Fatigue based three-dimensional structural design optimisation studies implementing the generalised Frost–Dugdale crack growth law

Experimental studies of fatigue crack growth in aluminium alloys have shown that, at the low-to-mid stress intensity factor range, there is often a log-linear relationship between the crack length and the fatigue life. These observations have led to the development of the generalised Frost–Dugdale crack growth law, which allowed the accurate prediction of fatigue crack growth from Region I. For this research paper the ‘generalised Frost–Dugdale’ law was used to perform an optimisation study of 7050-T7451 Aluminium structures. The structural optimisation procedure proposed integrates geometrical modelling, structural analysis and optimization into one complete and automated computer-aided design process. The results from the structural optimisation study compared the ‘generalised Frost–Dugdale’ law and the traditional Paris law. Gradient-less, gradient-based optimisation algorithm and an enumeration scheme were considered in this investigation. The enumeration scheme takes advantage of a cluster computer architecture which enables a visualisation of the solution space allowing verification and validation of the optimisation algorithm. The results indicated that the optimal geometrical shape and predicted fatigue life depended on the crack sizes, structural geometry, boundary conditions and fatigue crack growth law. As a result, this procedure illustrates that for the design of light weight structures, a fatigue based optimisation used in conjunction with visualisation of the solution space may provide a viable design methodology. The importance of non-destructive inspection (NDI) and its role in determining optimal structural geometries is also revealed. Furthermore, the possibility of the application of the generalised Frost–Dugdale model in design optimisation has been demonstrated. This procedure has the potential to be applied to structures with complex structural configurations taking into account crack propagation in Region I.     

Fatigue crack growth model for assessing reliability of box-girders for cable-stayed bridge combining SHMS with strain data

Enhancement of the computer algorithm developed for the Runyang cable-stayed bridge (RYCB) in China is made by incorporating the fatigue crack growth analysis in contrast to the SN curve approach. Strain data obtained from the structural health monitoring system (SHMS) and finite element calculations are used. This provides the application of a deterministic method in addition to the probabilistic approach with the added feature of crack growth. The choice of selecting the two-parameter fatigue crack growth criterion was based on the definition of reliability index β such that the new results can be compared with those using the SN curves. A gradual drop of the reliability index β with time with an upper limit was obtained for the crack growth model in contrast to the linear time relation for the SN curve model that had no upper limit. This difference is significant and reveals the importance for selecting the fatigue failure criterion. Deterministic and probabilistic crack growth models are used to assess the differences. The results are based on the box-girder component strain history data of the Runyang Cable-stayed Bridge (RYCB) in China, stress history recorded by structural health monitoring system (SHMS) is analyzed using the monitored stress amplitude, mean stress and stress ratio. Finite element calculations are used to supplement data at locations not accessible for measurements. Additional improvement with reference to damage accumulation and the physical meaning of the reliability index will be studies in relation to the fatigue damage of box-girder of long cable-stayed bridges.     

对裂纹扩展规律Paris公式物理本质的探讨

首先讨论了著名力学家K.Krausz和A.S.Krausz关于Paris公式物理本质研究的成果，从材料的微观结构和裂纹尖端的应力场出发，应用位错动力学理论，热激活能理论和速率过程理论对疲劳裂纹扩展规律进行了微观到宏观的探讨。最终推导出疲劳裂纹扩展速率的一个解析表示式，该式严格地定了Paris公式的两个试验常数，赋予了Paris公式明确的物理意义，从而真实地揭示了Paris公式的物理本质，为这一经验的普遍规律奠定了理论基础。     

Predicting the fatigue life and crack aspect ratio evolution in complex structures

This paper discusses a computationally efficient method for determining the behaviour of complex structures containing three-dimensional cracks. A simple method is presented for calculating the mode I stress intensities for semi-elliptical cracks emanating from the saddle point of two intersecting tubular members. This method, which gives results in good agreement with published values, uses the finite element technique, but does not require the crack to be modelled explicitly. The technique is then used, in conjunction with FASTRAN II, to study fatigue crack growth and the results are compared to experimental data. Good agreement is achieved between both the predicted and measured fatigue crack growth and the evolution of the crack aspect ratios.     

