Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material

0　INTRODUCTIONWeknowthatthemetalmaterialwillbegincreepwhenthetemperatureishigherthan 30 per centoftheirsmeltingpoint.Foraturbine,adieselengine,anaerospacestructureandothermotivepowermechanisms,thematerialsstillworkwhentheirtemperaturesovershootthecreepthresholdval ue.Thecreepdeformationwilloccuratnormaltem peratureforthepolymerstructures(e.g .plasticspipingelements) .Inthecaseofcreepingthefrac tureofthestructureoccursduetocreepfractureandcreepcrackgrowth.Thereforetheresearchonthecrackgro…     

The crack tip fields of Mode Ⅱ stationary growth crack on bimaterial interface

A mechanical model is established for mode Ⅱ interfacial crack static growing along an elastic-elastic power law creeping bimaterial interface. For frictional contact of boundary conditions on crack faces, asymptotic solutions of the stresses and strains of near tip-crack are got. It was shown that in stable creep growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, the stress and strain have the same singularity and there is not the oscillatory singularity the field. Through numerical calculation, it is shown that the frictional coefficient η notably influence the crack-tip field.     

Asymptotic field of mode Ⅱ dynamic growing crack in visco-elastic material

A mechanical model of visco-elastic material is established in order to investigate viscous effect in dynamic growing crack-tip field of mode Ⅱ. It is shown that in stable creep growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, the stress and strain have the same singularity, namely, (σε) ∝r^-1/(n-1). The asymptotic solutions of separatied variables of stress, stain and displacement in crack-tip field are obtained by asymptotic analysis, and the results of numerical value of stress and strain in crack-tip field are obtained by shooting method. Through numerical calculation, it is shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M. By the asymptotic analysis to the crack-tip field, the fracture criterion of mode Ⅱ dynamic growing crack of visco-elastic materials is put forward from the point of view of strain.     

动态载荷作用下焊接点线弹性裂纹的弯曲扩展路径的预测(英文)

利用二阶摄动方法研究了动态载荷作用下结构线弹性断裂裂纹的弯曲延伸扩展问题并求解了动态应力强度因子。利用二阶摄动方法研究了动载荷作用下裂纹路径预测时的应力准则与能量准则之间的关系。就均匀物质而言,在二阶摄动分析理论的框架内,两种准则指明了相同的动态裂纹路径。但在具有非均匀断裂韧度的物质中,能量准则优越于应力准则。作为二阶摄动方法的实际运用,研究了焊接结构中动态线弹性裂纹的形态特征和弯曲扩展路径问题,综合考虑了诸如远场动态作用应力、焊接残余应力、局部物质衰变以及不同尺寸的缺陷的存在等因素,绘制出动态载荷作用下退化区域中裂纹弯曲扩展的临界轨迹曲线。     

刚性-压力敏感性材料界面I型准静态扩展裂纹尖端场

为了研究船用工程复合材料的界面裂纹特性,建立了刚性-压力敏感粘弹塑性材料Ⅰ型准静态扩展裂纹的力学模型.在稳态扩展阶段,应力和应变具有相同的奇异量级,即(σ,ε)∝γ<'-1/(n-1)>.引入Airy应力函数,通过渐近分析得出了裂纹尖端应力和应变的分离变量形式的渐近解,并采用打靶法求得了裂纹尖端应力和应变的数值结果.数值计算结果表明,界而裂尖场主要受材料的泊松比和幂硬化指数的控制.通过对裂纹尖端场的渐近分析,从应变角度出发,提出了刚性一压力敏感性材料界面Ⅰ型准静态扩展裂纹的断裂判据.     

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.     

运用二阶摄动方法预测焊接点疲劳微弯裂纹的路径发展

利用二阶摄动方法分析研究了轻微弯曲疲劳裂纹尖端应力强度因子的变化幅度,进一步得到了在循环载荷下直线裂纹微弯延伸尖端应力强度因子变化幅值的近似表达式.以匹配渐进扩张的形式考虑了远区域边界条件的效果,研究了裂尖附近的渐进应力场.利用Irwin公式计算出了由于裂纹发展而引起的应变能释放率变化幅值.预测了在具有非均匀断裂韧度的物质中裂纹的延伸.考虑了循环载荷、残余应力,以及由于焊接而引起的物质衰变等因素,利用了二阶摄动方法预测了沿着焊接点传播的弹脆性裂纹路径.     

