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.     

Extended FEM modeling of crack paths near inclusions

The extended FEM is applied to model crack growth near inclusions. A procedure to handle different propagation rates at different crack tips is presented. The examples considered investigate uniform tension as well as equibiaxial tension under plane strain conditions. A parameter study analyzes the effects on the crack path when changing the relative stiffness between inclusion and matrix material, the relative distance between initial crack and inclusion, and the size of the inclusion. Both edge cracks and internal cracks are studied. An example with an internal crack near an inclusion is presented, where both crack tips propagate at different growth rates until one crack tip eventually stops growing, as the related energy release rate drops below the critical value. In another example, only one crack tip propagates initially, but eventually, the energy release rate of the second crack tip becomes critical, and both crack tips propagate. Finally, an example of two cracks near an inclusion is presented in which up to four crack tips propagate simultaneously. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of displacements around fatigue cracks using image analysis of in‐situ scanning electron microscope images

A technique to in‐situ measure the displacements in the vicinity of the crack tip during fatigue crack propagation has been developed. High‐resolution images of the crack tip were taken continuously throughout the fatigue load cycles with a scanning electron microscope (SEM), and an image analysis program was used to determine the displacements at different positions with respect to the crack tip. The displacements were then used to determine crack shapes and compliance curves. The measured crack shapes show a general √r dependence versus the distance to the crack tip. However, close to the crack tip the crack shape is clearly affected by plastic deformation, even in cases when small scale yielding prevails. The compliance curve measurements close to the crack tip can be used to determine the global stress level when the crack surfaces are separated, so that the exact opening and closure stresses can be determined.     

Role of plastic zone in crack growth direction criterion under mixed mode loading

An approach to determine the crack growth direction under mixed-mode loading conditions is presented. The plastic zone shape around the crack tip is applied for evaluating angle of crack propagation. It is proposed that a mixed-mode crack will extend along the plastic zone radius with a minimum value. The prediction of the proposed criterion is compared with the experimental data and other models. The agreement is fairly good.     

Determination of Fracture Parameters for Multiple Cracks of Laminated Composite Finite Plate

A predictive method for estimation of stress state at zone of crack tip and assessment of remaining component lifetime depend on the stress intensity factor (SIF). This paper discusses the numerical approach for prediction of first ply failure load (F_L), progressive failure load, SIF and critical SIF for multiple cracks configurations of laminated composite finite plate using finite element method (FEM). The Hashin and Chang failure criterion are incorporated in ABAQUS using subroutine approach user defined field variables (USDFLD) for prediction of progressive fracture response of laminated composite finite plate, which is not directly available in the software. A tensile experiment on laminated composite finite plate with stress concentration is performed to validate the numerically predicted subroutine results, shows excellent agreement. The typical results are presented to examine effect of changing the crack tip distance (S), crack offset distance (H), and stacking fiber angle (θ) on F_L, and SIF .     

Fatigue growth prediction of center slant crack in rectangular plate

This paper presents a numerical prediction model of mixed‐mode crack fatigue growth in a plane elastic plate. It involves a formulations of fatigue growth of multiple crack tips under mixed‐mode loading and a displacement discontinuity method with crack‐tip elements (a boundary element method) proposed recently by Yan is extended to analyse the fatigue growth process of multiple crack tips. Due to 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. Crack extension is conveniently modelled by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. As an example, the present numerical approach is used to analyse the fatigue growth of a centre slant crack in a rectangular plate. The numerical results illustrate the validation of the numerical prediction model and can reveal the effect of the geometry of the cracked plate on the fatigue growth.     

