Computations of modes I and II stress intensity factors of sharp notched plates under in-plane shear and bending loading by the fractal-like finite element method

The fractal-like finite element method (FFEM) is used to compute the stress intensity factors (SIFs) for different configurations of cracked/notched plates subject to in-plane shear and bending loading conditions. In the FFEM, the large number of unknown variables in the singular region around a notch tip is reduced to a small set of generalised co-ordinates by performing a fractal transformation using global interpolation functions. The use of exact analytical solutions of the displacement field around a notch tip as the global interpolation functions reduces the computational cost significantly and neither post-processing technique to extract SIFs nor special singular elements to model the singular region are required. The results of numerical examples of various configurations of cracked/notched plates are presented and validated via published data. Also, new results for cracked/notched plate problems are presented. These results demonstrate the accuracy and efficiency of the FFEM to compute the SIFs for notch problems under in-plane shear and bending loading conditions.     

拉伸载荷作用下单边缺陷-边裂纹应力强度因子研究

利用杂交位移不连续法研究拉伸载荷作用下矩形板中单边缺陷-边裂纹(半圆孔裂纹和半方孔裂纹)问题,给出了这三种平面弹性裂纹问题的应力强度因子的详细数值解。通过半圆孔裂纹问题和半方孔裂纹问题与单边裂纹问题的应力强度因子的比较,发现半圆孔和半方孔对单边裂纹有屏蔽影响。此外,本文的研究结果表明,杂交位移不连续法用于分析平面弹性有限体中复杂裂纹问题的应力强度因子简单且又准确。     

PZT-4紧凑拉伸试样的断裂分析

基于线性压电材料的复势理论,通过解析分析,导出了一种分析有限压电板裂纹问题的解析数值方法. 首先,计算了含中心裂纹有限板的断裂参数,与Woo和Wang的解析数值法(Int J Fract, 1993, 62: 203$\sim$218)相比较,表明该方法具有很高的精度和很好的计算效率. 随后,采用该方法和有限元法计算了PZT-4紧凑拉伸试样在绝缘裂纹面边界条件下断裂时的断裂参数,发现各断裂参数的临界值分散性很大,不能作为压电材料的单参数断裂准则. 进而,针对试样真实的裂隙形状,采用有限元法计算了裂隙尖端的应力、电位移场,比较了裂隙内介质的介电性能对裂隙尖端场的影响,计算了带微裂纹的真实裂隙模型的断裂参数并进行了理论分析.      

半无限板边缘裂纹的权函数解法与评价

权函数法是求解裂纹体在任意受载条件下的应力强度因子和裂纹面位移等断裂力学参量的高效、高精度方法,与有限元等数值方法相比,在求解效率和可靠性方面均具有明显优势.针对半无限板边缘裂纹,系统分析了在国际断裂力学界较有代表性的Wu-Carlsson、Glinka-Shen和Fett-Munz三种解析形式的权函数法,进而以在远端均匀加载下的半无限板边缘裂纹面位移Wigglesworth解析解导得的权函数及其对应的格林函数解(即裂纹面受一对单位集中力作用下的应力强度因子)为基准,沿整个裂纹长度对3种权函数的精度逐点进行比较,并与文献中基于其他方法求得的权函数做了广泛对比,包括Bueckner,Hartranft-Sih以及Wigglesworth利用不同解析方法推导出的高精度的权函数.研究了3种参考载荷(均布/正反向线性分布应力、集中力)及其不同组合,以及裂纹嘴位移的几何条件对权函数精度的影响.结果表明,基于一种参考载荷下的裂纹面张开位移比基于两种参考载荷下的应力强度因子所得到的权函数具有更高的精度,而且后一种方法的精度明显受到所选参考载荷组合的影响;裂纹面位移在裂纹嘴处三阶导数等于零的条件对基于一个参考解的权函数精度的改进效果较小.最后给出了利用各种权函数方法计算得到的4种载荷条件下的应力强度因子,并对结果进行了比较.     

Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

The stress–strain state near cracks on the boundary of a circular hole in a linear elastic orthotropic composite plate under tension is analyzed. The distribution of stress intensity factors (SIFs) at the crack tip is found from photoelectric measurements. The dependence of the SIFs on the ratio of crack length to hole radius and on the mechanical properties of the material is established     

Fracture of shape memory CuAlNi single crystals

The fracture behavior of shape memory CuAlNi single crystals loaded in tension is studied. Specimens cut from a single crystal are notched and loaded in tension until final fracture. Eight different crystallographic orientations of the notch and tensile axes are considered. The stress field at the notch tip triggers a cubic to orthorhombic phase transition in the crystal, which results in a set of twinned martensite plates emanating from the notch tip. As loading increases, a crack forms and grows off the notch tip, with the martensite plates continuing to appear at the growing crack. Details of the crack growth depend strongly on both the type of singular microstructures that forms and how this microstructure interacts with the growing crack. In one group of orientations a distinct transformation zone forms along one flank of the crack and the motion of this zone is directly connected to the crack growth. In a second group of orientations, the microstructure formation is not as strongly tied to the crack. Interestingly, in all specimens studied, the final crack direction is approximately 80° from the direction of the martensite plates.     

