CRACK TIP FIELDS UNDER NON-STEADY CREEP CONDITIONS—I. ESTIMATES OF THE AMPLITUDE OF THE FIELDS

Abstract— Under non-steady creep conditions, the stress and strain rate fields near the tip of a stationary crack can be described by the singular fields of Hutchinson, Rice and Rosengren for power-law creeping materials. Estimation formulae are presented for describing the amplitude of these fields under load and displacement controlled boundary conditions. For constant loading, the formulae reduce to the result of Riedel and Rice for short times after load application and to the steady state line integral C * for long times. At intermediate times, the estimate is validated by detailed finite-element computation. For displacement-controlled loading, the amplitude of the near-tip fields is shown to fall rapidly, consistent with finite-element analysis. The implications of the results for data collection and defect assessments are discussed in a companion paper.     

双压电材料界面力电耦合场奇异性研究

针对不同压电材料中界面裂纹尖端的扇形区域推导出了包含基本方程、裂纹面D-P边界条件和不同压电材料交界面处的边界条件的弱形式。在该弱形式的基础上,利用特征方程展开方法(eigenfunction expansion technique),可以得到一个分析压电材料裂纹尖端处力电耦合场奇异性的特殊的一维有限元列式。该一维有限元列式只需对扇形区域在角度方向上离散,最后的总体方程为一个二次特征根方程。求解该特征根方程就可以得到压电材料裂纹尖端处力电耦合奇异场的特征解。通过数值算例表明该方法可以准确而高效地计算压电材料裂纹尖端处力电耦合奇异场的特征解,进而用该方法研究了双压电材料界面力电耦合场的奇异性。     

PREDICTING THE EFFECTS OF LOAD RATIO ON THE FATIGUE CRACK GROWTH RATE AND FATIGUE THRESHOLD

The effect of the load ratio, R, on fatigue crack growth behaviour is analysed on the basis of the recently proposed inelastic discrete asperities model. A wide range of load ratios, both positive and negative, are examined. Particular emphasis is placed on compressive excursions, i.e. negative R loadings. The inelastic discrete asperities model is a micro-mechanical analysis based on the plastic crushing of a single asperity (or multiple asperities) located on the crack face close to the crack tip and under dominantly plane strain conditions. Experimental data have indicated that the primary crack face contacts which obstruct closure are immediately adjacent to the crack tip, although segments of the crack face more distant from the crack tip are not neglected. However, the more distant asperities are a part of the past crack advance history which does not influence current behaviour. By use of this model, it is shown that the effect of the load ratio can be adequately predicted once some baseline information on mechanical material properties and surface roughness is provided. The model also provides useful trend information and explains many of the observed phenomena, e.g. the ‘saturation’ of the compressive underload effects. For a constant applied nominal stress intensity factor range, ΔK_nom , it is shown that the effective stress intensity factor range, ΔK_eff , initially decreases as the positive R decreases (corresponding to the increasing influence of closure), reaches a minimum around R = 0, and then starts increasing with negative R (corresponding to the plastic crushing of the asperities which reduces closure), eventually reaching a saturation level below ΔK_nom . Conversely, for an assumption of a constant ΔK_eff , the applied ΔK_nom increases as the positive load ratio decreases, reaching a maximum around R = 0, and then decreases with more negative R values, eventually reaching again a saturation level (above ΔK_eff ). It is also shown that the effect of material hardness can be directly analysed based on this model.     

AN ASSESSMENT OF CRACK CLOSURE IN FATIGUE USING THE WESTERGAARD STRESS FUNCTION

Abstract— The residual stress fields at the tip of a fatigue crack have been evaluated using the Westergaard stress function. Using these values the loads at which the crack tip begins to open have been calculated to give U, Elber's effective stress range factor, as a function of stress ratio R, the ratio of applied stress range to yield stress, Δσ/σ_y, and the cyclic strain hardening exponent n. The computed values of U are shown to be in good agreement with measured values, and the predicted effect of prior high load cycles on the crack propagation rate at a lower cyclic load, on taking crack closure effects into account, is in excellent agreement with experimental results.     

