Characteristics of a transiently propagating crack in functionally graded materials

When a crack propagates with acceleration, deceleration and time rates of change of stress intensity factors, it is very important for us to understand the effects of acceleration, deceleration and time rates of change of stress intensity factors on the individual stresses and displacements at the crack tip. Therefore, the crack tip stress and displacement fields for a transiently propagating crack along gradient in functionally graded materials (FGMs) with an exponential variation of shear modulus and density are developed and the characteristics of a transiently propagating crack from the fields are analyzed. The effects of the rate of change of the stress intensity factor and the crack tip acceleration on the individual stresses at the crack tip are opposite each other. Specially, the isochromatics (constant maximum shear stress) of Mode I tilt backward around the crack tip with an increase of crack tip acceleration, and tilt forward around the crack tip with an increase of the rate of change of the dynamic mode I stress intensity factor. This paper was recommended for publication in revised form by Associate Editor Chongdu Cho Kwang-Ho Lee received a Ph.D. degree in Yeungnam University in 1993. Dr. Lee is currently a professor at the School of Mechanical and Automotive Engineering at Kyungpook National University in Korea. He also had worked in KOMSCO as an engineer and researcher (1982.3–1996.2). He is interested in the fields of fracture and stress analysis on the composite, interface, nano and functionally graded materials by theoretical and experimental mechanics. Specially, his major interest is analysis of dynamic crack tip fields. Young-Jae Lee received his B.S degree in Agricultural Civil Engineering from Gyeongsang National University (GNU) in 1982. He then received his M.S. and Ph.D. degrees from GNU in 1984 and 1995, respectively. Dr. Lee is currently a professor at the department of Civil Engineering at Kyungpook National University in Korea. From 2005 to 2006, he had served as an editor of Korea Institute for Structure Maintenance and Inspection. His research interests are in the area of evaluation, diagnosis and optimum design of structure. Sang-Bong Cho received a Ph. D. degree from Tokyo University in 1989. Dr. Cho is currently a professor at the division of Mechanical and Automation Engineering at Kyungnam University in Korea. His research interests are in the area of fracture mechanics, FEM stress analysis and fretting fatigue.     

激光冲击对金属板料裂纹的影响模型

研究了含有裂纹的金属板料在激光冲击波载荷作用下裂纹尖端应力强度因子和裂纹扩展速度的变化,利用断裂力学理论,对激光冲击加载下裂尖参数计算模型进行优化,采用应力强度因子叠加法,将外加载荷引起的应力强度因子和激光冲击后残留的残余压应力引起的应力强度因子叠加,推导出下裂纹尖端应力场强度因子表达式,由此可精确计算出金属板料的裂纹萌生寿命和裂纹扩展速度,实验验证了航空钛合金Ti6Al4V激光冲击后残余应力对裂纹扩展速度的影响,从而建立了激光冲击作用对板料裂纹扩展的影响的理论模型。     

工字型梁腹板中Ⅲ型裂纹应力强度因子分析

基于能量释放率研究Ⅲ型裂纹平面应变条件下的J积分能量表达式。采用有限元软件模拟了工字梁腹板受扭转时裂纹裂尖应力奇异场,通过数值模拟得出裂纹区的应力、位移分布状态,并计算应力强度因子和J积分,从而验证表达式的可行性。     

用杂交有限元法计算三维裂纹的应力强度因子

根据放松了连续性要求的修正势能原理及裂纹尖端的应力、位移场,推导了杂交单元的单元刚度矩阵。用杂交元法计算了纯扭转载荷下带有环形裂纹的圆柱体的应力强度因子。计算结果表明,这种计算方法具有较高的精确度。用杂交元法计算了裂面上作用有弯、切,扭载荷试件的应力强度因子,这类试件可用于进行三维断裂准则的实验研究。     

有限加筋板宽度对应力强度因子的影响

基于线性累积损伤理论,分析了含裂纹损伤的加筋板加强筋宽度的不同对裂纹尖端应力强度因子的影响。然后根据分析得到裂纹尖端应力强度因子随加强筋宽度的变化规律。结果表明,随着加强筋宽度的增大,结构应力强度因子的下降幅度逐渐增大,当裂纹尖端离筋条越近时,这种现象越明显。     

弹性半空间中平片裂纹问题的超奇异积分方程方法

使用边界积分方程方法,在有限部积分的意义下,将弹性半空间中垂于自边界面的平片裂纹归结为一组以裂纹面位移间数为示知函数的超奇异积仞氖限部积分蜞 建立了数值人出了用裂纹面位移间尖力强度因子的公式。通过对圆形、菜和矩形等贡型的平片裂纹问题的计算,分析了自由边界面对裂纹前沿应力强度因子的影响。     

基于ABAQUS的圆柱直齿轮齿根裂纹扩展与寿命估计

以渐开线直齿轮为研究对象,通过齿轮应力分析确定轮齿裂纹易萌生位置,利用ABAQUS软件建立齿轮裂纹扩展有限元模型,获取齿根裂纹扩展路径,计算不同阶段裂纹尖端应力强度因子.通过多种曲线拟合方式的对比,选取指数函数建立的裂纹长度与裂纹尖端应力强度因子幅之间的函数关系.运用Paris公式构建裂纹扩展速率模型,实现含齿根裂纹齿...     

