含曲线裂纹柱体扭转问题的新边界元法

研究了带曲线裂纹柱体的扭转断裂问题,推导出了可以直接应用于任意形状截面含有任意形状曲线裂纹的柱体扭转问题的新的边界积分方程,并建立了带裂纹柱体扭转问题的边界元数值计算方法,提出了裂纹尖端的奇异元和线性元插值模型,给出了抗扭刚度和应力强度因子的边界元计算公式。该文对含有圆弧裂纹、曲线裂纹及直线裂纹的不同截面形状柱体的典型问题进行了数值计算,所得结果证明了边界元方法的正确性和有效性。     

裂纹对弧齿锥齿轮扭转啮合刚度的影响分析

运用Pro/E软件建立了无裂纹和含裂纹弧齿锥齿轮完整的三维接触模型,并基于有限元分析软件ANSYS对模型进行了仿真模拟与数值计算,分析了两种运行状态下,不同接触位置上的扭转啮合刚度。仿真结果表明：裂纹使弧齿锥齿轮的扭转啮合刚度变化更加剧烈。     

圆轴扭转时最大剪应力和最小剪应力的计算

本文归纳了实心圆轴和空心圆轴扭转时横截面上剪应力分布规律以及最大剪应力和最小剪应力的计算。特别列举了空心圆轴扭转时最小剪应力计算的四种情况，通过学生讨论、分析，得出其中两种计算是正确的，而另两种是错误的，并找出错误的原因，让学生加深理解了空心圆轴扭转时最小剪应力的计算。     

裂尖具线性分布约束应力的运动裂纹模型及其解析解

以恒定速度运动的Griffith裂纹解析解为著名的Yoffe解。静止裂纹的条状屈服模型即Dugdale模型,将其推广到运动裂纹模型时发现,当裂纹运动速度跨越Rayliegh波速时,裂纹张开位移COD趋于(∞,且表现为间断。通过在裂尖引入一个约束应力区及两个速度效应函数,假设约束应力为线性分布,采用复变函数方法,求得动态应力强度因子SIF与裂纹张开位移COD的解析解。新的结果,在Rayleigh波速下裂纹张开位移连续且为有限值。给出裂纹张开位移的一些数值结果,获得了一些有意义的结论。     

基于主动艉支承的推进轴系横向振动抑制仿真与实验研究

提出一种基于主动艉支承的推进轴系横向振动传递控制方法,以抑制水下航行器的低频声辐射。该方法将传统的艉轴承支承方式由面支承改为点支承,通过六个主动作动器抑制螺旋桨横向激励力经由艉轴承向壳体的传递。建立包含主动艉支承的螺旋桨-推进轴系-壳体耦合系统动力学模型,分析系统振动传递特性及控制策略可行性;结合自适应控制算法,计算螺旋桨横向激励下的振动传递抑制效果。构建包含主动艉支承的螺旋桨-推进轴系-壳体实验系统,进一步验证控制方法的有效性。仿真与实验结果均表明主动艉支承对于螺旋桨横向激励力经由艉轴承向壳体的传递具有明显抑制效果,可有效降低壳体表面法向振动。     

H型截面钢梁约束扭转的简化计算

钢梁在外扭矩以及梁端约束的作用下,会产生翘曲正应力以及剪应力,传统上利用扇性坐标及双力矩法计算,计算过程很繁琐。许多工程师在设计中对钢梁扭转作用的处理带有一定的盲目性。根据约束扭转的受力及变形特点,以变形协调为基础提出一种新的计算钢梁约束扭转的简化计算方法,该方法可很好的计算钢梁在外扭矩作用下的受力情况。算例计算结果表明,该方法具有很好的精度和准确性,可供工程设计应用。     

