ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENING CERAMICS(Ⅱ)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.Project supported by the National Natural Science Foundation of China     

Electric-field-induced fatigue crack growth in ferroelectric ceramics

Electric-field-induced fatigue crack growth in pre-cracked PZT ferroelectric ceramics is experimentally investigated in this work. It is found that the crack open and close under an alternating electric field is a major mechanism of crack propagation. The experimental results also show that the frequency, waveform, as well as the amplitude ratio, of the electric loading, play important roles in electric-field-induced fatigue cracking. Empirical formulations of fatigue crack propagation rates are obtained based on the experimental results. It is revealed that the crack grows at a nearly constant rate when the loading frequency is below 100 Hz. However, with the increase of the loading frequency over 125 Hz, the crack propagation rate diminishes rapidly.     

Finite element analysis of void growth near a blunting crack tip

Large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack. The near crack tip stress and deformation fields are analyzed. The results show that the holes are pulled towards the crack tip and change their shape to approximately elliptical with the major axis radial to the crack. They also grow faster directly ahead of the crack than at an angle to the crack plane. Several crack-hole coalescence criteria are discussed and estimates for the conditions for fracture initiation are given and compared with experimental results. The range of estimates now available from finite element calculations coincides quite well with the range of experimental data for materials containing inclusions which are only loosely bonded to the matrix.     

Finite element analysis of mode III steady crack growth in anisotropic hardening materials

In this paper, the steady crack growth of mode III under small scale yielding conditions is investigated for anisotropic hardening materials by the finite element method. The elastic-plastic stiffness matrix for anisotropic materials is given. The results show the significant influences of anisotropic hardening behaviour on the shape and size of plastic zone and deformation field near the crack tip. With a COD fracture criterion, the ratio of stress intensity factorsk _ss/k_c varies appreciably with the anisotropic hardening parameterM and the hardening exponentN.     

Prediction of fatigue crack growth life under variable-amplitude loading using finite element analysis

This article presents an elastic-plastic study aiming at predicting the fatigue crack growth (FCG) of 2024-T3 aluminum alloys under variable-amplitude loading. The proposed analysis needs the estimation of the residual stress distribution ahead of the crack tip during propagation. An elastic-plastic FE analysis has been implemented for modeling FCG using Chaboche's model. The FE study has been carried out through consideration of the loading history effect using the memory rules. Three different loading spectra have been applied in this work. The obtained results have been compared to the experimental ones and it has been proved that the suggested model has a better prediction of the FCG lives of cracked 2024-T3 aluminum alloy structures subjected to variable-amplitude loading.     

Toughening analysis of mode III crack in transformation toughened ceramics

The fracture toughness enhancement of mode III crack in transformation toughened ceramics such as Ce-TZP and Mg-PSZ is predicted by using a pressure sensitive transformation criterion and the weight function method. The theoretical analyses of the toughening effect for both stationary and steady-state growing crack are given, respectively. The results show that the toughening is only associated with crack growth and there is no toughening effect for stationary crack.The project was supported by the National Science Foundation of China     

Finite element analysis of a bimaterial interface crack

In this investigation, the enriched element method developed by Benzley was extended to treat the stress analysis problem involving a bimaterial interface crack. Unlike crack problems in isotropic elasticity, where the stress singularity at the crack tip is of the inverse square root type, the interface crack contains an additional oscillatory singularity. Although the effect of this oscillatory characteristic is confined to a region very close to the crak tip, it nevertheless requires proper treatment in order to obtain accurate predictions on the stress intensity factors. Using appropriate crack tip stress and displacement expressions, the enriched element method can model the stress singularity for an interface crack exactly. The finite element implementation of this method has been made on the code APES. Stress intensity factor results predicted by the modified APES program compare favorably with those available in the literature. This indicates tha the enriched element technique provides an accurate and efficient numerical tool for the analysis of bimaterial interface crack problems.     

Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading

We have developed a three-dimensional cohesive element and a class of irreversible cohesive laws which enable the accurate and efficient tracking of three-dimensional fatigue crack fronts and the calculation of the attendant fatigue life curves. The cohesive element governs the separation of the crack flanks in accordance with an irreversible cohesive law, eventually leading to the formation of free surfaces, and is compatible with a conventional finite element discretization of the bulk material. The versatility and predictive ability of the method is demonstrated through the simulation of the axial fatigue tests of aluminum shafts of Thompson and Sheppard, 1992a, Thompson and Sheppard, 1992b, Thompson and Sheppard, 1992c . The ability of the method to reproduce the experimentally observed progression of beachmarks and fatigue life curves is particularly noteworthy.     

压电薄膜表面贯穿裂纹的有限元分析

基于有限元软件ANSYS数值模拟,计算了激光作用下的压电薄膜表面贯穿裂纹外场应力强度因子和电位移强度因子,并且研究了90°畴变所诱致的畴变增韧行为。首先,求解无裂纹压电薄膜在激光作用下的热-力-电响应,将求得的应力和电位移场反向作用于裂纹面,求解裂纹尖端处的外场应力和电位移强度因子,然后基于小范围畴变理论求解了90°畴变所致的屏蔽应力强度因子。讨论了薄膜表面裂纹的外场应力强度因子、电位移强度因子及屏蔽应力强度因子随激光作用时间和裂纹位置的变化关系,从而预测压电薄膜体系在加热工作状况下的裂纹扩展和断裂行为。     

Stratified model for estimating fatigue crack growth rate of metallic materials

Introduction Thefatiguedestructionisoneofthemaintypesofthemetaldamage.Therelationcurve betweenthefatiguecrackgrowthrateda/dNandthestressstrengthfactoramplitudeΔKisthe importantdatiumoffatiguecapabilityindesigningthemetaldamagetolerantlimitsandpredicting thelifeofmetalcomponentparts.Duetovariabilityofthefatiguecrackgrowthrate,alarge amountoftestsamplesareusuallyrequiredtoderiveahighlyreliableda/dN_ΔKcurve. However,inmostactualengineeringpractice,itishardtofindmultiplespecimenswithvery simil…     

A boundary element modeling of fatigue crack growth in a plane elastic plate

This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given.     