高频谐振载荷作用下Ⅰ型疲劳裂纹尖端力学参数变化规律

为研究高频谐振式疲劳裂纹扩展试验中带有Ⅰ型预制裂纹的紧凑拉伸(CT)试件裂纹尖端力学参数的变化规律,利用动态有限元方法,采用ANSYS和MATLAB软件编写程序,计算了CT试件在高频恒幅正弦交变载荷作用下,在一个应力循环及裂纹扩展到不同长度时裂纹尖端区域的位移、应变场及裂纹尖端的应力强度因子,并分析了其变化规律。在计算裂纹尖端应力强度因子时,首先采用静态有限元方法和理论公式验证了有限元建模和计算的正确性,然后采用动态有限元方法研究了裂纹扩展过程中裂纹尖端应力强度因子的变化规律。最后进行了高频谐振式疲劳裂纹扩展试验,采用动态高精度应变仪测量了裂纹扩展到不同阶段时裂纹尖端点的应变,并对有限元计算结果进行了验证。研究结果表明：在稳态裂纹扩展阶段,高频谐振载荷作用下Ⅰ型疲劳裂纹尖端位移、应变及应力强度因子均为与载荷同一形式的交变量;随着裂纹的扩展,Ⅰ型疲劳裂纹尖端的位移、应变及应力强度因子幅不断增大;静态应力强度因子有限元计算值和理论值的误差为2.51%,裂纹尖端点应变有限元计算结果和试验结果最大误差为2.93% 。     

轴承表面裂纹应力强度因子有限元分析

在ANSYS中建立152726QT铁路用滚动轴承的模型,在受力最大处建立裂纹,手动生成裂纹尖端处的奇异单元,建立接触对并且编写受力函数,设置路径在不同载荷作用下分别对不同长度的裂纹在不同深度的应力强度因子进行有限元计算,分析裂纹长度及载荷对应力强度因子的影响。     

基于ANSYS的焊接箱形梁裂纹断裂分析

以断裂力学理论为基础,推导了焊接箱形梁裂纹尖端应力强度因子计算公式,以ANSYS作为计算工具,模拟焊接箱形梁裂纹扩展,并采用奇异单元计算在不同长度初始裂纹下起重机焊接箱形梁应力强度因子范围。     

Influence of density variation on the arbitrarily propagating crack tip fields in functionally graded materials

The stress and displacement fields for an arbitrarily propagating crack tip in functionally graded materials (FGMs) with exponential variation of density and shear modulus are obtained. Nonhomogeneous parameters of density and shear modulus are different from each other. The solutions for higher order terms in the dynamic equilibriums are obtained by transforming the general differential equations to the scaled Laplace’s equations. Using the stress fields, the effects of the nonhomogeneous density on stress components is investigated. In addition, the contours of the constant maximum shear stress at a propagating crack tip are generated and the effects of the nonhomogeneous density on the isochromatics are discussed.     

The singular stress field and stress intensity factors of a crack terminating at a bimaterial interface

For the fracture evaluation of inclined cracks terminating at the dissimilar material interface, not only the singularities, but also the detailed stress field and its stress intensity factors are necessary. However, though there are many researches reported on the singularity analysis, the stress field and its stress intensity factors are still not clear. This paper has deduced theoretically the singular stress and displacement fields near the tip of a crack terminating at the interface between bonded dissimilar materials, for both cases of real and oscillatory singularities. From the deduced singular stress field, the stress intensity factors are defined for such a crack, and the corresponding numerical extrapolation methods are also proposed. Through the numerical examinations, it is found that the theoretical stress distributions agree well with the numerical results obtained by the finite element method. Moreover, the proposed extrapolation method shows a good linearity, thus it can be used as an efficient way to determine the characteristics of the stress and displacement fields near the tip of a crack terminating at interface.     

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only-0.621％;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is-11.29％.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05％.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.     

