Buckling analysis of pre-cracked beam-columns by Liapunov's second method

Interaction between reduced axial and lateral torsional buckling strengths of thin beam-columns of double symmetric sections with an edge crack at the middle is examined via Liapunov's second method. This is done in order to show how critical loads for pre-cracked thin-walled beam-columns can be obtained with out the rigour of meticulous solution of a set of differential equations. Having derived an asymptotic expression for the normalized energy release rates for the beam-column, a metric space and a Liapunov's Functional for a pre-cracked beam-column are proposed. By using Zubov's stability theorems and appropriate eigen value inequalities, expressions for reduced buckling strengths due to edge cracks are obtained. A crack reduction parameter k is proposed which is used to calculate reserve strengths for published lateral buckling strength equations. Results obtained using the proposed parameter are well in agreement with findings of earlier published works in the literature when the parameter is set to zero. The results also show that cracks cause loss of stiffness and can reduce the lateral buckling strengths of beam-columns considerably.     

开口复合材料柱壳屈曲与补救有限元分析

用有限元法对含有轴向裂纹的开口加强复合材料柱壳结构进行了补救研究;分析其压缩屈曲强度与模态情况,得到了裂纹长度与屈曲强度的关系,并与无裂纹的结构进行了对比.结果表明:裂纹长度在200mm以下时,对整个结构承载能力影响很小;当裂纹长度继续增大时,屈曲区域从开口上方转移到裂纹附近,屈曲强度开始急剧下降.为了加强裂纹所在区域结构的承剪能力,进行适当的修补后,可使屈曲模态与无裂纹柱壳相同,且屈曲强度稍有增加,从而证明了所提出补救方法的有效性.     

Buckling and vibration of a thin tensioned sheet with an elliptical hole

The out-of-plane deflection which can be developed in a thin tensioned sheet containing a central opening is discussed. It is noted that this behavior is of practical importance because it can alter the stress concentration and fatigue properties. The results of an experimental and analytical study of the buckling and vibration behavior of tensioned sheets with an elliptical opening are presented. Data from buckling and vibration experiments for several opening shapes ranging between a crack and a circle are presented. A generalized Galerkin method for solving the governing differential equations is used and the results obtained are presented in terms of buckling loads and natural frequencies. The experimental-buckling-stress estimates are correlated with the analytical results. The data from the vibration experiments indicate that the load-frequency behavior is dependent on the size of the test specimen and the opening shape. The analytical results display a load-frequency behavior which is experimentally observed for a narrow elliptical hole; i.e., for a small value of the ratio of minor axis to major axis. Some features of the analytical and experimental vibration results differ substantially, however. The analysis indicates that the frequency decreases to zero as the applied load approaches the buckling load. The experimental results do not exhibit this behavior. The sources of this difference in behavior are discussed.     

Gigacycle fatigue behaviors of two SNCM439 steels with different tensile strengths

Gigacycle fatigue behaviors of two SNCM439 steels with different tensile strengthes were experimentally studied by rotating bending tests,to investigate the effects of the tensile strength obtained by different heat treatment processes on very high cycle fatigue failure mechanisms.The material with higher tensile strength of 1 710 MPa exhibited typical gigacycle fatigue failure characteristics,whereas one with lower tensile strength of 1 010 MPa showed only traditional fatigue limit during the tests and no gigacycle failure could be found even when the specimen ran up to more than 10 8 cycles.Metallographic and fractographic analysis were carried out by an optical microscope (OM) and scanning electron microscope (SEM).It showed two different crack initiation mechanisms that for the specimen with lower tensile strength the crack prefers surface initiation and for that with higher strength the crack initiates from subsurface inclusions revealed by a fish-eye like microstructure.     

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.     

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.     