The asymptotic structure of small-scale yielding interfacial free-edge joint and crack-tip fields

Summary The problem of the small-scale yielding (SSY) plane-strain asymptotic fields for the interfacial free-edge joint singularity is examined in detail, and comparisons are made with the interfacial crack tip. The geometries are idealized as isotropic elasto-plastic materials with Ramberg-Osgood power-law hardening properties bonded to a rigid elastic substrate. The resulting fields are shown to be singular and are presented in terms of radial and angular distributions of stress and displacement, and as idealized plastic slip-line sectors. A fourth-order Runge-Kutta numerical method provides solutions to fundamental equations of equilibrium and compatibility that are verified with those of a highly focused finite element (FE) analysis. It is shown that, as in the case of the crack, the asymptotic singular fields are only dependent on the hardening parameter and only a small range of interfacial mode-mix ratios are permitted. The order for the stress singularity may be formulated in terms of the hardening parameter and the elastic solution for incompressible material. The rigid-slip-line field for the interfacial free-edge joint is presented, and it is shown that there is some significant similarity between the asymptotic fields of the deviatoric polar stresses for the joint and the crack-tip having an elastic wedge sector.     

THE GROWTH OF SMALL FATIGUE CRACKS IN A LOW CARBON STEEL; THE EFFECT OF MICROSTRUCTURE AND LIMITATIONS OF LINEAR ELASTIC FRACTURE MECHANICS

The growth characteristics of small fatigue cracks were studied under rotary bending in a low carbon steel prepared with two ferrite grain sizes of 24 and 84 μm, and were compared with the growth characteristics of large through cracks in fracture mechanics type specimens. The effect of microstructure on crack growth rates and the interaction in growth behaviour between two neighboring small cracks were examined experimentally, and also the critical crack lengths above which linear elastic fracture mechanics (LEFM) is applicable were evaluated for small crack growth and for fatigue crack thresholds. It is found that small cracks grow much faster than large ones and also show growth rate perturbations due to grain boundaries. It is indicated that the critical crack lengths for fatigue crack thresholds are significantly shorter than those for small crack growth.     

THE APPLICABILITY OF NEURAL NETWORKS IN MODELLING THE GROWTH OF SHORT FATIGUE CRACKS

This paper examines the use of a neural network to model the chaotic behaviour of the growth of short fatigue cracks which are characterized by a decreasing crack growth rate with increasing crack length. Fatigue crack growth is modelled in terms of the Hobson short fatigue crack growth law. The neural network is exclusively trained and tested on Hobson's experimental data of short fatigue cracks propagating in a 0.4% carbon steel. The empirical constants d, α and C of Hobson's growth law are determined from the neural network predictions and are found to be within the following approximate ranges 63 < d < 400 (μm), −0.27 < α < 0.08 and 1 × 10⁻⁴ < C < 509 × 10⁻⁴ with no proportional relationship observed between the constant C and the applied cyclic stress. It is shown that neural networks are a viable computational tool for modelling the chaotic behaviour of short fatigue crack growth.     

CYCLIC CRACK RESISTANCE OF WELDED JOINTS WITH NON-UNIFORM FIELDS OF RESIDUAL WELDING STRESSES

Abstract— The use of linear elastic fracture mechanics to describe the kinetics of fatigue fracture of welded joints with high welding residual stresses (WRS) is experimentally evaluated in this paper. A correction analysis is used to show that the crack propagation rate of cracks in joints, as a function of the applied stress intensity factor, is linear on a log-log scale in the Paris regime when non-uniform fields of WRS are superimposed on the applied cyclic loading. It is shown that crack growth rates in joints with high WRS do not depend on the characteristics of the loading cycle. The parameters of the Paris exponential equation are determined by the initial WRS distribution, by the range of cyclic stresses and by the load ratio. A method for calculating the cyclic crack resistance of joints is proposed which explicitly allows for a non-uniform field of WRS that influences the fatigue crack growth rate.     