Stability and dynamic analysis of partially cracked thin orthotropic microplates under thermal environment: an analytical approach

Abstract

An analytical model is proposed to analyze the vibration and buckling problem of partially cracked thin orthotropic microplate in the presence of thermal environment. The differential governing equation for the cracked plate is derived using the classical plate theory in conjunction with the strain gradient theory of elasticity. The crack is modeled using appropriate crack compliance coefficients based on the simplified line spring model. The influence of thermal environment is incorporated in governing equation in form thermal moments and in-plane compressive forces. The governing equation for cracked plate has been solved analytically to get fundamental frequency and central deflection of plate. To demonstrate the accuracy of the present model, few comparison studies are carried out with the published literature. The stability and dynamic characteristics of the cracked plate are studied considering various parameters such as crack length, plate thickness, change in temperature, and internal length scale of microstructure. It has been concluded that the frequency and deflection are affected by crack length, temperature, and internal length scale of microstructure. Furthermore, to study the buckling behavior of cracked plate, the classical relations for critical buckling load and critical buckling temperature is also proposed considering the effect of crack length, temperature, and internal length scale of microstructure.     

Prediction and observation of crack tip microstructure in shape memory CuAlNi single crystals

The formation of martensite at a notch tip in a CuAlNi shape memory alloy loaded in tension is studied. The geometry of the initial martensite plate to form at the notch is predicted theoretically, using the stress field at a crack tip in an anisotropic linearly elastic body together with a listing of all possible austenite-martensite interfaces from the Crystallographic Theory of Martensite (CTM). The stress field and CTM analyses are combined through a selection criterion based on computing the work available from the stress field to transform to each austenite-martensite interface. The resulting predictions are compared to experimentally observed microstructures in notched specimens of single crystal CuAlNi loaded in tension for eight notch orientations. Results show that the available work criterion accurately predicts the orientation, number and order of the austenite-martensite interfaces that initially form near a crack.     

Influence of aggregate size on fracture toughness of concrete

Employing an extension of the splitting tensile by using a notched cylinder specimen, we have studied effects of initial notch length and maximum aggregate size on fracture toughness of concrete. Experimental results show that maximum aggregate size does influence ductility, with increasingly ductile behavior associated with increasing aggregate size. The results also support previous work in that initial notch length and maximum load do not yield a constant value for fracture toughness, whereas maximum linear load and initial notch length minimize the effects of slow crack growth and do produce a more constant value.     

焊接残余应力平板多个共面表面裂纹的应力强度因子

采用线弹簧模型求解含焊接残余应力平板多个共面任意分布表面裂纹的应力强度因子.利用边裂纹权函数给出了裂纹表面上沿厚度非线性分布的残余应力向线性分布的转化公式.基于Reissner板理论和连续分布位错思想,将含多个共面任意分布表面裂纹的无限平板问题归结为一组Cauchy型奇异积分方程,并采用Gauss-Chebyshev方法获得了奇异积分方程的数值解.以三共面表面裂纹为例,计算了表面裂纹的应力强度因子,并讨论了裂纹间距、裂纹几何形状等因素对应力强度因子的影响.     

Investigation on 3D fatigue crack propagation in surface-cracked specimens

In the present work the fatigue crack growth in AISI304 specimens is investigated experimentally. In 3D finite element analysis the virtual crack closure technique is applied to calculate distributions and variations of the stress intensity factor along the surface crack front. It is confirmed that the stress intensity factor along the surface crack front varies non-uniformly with crack growth. Crack growth rate is proportional to the stress intensity factor distribution in the 3D cracked specimen. The fatigue crack growth in surface cracked specimens can be described by the Forman model identified in conventional compact tension specimens. For crack growth in the free specimen surface the arc length seems more suitable to quantify crack progress. Geometry and loading configuration of the surface cracked specimen seem to not affect the fatigue crack growth substantially.     

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed mathematically using a complex variable approach in two-dimensional(2 D) semipermeable piezoelectric media. In this model, an existing polarization saturation(PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displacement(COD), the crack opening potential(COP), and the local stress intensity factors(SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.     

中心直裂纹平台巴西圆盘复合型动态应力强度因子

为了指导用中心直裂纹平台巴西圆盘(CSTFBD)试样进行岩石复合型动态断裂 试验,利用有限元法首先验证了文献中对中心直裂纹巴西圆盘(CSTBD)得到的有关结果,分析 比较了不同无量纲裂纹长度(即裂纹半长和圆盘半径之比)时两种圆盘的I, II型动态应力 强度因子的时间历程,发现两者的差异大部分在10{\%}以内,同时验证了该文数值方法的可 靠性. 然后讨论了CSTFBD试样I, II型动态应力强度因子的复合比、起裂角以及纯II型加 载角. 研究成果可为复合型动态断裂试验中CSTFBD试样的加工、试样上应变片的粘贴、起裂 方向和起裂时间的估计等提供参考.     

