Prediction of non-propagating fretting fatigue cracks in Ti6Al4V sheet tested under pin-in-dovetail configuration: Experimentation and numerical simulation

This paper presents the results of fretting fatigue tests carried out on Ti6Al4V sheet specimens in contact with carbide rod in a cylinder-on-flat contact configuration. A new methodology of carrying out fretting fatigue experiments is proposed and successfully implemented using a pin-in-dovetail and pin-in-hole configuration. The advantage of this configuration is the simplicity and ease of application. The tests are carried out on MTS 810 at different loads, constant frequency (30 Hz) and ambient conditions. These tests reveal that the crack initiation and propagation are dependent on the applied load and the configuration of the contact. At low loads, non-propagating cracks are observed in the pin-in-dovetail configuration using metallurgical microscope. At high loads these cracks become longer but are still non-propagating. Numerical simulation using elastic–plastic material model is carried out to determine stress intensity factor and the mode of crack propagation. Maximum principal stress damage criteria approach is used to predict the crack initiation sites under different loads and a strong correlation with experimental results is observed. The crack propagation is simulated using XFEM, which successfully simulates the non-propagating crack length.     

Prediction of crack propagation in layered ceramics with strong interfaces

The crack propagation under flexure in layered ceramics designed with strong interfaces and high compressive residual stresses is investigated by means of FE simulations and compared with experimental observations on Al₂O₃-ZrO₂ multilayered ceramics. The change of crack propagation direction on the interface is assessed based on the strain energy density and maximum tangential stress criteria. The influence of the layer thickness on the crack propagation direction is evaluated. The estimated crack path (crack deflection angle) obtained through FE calculations is in agreement with the experimental observations. The results can be used for the design of layered ceramics with enhanced crack growth resistance.     

Fatigue crack propagation simulation in an aircraft engine fan blade attachment

This paper discusses the computation of three-dimensional fatigue crack growth rates in a typical military aircraft engine fan blade attachment under centrifugal and aerodynamic loads. The three-dimensional crack growth simulations utilize FRANC3D, a state-of-the-art crack propagation software developed at Cornell University, which uses boundary elements and linear elastic fracture mechanics. With an existing three-dimensional finite element contact stress analysis with a prescribed coefficient of friction (COF) along the contact surface, the displacements and stress intensity factors are calculated on the crack leading edge to yield crack propagation trajectories and growth rates. Due to complex geometry of the fan blade attachment and loading conditions, all three-fracture modes are considered and the associated stress intensity factors (SIF) are calculated using the Crack Opening Displacement (COD) approach. Crack propagation trajectories under mixed-mode conditions are obtained using the planar and maximum tangential stress crack-extension criteria. The fatigue crack in the blade attachment is subjected to an over speed mission cycle that includes high cycle frequencies (i.e., spectrum load) and the crack growth rate is predicted utilizing the Forman–Newman–de Koning (FNK) model. Scanning Electron Microscope (SEM) images of a cracked component from an engine ASMET (Accelerated Simulated Mission Endurance Test) are used to evaluate and compare the simulation results. The calculated SIF's from the simulations indicate a strong Mode-I (K_I) and Mode-III (K_III) interaction at the edge of contact (EOC). However, on the free surface it is primarily a crack opening (K_I) condition only. The crack growth rates are determined using the planar extension criterion which correlates better with the test data than the maximum tangential stress extension criteria.     

A fracture mechanics model for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems

A computational model is presented for the analysis of micro-pitting in regard to lubricated rolling–sliding contact problems. This model assumes the appearance of an initial microcrack on the contact surface due to the mechanical or thermal treatment of the material, and as a consequence of an on-going process in early the stage of exploitation. The discretised model of the contacting mechanical elements is subjected to normal loading (Hertzian contact pressure), tangential loading (friction between contacting surfaces) and internal pressure to the crack surfaces. Crack propagation is predicted as follows: (1) using modified maximum tangential stress criterion, which takes into account the influence of stress intensity factors K_I and K_II, T-stress, stress on the crack’s surface caused by lubricant pressure inside the crack, and the critical distance ahead of the crack tip and (2) the classical maximum tangential stress criterion, which only takes into account the influence of the stress intensity factors K_I and K_II. The stress intensity factor based on these two criteria is then used in a short crack growth theory to determine the fatigue life of an initial crack to extent up to micro-pit. The developed model is applied to a real spur gear pair.     

Modelling dynamic crack propagation using the scaled boundary finite element method

This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi‐analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack‐tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode‐I and mix‐mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. Copyright © 2011 John Wiley & Sons, Ltd.     