高速列车锻钢制动盘热疲劳裂纹耦合扩展特性研究

据制动盘裂纹剖面的宏观形貌,发现盘面长裂纹的形成以多条半椭圆表面裂纹连通为主。针对制动盘在运行过程中的典型运用工况,采用有限元法计算制动盘在300 km/h紧急制动后的热应力,发现周向残余应力较大,并以此推测周向残余应力是驱动制动盘热疲劳裂纹扩展的主要原因。在此基础上,建立制动盘盘面的裂纹网格,研究了裂纹扩展过程中的应力强度因子和多裂纹耦合扩展规律。通过研究发现对于给定的载荷条件,不同初始形状比时,裂纹前缘应力强度因子的分布规律存在一定的规律性,随着裂纹的扩展,裂纹形状趋于扁平化;多裂纹扩展时,裂纹间距越小,裂纹间的相互作用越明显,扩展速度越快;但受制动盘结构和尺寸限制,共线裂纹数越多,每条裂纹扩展到临界值时的应力强度因子越小。     

动车组铸钢制动盘裂纹扩展寿命预测

为研究动车组铸钢制动盘出现裂纹后裂纹扩展速率和扩展寿命,根据制动盘材料参数,使用ANSYS软件建立制动盘的循环对称三维瞬态计算模型,采用间接耦合方法计算制动盘的温度场和应力场,得到在动车组速度为300 km/h的工况下,裂纹处的温度为355.33℃。以温度计算结果作为初始载荷计算制动盘热应力,制动盘最大热应力为899 MPa,盘面裂纹处的应力为501 MPa。并将计算结果作为计算制动盘的载荷输入到NASGRO中,对裂纹扩展速率和扩展寿命进行计算和分析。计算和分析结果表明,此材料制动盘径向裂纹长度尖端处的应力强度因子和扩展速率均高于深度尖端处;计算得出制动盘裂纹扩展寿命为制动48 831次,为该制动盘的使用提供参考。     

压电材料平面渗透裂纹的机电耦合场

为提高压电传感器和换能器的品质,针对材料缺陷导致的压电元器件失效或不稳定,用复变函数的方法,结合椭圆形夹杂内的电场强度和电位移为常量这一早期研究结果,研究了压电材料平面电渗透裂纹的机电耦合场及其奇异性。解答表明,切向电场强度和法向电位移在裂纹尖端有由机械载荷引起的奇异,而与电载荷无关;应力强度因子与纯弹性材料结果一致。     

疲劳裂纹残余应力与应力强度因子研究

聚碳酸酯紧凑拉伸试件的疲劳试验和光弹性试验表明，尽管是低应力疲劳问题，但随着裂纹的扩展在裂尖附近出现残余应力场。给出了与循环周次相对应的卸载残余应力场，从而揭示出闭合效应的存在并提出其度量准则。试验表明，闭合效应使得应力强度因子降低，因此原有应力强度因子理论计算式不再适用，对此提出了一种简便有效的修正方案。     

Stress field near circular-arc interface crack tip based on electric saturation concept

Within the framework of nonlinear electroelasticity, the anti-plane problem of a circular-arc interfacial crack between a circular piezoelectric inhomogeneity and an infinite piezoelectric matrix subjected to a far-field uniform loading is investigated by an electrical strip saturation model, the complex variable method, and the method of analytical continuation. Explicit closed form expressions for the complex potentials in both the matrix and the inclusion, and the stress intensity factor at the crack tip are presented. Comparison with some related solutions based on the linear electroelastic theory shows the validity of the present solutions     

V形切口尖端裂纹起裂方向的主应力判别准则及其验证

围绕V形切口尖端裂纹起裂方向,分析了V形切口尖端裂纹应力场、位移场、应力强度因子,提出了裂纹起裂方向的主应力判别准则。首先,详细给出了V形切口尖端应力应变场的求解方法,通过裂纹尖端场本征值的三次线性拟合及误差分析,确定了V形切口尖端裂纹位移场;然后,建立了V形切口尖端的数值分析模型,运用数值计算方法确定了应力强度因子和切口强度因子,提出了V形切口尖端裂纹起裂方向的主应力判断准则,给出了外推法求解分析过程;最后,以LY8为试验材料,在张角2β＝60°的V形切口情况下,对提出的V形切口尖端裂纹起裂方向计算方法与判别准则进行了试验验证。     

应力比r对构件疲劳裂纹扩展的影响分析

应用能量释放率法及Paris公式对疲劳裂纹扩展问题进行了研究,详细分析比较了在不同应力比r作用下,对箱形构件未穿透型裂纹剖面各积分点的应力强度因子及裂纹扩展速率的影响.所得结论可为工程设计及裂纹无损检测人员提供一定参考.