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.     

随机载荷作用下焊接结构表面裂纹扩展研究

随机载荷作用下焊接结构表面裂纹的扩展问题是工程结构中常见的问题.文中设计了随机载荷作用下焊接结构的疲劳断裂试验,试样由平板以一定的角度焊接而成,配合相应的夹具采用轴向加载,在MTS疲劳试验机上进行试验,采用应变片对裂纹的萌生进行监测,用降载勾线法描绘裂纹的扩展形貌,最后利用试验数据对文献中提到的等效厚度法和等效应力强度因子法进行了验证,结果表明:这两种方法的计算结果都与试验结果比较接近,可以用于计算表面裂纹的疲劳扩展.     

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.     

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.     

基于裂纹扩展理论的船体结构疲劳评估

疲劳破坏是船舶结构的主要破坏形式之一。为了保证船舶结构有足够的疲劳强度,各国船级社、船厂等均建立了船舶结构疲劳强度校核规范作为船舶疲劳评估的指导性文件,尽管这些规范均是建立在S-N曲线方法基础上的,但由于S-N曲线方法存在自身无法克服的缺陷(如忽略材料的初始缺陷等),对同一节点进行计算得到的疲劳寿命大相径庭。该文作者在基于裂纹扩展理论的基础之上,给出了一套详细的船体结构疲劳评估方法,并应用此方法对大型船舶结构典型节点的疲劳寿命进行评估,以期能为完善船舶结构疲劳寿命的评估提供参考。     

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。     

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.     

复杂载荷作用下潜艇结构疲劳裂纹扩展预报方法

统一疲劳裂纹扩展模型是课题组在McEvily模型基础上提出来的,它将疲劳裂纹扩展的3个扩展区域统一起来,并能解释更多的疲劳试验现象.本文介绍了统一疲劳裂纹扩展模型的基本表达式.将此模型与焊缝焊趾表面裂纹应力强度因子的计算方法结合起来,探讨复杂载荷作用下潜艇结构疲劳裂纹扩展预报方法.将服从Weibull分布的随机载荷系列编排为升序、降序载荷谱及随机载荷谱,预报潜艇锥柱结合壳焊缝焊趾处表面裂纹在3种载荷谱下的疲劳裂纹扩展情况,并分析随机载荷谱下载荷次序效应及初始裂纹尺寸对疲劳裂纹扩展行为的影响.结果表明,载荷次序效应对潜艇结构疲劳寿命的影响很明显,且合理的确定初始裂纹尺寸对潜艇结构的疲劳寿命预报是非常重要的.     

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。     

不同数值积分方式对海洋结构物疲劳裂纹扩展模拟结果的影响

海洋结构物的疲劳寿命预报是当前的研究热点,文章根据第二作者率领的课题组提出的海洋结构物疲劳寿命预报统一方法比较了疲劳裂纹扩展模拟的三种数值积分方法：逐周数值积分法、△N积分法和△a积分法,并分析了每种方法的适用条件。随后,以中心表面裂纹承受单向交变拉伸载荷的平板为例,分别运用三种方法计算了裂纹扩展寿命和最终裂纹尺寸。同时,研究了△N和△a取值不同对结果的影响。最后,综合考虑计算耗时和计算结果精度,给出了△N积分法和△a积分法的建议值,即△N/N≤1.0%,△a≤0.1 mm。     

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。     

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.     

船舶腐蚀断裂力学的一种数值计算方法

基于船体表面微裂缝在应力和海水腐蚀耦合作用下的扩展机理,根据Charles-Hillig模型用数值方法模拟了裂缝的动态扩展过程,并用front-tracking图形技术开发了有限元网格剖分软件,从根本上解决了以往该模型无法进行数值模拟的难题.文中侧重于对腐蚀断裂问题进行一般性的基础研究,探索裂缝扩展时的形态以及速度与外荷载之间的关系,数值计算表明,计算结果和实验得出的曲线在形态上比较吻合.     

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.     

Comparison of different structural stress approaches for fatigue assessment of welded ship structures

The structural stress approach, which considers the stress increase due to the structural configuration, allows the fatigue strength assessment of welded ship structures with various geometries on the basis of an S–N curve depending only on the type of weld. However, a unique definition and the numerical calculation of the structural stresses are problematic, which has resulted in the development of different variants of the approach. These are discussed and compared with each other in the present paper. The application to three examples shows the variation and differences in the analysed stresses and predicted fatigue lives, which are compared with those derived from fatigue tests.     

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.     

潜艇锥柱典型节点表面裂纹扩展数值模拟

锥柱结合处是潜艇结构疲劳破坏的热点区域。本文以潜艇锥柱结合壳结构典型节点为研究对象,以断裂力学为理论基础,使用APDL语言对ANSYS软件进行2次开发,分析潜艇耐压壳结构典型节点表面裂纹在交变载荷作用下的扩展过程,并与试验结果进行对比,结果表明本方法可较好地模拟表面裂纹的疲劳扩展。     

冲击载荷下含表面裂纹潜艇典型结构的动态断裂研究

文章基于大型通用有限元分析软件ANSYS研究了带有初始表面裂纹的潜艇典型结构在不同下潜深度、不同爆心到船壳距离R和不同作用方位冲击载荷作用下的动态应力强度因子及其最大值与冲击因子的变化规律,然后以921A钢为例对多种工况下结构是否发生失稳断裂作出初步判断。     

一种基于累积损伤理论和裂纹尖端弹塑性应力场的裂纹扩展预测方法

文章提出了一种预测疲劳寿命的应力循环叠加和损伤循环叠加的双重叠加方法。该方法依据累积损伤理论,通过分析变幅载荷下裂纹尖端的应力场,采用应力循环叠加的方法反映残余应力的影响;同时利用SWT应力应变和寿命的关系,循环叠加裂尖损伤。该方法能够很好地反映过载时裂纹扩展的迟滞效应,适合变幅载荷下疲劳寿命的评估分析。