Growth prediction of two interacting surface cracks of dissimilar sizes

When multiple cracks approach one another, the stress intensity factor changes due to the interaction of the stress field. This causes variation in the crack growth rate and shape of cracks. In particular, when cracks are parallel to the loading direction, their shape becomes non-planar due to the mixed mode stress intensity factor. In this study, the growth of interacting surface cracks was simulated by using the S-version finite element method, in which a local detailed finite element mesh (local model) is superposed on a coarse finite element model (global model) representing the global structure. First, simulations were performed for fatigue crack growth experiments and the method validity was shown. Second, simulations were conducted for various relative sizes and spacings of twin cracks. It was shown that the offset distance and the relative size were both important parameters to determine the interaction between two surface cracks; the smaller crack stopped growing when the difference in size was large. It was possible to judge whether the effect of interaction should be considered based on the correlation between the relative spacing and relative size.     

Cohesive and non-cohesive fracture by higher-order enrichment of XFEM

A comprehensive study is performed on the use of higher-order terms of the crack tip asymptotic fields as enriching functions for the eXtended FEM (XFEM) for both cohesive and traction-free cracks. For traction-free cracks, the Williams asymptotic field is used to obtain highly accurate stress intensity factors (SIFs), directly from the enriched degrees of freedom without any post-processing. The low accuracy of the results of the original research on this subject by Liu et al. [Int. J. Numer. Meth. Engng., 2004; 59:1103–1118] is remedied here by appropriate modifications of the enrichment scheme. The modifications are simple and can be easily included into an XFEM computer code. For cohesive cracks, the relevant asymptotic field is used, and two widely used criteria including the SIFs criterion and the stress criterion are examined for the crack growth simulation. Both linear and nonlinear cohesive laws are used. For the stress criterion, averaging is avoided due to the highly accurate crack tip approximation because of the higher-order enrichment. Then, a modified stress criterion is proposed, which is shown to be applicable to a wider class of problems. Several numerical examples, including straight and curved cracks, stationary and growing cracks, single and multiple cracks, and traction-free and cohesive cracks, are studied to investigate in detail the robustness and efficiency of the proposed enrichment scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Complete Tangent Stiffness for eXtended Finite Element Method by including crack growth parameters

The eXtended Finite Element Method (XFEM) is a useful tool for modeling the growth of discrete cracks in structures made of concrete and other quasi‐brittle and brittle materials. However, in a standard application of XFEM, the tangent stiffness is not complete. This is a result of not including the crack geometry parameters, such as the crack length and the crack direction directly in the virtual work formulation. For efficiency, it is essential to obtain a complete tangent stiffness. A new method in this work is presented to include an incremental form the crack growth parameters on equal terms with the degrees of freedom in the FEM‐equations. The complete tangential stiffness matrix is based on the virtual work together with the constitutive conditions at the crack tip. Introducing the crack growth parameters as direct unknowns, both equilibrium equations and the crack tip criterion can be handled within the same standard nonlinear iterations. This new solution strategy is believed to provide the modeling capabilities to deal with simultaneous growth of several cracks. A cohesive crack modeling is used. The method is applied to a partly cracked XFEM element of linear strain triangle type with the crack length as the unknown crack growth parameter. In this paper, two examples are given. The first example verifies the theory and the implementation. The second example is the benchmark test three point bending test, where the efficiency of the complete tangential behavior is shown. Copyright © 2013 John Wiley & Sons, Ltd.     

A plastic fracture mechanics model for characterization of multiaxial low-cycle fatigue

The near-tip stress and strain fields of small cracks in power-law hardening materials are investigated under plane-stress, general yielding, and mixed mode I and II conditions by finite element analyses. The characteristics of the near-tip strain fields suggest that the experimental observations of shallow surface cracks (Case A cracks) propagating in the maximum shear strain direction can be explained by a fracture mechanics crack growth criterion based on the maximum effective strain of the near-tip fields for small cracks under general yielding conditions. The constant effective stress contours representing the intense straining zones near the tip are also presented. The results of the J integral from finite element analyses are used to correlate to a fatigue crack growth criterion for Case A cracks. Based on the concept of the characterization of fatigue crack growth by the cyclic J integral, the trend of constant J contours on the Γ-plane for Case A cracks compares well with those of constant fatigue life and constant crack growth rate obtained from experiments.     

