Automated simulation of fatigue crack propagation for two-dimensional linear elastic fracture mechanics problems by boundary element method

In this paper, automated simulation of multiple crack fatigue propagation for two-dimensional (2D) linear elastic fracture mechanics (LEFM) problems is developed by using boundary element method (BEM). The boundary element method is the displacement discontinuity method with crack-tip elements proposed by the author. Because of an intrinsic feature of the boundary element method, a general growth problem of multiple cracks can be solved in a single-region formulation. In the numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not necessary. Local discretization on the incremental crack extension is performed easily. Further the new adding elements and the existing elements on the existing boundaries are employed to construct easily the total structural mesh representation. Here, the mixed-mode stress intensity factors are calculated by using the formulas based on the displacement fields around crack tip. The maximum circumferential stress theory is used to predict crack stability and direction of propagation at each step. The well-known Paris’ equation is extended to multiple crack case under mixed-mode loadings. Also, the user does not need to provide a desired crack length increment at the beginning of each simulation. The numerical examples are included to illustrate the validation of the numerical approach for fatigue growth simulation of multiple cracks for 2D LEFM problems.     

Crack Growth analysis of plates Loaded by bending and tension using dual boundary element method

This paper presents an extension of the dual boundary element method to analysis of crack growth in plates loaded in combine bending and tension. Five stress intensity factors, two for membrane behaviour and three for shear deformable plate bending are computed using the J-Integral technique. Crack growth processes are simulated with an incremental crack extension analysis based on the maximum principal stress criterion. The method is considered effective since no remeshing is required and the crack extension is modelled by adding new boundary elements to the previous crack boundaries. Several incremental crack growth analysis for different configurations and loadings are presented.     

Non‐planar mixed‐mode growth of initially straight‐fronted surface cracks,in cylindrical bars under tension,torsion and bending,using the symmetric Galerkin boundary element method‐finite element method alternating method

In this paper, the stress intensity factor (SIF) variations along an arbitrarily developing crack front, the non‐planar fatigue‐crack growth patterns, and the fatigue life of a round bar with an initially straight‐fronted surface crack, are studied by employing the 3D symmetric Galerkin boundary element method‐finite element method (SGBEM‐FEM) alternating method. Different loading cases, involving tension, bending and torsion of the bar, with different initial crack depths and different stress ratios in fatigue, are considered. By using the SGBEM‐FEM alternating method, the SIF variations along the evolving crack front are computed; the fatigue growth rates and directions of the non‐planar growths of the crack surface are predicted; the evolving fatigue‐crack growth patterns are simulated, and thus, the fatigue life estimations of the cracked round bar are made. The accuracy and reliability of the SGBEM‐FEM alternating method are verified by comparing the presently computed results to the empirical solutions of SIFs, as well as experimental data of fatigue crack growth, available in the open literature. It is shown that the current approach gives very accurate solutions of SIFs and simulations of fatigue crack growth during the entire crack propagation, with very little computational burden and human–labour cost. The characteristics of fatigue growth patterns of initially simple‐shaped cracks in the cylindrical bar under different Modes I, III and mixed‐mode types of loads are also discussed in detail.     

HT有限元在Ⅰ、Ⅱ与Ⅲ型复合弹性断裂问题中的应用

探讨了HT有限元应用于Ⅰ、Ⅱ和Ⅲ型复合裂纹的弹性断裂问题。分析了Ⅲ型弹性断裂问题的HT有限元方法及高阶奇异性应力强度因子KΙΙΙ,同时,对Ⅰ和Ⅱ型断裂问题的HT有限元原理及断裂强度因子KΙ和KΙΙ的计算也进行了阐述。特别地,在计算三个强度因子时,引入了一种新的方法——附加试函数法,它主要用于满足裂尖特殊的边界条件,提高了三个奇异应力强度因子的精确性与可靠性。最后,根据HT有限元计算结果,讨论了奇异应力强度因子无量纲化系数K/Kc随裂纹单元特殊T函数项数、细划单元数、单元高斯点数及裂尖不同附加试函数的变化规律;获得了应力强度因子精确度和可靠度,并与其它有限元结果进行了比较,阐述了此方法的优越性。     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

7050铝合金Ⅰ-Ⅱ复合型疲劳裂纹研究

为研究7050铝合金在Ⅰ-Ⅱ型复合加载下疲劳裂纹扩展规律,在Amsler HFP5000高频试验机上利用Richard加载装置,完成紧凑拉剪(CTS)试样疲劳裂纹扩展试验,利用有限元对Ⅰ-Ⅱ复合型裂纹进行数值模拟,采用APDL命令流计算不同裂纹长度的应力强度因子,并引入最大周向应力准则计算裂纹扩展角,用有限元计算等效应...     

