载流金属材料裂纹尖端电磁应力的数值模拟

用数值模拟方法研究了金属裂纹尖端电磁应力的分布情况,给出了电流分布、磁场分布和电磁应力的分布.模拟结果表明,金属材料裂纹尖端受的电磁应力是最大的,并且这个力的大小随着电流密度的增加而增大,裂纹尖端的电磁力指向金属的内部.通过具体算例表明,在金属能承受的电流密度下,金属材料裂纹尖端的电磁应力约能达到1MPa的数量级.因此,在研究电磁场处理金属裂纹时,不能忽略电磁应力.     

导电薄板内裂纹尖端区域的电磁应力

为了研究电磁应力对导电薄板内裂纹尖端的作用,从基本电磁理论出发,通过对导体表面所受电场力的分析,推得了导电薄板内裂纹边缘处电场力的表达式.在此基础上,通过导电薄板内裂纹尖端区域磁场的确定,得到裂纹尖端区域的电磁应力表达式.裂纹尖端电磁应力的计算表明,金属薄板中裂纹尖端的电磁应力是由裂纹尖端指向金属内部的压应力,并且当电流密度为103～104A/mm2的数量级时,裂纹尖端的压应力数值可达数兆帕到数百兆帕.因此,在研究裂纹止裂问题上,其影响不容忽视.     

通电瞬时板内半无限长裂纹尖端域的应力场

以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了在向含半无限长直线裂纹的无限大导电薄板内通入电流的瞬时,裂纹尖端附近电流密度的表达式。在此基础上,得到了裂纹尖端区域处温度和应力的具体表达式。算例表明,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,并伴有压应力的产生,从而可达到阻止裂纹扩展的目的。     

带有空间裂纹的拉伸试件电磁热止裂及机械性能测试

首先应用ZL-2超强脉冲电流发生装置对带有预制裂纹的标准拉伸试件进行脉冲放电止裂。放电后裂纹尖端熔化形成堆焊和高压应力区,使裂纹尖端钝化,达到了止裂的目的,采用数值模拟确定了止裂工艺参数。对止裂后的拉伸试件通过微机控制电子万能试验机进行了拉伸实验,研究结果表明:电磁热裂纹止裂有效提高了试件的抗拉强度,放电电压是影响其机械性能的最主要因素。     

The stresses in the neighborhood of a crack tip under effects of electromagnetic forces

In recent work, some basic problems of the stresses in the neighborhood of a crack tip under the effects of electromagnetic forces are studied, and the basic concept of Maxwell electromagnetic stress tensor is illustrated and used to express the effects of the electromagnetic field to the solid body. The basic governing equations of elastic stress of both potential electromagnetic force and Maxwell stress tensor and the approaches for solving these equations are provided. Two kinds of affects of the electromagnetic field on stress singularity of a crack tip are presented and analyzed. Lastly, several examples about the stress analysis on the effects of the electromagnetic field are provided     

金属构件中裂纹的电磁热效应局部跨越止裂

采用理论分析和实验研究的方法讨论了应用电磁热效应对金属构件中裂纹实施局部跨越止裂的技术。在带有裂纹的模具钢构件上取样,对裂纹处通过点电极进行局部跨越脉冲放电。实验研究和理论分析结果均表明:跨越止裂可以使导体中局部裂纹在裂纹尖端处很小的范围内熔化形成微小的焊口,实现了钝化止裂,遏制了裂纹的扩展。通过对止裂后裂尖的金相组织观察和力学性能测试发现:超细化的条状马氏体、极少量残余奥氏体和细颗粒碳化物的出现极大地提高了裂纹尖端的硬度、韧性和耐磨性。     

Quantitative evaluation of the displacement distribution and stress intensity factor of fatigue cracks healed by a controlled high‐density electric current field

Fatigue cracks were healed by controlling a high‐density electric current. The changes in the displacement distribution around the crack tip and the stress intensity factor before and after crack healing were evaluated quantitatively with a digital image collation method. According to the results, it was determined that the cracks were closed by approximately 2 to 7 µm in this study. On the other hand, the stress intensity factor decreased or increased depending on the conditions of the crack and the current applied. The physical restriction between the crack surfaces, such as bridging, is important with respect to lowering the stress intensity factor after healing.     