Fracture of Plates with an Inclined Edge Crack under Tension

The paper discusses experimental results on tension fracture of D16AT plates with an inclined crack with and without local buckling. The influence of crack geometry (initial length and crack angle) on fracture kinetics and strength of the plates is studied. Also the effect of local buckling on the fracture characteristics is evaluated     

The influence of tempering martensite containing microstructures on the near threshold fatigue crack propagation behaviour

Fatigue crack growth studies have been conducted in a humid air environment for various martensite containing microstructures under low and high R-ratio testing conditions.Tempering reduced the yield strength properties; the greater the amount of martensite the greater the reduction.Tempering generally (i) increased the threshold for fatigue crack growth ΔK_th, and (ii) decreased near threshold fatigue crack growth rates for both low and high R-ratio testing conditions. Also tempering inhibited the occurrence of subcritical transgranular cleavage in the high R-ratio tests of the ferrite-martensite microstructures and consequently affected Stage II fatigue crack growth behaviour.Finally the fully martensitic microstructure did not exhibit cracking and the present ΔK_th data exhibited good agreement with other data for steels in the tempered condition.     

Stability and residual strength of panels with straight and curved cracks

Loss of local stability and residual strength of panels with a through crack in tension is studied whereby the crack can take different configurations, namely, straight, inclined and curved. The critical stresses corresponding to buckling and crack initiation are determined. Here, buckling corresponds to the panel deflecting out of its own plane.     

A simpliied fatigue assessment method for transverse illet welded joints

Under the as-welded condition the fatigue crack initiation period was considered nonexistent and Linear Elastic Fracture Mechanics(LEFM) was used to calculate fatigue strength for a range of weld geometries. Fracture mechanics assessment of welded joints requires accurate solutions for stress intensity factor(SIF). However, the solutions for the SIF of complex welded joints are dificult to determine due to the complicated correction factors. Three methods for SIF prediction are discussed on illet welded specimens containing continuous or semi-elliptical surface cracks, including the traditional correction method Mk, the approximate correction method Kt, and the suggested additional crack size method(ac+ae).The new additional crack parameter ae is used to replace the stress concentration effect of weld proile Mk, which simpliies the calculation process. Experimental results are collected to support fatigue strength assessment of the additional crack size method.     

Fatigue life prediction of in-plane gusset welded joints using strain energy density factor approach

Fatigue crack growth behavior of in-plane gusset welded joints is studied using the strain energy density factor approach. Fatigue tests were performed in order to estimate fatigue strength under tension. Fatigue crack growth analysis was carried out to show the effects of the initial crack shape, the initial crack length, and the stress ratio on the crack types of in-plane gusset welded joints. The assumed crack types were edge crack, semi-elliptical crack, and corner crack. Fatigue crack growth parameters were obtained from crack growth curves assuming constant crack shapes for the given crack types. The results of analysis for the assumed crack types agreed well with the experimental data. The fatigue life did not change as initial crack shape varied for a given initial crack length.     

降载勾线法在高强钢疲劳断裂试验中的应用

制作高强钢特征试件,在压、弯应力共同作用下进行疲劳断裂试验;结合疲劳辉纹产生机理,采用降载勾线法在试件断面制造出“海滩状花纹”;利用CAD软件描绘断面形貌并测量裂纹长度,用Newman-Raju理论进一步研究表面裂纹扩展的规律,并与试验值比较.结果表明降载勾线法可以解决高强度钢表面裂纹不易测量及断面难以观测到疲劳辉纹的问题;采用Newman-Raju公式模拟压弯组合应力下表面裂纹扩展形貌是合适的,但由此计算的疲劳寿命偏于保守.另外,当压弯应力比值较小时,计算扩展形貌时压应力可以忽略,而计算疲劳寿命时压应力不可忽略.     

Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory

The elastic buckling analysis and the static postbuckling response of the Euler–Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Kármán nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.     