An analytical method for mixed-mode propagation of pressurized fractures in remotely compressed rocks

An analytical method for mixed-mode (mode I and mode II) propagation of pressurized fractures in remotely compressed rocks is presented in this paper. Stress intensity factors for such fractured rocks subjected to two-dimensional stress system are formulated approximately. A sequential crack tip propagation algorithm is developed in conjunction with the maximum tensile stress criterion for crack extension. For updating stress intensity factors during crack tip propagation, a dynamic fictitious fracture plane is used. Based on the displacement correlation technique, which is usually used in boundary element/finite element analyses, for computing stress intensity factors in terms of nodal displacements, further simplification in the estimation of crack opening and sliding displacements is suggested. The proposed method is verified comparing results (stress intensity factors, propagation paths and crack opening and sliding displacements) with that obtained from a boundary element based program and available in literatures. Results are found in good agreements for all the verification examples, while the proposed method requires a trivial computing time.     

自适应有限元-离散元算法、ELFEN软件及页岩体积压裂应用

该文介绍流体-固体-断裂耦合分析的自适应有限元（FE）-离散元（DE）算法,引进一款新近基于该方法研发的数值计算软件ELFEN,并将其应用于页岩分段体积压裂的三维数值计算和机理分析。该方法引入有限元应力恢复的超收敛拼片恢复（SPR）法,获得应力的超收敛SPR解,利用SPR解估计常规有限元解的误差,通过裂纹尖端局部区域的自适应网格重划分获得高精度应力解答并得以有效描述裂纹动态扩展,形成分析策略和求解方案。数值算例表明该算法和软件分析流体-固体-断裂耦合作用下单一、多水平井分段体积压裂的可靠性、有效性和实用性。     

Crack propagation from a pre-existing flaw at a notch root. I. Introduction and general form of the stress intensity factors at the initial crack tip

This paper and its companion are devoted to the study of crack kinking from some small pre-existing crack originating from a notch root (the notch root radius being zero). Both the notch boundaries and the initial crack are allowed to be curved; also, the geometry of the body and the loading are totally arbitrary. The ingredients required are knowledge of the stress intensity factors at the initial crack tip and use of a suitable mixed mode propagation criterion. This paper is devoted to the first point, and more specifically to establishing the general (that is, not yet fully explicit) form of the formulae giving these stress intensity factors. The method used is based on changes of scale (homogeneity properties of the equations of elasticity) on the one hand, and on continuity of the displacement and stresses at a given, fixed point with respect to the crack length on the other hand. The formulae derived for the stress intensity factors at the tip of the small crack are of universal value: they apply to any situation, whatever the geometry of the body, the notch and the crack and whatever the loading, the stress intensity factors depending always only upon the `stress intensity factor of the notch' (the multiplicative coefficient of the singular stress field near the notch root in the absence of the crack), the length of the crack, the aperture angle of the notch and the angle between its bisecting line and the direction of the crack.     

Cleavage to quasicleavage fracture transition in steels

Abstract

The cleavage behaviour of plain carbon steels containing from 0· 2 to 0·8%C has been investigated. It is observed that each steel displays two characteristic temperatures at which a transition in the mode of fracture occurs. These are the transition temperatures for cleavage T_c and for general yielding T_g. At temperatures below T_c, the steels fail by pure cleavage. This involves the generation of a cleavage crack nucleus in a carbide particle followed by cleavage crack propagation. The cleavage fracture stress σ _f is independent of temperature. Between temperatures T_c and T_g, the steels fail by quasicleavage. This involves the generation of a crack nucleus by a localised fibrous process followed by cleavage crack propagation. The crack nucleation stage is shear stress controlled and therefore the quasicleavage fracture stress σ_q increases with decreasing test temperature. Above temperature T_g, failure occurs at or after general yielding.

MST/1045     

基于分形理论不同装药量的爆破动焦散线实验研究

为研究装药量对爆生裂纹扩展行为的影响。采用透射式数字激光动态焦散线实验系统,分析了不同装药量的爆生裂纹扩展规律,并基于计盒维数的计算原理,编写MATLAB程序计算爆生裂纹的分形维数。结果表明:①起爆后裂纹扩展分2阶段,Ⅰ阶段(0～114.3μs)为爆炸应力波与爆生气体对裂纹尖端的作用,在裂纹的起裂时刻扩展速度达到峰值,随即迅速降低;Ⅱ阶段(114.3μs～裂纹止裂)在反射应力波对裂纹尖端的作用下,裂纹扩展速度继续提升;②裂纹扩展速度峰值、动态应力强度因子峰值、粉碎区面积、爆生裂纹分形维数与装药量正相关;③采用回归分析与线性拟合的方法,得到了裂纹扩展速度与裂纹扩展轨迹分形维数的线性关系,同一裂纹扩展速度的变化符合分形规律。     

Stress intensity factors at tips of branched cracks under various loadings

Several papers have been published on branched cracks by using various analytical methods, but most of them are concerned with special crack geometries or special loading conditions, and often give unreliable values for cracks with short branches or with small branching angles. The purpose of this paper is to give reliable formulae and new results of the stress intensity factors of various branched cracks in a wide plate. The analysis is based on the body force method combined with a perturbation procedure, and the stress intensity factors at the tips of all the branches and the main crack are given by power series formulae. Numerical results for typical branched cracks are discussed.     

