Experimental study and BEM analysis of fatigue crack growth in a cracked heterogeneous body

A model for analysing a soft-hard heterogeneous body with a crack in the hard region is presented in this paper. The result of fatigue experiments shows that mechanical heterogeneity affects the rate of propagation of fatigue crack. Meanwhile the results computed by BEM for cracked heterogeneous bodies under cycling loading indicate that the smaller the distance between the crack and the interface of hard and soft regions is, the smaller the amplitude of crack opening displacement, COD and ofJ-integral as well at the same step during the fatigue crack growth will be. The effect of heterogeneity on the rate of fatigue crack propagation is shown by the variation of J. The smaller the distance of the crack to the interface is, the smaller the rate of fatigue crack growth will be.     

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well.The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (a>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (a>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition.This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.     

A phenomenological model of fatigue crack growth in perfectly plastic infinite plates under completely reversed uniaxial loading

The fatigue failure of a thin infinite center-cracked plate under completely reversed uniaxial loading is considered. A two-stage fatigue crack model including the incubation and crack propagation stages is constructed. The stress distribution in the vicinity of the crack tip is described using the concept of a conventional elastic crack. The crack-tip plastic zone is simulated by a Dugdale thin plastic zone, and the condition for the movement of the failure front is given by criteria of damage mechanics. It is shown that the fatigue crack growth rate in perfectly plastic materials with a plastic zone of constant length is a power-law function of the stress intensity factor range. This relationship is quadratic when the length of the plastic zone is not constant Published in Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 116–127, December 2005.     

Fatigue crack propagaion under mixed mode loading

Mixed model fatigue crack propagation is analyzed in this paper, using a centre cracked plate geometry, loaded under un-iaxial cyclic tension. Based on maximum principal stress criterion, a modified Paris expression of fatigue crack growth rate is derived in terms of ΔK and crack angle β_α for an inclined crack. It is also shown that it is more convenient to express the Paris equation by means of crack length projected on the x -axis, α_x rather than the actual length, α itself. The crack trajectory due to cyclic loading is predicted, β is varied from 29° to 90°. Experimental data on Type L3 aluminium agree fairly well with predicted values when β_α exceeds 30°.     

Prediction models of fatigue crack closure and growth under random loading

The effects of plastic zones both in front of and behind crack tip on crack closure have been analysed. The total residual deformations of crack surfaces involve two parts, that is, the amount of plastic blunting of crack tip and the residual deformation in the wake of the tip. This paper presents a fatigue crack closure model in which the influences of compressive load on closure stress are discussed. The model is applied to random loading conditions by the assumption of limited memory properties. The fatigue lives are predicted using the proposed crack growth model for CCT plane stress specimen cut from 2219-T851 aluminum alloy under flight spectrum loadings, and the prediction values agree with the test results.The project was supported by the natural science foundation of China.     

Perfectly plastic stress field at a stationary crack tip

Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.     

过载作用下聚乙烯疲劳裂纹扩展行为研究

论文针对中密度聚乙烯材料(MDPE)，采用平板试样进行了I型疲劳裂纹扩展和单次过载下裂纹扩展试验．发现与金属材料类似，单次拉伸过载对聚乙烯(PE)的疲劳裂纹扩展有明显的迟滞作用，降低了裂纹扩展速率．试验还通过变载荷刻线法获取疲劳裂纹扩展前缘的实际形貌和变化规律，对常规变载荷刻线方法进行了调整和验证，其修正方法对高分子材料的疲劳裂纹扩展前缘刻线具有较好的效果．通过观察发现含楔形塑性区的裂尖钝化是裂纹迟滞的主要原因．过载引入的塑性区内残余应力对裂纹迟滞也起了重要作用．论文利用Dugdale模型计算了塑性区尺寸，使用基于残余应力的Wheeler模型对过载迟滞进行了很好的拟合．     

Perfectly plastic stress field at a rapidly propagating plane-stress crack tip

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of only, making use of the Treasca yield condition, steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly palstic stress field at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic stress field at the rapidly propagating tips of models I and II plane-stress cracks.     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

Numerical analysis of fatigue striations

A computational model was developed to numerically analyse fatigue striations. The inclined strip yield model with continuous distributions of infinitesimal dislocations was utilized to express the crack tip plasticity in this model. The fatigue crack tip blunting process was approximated by sequential activation of two slip lines under loading, and crack closure during unloading was taken into account. The plastic zone at a growing fatigue crack tip at the maximum load was independent of the crack growth up to ten cycles while the reversed plastic zone decreased in a size to one twentieth of that at the maximum load as the crack grew. The ratio of these plastic zone sizes and also the crack tip opening displacement were quite different from the simple prediction by J.R. Rice for a stationary crack. The computed striation spacings were compared with the observed ones and moderate agreement between them obtained.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

一种经验型疲劳小裂纹扩展模型

金属材料疲劳寿命由裂纹萌生和裂纹扩展寿命两部分组成,其中对于萌生寿命中的小裂纹分析是精确描述裂纹萌生寿命的关键．而小裂纹在扩展过程中由于尺寸相对较小,导致传统线弹性断裂力学预测方法失效,需要对其进行改进,考虑裂纹尖端塑性区引起的残余压应力对小裂纹扩展速度的影响．本文针对此问题进行了初步分析,通过对塑性区引起的残余应力的量化,结合小裂纹门槛值特性,提出了一种经验型修正的小裂纹扩展模型,用于定量预测裂纹的萌生寿命．使用铝合金6082-T6缺口试样进行了疲劳实验,并与理论结果进行了对比,验证了所提模型的有效性．     