定向断裂控制爆破爆生裂纹扩展机理的实验研究

采用新型数字激光动态焦散线实验系统,对缺陷介质双孔定向断裂控制爆破裂纹扩展的动态行为进行了研究。结果表明,预制斜裂纹阻断了爆生主裂纹的扩展,最终两条主裂纹分别与翼裂纹形成相互勾连的形状。爆生主裂纹尖端以张拉应力场为主,其断裂为近似I型断裂。当爆生主裂纹运动到预制裂纹附近时,主裂纹端部应力场与预制裂纹尖端奇异应力场相互叠加,在预制裂纹尖端形成较强的拉剪应力场,且受已有主裂纹面的影响,预制裂纹扩展表现为弯向主裂纹面的弯曲断裂。研究结果可为含节理岩体定向断裂控制爆破提供理论依据。     

FATIGUE CRACK PROPAGATION BEHAVIOUR OF SHORT CRACKS; THE EFFECT OF MICROSTRUCTURE

–Fatigue cracks shorter than some critical length tend to propagate anomalously quickly. This paper examines the concept of a ‘critical length’, identifying three regimes of behaviour for different crack lengths. Some published work is examined, covering a wide range of different materials. It is concluded that there is an approximate correlation between the critical length for short crack behaviour and the scale of the microstructure. LEFM is difficult, if not impossible, to apply to cracks shorter than this critical length because the material surrounding a crack cannot be assumed to approximate to a homogeneous continuum. Suggestions are made for a fatigue design philosophy which incorporates short crack behaviour.     

金属材料疲劳裂纹扩展曲线的拟合方法研究

提出了一种金属材料疲劳裂纹扩展曲线(a~N曲线)的拟合方法,即修正的双曲函数拟合方法。为检验这种曲线拟合方法的适用性,利用2024-T42铝合金CCT试样的疲劳裂纹扩展试验数据,对该铝合金的疲劳裂纹扩展曲线进行了拟合分析,并给出了疲劳裂纹扩展速率和扩展寿命。通过疲劳裂纹扩展寿命计算结果和试验结果的对比分析,证明这种拟合方法具有较高的拟合精度。     

THE INFLUENCE OF TEST VARIABLES ON THE FATIGUE CRACK GROWTH THRESHOLD

Abstract— A microcomputer controlled fatigue crack growth and threshold testing system has been used to investigate the influence of test variables on the measured values of Δ K _th, the threshold for fatigue crack growth, using a C-Mn steel. The work has examined: (1) the influence of crack length and test management; (2) the basic material scatter from repeated testing; (3) the effect of unloading rate C where C = (1/Δ/ K )(d Δ K /d a ); (4) the effect of step unloading; (5) the influence of minimum stress intensity factor, K _min . Comparisons have been made between the results of this computer controlled work and those published previously but made using a manual load shedding technique. The results of Δ K _th and fatigue crack growth rates are in general agreement with previous data and confirm the K _min dependence of Δ K _th and d a /d n. The value of Δ K _th is shown to be generally independent of the other test variables for a wide range of conditions and is reproducible with a low degree of scatter.     

NUMERICAL ANALYSIS OF CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

The formulation of an isoparametric displacement – electric potential finite element method that accounts for the electro-mechanical coupling effect of piezoelectric materials is briefly presented in this paper. The crack propagation behaviour and the elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and mechanical – electrical mixed loads are investigated using this electro-mechanical finite element method. From the numerical results, it can be seen that crack propagation along the crack plane direction will be impeded and the crack will tend to propagate at an angle of about 84° to the crack plane under a negative electric field on the basis of the maximum stress criterion. The physical explanation of the phenomena is presented in this paper and it is shown that the mechanical strain energy release rate is not a good criterion for predicting crack propagation in the case where the ratio of the electric field to the mechanical load becomes large.     

THE EFFECT OF GRAIN SIZE ON FATIGUE CRACK GROWTH IN AN ALUMINIUM MAGNESIUM ALLOY

Abstract Fully reversed uniaxial fatigue tests were performed on aluminium magnesium alloy Al 5754 with four different grain sizes in order that the effect of grain size on fatigue crack growth could be examined. Surface cracks were monitored by a plastic replication technique. Fatigue strength was shown to improve with a decrease in grain size. The endurance stress is a function of the inverse square root of the grain size and is described empiricdty by a Hall-Petch type relation. The effect of grain size on fatigue crack growth is most significant when the crack length is of the order of the microstructure. Fluctuations in the growth rate of microstructurally short cracks are most marked in a fine grained microstructure and may be related to the need to transfer slip to adjacent grains. Crack path deviation is greatest in the coarsest grained microstructure and SEM fractography reveals a more pronounced crack surface roughness in the coarser grained alloy than in the finer grained alloy.     