Nanoscale void nucleation and growth and crack tip stress evolution ahead of a growing crack in a single crystal

A constrained three-dimensional atomistic model of a cracked aluminum single crystal has been employed to investigate the growth behavior of a nanoscale crack in a single crystal using molecular dynamics simulations with the EAM potential. This study is focused on the stress field around the crack tip and its evolution during fast crack growth. Simulation results of the observed nanoscale fracture behavior are presented in terms of atomistic stresses. Major findings from the simulation results are the following: (a) crack growth is in the form of void nucleation, growth and coalescence ahead of the crack tip, thus resembling that of ductile fracture at the continuum scale; (b) void nucleation occurs at a certain distance ahead of the current crack tip or the forward edge of the leading void ahead of the crack tip; (c) just before void nucleation the mean atomic stress (or equivalently its ratio to the von Mises effective stress, which is called the stress constraint or triaxiality) has a high concentration at the site of void nucleation; and (d) the stress field ahead of the current crack tip or the forward edge of the leading void is more or less self-similar (so that the forward edge of the leading void can be viewed as the effective crack tip).     

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.     

A MICRO-MECHANICS MODEL OF CORROSION-FATIGUE CRACK GROWTH IN STEELS

Principles of Microstructural Fracture Mechanics (MFM) are used to develop a model for the characterization of environment-assisted short fatigue crack growth. Fatigue cracks are invariably initiated at corrosion pits formed at inclusions, hence the analysis includes stress concentration effects at pits that lead to the propagation of fatigue cracks the rates of which are considered to be proportional to the crack tip plastic displacement. This plasticity is constrained by microstructural barriers which are overcome in a non-aggressive environment at critical crack lengths only when the applied stress is higher than the fatigue limit. However, the superposition of an aggressive environment assists fatigue damage via crack tip dissolution, enhancement of crack tip plastic deformation, the introduction of stress concentrations at pits and a reduction of the strength of the microstructural barrier. These environment effects are manifested in a drastic reduction of the fatigue limit and higher crack propagation rates. The model is compared with fatigue crack propagation data of a BS251A58 steel tested in reversed torsion when submerged in a 0.6M NaCl solution.     

On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems

The accurate calculation of the opening and closing stresses is an important issue in fatigue crack closure problems, since the effective driving force for crack growth is dependent on accurate calculation of the opening stresses. Often numerical methods such as finite element analysis are used to model plasticity-induced fatigue crack closure problems. There are many difficulties associated with this modelling work, since the results may depend on a wide range of parameters such as mesh refinement, node release scheme and modelling of the contact between the crack faces etc. Even after a great deal of modelling work some arbitrariness is evident in the technique used for assessing the opening and closing stresses. A number of techniques have been proposed in the literature and the current work will assess and compare these approaches. The node displacement method, the change in stresses at the crack tip, and the weight function technique will each be applied to a finite element model of a plane stress crack for a range of stress levels. In addition, an analytical model for plasticity-induced crack closure under plane stress conditions will be used to discuss the accuracy of these techniques. The investigation shows that all these techniques are equivalent provided that the displacement and stress at the crack tip are assessed accurately. However, it will be shown that use of the tensile tip stress method, proposed by some authors for assessing the closing stress, is erroneous.     

A hybrid experimental/computational approach to the assessment of crack growth criteria in composite laminates

While a number of criteria have been proposed for predicting the onset of crack growth in composite laminae, there has hitherto been no accepted method of assessing the value of alternative proposals. This study integrates the use of computational modelling, along with moiré interferometry for the quantitative mapping of near crack tip deformation fields. The moiré method was used to validate the computational model. It was then possible to use the computational model on its own to predict crack tip behaviour in more detail than could be done with the optical system alone.
This study chose one crack growth criterion - the normal stress ratio - to demonstrate the assessment routine. The value of the normal stress ratio (NSR) was calculated as a function of the ply angle to the loading direction. In order to obtain sensitive predictions of crack growth direction, it was desirable to proceed by analysing the crack tip behaviour down to radial distances from the crack tip of a few tens of microns. By a suitable choice of elements around the crack tip, the finite element model was able to predict values of the NSR down to a radius of 80 times10^-3 mm around the crack tip.     