方形截面管横向裂纹的应力强度因子KI

利用裂纹张开能量释放率建立了一个求解方形截面管横向裂纹应力强度因子的一个方法。给出了方形截面管裂纹张开能量释放率的 G*-积分表征,以及和应力强度因子的关系。同时也给出了 G*-积分与载荷、几何参量以及机械性能参数的关系,进而得到方形截面管横向裂纹的应力强度因子。给出的方法不仅适用于一般箱形结构件的裂纹问题,也适用于其它有限边界多边管状结构的三维裂纹问题,过程极为简单。     

含多个椭圆孔或裂纹的圆柱体扭转问题

基于复势函数理论,提出了一种既简洁又直观的方法来研究含多个椭圆孔或裂纹的圆柱体的Saint-Venant扭转问题.首先,应用保角变换技术以及Faber级数和Fouriier级数展开方法,给出了孔边应力和抗扭刚度的半解析解;然后,当椭圆退化成裂纹时推导了裂纹尖端的应力强度因子解.最后,通过几组数值算例,讨论了各种参数的变...     

椭圆形半露头裂纹的线弹簧模型

建立了无限平板椭圆形半露头裂纹线弹簧模型,由积分变换方法推导了问题的控制方程和应力强度因子表达式,给出了相应于表面裂纹及内埋裂纹的计算结果,通过与现有有限元解或交替迭代解比较,表明了解的良好性。由此说明半露头裂纹的线弹簧模型解也将是合理的可靠的。     

一个简化的表面裂纹应力强度因子的计算公式

通过三点弯曲加载的表面裂纹试样研究了碳氮共渗、渗氮及调质几种不同热处理的(?)面裂纹疲劳扩展行为。试验证实:半椭圆表面疲劳裂纹的长轴(c)、短轴(α)与试样厚度(B)符合α/c α/B=0.99±,,12的关系式。并且在我们的试验范围内(0.33≤α/c≤0.71;0.29≤α/B≤0.67),其长轴端应力强度因子可用简单的放学式进行计算:△K_c=A·△,(πc)/(1/2)·M_w.其中A≈0.5。由此大大简化了表面裂纹应力强度因子的计算。     

Effects of the transverse stress on biaxial fatigue crack growth predicted by plasticity-corrected stress intensity factor

The transverse stress has an important effect on the biaxial fatigue crack behavior. However, the experimental evidence has provided conflicting indications: it is sometimes considered to increase, decrease or have no effect. These complex phenomena cannot be rationally explained by the existing mechanical models. The effect of the transverse stress on the fatigue crack growth behavior is still one of the most puzzling questions in biaxial fatigue. Physically, this effect is a transverse stress induced plasticity phenomenon. In this paper, a plasticity-corrected stress intensity factor (PC-SIF) is proposed to describe the effect of transverse stress on biaxial fatigue. By use of this new crack driving force some important phenomena associated with transverse stress are predicted. Comparisons with experimental results showed that the PC-SIF as an effective mechanical parameter is capable of predicting the effects of the crack length, the stress level, cyclic stress ratio, biaxial stress ratio and phase difference on the biaxial fatigue crack growth. Consequently, the alleged conflicting experimental results have been rationally explained by the PC-SIF.     

Dynamic stress field for torsional impact of a penny-shaped crack in a transversely isotropic functional graded strip

The torsional impact response of a penny-shaped crack in a transversely isotropic strip is considered. The shear moduli are assumed to be functionally graded such that the mathematics is tractable. Laplace and Hankel transforms are used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Investigated are the effects of material nonhomogeneity and orthotropy and strip’s highness on the dynamic stress intensity factor. The peak of the dynamic stress intensity factor can be suppressed by increasing the shear moduli’s gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface. The dynamic behavior varies little with the increasing of the strip’s highness.     