THE EFFECT OF GRAIN SIZE ON THE FATIGUE OF COMMERCIALLY PURE ALUMINIUM

Abstract— Fully reversed uniaxial fatigue tests were performed on polished hour-glass specimens of commercially pure aluminium with three different grain sizes, in order to examine the effect of grain size on fatigue. The growth of surface cracks was monitored by a plastic replication method. An improvement in fatigue strength was observed, as the polycrystal grain size was refined. The endurance limit stress was shown to depend on the inverse square root of the grain size as described empirically by a type of Hall-Petch relation. The effect of refining grain size on fatigue crack growth is to increase the number of microstructural barriers to the advancing crack and to reduce the slip length ahead of the crack tip, and thereby lower the crack growth rate. Multiple crack initiation and growth is a feature of the fatigue of aluminium, while the grain size influences the specific detail of crack coalescence. Crack path deviation is greatest in the coarse grained microstructure and crack surface roughness is more pronounced. SEM fractography reveals that crack initiation and early crack growth takes place along crystallographic slip planes, and that fatigue striations, characteristic of stage II cracking, extend to the very edge of the specimen section, suggesting extensive crack tip blunting.     

INCOMPLETE SELF-SIMILARITY OF FATIGUE IN THE LINEAR RANGE OF CRACK GROWTH

Abstract —The application of dimensional analysis and similarity methods to the study of the speed of fatigue crack growth is considered. It is shown that the Paris range of the crack propagation diagram is an intermediate-asymptotic stage of the crack growth process. Over this stage the influence of the initial conditions on the process of fatigue crack growth has disappeared but the influence of the instability has not yet intruded. So-called incomplete self-similarity prevails at this stage with respect to a basic similarity parameter, equal to the ratio of the stress intensity factor amplitude to the fracture toughness. It is shown that for a certain material under fixed external loading conditions the exponent in the Paris power law is a universal function of the ratio of specimen thickness to the ultimate size of the cyclic plastic zone. Processing of available experimental data confirmed the results obtained by this approach.     

阶跃递增电流作用下导电薄板中的裂纹止裂效应

研究了在带有有限长裂纹的无限大导电薄板中，垂直裂纹通入阶跃递增电流的情况下，裂纹尖端处的电磁场和温度场．给出了裂纹尖端温度的计算方法和算例．指出适当调整阶跃电流的变化值和阶跃次数，可使裂纹尖端处熔化形成焊点，从而遏制了裂纹的扩展．     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

两种材料界面裂纹的应力强度因子

选用复变函数的幂级数作为应力函数,分析在两种材料界面上存在裂纹的情况。利用裂纹自由表面力的边界条件及材料界面上的连续条件求得特征值及待定系数之间的关系式,从而求得应力、位移及应力强度因子表达式。本文修改了Lin[1]和Mar[2]的应力函数表达式,使所得应力、位移表达式与Williams[6]及Sih—Rice[3,4]结果一致。基于上述解析解建立了裂纹尖端的奇异元。并以含有界面中心裂纹平板拉伸情况作为计算实例。      

多裂纹导电薄板电热温度场和应力场的计算

讨论了对带有n个共线裂纹的薄板,在无穷远处加载电流实施止裂时板内的温度场和应力场。文中利用了复变函数的方法计算得到了电流场、温度场和应力场的分布状态。计算中考虑了材料热传导系数、线胀系数、弹性模量随温度的变化。作为算例,以带有两个共线裂纹、牌号为2132GH的高温合金制成的薄板进行了计算,给出了应力、温度与加载的电流密度及裂纹尺寸的关系;分析了导热系数随温度的变化对温度场数值的影响。