Simulation of crack extension in shell structures and prediction of residual strength

Two models for the numerical simulation of ductile crack extension in shell structures are presented and compared. They are based on the crack tip opening angle and a cohesive zone approach. After identification of the model parameters and investigations of the mesh dependence, the models are applied to various specimen configurations and structural components. Their excellent numerical performance favors their application for predicting the residual strength of lightweight components like aircraft fuselages.     

Mixed mode fatigue crack growth in test coupons made from 2024-T3 aluminum

In this paper, two different fracture criteria are applied to determine the crack trajectory or angle of crack propagation in test specimens containing inclined cracks emanating from open holes. Also, different crack growth rate models are assumed for each criterion. The maximum principal stress criterion is used with a crack growth-rate equation based on an effective stress intensity factor. The strain energy density criterion is used with a crack growth-rate equation corresponding to an effective strain energy density factor. The crack growth-rate models for each criterion were constructed using unpublished fatigue crack growth data for 2024-T3 aluminum.     

Scaling of size/time/temperature — Part 2: Progressive damage in uniaxial compressive specimen

This work is concerned with predicting the fatigue failure initiation of a wing/fuselage bolt assembly. Accounted for in the analysis are both the influence of energy dissipation and damage accumulation as the structure is subjected to repeated cyclic loading. Results involving the location and number of cycles to initiate a fatigue crack 10⁻² in. are obtained. They agreed both qualitatively and quantitatively with the experimental findings. Also discussed is the influence of pre-torque in the bolt which tends to decrease the number of cycles to fatique crack initiation. Fatigue life may be extended by altering the load path so as to decrease the accumulation of energy near the site of failure initiation. This can be accomplished without major modification of the design. The methodology that makes use of the strain energy density criterion can be used to optimize the fatigue strength of other structural sub-assemblies by appropriate combination of material and geometry for specified load conditions.     

Fracture mechanics of plates and shells applied to fail-safe analysis of fuselage Part II: Computational results

In this paper, the problem of the fracture of a fuselage stiffened by longitudinal longerons and circumferential frames is analyzed by means of the finite element method. Our research is motivated by the fail-safety design concept of fuselage for civil aircraft. In this study, the total energy release rate are evaluated for five types of basic loading, namely, axial extension, pure bending, twisting, transverse shearing, and radial expansion due to internal pressure. The crack is located either at the mid-point or near the end of the fuselage. It extends in two bays with the stiffener at its center. The stiffener which bisects the crack is assumed to be broken at the location of the crack. Computational results indicate that the total energy release rate G_t increases with the increasing crack length. However, when the crack tip approaches the stiffener, the value of G_t decreases as a result of the reinforcement from the stiffener. For a crack near the end of the fuselage, as a result of boundary effect, the value of G_t is larger in comparison with the case of the crack at the mid-point of the fuselage. We also find that the effect of geometrical nonlinearity can reduce the value of G_t for the fuselage under axial tension or pure bending. For the fractured fuselage under pure bending, shell buckling can occur at the concave side of the fuselage prior to crack growth. The maximum tensile stress in the stiffener in front of the crack tip is also investigated.     

停歇对疲劳裂纹扩展超载迟滞效应影响的研究

本文用 16 Mn和 A 537 两种普通低合金钢试件,较系统地研究了停歇对疲劳超载迟滞效应的影响。研究表明,疲劳载荷中的停歇对超载迟滞效应有明显影响,其影响的程度大小与停歇时的载荷 P_H,停歇时间 t_H 等因素密切相关;不但可能使试件的疲劳寿命减少,也可能使试件的疲劳寿命增加。在工程结构疲劳设计、分析及应用超载迟滞效应时应予以注意。     

Fatigue crack growth simulation in coated materials using X-FEM

In the present work, the eXtended Finite Element Method (XFEM) is used to study the effect of bi-material interfaces on fatigue life in galvanised panels. X-FEM and Paris law are implemented in ABAQUS software using Python code. The XFEM method proved to be an adequate method for stress intensity factor computation, and, furthermore, no remeshing is required for crack growth simulations. A study of fatigue crack growth is conducted for several substrate materials, and the influence of the initial crack angle is ascertained. This study also compares the crack growth rate between three types of bi-materials alloys zinc/steel, zinc/aluminium, and zinc/zinc. The interaction between two cracks and fatigue life, in the presence of bi-material interface, is investigated as well.     