Fatigue crack propagation and cyclic deformation at a crack tip

The fatigue crack propagation relation da/dN = f(R)ΔK² can be derived with three assumptions: small scale yielding, material homogeneity and that crack tip stresses and strains are not strongly affected by plate thickness. f(R) is a constant at a given stress ratio, R. The effects of plate thickness and stress ratio on crack tip deformation and fatigue crack growth in 2024-T351 aluminum alloy were studied. High ΔK level in a thin specimen causes crack tip necking. Necking is more pronounced at high stress ratio. Necking causes high maximum strain near a crack tip, ε_max, and fast crack growth rate. In order to avoid the effects of crack tip necking, plates thicker than 2.5 (ΔK/σ_Y(c))² should be used.     

Extended structural criterion for numerical simulation of crack propagation and coalescence under compressive loads

An extension of the Neuber-Novozhilov structural fracture propagation criterion is presented for mode I (tensile) and mode II (shear) propagation under compressive loads. In addition to allowing numerical simulation of crack growth, the criterion can be used to model change of propagation mode, crack branching, and coalescence. The criterion can be applied effectively when the SIF is calculated accurately (at least three significant digits). A numerical method is suggested for this purpose that consists of complementing the complex variable hypersingular boundary element method (CVH-BEM) with special procedures for automatically tracing crack propagation and coalescence. The CVH-BEM code with the structural criterion has been used to investigate crack propagation in compression for both small and non-small fracture process zone (FPZ). The results of numerical experiments are in agreement with the analytical conclusions available for the case of small FPZ that indicates the possibility of three distinct patterns of crack propagation under external compressive loads. These are: (i) smooth curvilinear tensile (wing) cracks, (ii) stair-step propagation pattern with changing modes, and (iii) in plane shear propagation. The numerical study also indicates that when the critical size of the FPZ is large enough, the non-singular terms in the expansion of the stress functions strongly influence the crack trajectories. Specifically, this occurs when the size of the FPZ approaches a quarter of the half-length of the initial crack. Calculations for a closed initial crack in a half-space under compression illustrate the general features of crack propagation. Although the dominant direction of crack growth is that of the applied compressive stress, the pattern of propagation strongly depends on the particular geometry, critical size of the FPZ, and the ratio of shear-to-tensile microscopic strength.     

Quasi‐static crack propagation in plane and plate structures using set‐valued traction‐separation laws

We introduce a numerical technique to model set‐valued traction‐separation laws in plate bending and also plane crack propagation problems. By using of recent developments in thin (Kirchhoff–Love) shell models and the extended finite element method, a complete and accurate algorithm for the cohesive law is presented and is used to determine the crack path. The cohesive law includes softening and unloading to origin, adhesion and contact. Pure debonding and contact are obtained as particular (degenerate) cases. A smooth root‐finding algorithm (based on the trust‐region method) is adopted. A step‐driven algorithm is described with a smoothed law which can be made arbitrarily close to the exact non‐smooth law. In the examples shown the results were found to be step‐size insensitive and accurate. In addition, the method provides the crack advance law, extracted from the cohesive law and the absence of stress singularity at the tip. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of microstructure on fatigue crack propagation behavior in a bi-modal TC11 titanium alloy fabricated via laser additive manufacturing

In this study, the crack propagation behaviors in the equiaxed and equiaxed-columnar grain regions of a heat-treated laser additive manufacturing (LAM) TC11 alloy with a special bi-modal microstructure are investigated. The results indicate that the alloy presents a special bi-modal microstructure that comprises a fork-like primary α (α_p) phase surrounded by a secondary α colony (α_s) in the β phase matrix after the heat treatment is completed. The samples demonstrate a fast crack growth rate with larger da/dN values through the equiaxed grain sample versus across the equiaxed-columnar grain sample at low ΔK values (<13.8). The differences that are observed between the crack propagation behaviors (in the crack initiation stage) of the samples can be mostly attributed to the different size and morphology of the α_p lamellae and α_s colony within the grains in the equiaxed and columnar grain regions rather than the grain boundaries. The cracks prefer to grow along the α/β boundary with a smooth propagation route and a fast propagation rate in the equiaxed grain region, where the α_p and α clusters have a large size. However, in the columnar grain region, small and randomly distributed α_p lamellae generate a zigzag-shaped propagation path with a reduction in the da/dN value. Additionally, the change in the size of the α_p lamellae in the equiaxed grains (heat affected bands, HAB) is also observed to influence the propagation behavior of the crack during the crack initiation stage.     

