周疲劳寿命,锥柱结合壳模型的数值算例表明本文的计算结果与试验测试结果相吻合.     

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.     

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。     

基于裂纹扩展的海洋平台疲劳可靠性分析

文章基于裂纹疲劳基本理论,针对在役导管架平台出现初始裂纹状态下结构承载力进行分析,考虑结构损伤与腐蚀等因素,建立了典型导管架平台整体结构模型和局部子模型,分析了在该工况下平台整体结构的疲劳强度,并确定了平台结构的疲劳关键部位。采用几何应力外插法计算了热点应力,基于疲劳裂纹扩展的疲劳分析方法,计算了疲劳关键节点的疲劳寿命与疲劳可靠度。该方法能够为海洋平台结构的维护和保养提供一定参考。     

Fatigue life prediction of welded stiffened 350WT steel plates

The propagation of fatigue cracks under constant amplitude cyclic loading was studied in welded stiffened steel plates. The residual stresses in the stiffened plates were measured using the neutron diffraction strain-scanning technique. A finite element model of the stiffened plate was constructed to simulate the residual stresses by an uncoupled thermal and thermo-mechanical analysis. Both the finite element model and the neutron diffraction measurements indicated that in general the residual stresses were tensile near the welded stiffeners and compressive between the stiffeners and ahead of the starter notch tip. Fatigue testing indicated that the fatigue crack growth rates of the stiffened plates were in general lower than that of a corresponding unstiffened plate, especially near the notch tip where compressive residual stresses existed. Both the finite element method and Green's function predicted the fatigue crack growth rates with reasonable accuracy.     

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。     

钛合金疲劳裂纹扩展速率试验及预报方法

本文针对深海载人潜水器耐压壳用钛合金,开展疲劳性能试验研究,得到该类型钛合金的室温断裂韧性,载荷比R=0.1下的疲劳裂纹扩展门槛值及疲劳裂纹扩展速率,基于选用的疲劳裂纹扩展预报模型,对载荷比R=0.1下的钛合金疲劳裂纹扩展行为进行了预报研究。结果表明:在载荷比不变的前提下,应力强度因子范围是疲劳裂纹扩展速率的主要影响因素,应力强度因子范围的增加会导致疲劳裂纹扩展速率增加;考虑小裂纹效应的疲劳裂纹扩展预报模型可对钛合金的疲劳裂纹扩展行为进行准确预报。