STOCHASTIC MODELLING OF FATIGUE CRACK GROWTH UNDER CONSTANT AMPLITUDE LOADING

Two stochastic models of fatigue crack growth under constant amplitude cyclic loadingare proposed and studied by using the stochastic averaging method and total probability theorem to ac-count for high frequency component and low frequency component, respectively, of the irregular na-ture of fatigue crack growth observed in Virkler's experiment. Particular attention is paid to the predic-tion performance of the models under a change in the initial crack length. It is shown that the modelsproposed in the present paper yields better agreement with experimental data than other models avail-able in literature.     

Study of multi-site damage of fuselage lap joints

The downturn in the world economy coupled with the cost of new aircrafts has meant that there are now ageing fleets whose continued airworthiness requires special attention to corrosion treatments, repair design, fatigue and fracture analysis, and improved crack detection techniques. To assist in this goal the present paper first summarises recent Australian efforts into the development of a simple experimental test specimen which is capable of reproducing the crack growth and failure mechanisms seen in the fuselage lap splice of a wide bodied transport aircraft. The development of a composite repair to overcome these phenomena is then discussed.     

Fourier and wavelet analyses for fatigue assessment of concrete beams

We investigate damage detection in a simply-supported pre-stressed beam. A crack was propagated by fatigue loads, which were applied up to two million cycles. Both fast Fourier transform (FFT) and continuous wavelet transform (CWT) are used in the analysis of the structural response to impulse loads. The acceleration response of the full-scale beam was measured each time a certain number of cycles of fatigue loads were applied. The results of this study show that both methods can clearly identify the crack growth induced by fatigue loads. The natural frequencies found by FFT are sensitive to the crack progression. The results from the CWT analysis show a clear difference in structural responses between the initial and damaged states of the structure. The response accelerations are de-noised by a soft-thresholding method before they are analyzed by CWT. In addition to the frequency components, the CWT shows the moment in time when particular frequencies occur. Therefore, wavelet analysis has the potential of becoming an effective tool for damage detection and health monitoring of structures for which the natural frequencies are irregularly changing. As the crack grows, the magnitude of ridges obtained by CWT analysis decreases significantly, which indicates the reduction in structural stiffness.     

Evaluation of stress intensity factors for bi-material interface cracks using displacement jump methods

The aim of the present work is to investigate the numerical modeling of interfacial cracks that may appear at the interface between two isotropic elastic materials. The extended finite element method is employed to analyze brittle and bi-material interfacial fatigue crack growth by computing the mixed mode stress intensity factors (SIF). Three different approaches are introduced to compute the SIFs. In the first one, mixed mode SIF is deduced from the computation of the contour integral as per the classical J-integral method, whereas a displacement method is used to evaluate the SIF by using either one or two displacement jumps located along the crack path in the second and third approaches. The displacement jump method is rather classical for mono-materials, but has to our knowledge not been used up to now for a bi-material. Hence, use of displacement jump for characterizing bi-material cracks constitutes the main contribution of the present study. Several benchmark tests including parametric studies are performed to show the effectiveness of these computational methodologies for SIF considering static and fatigue problems of bi-material structures. It is found that results based on the displacement jump methods are in a very good agreement with those of exact solutions, such as for the J-integral method, but with a larger domain of applicability and a better numerical efficiency (less time consuming and less spurious boundary effect).     

Experimental Investigation and Finite Element Analysis of Fatigue Crack Growth in Pipes Containing a Circumferential Semi-elliptical Crack Subjected to Bending