Crack growth prediction and non-linear analysis for an elasto-plastic solid

In this paper, a variable radius for the plastic zone is introduced and a maximum principal stress criterion is proposed for the prediction of crack initiation and growth. It is assumed that the direction of crack initiation coincides with the direction of the maximum principal stress. The von Mises yield criterion is applied to define the plastic zone, instead of assuming a plastic zone with a constant distance r from the crack tip. An improvement is made to this fracture criterion, and the criterion is extended to study the crack growth characteristics of mixed mode cracks. Based on the concept of frictional stress intensity factor, k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The proposed crack growth model is discussed by comparing the experimental results with those obtained using the maximum principal stress criterion.     

Mixed mode fatigue crack growth: A literature survey

The applications of fracture mechanics have traditionally concentrated on crack growth problems under an opening or mode I mechanism. However, many service failures occur from growth of cracks subjected to mixed mode loadings. This paper reviews the various criteria and parameters proposed in the literature for predictions of mixed mode crack growth directions and rates. The physical basis and limitations for each criterion are briefly reviewed, and the corresponding experimental supports are discussed. Results from experimental studies using different specimen geometries and loading conditions are presented and discussed. The loading conditions discussed consist of crack growth under mode II, mode III, mixed mode I and II, and mixed mode I and III loads. The effects of important variables such as load magnitudes, material strength, initial crack tip condition, mean stress, load non-proportionality, overloads and crack closure on mixed mode crack growth directions and/or rates are also discussed.     

拉—拉疲劳下15MnMoVN多裂纹扩展研究

为分析单裂纹或多裂纹在裂纹面承受疲劳拉伸载荷作用下尖端应力强度因子变化规律和裂纹形貌变化以及疲劳寿命情况,以含不同初始长深比的半椭圆单裂纹或双裂纹的薄片试样为研究对象,对试样在应力比R=0.1的疲劳拉伸载荷下单裂纹或双裂纹情况进行了仿真分析。建立含裂纹试样的有限元模型,仿真分析了裂纹在扩展过程中尖端应力强度因子的分布情况,并将单裂纹扩展结果与双裂纹相互作用影响下的结果进行了对比研究;进行含裂纹试样的疲劳实验,分析了含单裂纹或双裂纹的试样的断裂面的形成原因,并验证仿真结果正确性。结果表明,裂纹面之间的相互作用会逐渐影响裂纹的扩展方向、扩展速率以及在扩展过程中尖端应力强度因子的变化趋势;而且初始形貌为半椭圆形的双裂纹在相互作用影响下会逐渐过渡到半圆形。     

Analysis of crack interactions at adjacent holes and onset of multi-site fatigue damage in aging airframes

Focusing on the geometry of one hot spot in airframes, this paper discusses the onset of the interaction of two collinear cracks at adjacent holes and defines the onset as a criterion for multi-site fatigue damage failure. The finite element method is used to calculate the stress intensity factors at the tips of two collinear cracks at adjacent holes growing towards each other. The stress intensity factor is found to increase rapidly at the onset of interaction. Since a rapid increase in stress intensity factor results in a rapid and unstable growth of the crack, the onset of the interaction is proposed as the point where the multi-site fatigue damage starts. A criterion to avoid multi-site fatigue damage locally is then established based on the separation distance of two crack tips at the onset of the interaction. To speed up the simulation of crack growth under multi-site fatigue damage with the finite element method, a semi-empirical criterion is derived to determine the time at which the stress intensity factors at the tips of the cracks correlate. The numerical examples show that the proposed criterion saves simulation time while incurring negligible relative error in the computation of the final crack length.     