悬臂弯曲加载表面裂纹长度与施力点位移的相关性研究

在悬臂弯曲加载方式下,采用五件带缺口光滑板状试样,通过循环载荷控制模式,研究了表面裂纹长度2c与试样施力点位移的相关性,结果表明:表面裂纹长度与施力点位移的谷值无相关性,但与施力点位移的峰值DP具有明显的相关性,即在表面裂纹扩展初期,DP几乎不发生变化,但随着表面裂纹的进一步扩展,DP开始增加,在表面裂纹扩展的后期,DP显著增加;在表面裂纹扩展的中后期,2c与DP满足递增多项式关系。根据2c与DP的函数关系,可为实现复杂环境条件下表面裂纹长度的自动化测量提供依据。     

Crack tip shielding by asperity contact as determined by acoustic measurements

Asperity contact along the fracture surface of a crack is one of the mechanisms of crack closure. This contact shields the crack tip, in part, from the externally applied driving force. We have now succeeded in using information from acoustic transmission and diffraction experiments, obtained under plane strain conditions, to determine the size and density of the contacting asperities in the closure region. We have also succeeded in estimating values for the static stress across a partially closed crack as well as the stress intensity factor,K_I (local), which shields the crack tip below the stress intensity factor K_Iclosure at which the first contact during unloading occurs. It is suggested that when crack closure has an important influence on crack propagation, the shielding stress intensity factor provides information that can be used to estimate the fatigue crack propagation rate.     

Finite element modelling and analysis of crack shape evolution in mode-I fatigue Middle Cracked Tension specimens

A numerical procedure was employed to study the shape evolution of fatigue cracks in Middle Cracked Tension specimens. This iterative procedure consists of a 3D finite element analysis to obtain the displacement field in the cracked body, calculation of stress intensity factors along crack front and definition of local crack advances considering the Paris law. Numerical predictions were compared with experimental crack shapes with a good agreement. The evolution of crack shape was analysed for different propagation conditions considering robust dependent parameters. Two main propagation stages were identified: an initial transient stage highly dependent on initial crack shape and a stable stage where the crack follows preferred paths. Mathematical models were proposed for transient and stable stages consisting of exponential and polynomial functions, respectively. The transition between both stages was defined considering two criteria: the rate of shape variation and the distance to stable shape. Finally, the crack shape change was linked with the distribution of stress intensity factor along crack front.     

Modelling of Surface Crack Growth under Lubricated Rolling–Sliding Contact Loading

The paper describes modelling approach to computational simulation of surface crack growth subjected to lubricated rolling–sliding contact conditions. The model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact and the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The motion of the contact sliding load is simulated with different load cases. The strain energy density (SED) and maximum tangential stress (MTS) crack propagation criteria are modified to account for the influence of internal pressure along the crack surfaces due to trapped fluid. The developed model is used to simulate surface crack growth on a gear tooth flank, which has been also experimentally tested. It is shown that the crack growth path, determined with modified crack propagation criteria, is more accurately predicted than by using the criteria in its classical form.     

Fatigue Crack Growth and Fracture of 30 wt% B4C/6061Al Composites

This paper focuses on studying the fatigue crack growth (FCG) characteristics and fracture behaviours of 30 wt% B₄C/6061Al composites fabricated by using powder metallurgy and hot extrusion method. Compact tension (CT) specimens having incisions parallel to the extrusion direction (T‐D) and perpendicular to the extrusion direction (E‐D) were investigated through FCG tests. Results show that, at low/medium stress‐intensity factor range levels (ΔK ≤ 9), crack propagation rate in E‐D specimens is lower than that in T‐D specimens because the elongated B₄C particles parallel to the extrusion direction in E‐D specimens can deflect the crack. The scanning electron microscope micrographs of the fractured surface illustrate that crack mainly propagates in the matrix alloy at the initial stage of its propagation and propagates more remarkably near the particle‐matrix interface with the increase of ΔK value. B₄C particles are also found to be easy to fracture during the rapid crack propagation. Based on fracture analyses, considering the impacts of factors like crack deviation, plastic zone size at the crack tip, and crack driving force, a 2‐D crack propagation model was developed to study the fatigue crack propagation mechanism in the 30 wt% B₄C/6061Al composite.