The asymptotic field of a dynamically growing crack in a viscoelastic materia

A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field. It was shown that in the stable creep-growing phase,elastic deformation and viscous deformation are equally dominant in the near-tip field,and stress and strain have the same singularity,namely,(σ,ε ) ∝ r?1 /( n?1) . The asymptotic solution of separating variables of stress,stain and displacement in the crack-tip field was obtained by asymptotic analysis,and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack. Through numerical calculation,it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M . When n →∞,the asymptotic solution of a viscoelastic material can be degenerated into that of Freund's elastic-ideally plastic material by analyzing basic equations.     

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.     

用扩展有限元方法来分析含裂纹板时剪切闭锁问题消除

文章介绍了扩展有限元计算含裂纹板问题的基本方法,该方法以常规有限元为基础,通过在位移场中增加反映裂纹面的不连续函数及反映裂尖局部特性的裂尖渐近位移场函数,体现裂纹的存在,从而使裂纹与有限元模型相互独立,方便了裂纹扩展的模拟。采用求解 Reissner 板问题的混合插值单元 MITC4,可以有效地避免剪切闭锁现象。通过相互作用能量积分确定混合模型的应力强度因子。最后,通过一系列的数值算例验证了该方法的正确性。     

Fitness-for-purpose assessment of cracked offshore wind turbine monopile

In this paper, the procedure for flaw acceptability assessment is examined through a case study of a semi-elliptical surface crack in an offshore monopile as it grows till it forms a through thickness crack. Using the procedure prescribed in an industrial standard (BS 7910), the fracture ratio, K_r is shown to increase monotonically with increasing crack depth. The load ratio, L_r, is initially insensitive to the crack depth. However, there is a rapid increase in L_r when the crack depth to thickness ratio exceeds 80%. L_r values obtained from detailed 3D FE limit analysis using elastic-perfectly-plastic material behaviour do not exhibit the asymptotic behaviour predicted by BS 7910 as the flaw transitions from deep crack to through-thickness crack. Furthermore, K_r predicted by BS 7910 is shown to be an over-estimation for the typical dimensions of offshore monopiles. The findings suggest that a structure with a deep flaw may be identified as unacceptable based on BS 7910 when it may still possess a non-trivial amount of structural residual life. This is a concern for monopiles where crack growth as a large flaw forms a significant part of the total life.     

Approximate weight functions of stress intensity factor for a wide range shapes of surface and an embedded elliptical crack

This paper describes the application of weight function for stress intensity factor in a surface crack with a wide range of crack shapes. Based on the weight function representation proposed by Wang and Glinka (2009), an extended formulation of the weight function for surfaces and embedded cracks is performed. The unknown parameters in the formulations were determined from reference values of stress intensity factor for a surface and an embedded crack given by finite element analysis with the J integral method. The effectiveness of the proposed weight functions has been verified by comparing with the stress intensity factors given by finite element analysis and available approximated solutions under several loading conditions.     

轴力作用下X型焊接管节点热点应力的分布规律

海洋平台中的焊接管节点的疲劳寿命是由热点应力的大小和分布决定。热点应力的大小决定了管节点在疲劳失效前所能承受的循环荷载的次数,而热点应力的位置则决定了疲劳裂纹的萌生位置和扩展方式。文中采用有限元方法分析了承受轴向拉力作用的X型焊接管节点在焊缝周围的热点应力的分布情况,通过对112个X节点进行的模型分析,研究了节点几何参数对热点应力大小和分布规律的影响。     

复杂应力场中裂纹疲劳扩展寿命预报

船舶作为一种大型焊接结构,其疲劳热点部位的应力应变场分布很复杂,要预报这些部位的裂纹疲劳扩展寿命,必须解决复杂场中裂纹的应力强度因子计算及其裂纹扩展方向问题.该文对船舶肘板处两种不同原因产生的裂纹的扩展路径、扩展速率进行了研究.裂纹扩展方向用第一主应力准则确定,在裂纹扩展方向上给定不同的裂纹增量,得到不同长度裂纹的复合裂纹等效应力强度因子,并拟合这些计算结果得出船舶肘板的应力强度因子计算式.结合裂纹扩展率单一曲线模型对肘板裂纹扩展寿命进行了预报,预报结果与实验结果符合得较好,说明所采用的方法可行.对建立船舶典型节点的裂纹扩展寿命预报方法有参考价值.     