Fatigue crack growth in fibre metal laminates with multiple open holes

The fatigue crack growth behaviour of hybrid S2‐glass reinforced aluminium laminates (Glare) with multiple open holes was investigated experimentally and analytically. It was observed that the presence of multiple‐site fatigue damage would increase crack growth rates in the metal layers as two propagating cracks converged. An analytical crack growth model was established for predicting crack growth rates based on empirical Paris equation. The effective stress intensity factor at crack tips is a function of mode I far‐field stress intensity factor, crack opening stress intensity factor and effective non‐dimensional stress intensity factor that incorporated the crack‐bridging effect in fibre metal laminates. The predicted results under different applied stress can capture the trend of averaged crack growth rates in experiments, although deviation exists in the predictions.     

Experimental fatigue crack growth analysis and modelling in part‐through circumferentially pre‐cracked pipes under pure bending load

In the present work, an attempt has been made to study the fatigue crack growth in a part‐through circumferentially notched pipe specimen. It has been observed that under four‐point bend cyclic load, the crack propagates in a transverse plane in the radial direction initially followed by propagation in the circumferential direction. The crack extension in the circumferential direction resulted crack growth retardation in the radial direction. This behaviour of the fatigue crack growth has been modelled, and a fatigue life prediction methodology based on an exponential model has been applied for prediction of fatigue crack growth.     

Multiple-cracked fatigue crack growth by BEM

The dual boundary element method is applied for the two-dimensional linear elastic analysis of fatigue problem of multiple-cracked body. The traction integral equation is applied on ones of surfaces of cracks while the usual displacement integral equation simultaneously on the others. General multiple crack growth problem is solved in a single-region formulation. All crack surfaces are discretized with discontinuous quadratic boundary elements. J-integral technique is used to evaluate stress intensity factors. The real extension path of cracks is simulated by a linear incremental crack extension, based on the maximum principal stress criterion. For each increment analysis of the cracks, crack extension is conveniently modelled with new boundary elements. Remeshing is no longer necessary. Fatigue life analysis is carried out with Paris' formulae. Several numerical examples show high efficiency of present method.     

Simulation of stage I-crack growth using a hybrid boundary element technique

Short fatigue crack propagation often determines the service life of cyclically loaded components and is highly influenced by microstructural features such as grain boundaries. A two-dimensional model to simulate the growth of these stage I-cracks is presented. Cracks are discretised by displacement discontinuity boundary elements and the direct boundary element method is used to mesh the grain boundaries. A superposition procedure couples these different boundary element methods to employ them in one model. Varying elastic properties of the grains are considered and their influence on short crack propagation is studied. A change in crack tip slide displacement determining short crack propagation is observed as well as an influence on the crack path.     

Prediction of fatigue crack growth path in mechanical joints using a weight function approach

Cracks often initiate from the mechanical joints which are widely used in structural components. It has been reported that cracks in mechanical joints are under mixed‐mode condition and there is a critical angle at which mode I stress intensity factor becomes maximum. The crack propagates in an arbitrary direction and the prediction of fatigue crack growth path is needed to provide against crack propagation and examine safety. In this study, mixed‐mode fatigue crack growth tests are performed for horizontal and critical inclined cracks in mechanical joints. Fatigue crack growth paths are predicted using a weight function approach and maximum tangential stress criterion.     

Prediction on fatigue life of U‐notched PMMA plate

In this paper, fatigue life prediction of U‐notched polymethyl methacrylate (PMMA) plate is numerically investigated based on the combination of fatigue damage mechanism and fatigue crack propagation mechanism. First, strength and stiffness degeneration criterions during the fatigue process are established on the basis of nonlinear progressive damage evolution, and the fatigue crack initiation life is estimated. Second, fatigue crack propagation phase is analysed through virtual crack closure technique. The fatigue crack propagation life before totally fracture is also predicted. Finally, finite element models of PMMA plate weakened by lateral symmetric U‐notch are built up using ABAQUS, and the total fatigue life of notched plate is calculated by combining the crack initiation life with the crack propagation life. These results will play an important role for evaluating the fatigue life of U‐notched PMMA plate.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

Fatigue growth analysis of interacting and coalescing surface defects

Fatigue crack-growth is simulated for multiple surface cracks in a plate subjected to different combinations of tension and bending loads. The numerical technique employed is based on the step-by-step integration of a Paris' type of fatigue crack-growth law at a set of points of crack front, which enables the crack shape change during propagation to be traced. The stress intensity factors along the crack front are estimated by the three-dimensional finite element method. The technique has also accommodated an automatic procedure for the regeneration of finite element models as the crack grows, so that the prediction of complex crack shape change undergoing particularly during the crack coalescence is made possible and easy. The fatigue growth behaviours at three typical growth stages, i.e. pre-coalescence, coalescence and post-coalescence, are analysed for two multiple crack configurations. The predicted results are also compared with those obtained by the ASME XI code and a ‘no interaction and immediate transition (NIIT)’ simplified method. It is shown that each individual crack before they touch propagates almost independently and the interaction between them is generally limited despite being dependent on actual crack configurations. The analyses of fatigue lives show that both the ASME XI code and the NIIT method give more conservative results than the present simulation technique; however, the NIIT method is relatively less conservative than the ASME XI code which is excessively conservative for the crack configuration examined. This revised version was published online in July 2006 with corrections to the Cover Date.     