拉压循环载荷下正交异性钢桥面板肋-面板焊缝裂纹扩展分析

采用四步法计算了考虑循环载荷中压应力影响的正交异性钢桥面板的肋-面板焊缝表面裂纹扩展。第一步是基于正交异性钢桥面板的疲劳分析模型,计算肋-面板焊缝处的应力,第二步是通过肋-面板焊缝的三维局部模型,用Schwartz-Neumann交替法计算焊缝表面裂纹的应力强度因子分布,第三步是用二维断裂力学模型和增量塑性损伤模型,计算循环载荷中的压应力对裂纹扩展的影响,第四步是用第二步中的三维裂纹分析结果和第三步中的二维断裂力学模型得到的裂纹扩展公式,计算钢桥面板的肋-面板焊缝表面裂纹扩展。计算结果表明,对应于正交异性钢桥面板肋-面板焊缝处的循环应力,本文所用模型的裂纹尖端反向塑性区导致裂纹扩展率增加50%以上。研究结果为正交异性钢桥面板肋-面板焊缝裂纹的疲劳寿命分析提供了研究基础。     

Cohesive zone laws for fatigue crack growth: Numerical field projection of the micromechanical damage process in an elasto-plastic medium

Cohesive zone failure models are widely used to simulate fatigue crack propagation under cyclic loading, but the model parameters are phenomenological and are not closely tied to the underlying micromechanics of the problem. In this paper, we will inversely extract the cohesive zone laws for fatigue crack growth in an elasto-plastic ductile solid using a field projection method (FPM), which projects the equivalent tractions and separations at the cohesive crack-tip from field information outside the process zone. In our small-scale yielding model, a single row of discrete voids is deployed directly ahead of a crack in an elasto-plastic medium subjected to cyclic mode I K-field loading. Damage accumulation under cyclic loading is captured by the growth of voids within the micro-voiding zone ahead of the crack, while the evolution of the cohesive zone law representing the micro-voiding zone is inversely extracted via the FPM. We show that the field-projected cohesive zone law captures the essential micromechanisms of fatigue crack growth in the ductile medium: from loading and unloading hysteresis caused by void growth and plastic hardening, to the softening damage locus associated with crack propagation via a void by void growth mechanism. The results demonstrate the effectiveness of the FPM in obtaining a micromechanics-based cohesive zone law in-place of phenomenological models, which opens the way for a unified treatment of fatigue crack problems.     

Damage accumulation for growth of anti-plane crack in work-hardening material

Elastic–plastic solutions of an anti-plane crack in an infinite body are used in conjunction with a continuum damage model to describe the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to time dependent events. A power law relates the stress to the strain of the material. The damage, which invokes nucleation, growth and coalescence of microvoids due to elevated strain, is confined to the plastic zone surrounding the crack tip. For applied loading below the yield stress, the small-scale and large-scale yielding solutions are used to determine the influence of strain hardening on crack instability and failure. Crack growth due to cyclic loading and time-dependent deformations are studied using the small-scale yielding solution of the deformation theory of plasticity.     

Fundamental study on rupture by low-cycle fatigue of polymers applying the fine-grid method

Few studies have been made on the fracture mechanics of polymers, their resistance to plastic failure, fatique rupture, and the adverse effects of environmental conditions, in contrast to the numerous studies conducted on metallic materials. Since fatigue is characterized by very local and cyclic fractures, in the present study a real-time fine-grid method was applied to study the fatigue rupture of polymers: to examine changes in local strain at the root of the notch during the process of crack initiation, the local strain at the tip of the crack during crack propagation and the relation between the plastic zone formed in front of the crack tip and the rate of crack propagation. As a result, strong correlation between three proposed parameters of the local crack-tip strain, the crack initiation and the propagation rate was obtained, and the mechanism of low-cycle fatigue rupture of polymers could be discussed.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

The size of plastic zones in cracked plates made of polycarbonate

The influence of the thickness of a cracked plate, made of Polycarbonate of Bisphenol A, on the plastic zones developed at the crack tip was studied. The three-dimensional character of yielding at the vicinity of the crack tip is revealed. The study of the thickness variation in the plastic zones is made by applying the shadow-moiré method. It has been derived that the thickness variation in the plastic zones is discontinuous with successive dimples of different thickness. The influence of the overall thickness of the specimen on the size and length of the plastic zone was studied for different crack lengths. Irwin's theory for small yielding, as well as the simple and modified Dugdale-Barenblatt models, were applied for the study of plastic zones. By comparing the plastic-zone lengths in relation to their shape, with those given by the above theories, it may be concluded that, for small loads where the applied stress σ is not exceeding 0.40 of the yield stress \(\sigma _o \) in tension and small values of the ratio of crack lengtha to plate thicknesst, (a/t<4) a state of plane strain dominates at the vicinity of the crack tip, while, by increasing the load and ratioa/t, the plastic zones approach in shape and size those given by the modified Dugdale-Barenblatt model.     

Limiting state of an elastoplastic orthotropic plate with a periodic system of collinear cracks

A modified Dugdale model is used to study the fracture of an orthotropic elastoplastic plate with a periodic system of rectilinear cracks. The material of the plate obeys a general yield criterion. The general form of solution is obtained in terms of Kolosov-Muskhelishvili potentials. The size of the plastic zone is expressed in terms of the external load and geometrical parameters. The equations for the determination of the stresses in the plastic zone and the crack opening displacement are derived. The effect of anisotropy on the formation of the plastic zones at the crack tip is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 80–88, May 2007.