In this paper, a circumferential external surface flaw in a metallic round pipe under cyclic bending loading is considered. Because of very rapid changes in the geometrical parameters around the crack front region, the mesh generation of this region must be done with great care. This may lead to an increase in the run time which makes it difficult to reach valid results and conclusions. Because of the advantages of the sub-modeling technique in problems which need very high mesh density, this method is used. Stress intensity factors in mode I condition are determined using three-dimensional finite element modeling with 20 node iso-parametric brick elements in the ANSYS 9.0 standard code and the singular form of these finite elements at the crack front. In order to estimate the analysis error, the structural parameter error in energy norm criterion was used. Because of the advantages of non-dimensional analysis, this method is employed, and the stress intensity factors are normalized. For the analysis of the fatigue crack growth, the Paris law is used. The propagation path of the surface flaw is obtained from the diagram of aspect ratio versus relative crack depth. The fatigue crack growth analysis (the relative crack depth against loading cycles diagram) of different initial crack aspect ratio under cyclic loading is also considered. Fatigue shape development of initially semi-elliptical external surface defects is illustrated. The effect of the Paris exponent (material constant) on fatigue crack propagation is shown as well. Moreover, the fatigue crack growth of several specimens is assessed experimentally using a manually-constructed experimental set up. Finally, the experimental results obtained by cyclic bending loading tests are compared with the numerical results. The experimental results show good conformity with the finite element results.     

基于多因素的焊接结构疲劳裂纹扩展速率分析

以Donahue等提出的疲劳裂纹扩展速率计算模型为基础,通过引入形状系数、张开比和残余应力等参数,建立了适用于焊接结构的疲劳裂纹扩展速率计算模型,分析了多种因素对焊接结构疲劳裂纹扩展速率的影响规律。结果表明,焊板厚度和焊缝余高的变化均会对焊接结构疲劳裂纹的扩展速率产生影响,在对焊接结构表面形状进行设计时应保有一定的焊缝余高;有效应力比的增大会降低焊接结构疲劳裂纹的扩展速率,且裂纹深度的变化不会改变有效应力比对焊接结构疲劳裂纹扩展速率的影响;残余应力的增大会提高焊接结构疲劳裂纹的扩展速率,且残余应力对疲劳裂纹扩展速率的促进作用随着裂纹深度的增加而增大,在对焊接结构的疲劳性能进行设计时须考虑残余应力对结构性能的影响。     

Similitude: Fatigue cracking in steels

The ability to understand and predict fatigue crack growth is central to both the design and the continued operational safety of aircraft, rail, offshore structures, nuclear power plants, and many other engineering assets. However, most current crack growth models are based on the concept of similitude. This paper examines cracking in a range of steels and reveals that the similitude hypothesis is invalid in Region I, where the crack growth rate is low.     

构件三维断裂与疲劳力学及其在航空工程中的应用

本文总结评述了断裂力学由二维理论到三维理论的发展历程。介绍了三维裂纹端部场的K-Tz和J-Tz双参数描述、K-T-Tz和J-QT-Tz三参数描述,以及三维弹塑性断裂准则和三维疲劳裂纹闭合模型等。通过具体的实例介绍了三维断裂理论在航空结构损伤容限分析中的应用。正确考虑离面约束和面内约束对裂纹端部场以及材料断裂和疲劳裂纹扩展性能的影响,能够发展航空结构损伤容限可预测设计能力。     

Axial crack propagation and arrest in a pressurized cylinder: An experimental-numerical analysis

The feasibility of using a previously developed crack-kinking criterion to predict crack arrest at a tear strap in a pressurized fuselage was studied with instrumented axial rupture tests of 21 models of an idealized fuselage. A rapidly propagating axial crack, which was initiated from a precrack, kinked immediately upon extension and propagated diagonally until it turned circumferentially and propagated along the tear straps. An elastodynamic finite element analysis of the rupturing model fuselage yielded the mixed-mode stress intensity factors,K _I andK _II , and the remote stress component, σ _OX . This numerical procedure was also used to predict the crack trajectories in full-scale fuselage rupture tests. All numerical results agreed well with their measured counterparts regardless of size.     

负超载对Al-2024疲劳裂纹扩展的影响

本文讨论了负超载对Al-2024铝合金材料疲劳裂纹扩展的影响,试验发现在大量负超载循环周次之后也有裂纹停滞现象发生。这种停滞现象的产生与剪切唇的形成有关。本文发现负超载期间的剪切唇(简称剪切唇Ⅰ)和负超载之后的剪切唇(简称剪切唇Ⅱ)对疲劳裂纹扩展速率影响的程度不同。从裂纹闭合的观点建立了负超载对疲劳裂纹扩展影响的计算模型。