Boundary element analysis of three‐dimensional cracks in anisotropic solids

This paper presents a boundary element analysis of linear elastic fracture mechanics in three‐dimensional cracks of anisotropic solids. The method is a single‐domain based, thus it can model the solids with multiple interacting cracks or damage. In addition, the method can apply the fracture analysis in both bounded and unbounded anisotropic media and the stress intensity factors (SIFs) can be deduced directly from the boundary element solutions. The present boundary element formulation is based on a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. While the former is collocated exclusively on the uncracked boundary, the latter is discretized only on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (COD) (i.e. displacement discontinuity, or dislocation) is treated as a unknown quantity on the crack surface. This formulation possesses the advantages of both the traditional displacement boundary element method (BEM) and the displacement discontinuity (or dislocation) method, and thus eliminates the deficiency associated with the BEMs in modelling fracture behaviour of the solids. Special crack‐front elements are introduced to capture the crack‐tip behaviour. Numerical examples of stress intensity factors (SIFs) calculation are given for transversely isotropic orthotropic and anisotropic solids. For a penny‐shaped or a square‐shaped crack located in the plane of isotropy, the SIFs obtained with the present formulation are in very good agreement with existing closed‐form solutions and numerical results. For the crack not aligned with the plane of isotropy or in an anisotropic solid under remote pure tension, mixed mode fracture behavior occurs due to the material anisotropy and SIFs strongly depend on material anisotropy. Copyright © 2000 John Wiley & Sons, Ltd.     

Fatigue crack growth in a coarse-grained iron–silicon alloy

The fatigue crack growth in a coarse-grained Fe-2 wt% Si alloy is investigated in considerable detail. At room temperature, the material is quasi-brittle and the failure mode is mixed cleavage. Under a mode-I cyclic loading, the crack can overcome the barrier effect of grain boundaries, which dominates the overall damage evolution. Associated with the geometrically necessary crack front branching, there are two possible break-through modes for a fatigue crack to propagate across a high-angle grain boundary.     

Coupled meshfree and fractal finite element method for mixed mode two‐dimensional crack problems

This paper presents a coupling technique for integrating the element‐free Galerkin method (EFGM) with the fractal finite element method (FFEM) for analyzing homogeneous, isotropic, and two‐dimensional linear‐elastic cracked structures subjected to mixed‐mode (modes I and II) loading conditions. FFEM is adopted for discretization of the domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the EFG and the finite element (FE) shape functions, satisfies the consistency condition thus ensuring convergence of the proposed coupled EFGM–FFEM. The proposed method combines the best features of EFGM and FFEM, in the sense that no special enriched basis functions or no structured mesh with special FEs are necessary and no post‐processing (employing any path independent integrals) is needed to determine fracture parameters, such as stress‐intensity factors (SIFs) and T‐stress. The numerical results show that SIFs and T‐stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also, a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack length to width ratio on the quality of the numerical solutions. A numerical example on mixed‐mode condition is presented to simulate crack propagation. As in the proposed coupled EFGM–FFEM at each increment during the crack propagation, the FFEM mesh (around the crack tip) is shifted as it is to the new updated position of the crack tip (such that FFEM mesh center coincides with the crack tip) and few meshless nodes are sprinkled in the location where the FFEM mesh was lying previously, crack‐propagation analysis can be dramatically simplified. Copyright © 2010 John Wiley & Sons, Ltd.     

Fatigue crack propagation under in‐phase and out‐of‐phase biaxial loading

Fatigue damage characteristics of aluminium alloy under complex biaxial loads such as in‐phase and out‐of‐phase loading conditions and different biaxiality ratios have been investigated. The effects of microscale phenomena on macroscale crack growth were studied to develop an in‐depth understanding of crack nucleation and growth. Material characterization was conducted to study the microstructure variability. Scanning electron microscopy was used to identify the second phase particles, and energy dispersive X‐ray spectroscopy was performed to analyse their phases and elements. Extensive quasi‐static and fatigue tests were conducted on Al7075‐T651 cruciform specimens over a wide range of load ratios and phases. Detailed fractography analysis was conducted to understand the crack growth behaviour observed during the fatigue tests. Significant differences in crack initiation and propagation behaviour were observed when a phase difference was applied. Primarily, crack retardation and splitting were observed because of the constantly varying mode mixity caused by phase difference. The crack growth behaviour and fatigue lives under out‐of‐phase loading were compared with those under in‐phase loading to understand the effect of mixed‐mode fracture.