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在空气和腐蚀介质中对低合金钢分别的进行疲劳试验,获得了S-N曲线,并对疲劳试样表面和断口形貌进行了观察。结果表明：与空气相比,腐蚀介质使低合金钢的疲劳强度显著降低;空气中疲劳试样只有一个萌生于试样表面基体的裂纹源,而腐蚀介质中的疲劳试样一般有多个裂纹源,多数裂纹源均萌生于点蚀坑;空气中疲劳裂纹扩展区以疲劳辉纹为主,而腐蚀疲劳则以沿晶开裂等脆性特征为主;此外还对空气中的疲劳极限进行了预测,预测值与试验值比较吻合     

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.     

16Mn钢在不同条件下的疲劳行为研究

对截面为3 mm×3mm的16Mn钢试件在空气和3.5%NaCl溶液中分别进行疲劳试验,获得了S-N曲线,并对疲劳试样表面和断口形貌进行了观察.结果表明:与空气相比,3.5%NaCl腐蚀溶液使16Mn钢的疲劳强度显著降低;在空气中疲劳试样只有一个萌生于试样表面基体的裂纹源,而在3.5%NaCl溶液中一般有多个裂纹源,而...     

DETERMINATION OF CRACK SURFACE DISPLACEMENTS FOR A RADIAL CRACK EMANATING FROM A SEMI-CIRCULAR NOTCH USING WEIGHT FUNCTION METHOD

A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate.Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained with the weight function method. It is demonstrated that the WuCarlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required.     

Analytical and experimental evaluations of the influence of fracture surface roughness,its sliding actions and the associated plasticity on fatigue crack propagation

An investigation of fatigue crack propagation in rectangular AM60B magnesium alloy plates containing an inclined through crack is presented in this paper. The behavior of fatigue crack growth in the alloy is influenced by the fracture surface roughness. Therefore, in the present investigation, a new model is developed for estimating the magnitude of the frictional stress intensity factor, k_f, arising from the mismatch of fracture surface roughness during in-plane shear. Based on the concept of k_f, the rate of fatigue crack propagation, db/dN, is postulated to be a function of the effective stress intensity factor range, Δk_eff. Subsequently, the proposed model is applied to predict crack growth due to fatigue loads. Experiments for verifying the theoretical predictions were also conducted. The results obtained are compared with those predicted using other employed mixed mode fracture criteria and the experimental data.     

Compressive response of a sandwich plate containing a cracked diamond-celled lattice

The compressive strength is determined for a sandwich plate containing a centre-cracked core made from an elastic–brittle, diamond-celled lattice. It is assumed that the lattice fails when the major component of principal stress anywhere in the lattice attains the compressive or tensile strength of the solid, or when local buckling intervenes. First, analytical and numerical predictions are given for the unnotched strength of the core and for the compressive fracture toughness of the lattice K_IC. Second, finite element simulations and analytical models are reported for the fracture response of the sandwich plate with cracked core. The active failure mechanism in the cracked core is sensitive to core height, crack length, lattice geometry and material choice; this is illustrated by means of material-property charts.     

基于子模型法的带有表面裂纹钢丝应力强度因子研究

钢丝裂纹应力强度因子是进行钢丝疲劳断裂寿命评估、疲劳裂纹扩展分析和钢丝断裂强度评估等工作的重要参数。本文首先介绍了裂纹扩展分析软件FRANC3D,然后基于子模型法模拟研究了拉伸荷载作用下带有表面裂纹钢丝的应力强度因子,裂纹种类包括直线形裂纹和半圆形裂纹,最后拟合得到拉伸荷载作用下带表面裂纹钢丝的应力强度因子形状修正系数表达式,分析了利用该公式进行承载力评估时产生误差的原因。研究结果表明,利用子模型模拟分析拉伸荷载作用下带有表面裂纹的钢丝应力强度因子时计算精度高,计算速度快,对计算机硬件要求低;利用该方法得到的钢丝裂纹应力强度因子,在进行索承式桥梁吊索安全性能评估时,评估结果更精确。