Elastodynamic stress intensity factors for a semi-infinite crack due to three-dimensional concentrated shear loadings on the crack faces

The dynamic stress intensity factors for a semi-infinite crack in an otherwise unbounded elastic body is investigated. The crack is subjected to a pair of suddenly-applied shear point loads on its faces at a distance l away from the crack tip. This problem is treated as the superposition of two problems. The first problem considers the disturbance by a concentrated shear force acting on the surface of an elastic half space, while the second problem discusses a half space with its surface subjected to the negative of the tangential surface displacements induced by the first problem in the front of the crack edge. A fundamental problem is proposed and solved by means of integral transforms together with the application of the Wiener–Hopf technique and Cagniard–de Hoop method. Exact expressions are then derived for the mode II and III dynamic stress intensity factors by taking integration over the fundamental solution. Some features of the solutions are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of initial stress on fracture of a halfspace containing a penny-shaped crack under radial shear

In this study, an axisymmetrical problem for a penny-shaped crack under radial shear is considered. The crack is located parallel to the surface of a halfspace, which is subjected to initial stress parallel to the crack plane. An approach proposed by Guz (1983) in the framework of the three-dimensional linearised solid mechanics is used. Analysis involves reducing the problem to a system of Fredholm integral equations of the second kind, where the solutions are identified with harmonic potential functions. The representations of the stress intensity factors K _I and K _II near the crack edges are obtained. These stress intensity factors are both influenced by the initial stress.     

Influence of effective stress intensity factor range on mixed mode fatigue crack propagation

ABSTRACT The behaviour of fatigue crack propagation of rectangular spheroidal graphite cast iron plates, each consisting of an inclined semi‐elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the growth of the fatigue crack was monitored using the AC potential drop technique, and a series of modification factors, which allow accurate sizing of such defects, is recommended. The rate of fatigue crack propagation db/dN is postulated to be a function of the effective strain energy density factor range, ΔS_eff. Subsequently, this concept is applied to predict crack growth due to fatigue loads. The mixed mode crack growth criterion is discussed by comparing the experimental results with those obtained using the maximum stress and minimum strain energy density criteria. The threshold condition for nongrowth of the initial crack is established based on the experimental data.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

A new numerical analysis for a semi-circular surface crack

This note is concerned with a surface semi-circular crack by using the fracture analysis software FRANC3D developed by a fracture mechanics investigation group of Cornell University. Attention is specifically paid to the effect of the boundaries parallel to the crack on the stress intensity factors (SIFs).     

Interaction of a penny-shaped crack with an elliptic crack under shear loading

The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter _i up to the order _i⁵,(i=1,2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289–313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.     

An arc-shaped crack in an electrostrictive material

The plane problem of a circular-arc crack in an infinite electrostrictive solid under remote electric fields is studied based on the complex variable method. First, explicit solutions for the complex potentials are presented in closed-form. Secondly, intensity factors of total pseudo stresses are derived by taking the Maxwell stresses around the infinite surrounding space and inside the crack into account. Then, numerical results are given to discuss the effects of electric fields on the fracture of electrostrictive materials. It is found that when the interior of the crack is filled with the same gas as that at infinity, the applied electric field has no effects on crack growth; however, when the interior of crack and the surrounding space at infinity are filled with different gases, the applied electric field may either enhance or retard crack growth, which depends on the electric boundary conditions adopted on the crack faces, the Maxwell stresses on the crack faces and at infinity, and the central angle of the crack.     

Three-dimensional stress and displacement fields near an elliptical crack front

Local stress and deformation fields for an elliptical crack embedded in an infinite elastic body subjected to normal, shear and mixed loads are considered. Particular emphasis is placed on the direction of propagation of points along the crack border. A confocal curvilinear coordinate system related to a fundamental ellipsoid, and a local spherical coordinate system attached to the crack border are adopted. Using asymptotic analysis, this paper obtains the stress and displacement fields in a plane inclined to the 3D crack front. Results show that the present solutions are independent of the curvature of the ellipse, and different from those given by Sih (1991). Based on two different fracture criteria, crack growth analysis shows that a 3D crack would propagate in the direction of the normal plane along the crack front. As a result, the fracture initiation and propagation of a 3D flat crack can be analyzed in the plane normal to the crack front, and the local fields in the normal plane are the linear superposition of the plane strain mode-I, mode-II, and mode-III crack-tip fields.