Crack growth rate and cracking velocity in fatigue for a class of ceramics

Fatigue crack growth rate data and cracking velocity data are studied for a class of ceramics including SiC, TiB₂, Si₃N₄, ZrO₂ and Al₂O₃. Both sine and square wave cyclic loading are combined such that the data could be converted to cracking velocity for a given frequency of cyclic load. An effective stress intensity factor range is defined and used in an relation for computing the crack growth rate and cracking velocity. As for the metal alloys, the data for ceramics also fall into three regimes identified with near-threshold, stable growth and rapid crack extension, except that the slope of the da/dN (the crack growth rate) curves for ceramics are steeper in comparison with that for metals. Reported are the empirical constants in the relations for the crack growth rate and the cracking velocity for a variety of ceramics.     

Statistical analysis of high cycle fatigue crack growth: center crack in aluminum panel

High cycle fatigue crack growth results are obtained from a statistical analysis and compared with test data for an aluminum panel with a center crack under constant amplitude cyclic load. The analysis makes use of a generalized Fock-Planck equation that is satisfied by a union probabilistic density of stochastic variables of cycle number and crack length. Obtained are high degrees of modified expressions of the equation's coefficients and hence the analytical solution. A two-parameter fatigue crack growth rate relation is assumed together with a logarithmic average life distribution. Good agreement is obtained with test data for different initial crack lengths.     

疲劳裂纹扩展寿命的可靠性及灵敏度分析

将影响结构疲劳裂纹扩展寿命的不确定因素视为随机变量,用随机有限元和可靠性分析理论,从概率论和数理统计的角度出发对含裂纹平面结构的断裂过程进行了可靠性分析。通过疲劳裂纹扩展寿命可靠度对随机变量的灵敏度分析,可以看出不同因素对疲劳裂纹扩展寿命可靠度影响的差别很大。     

基于多因素的焊接结构疲劳裂纹扩展速率分析

以Donahue等提出的疲劳裂纹扩展速率计算模型为基础,通过引入形状系数、张开比和残余应力等参数,建立了适用于焊接结构的疲劳裂纹扩展速率计算模型,分析了多种因素对焊接结构疲劳裂纹扩展速率的影响规律。结果表明,焊板厚度和焊缝余高的变化均会对焊接结构疲劳裂纹的扩展速率产生影响,在对焊接结构表面形状进行设计时应保有一定的焊缝余高;有效应力比的增大会降低焊接结构疲劳裂纹的扩展速率,且裂纹深度的变化不会改变有效应力比对焊接结构疲劳裂纹扩展速率的影响;残余应力的增大会提高焊接结构疲劳裂纹的扩展速率,且残余应力对疲劳裂纹扩展速率的促进作用随着裂纹深度的增加而增大,在对焊接结构的疲劳性能进行设计时须考虑残余应力对结构性能的影响。     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

Correlation of crack growth rate and stress ratio for fatigue damage containing very high cycle fatigue regime

A model is proposed to correlate the crack growth rate and stress ratio containing very high cycle fatigue regime. The model is verified by the experimental data in literature. Then a formula is derived for the effect of mean stress on fatigue strength, and it is used to estimate the fatigue strength of a bearing steel in very high cycle fatigue regime at different stress ratios. The estimated results are also compared with those by Goodman formula.     

Three-dimensional transverse fatigue crack growth in rail head

Results are given in terms of crack growth area and tonnage of train load. A three-dimensional finite element procedure is developed for analyzing multiple-mode transverse fatigue crack growth in a rail section. Stress and failure analysis are performed for each increment of non-self-similar crack growth up to the point of global instability that is assumed to be governed by the fracture toughness of the rail steel. The strain energy density criterion is adopted to predict the crack profiles developed from a two-stage fatigue loading cycle where both Mode I and III crack extension are present. Use is made of the material data obtained from the past and present TSC programs for predicting the remaining life of a 132 lb/ft rail head with an initial transverse circular crack of 0.50 in. in diameter. The number of cycles to failure are estimated for four different vertical load and initial crack positions.     

混凝土裂缝开展宽度计算的有限单元法

本文采用“最大拉应力单元开裂”准则，改进了非线性分析的迭代流程，使其最大可能地模拟实际结构的开裂情况，进而可以基于分布裂缝模式计算裂缝发生位置，裂缝间距，裂缝开展深度和宽度。算例表明，该法所计算的裂缝分布规律是正确的，计算裂缝宽度与试验实测值及规范公式计算值基本吻合，可以推广应用。     

广义扩展有限元法及其在裂纹扩展分析中的应用

结合广义有限元法(GFEM)和扩展有限元法(XFEM)的特点,提出了一种新的数值方法——广义扩展有限元法(GXFEM)。阐述了广义扩展有限元法的基本原理,对相关公式进行推导,探讨数值实施中需注意的重要问题,给出利用广义扩展有限元法进行断裂分析时应力强度因子的计算方法,编写了广义扩展有限元法程序。通过算例进行了应力强度因子的计算,模拟了结构裂纹的扩展过程。算例结果表明,利用广义扩展有限元法计算裂纹扩展问题,不需要进行过密的网格划分,且网格在裂纹扩展后无需重新剖分,具有相当高的计算精度。