考虑裂纹扩展的周向裂纹损伤圆柱壳的极限强度

为了正确评价和预测大型海洋平台结构在疲劳裂纹损伤条件下的承载能力,须要全面、系统地研究圆柱壳这类基本构件在考虑裂纹扩展条件下的极限强度。针对含周向壁穿裂纹损伤的圆柱壳,利用已有的关于弹塑性裂纹及裂纹扩展的理论解析解,通过系列计算,探讨了裂纹初始长度、圆柱壳直径板厚比、材料的临界CTOD、临界CTOA、屈服应力及杨氏模量等参数对极限强度的影响,并就其对各参数的敏感度作了相应的分析。提出极限强度损失系数κ、强度冗余系数λ及裂纹剩余扩展长度ξ等无因次参数,并以此定量地评价由裂纹扩展所引起的结构承载能力的变化。这项研究为进一步合理地评估含裂纹损伤的结构系统整体的极限强度完成了一项基础性工作。     

Experimental investigation of structural system capacity with multiple fatigue cracks

Few experimental data sets exist in the literature to support the development and evaluation of digital twins predicting structural degradation. The literature is especially sparse for system tests where multiple failures occur and interact. In this work, a laboratory-level experiment is conducted to mimic many of the properties of larger and more complex marine structures with redundant load paths, failure interaction, and component-to-system level integration. In the experiment, such properties are reflected by a hexagon tension specimen with four propagating fatigue cracks tested under displacement-controlled loading. The applied loading cycles and corresponding crack lengths are recorded as the major time-varying data of degradation, with the resisting force at maximum extension used as the system capacity. A novel computer vision method is used to measure the crack length. Strain gauges are also used to monitor the structure’s status. The experimental data is presented and analyzed in this paper. The resulting data sets can be used to evaluate the performance of different digital twin updating approaches.     

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.     

一类带存放率的渐近周期竞争扩散系统的稳定性

应用上、下解方法和抛物型方程的极值原理,研究了带存放率的渐近周期竞争系统ut-D1Δu=u（a-bu-cv）＋h,vt-D2Δv=v（d-eu-fv）＋k在齐次Neum ann边界条件下解的渐近性态,得到了该系统的全局渐近稳定性.     

基于结构疲劳动态可靠性分析的船舶结构概率损伤容限设计

本文根据结构可靠性理论，提出了一种基于结构疲劳动态可靠性分析的损伤容限分析方法，给出结构疲劳裂纹随机扩展过程中疲劳寿命分布和结构疲劳可靠性的表达式。在给定与疲劳寿命有关的各参数条件下求得动态可靠性曲线，从而在结构设计中根据可靠性要求确定或选择设计参数。     

Development of super element to perform direct analysis on failure assessment of hull structures based on FAD

Failure assessment diagram (FAD) has great potentials to be a powerful tool to assess the integrity of hull structures. However, the current methodology to obtain the fracture ratio and the load ratio, two axes of FAD, for hull structures is tedious and burden which is one of the major obstacles to advance the further application of FAD. In this paper, a super element is introduced to obtain those two ratios simultaneously in the framework of linear elastic analysis within a single step. Besides, the virtual section closure technique is proposed to compute the reference stress under the inspiration of virtual crack closure technique to compute the stress intensity factor. The capacity of the proposed super element has been assessed by two classic examples of a plate with central crack and a cylinder with circumferential crack. The results obtained from the super element are compared to the corresponding analytical solutions. Finally, the cracked Nishihara specimen (NST-3) was examined and the facture ratio and the load ratio obtained by the super element were compared to those obtained by the global analyses. The comparisons indicate that the proposed super element is accurate. No convergence troubles were encountered. Therefore, the methodology developed in this paper could be a very useful addition to perform the direct analysis on the failure of hull structures due to large crack extensions based on the failure assessment diagram.