虚拟裂缝尖端拉应力大小的确定

针对单边切口的混凝土轴心受拉构件,基于虚拟裂缝模型提出一种计算极限承载力的解析模型,并在此基础上确立了虚拟裂缝尖端拉应力与混凝土轴心抗拉强度之间的关系。结果表明:二者的比值随初始缝高比的增大呈线性增加,但对混凝土强度等级的变化不敏感。其原因是由于所有的混凝土试件都存在初始缺陷,导致截面上存在明显的应力梯度,因而得到的混凝土轴心抗拉强度值是截面应力的平均值,而虚拟裂缝尖端拉应力为截面上的最大应力。很显然,轴心受拉构件的初始缺陷越长,截面的应力梯度越大,虚拟裂缝尖端拉应力与平均应力的比就越大。通常情况下,虚拟裂缝尖端的拉应力大小约为混凝土轴心抗拉强度值的1.22倍,约等于混凝土的抗折强度。     

Technique for producing crack arrest by electromagnetic heating

Abstract

Crack arrest in current conducting materials by electromagnetic heating can be used effectively to extend the service life and improve the safety and reliability of structures and components. Theoretical analysis and experimental investigations have shown that due to heat concentration around the crack tip, small welded joints are formed by metal melting. Thus, the formation of the main crack source is prevented. From metallography, it has been found that a typical fine phase transformation microstructure can be obtained in the crack tip region as a result of rapid heating and cooling. The intensity, ductility, and wear capacity are promoted under the combined influence of superfine structure, thermal compressive stresses, and phase transformation compressive stresses. Microcracking and subsequent main crack propagation can both be prevented. The basic principles of the electromagnetic heating effect and the results of experimental work based on the theory are presented.     

Transient response of a cracked magnetoelectric material under the action of in-plane sudden impacts

Dynamic analysis of a crack embedded in a magnetoelectric material is made when subjected to in-plane mechanical, electric and magnetic impacts. The Laplace and Fourier transforms are applied to reduce the associated initial- and mixed-boundary value problem to dual integral equations, and then to singular integral equations with Cauchy kernel. By numerically solving the resulting equation, the dynamic field intensity factors as well as CODs, and energy release rates near the crack tip are evaluated and presented graphically. The effects of applied magnetic and electric impacts on crack growth are discussed. Obtained results show that, different from the static results, applied magnetic and electric impacts can strongly affect dynamic stress intensity factors.     

Analysis of the effects of compressive stresses on fatigue crack propagation rate

In this study, the effects of compressive stresses on the crack tip parameters and its implication on fatigue crack growth have been studied. Elastic–plastic finite element analysis has been used to analyse the change of crack tip parameters with the increase of the applied compressive stress level.The near crack tip opening displacements and the reverse plastic zone size around the crack tip have been obtained. The finite element analysis shows that when unloading from peak tensile applied stress to zero applied stress, the crack tip is still kept open and the crack tip opening displacement gradually decreases further with the applied compressive stress. It has been found that for a tension–compression stress cycle these crack tip parameters are determined mainly by two loading parameters, the maximum stress intensity K_max in the tension part of the stress cycle and the maximum compressive stress σ_maxcom in the compression part of the stress cycle.Based on the two parameters, K_max, and σ_maxcom, a fatigue crack propagation model for negative R ratios only has been developed to include the compressive stress effect on the fatigue crack propagation rate.Experimental fatigue crack propagation data sets were used for the verification of this model, good agreements have been obtained.     

A multilayer hybrid-stress finite element analysis of a through-thickness edge crack in A ± 45° laminate

A solution is given for the three-dimensional stress field near a through-thickness edge crack in a thin ± 45° laminate having elastic ply moduli typical of graphite/epoxy. The stress distribution was obtained by a three-dimensional multilayer finite element analysis based on the hybrid stress model, formulated through the minimum complementary energy principle. The results indicate that the in-plane stresses of each individual ply follow the classical $\text{1}\text{√r}$ stress singularity, but that the shape of isostress contours in the crack tip region is strongly distorted from predictions based on two-dimensional anisotropic fracture mechanics theory. The interlaminar shear stresses increase rapidly as the crack tip is approached, but are restricted to a local region around the crack tip and flanks. The interlaminar normal stress is assumed to be negligible in the formulation of the analysis.     

Influence of minimum element size to determine crack closure stress by the finite element method

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results.In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.     

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.