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.     

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.     

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。     

金属疲劳裂纹扩展率曲线与S-N曲线之间的关系

目前有两种不同的理论用于预报金属结构的疲劳寿命。一种是基于S－N曲线的累积疲劳损伤理论，另一种是基于裂纹扩展率曲线的疲劳裂纹扩展理论，如果都把一个构件的最终断裂作为疲劳破坏的定义，则S－N曲线和裂纹扩展率曲线均是反映金属在疲劳载荷作用下的基本材料特性。尽管在过去这两种曲线是分别测试的，但它们之间应该存在一些相互关系。本文的主要目的就是讨论它们之间的关系。基于S－N曲线的一个一般表达式和裂纹扩展率曲线的一个有代表性的表达式，本文建立了两种曲线之间的一个正式关系，这表明只需要测试一种曲线，而另一种曲线就可以根据已有的试验结果导出。文章以一个中央裂纹平板作为例子，演示了如何根据一种曲线推导另一种曲线。     

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。     

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.     

Fracture control of extremely thick welded steel plates applied to the deck structure of large container ships

The rapid enlargement of the size of container ships has led to the application of extremely thick plate in the deck structures, which may grow concerns about the fracture toughness at the butt-weld with large amount of heat input, and the arrest toughness of brittle crack propagation in the base metal of such thick plates. Also, slam-induced whipping stresses might affect the fatigue crack propagation and the initiation of a brittle crack in a container ship. In order to prevent the catastrophic failure of deck structures by brittle fracture, national joint research projects, which focused on the safety-related issues of extremely thick steel plate applied to hull of large container ships, were formed from April 2007 to March 2011 organized by the Japan Ship Technology Research Association (JSTRA) supported by the Japanese Government in collaboration with universities, national research institute, classification societies and relevant industries including shipbuilding, steel manufacturing and shipping companies. The joint research projects have carried out the investigations on crack initiation toughness of the weld, fatigue crack propagation under seaway loading, the potential of defect detection by ultrasonic testing, and the crack-arrest methods after brittle crack propagation. Practical recommendations to prevent brittle fracture of large container ships were proposed based on these comprehensive investigations. The essential parts of the above research activities are presented in this paper.     

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。     

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.     

HTS-A钢对接接头的双轴疲劳试验研究

开展了HTS-A钢对接焊接试件的双轴疲劳试验.通过一组试件在纵向受弯和垂向受压循环载荷作用下的试验研究,得到了不同双轴载荷比情况下的试件断口形式及疲劳寿命.根据试验过程中记录的裂纹扩展数据,回归了不同载荷比情况下的Paris公式,从而推算裂纹扩展寿命.进而通过总寿命减去裂纹扩展寿命得到裂纹的萌生寿命.结果表明,垂向循环压力载荷缩短了试件的疲劳寿命,且对萌生寿命的影响大于对扩展寿命的影响.     

低周疲劳载荷下考虑累积塑性的船舶裂纹板剩余极限强度研究

研究表明在恶劣海洋环境中船体结构整体断裂破坏往往是低周疲劳破坏和累积塑性破坏的耦合结果。考虑这两者耦合作用的影响,评估船体结构的极限承载力更为实际。基于累积塑性和低周疲劳裂纹扩展,从理论上分析了平面内低周疲劳载荷下裂纹板的残余极限强度。经过一系列数值模拟,首先讨论低周疲劳裂纹扩展行为的影响,然后随着疲劳裂纹扩展的发展,主要讨论了初始变形,焊接残余应力,裂纹扩展长度,裂纹分布和裂纹板厚度对低周疲劳载荷下船体裂纹板极限强度的影响。     

A probabilistic damage tolerance concept for welded joints. Part 1: data base and stochastic modelling

The present paper presents the necessary crack growth statistics and suggests stochastic models for a reliability analysis of the fatigue fracture of welded steel plate joints. The reliability levels are derived from extensive testing with fillet-welded joints for which the entire crack growth history has been measured, not only the final fatigue life. The statistics for the time to reach given crack depths are determined. Fracture-mechanics-derived crack growth curves are fitted to the measured experimental curves and the best fit defines the growth parameters involved for each test specimen. The derived statistics and distribution function for these parameters are used as variables in a Monte Carlo simulation (MCS). In addition a Markov model is developed as an alternative stochastic model. It is a Markov chain for which the discrete damage states are related to chosen crack depths in the material. This model works directly with the experimental time statistics. It is a “stochastic bulk approach” not involving any random variables or fracture mechanics modeling. Both models are fitted to the data base and scaled to in-service conditions. Both methods are compared and discussed. The aim is to provide data for the variables used in a MCS and to develop a Markov chain for fast reliability calculation, especially when predicting the most likely influence of numerous future inspections.     

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.     

Full-scale fatigue tests of ship structures to validate the S–N approaches for fatigue strength assessment

Ships belong to those welded structures which are prone to fatigue due to high cyclic loads. Different approaches exist for the fatigue strength assessment which are varying between the industrial sectors. Therefore, deeper fatigue strength investigations were performed in Germany within an industry-wide joint research project aiming at the harmonization of the approaches. Regarding ship structures, two types were selected for full-scale tests. The first concerned web frame corners being typical for roll-on/roll-off ships (ro/ro) ships, from which three models were tested under constant amplitude loading. The second type was the intersection between longitudinals and transverse web frames, which recently showed fatigue failures in containerships. Five models were tested, three under constant and two under variable amplitude loading. All tests showed a relatively long crack propagation phase after first cracks had appeared, calling for a reasonable failure criterion. For the numerical analysis, the structural hot-spot stress as well as the effective notch stress approach have been applied. The latter allows the consideration of the weld shape which could partly explain differences in the observed and calculated failure behaviour. Another factor is the distribution of welding-induced residual stresses, which obviously affected the failure behaviour in the web frame corner as well. Insofar the investigations give a good insight into the strength behaviour of complex welded structures and into current problems and opportunities offered by numerical analyses.     

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。     

考虑累积塑性的船体裂纹板变幅低周疲劳裂纹扩展行为研究

船舶结构的扩展断裂失效往往是低周疲劳破坏和累积递增塑性耦合作用的结果,疲劳裂纹的扩展就是裂纹尖端前缘材料刚度不断降低、延展性不断耗失而逐渐分离的过程。基于弹塑性断裂力学理论,文章在作者对常幅载荷下提出的考虑累积塑性损伤的低周疲劳裂纹扩展速率预测模型的基础上对具有单个过载峰的拉伸/压缩过载下的扩展行为进行了研究。通过低周疲劳裂纹扩展试验进一步验证了该预测模型能合理评估具有单个过载峰的拉伸/压缩过载下的低周疲劳裂纹扩展行为。     

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.     

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。