A numerical study on the effect of symmetric crack flank holes on fatigue life extension of a SENT specimen

The crack growth retardation is studied theoretically by drilling two symmetric holes at appropriate locations along the crack flanks. A fatigue crack growth code for two‐dimensional elastic problems is developed to approve the effectiveness of this method. The crack growth retardation was examined using a parametric study both on the arrangements of the flank holes and the diameters of holes. The numerical results reveal that for some cases, the presence of flank holes significantly decreases the stress concentration around the crack tip and its stress intensity factor. The best positions for crack flank holes to provide the highest crack growth retardation are shown to be where the line connecting the two centres of holes passes the crack tip. A larger hole diameter and a closer distance between the flank holes and the crack tip result in lower crack growth rate and higher fatigue life.     

J-Q characterization of propagating cracks

An investigation is performed to determine to what extent the state at a growing crack tip vicinity can be characterised by J and Q calculated from FE analyses of successively stationary crack tip positions. FE models in two-dimensionals of single edge notch bend and double edge cracked panel specimens with several different crack lengths are used to cover a range of load and constraint levels. The stress and strain fields are compared between different specimens keeping J- and Q-values equal. A remeshing technique in the commercial FE-code ABAQUS is used to enhance the efficiency of the analysis. The results show that the J-Q-theory provides reasonably accurate crack tip characterization also for growing cracks. This leads to the conclusion that FE analyses of successive stationary cracks rather than full FE propagation analyses are sufficient. The limit of validity for propagation is similar to the validation limit for the stationary case, although somewhat more restrictive.     

Crack interaction modelling

The growth characteristics of short fatigue cracks under axial loading were investigated using specimens of the ferritic–martensitic steel F82H-mod. Interest focused on crack propagation due to coalescence, which proved to be the dominant mechanism of crack growth. Crack propagation due to coalescence under a certain loading state is strongly influenced by the microstructure of the material on the one hand and by the interaction of cracks on the other. This study deals with an elasto-plastic fracture mechanics analysis of two interacting cracks neglecting the microstructural influence. Finite element calculations based on a Ramberg–Osgood model for the material properties were performed to quantify the interaction of two cracks in terms of an interaction function Y depending on the material and crack configuration. Finally, a neural network was trained to determine the interaction function for two cracks within the range of interest.     

Dynamic initiation and propagation behaviour of sub-interfacial cracks in PMMA/aluminium bi-material system

The paper describes studies on the dynamic initiation and growth of sub‐interfacial cracks in a PMMA/aluminium bi‐material system using high‐speed photography combined with the method of caustics. Dynamic fracture phenomena such as crack propagation trajectories, crack velocity, phase angle and stress intensity factor were determined from recordings of a series of dynamic caustic patterns surrounding the propagating sub‐interfacial crack tip.. There is a considerable influence of the distance between the interface and the crack on fracture characterization.     

Corrosion Fracture of Structural Metallic Materials: Effect of Electrochemical Conditions in Crack

Abstract: The work is a compressed review based on the summarised results and the original approach for study of corrosion crack growth, taking into account local electrochemical conditions in the crack tip, which was developed at the Karpenko Physico‐Mechanical Institute of NASU. The model scheme of the pre‐fracture zone in the corrosion crack tip, which can be defined by the local values of pH of solution, electrode potential of metal E and stress intensity factor K_I is proposed. For its realisation, the special method and testing equipment for corrosion crack growth study and local electrochemical measurements in the crack were developed. The variation of the electrochemical conditions in corrosion cracks was studied, and it has been found that some stabilised levels of the pH and E values can be achieved in the tip of a non‐propagating and a propagating crack under static and cyclic loading during of exposure time. On this ground, the method for forecasting of the threshold stress intensity factor K_ISCC under stress corrosion cracking was proposed using these characteristic values of pH and E. This method was also adopted for the determination of the threshold stress intensity factor K_th under corrosion fatigue. The special method for determining corrosion fatigue crack growth rate diagrams based on consideration of extreme electrochemical conditions in the crack tip was developed. It has been proven that such diagrams reflect the extreme influence of the environmental factor on corrosion fracture of material, and they may be recommended as the base for the remaining lifetime calculation of the structural elements exploited under environmental conditions.