垂直于界面V型缺口尖端的应力奇异性及其应用

基于双材料垂直于界面V型缺口理论,给出了单一材料和双材料裂纹问题、V型缺口问题应力强度因子的统一定义,得到了应力外推法计算双材料K_I的公式,数值算例验证了本文方法的有效性.以双材料单向拉伸和三点弯曲模型为对象,深入研究了双材料中弹性模量、泊松比、缺口深度、缺口张角对缺口尖端奇异应力场的影响,获得了一定范围内各种参数变化对缺口尖端奇异应力场的影响规律,为异体材料形成的V型缺口在应力断料中的应用提供了必要的参考依据.     

Modeling of fatigue crack growth from a notch

When a fatigue crack is nucleated and propagates into the vicinity of the notch, the crack growth rate is generally higher than that can be expected by using the stress intensity factor concept. The current study attempted to describe the crack growth at notches quantitatively with a detailed consideration of the cyclic plasticity of the material. An elastic–plastic finite element analysis was conducted to obtain the stress and strain histories of the notched component. A single multiaxial fatigue criterion was used to determine the crack initiation from the notch and the subsequent crack growth. Round compact specimens made of 1070 steel were subjected to Mode I cyclic loading with different R-ratios at room temperature. The approach developed was able to quantitatively capture the crack growth behavior near the notch. When the R-ratio was positive, the crack growth near a notch was mainly influenced by the plasticity created by the notch and the resulted fatigue damage during crack initiation. When the R-ratio was negative, the contact of the cracked surfaces during a part of a loading cycle reduced the cyclic plasticity of the material near the crack tip. The combined effect of notch plasticity and possible contact of cracked surface were responsible for the observed crack growth phenomenon near a notch.     

Delamination effects on cracked steel members reinforced by prestressed composite patch

Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce crack closure effect. Moreover, it modifies the crack geometry by bridging the crack lips and reduces the stress range at crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A debond crack in the adhesive–plate interface was observed by optical technique. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique. A parametric analysis is performed in order to investigate the influence of some design parameters such as the composite patch Young’s modulus, the adhesive thickness and the pretension level on the adhesive–plate interface debond.     

Photoelastic modeling of the fracture of viscoelastic orthotropic plates with a crack

The well-known equations of photoelasticity of linear viscoelastic bodies are used to describe the photoelastic behavior of a viscoelastic orthotropic plate with a crack. Expressions for the stress intensity factors (SIFs) at the crack tip are obtained using photoelastic measurements. The time dependence of the SIFs is analyzed and shown to be determined by the angles between directions of the crack and tension     

Fracture in single crystal NiTi

This paper presents an investigation of the pseudoelastic transformation of two crystallographic orientations of a single crystal NiTi shape memory alloy (SMA). Both uniaxial tension and notched tension samples are considered with the tensile axes along the [1 0 0] and [1 1 1] directions. The phase transformation is observed using optical techniques in situ. For the uniaxial tension samples, martensite plates and Lüders-band structures are observed. For the notched samples, transformation structures in the [1 0 0] sample appeared predominantly on the sides of the notch and crack tip with stable crack propagation. In the [1 1 1] notched samples transformation occurs directly ahead of the notch and unstable crack propagation is observed. An available work criterion is used to predict the location of the transformation, with good agreement to the experimental observations. The different fracture behavior of the two notched sample orientations is explained utilizing the available work calculations.     

CTS试样I/II混合型断裂特性数值计算研究

采用CTS试样研究I/II混合型断裂特性计算裂纹前缘应力强度因子时可采用解析公式,一旦裂纹发生扩展,解析公式便不再适用。文中采用有限元法研究紧凑拉伸剪切（CTS）试样在I/II平面混合型加载下的裂纹扩展行为。采用ANSYS建立CTS试样I/II混合型测试系统有限元模型,为模拟真实受力状态,在CTS试样-销-扇型夹具以及扇型夹具-销-U型夹具之间分别建立接触对进行接触力学分析。通过与解析公式结果进行对比验证了该数值方法的可靠性。采用最大环向应力准则（MTS）,模拟了CTS试样不同加载角度下的裂纹扩展路径,获得了裂纹扩展路径中应力强度因子随裂纹长度的变化曲线,解释了裂纹扩展路径不与外载荷方向垂直的原因。结合文中计算结果,在CTS试样I/II混合型裂纹扩展速率实验测得裂纹长度与寿命的关系曲线a-N的基础上,便可得到材料I/II型混合型裂纹扩展速率曲线。