Convolution of the impact three-dimensional elasto-dynamics and dynamic stress intensity factor for an elliptic cracks

This paper presents a formulation for three-dimensional elastodynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method. The project supported by the National Natural Science Foundation of China (K19672007)     

拉伸荷载下分支裂隙破坏机理研究

为研究拉伸荷载下分支裂隙对破坏模式的影响,保持主裂隙参数不变,改变分支裂隙倾角和长度,利用扩展有限元方法模拟了弯折裂隙的动态扩展,总结了分支裂隙参数变化对破坏模式的影响.利用ABAQUS中的轮廓积分计算了分支裂隙尖端应力强度因子,并根据最大周向应力准则计算起裂角.结果表明:拉伸荷载下分支裂隙出现三种破坏模式;分支裂隙倾...     

A half plane crack under three-dimensional combined mode impact loading

The dynamic stress intensity factor history for a half plane crack in an otherwise unbounded elastic body, with the crack faces subjected to a traction distribution consisting of two pairs of suddenly-applied shear line loads is considered. The analytic expression for the combined mode stress intensity factors as a function of time is obtained. The method of solution is based on the application of integral transforms and the Wiener-Hopf technique. Some features of the solutions are discussed and graphical numerical results are presented. The project supported by the National Natural Science Foundation of China     

冲击载荷作用下裂纹动态响应的数值模拟

对垂直、剪切以及斜向等各种冲击载荷作用下裂纹的动态响应进行了数值模拟,得到了一系列随时间变化的动态应力场以及应变场图;根据其定义,计算出了相应的动态应力强度因子,进而分析了斜向载荷作用下裂纹起裂情况,并对最优断裂问题进行了阐述。     

Crack growth under alternating loading

Crack propagation under alternating loading is investigated. Relations between the growth rate of a fatigue defect and loading parameters and the expression for the stress intensity factor are derived for compression of a cracked solid taking into account the possible contact of the crack faces. A model for the deformation of a small region near the crack tip is proposed which allows one to formulate the conditions of residual opening of a growing fatigue crack. The experimental data obtained in tests of steel samples are compared with the results of calculation using the developed procedure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 190–198, September–October, 2008.     

Stress state in the plastic zone on the continuation of an elliptic mode I crack under bi-and tri-axial loading

The spatial stress state in a circular plastic zone near an elliptic crack under bi-and tri-axial asymmetric loading at infinity is studied. It is shown that the plastic constraint factor peaks at the points with maximum external tensile tangential stresses on the crack boundary. The use of a two-parameter failure criterion leads to the conclusion that the limit state can first be reached at the ends of the major axis of the elliptic crack depending on the relation between the external stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 24–30, November 2007.     

辛解析奇异元在动荷载作用下V型切口问题中的应用

利用辛解析奇异单元,结合时域精细算法,研究了动荷载作用下的含平面V型切口问题。时域上,采用时域精细算法,并结合自适应算法控制展开项数,保证了计算精度。空间域上,切口尖端附近采用辛解析奇异单元,其余区域采用常规有限单元,避免了局部网格加密。本文使用的辛解析奇异单元不需要过渡单元和局部网格加密,且能够通过奇异单元内部的参数关系直接给出切口尖端的应力强度因子,不需要复杂的后处理过程。数值结果表明,本文方法具有良好的精度和稳定性,可以准确地计算动态应力强度因子。     

三点弯曲试样动态冲击特性的有限元分析

本文使用动态有限元技术，对于两种不同几何尺寸，两种不同材料的三点弯曲试样在三类七种不同冲击载荷作用下的动态响应进行了分析，求得了动态应力强度因子随时间的变化规律。并与准静态应力强度因子进行了比较。计算结果表明：将冲击载荷历史代入静态公式确定动态应力强度因子的做法是不正确的，要求得动态应力强度因子，必须对试样进行完全的动态分析。当材料的Ｅ／ρ值相同时，动态应力强度因子的响应曲线完全相同。而动态应力强度因子分别与加载点的位移及裂纹的张开位移之间存在着与准静态情况下各自相同的线性关系。这与资料［５］［６］中的结论完全相同。     

基于圆弧底试件的动态裂纹扩展及止裂规律研究

为了研究脆性材料的动态裂纹扩展及止裂规律,设计了一种带圆弧形底边的梯形开口边裂纹（trapezoidal opening crack with arc bottom,TOCAB）构型的试件。在落锤冲击设备加载下,对圆心角为0°、60°、90°和120°的TOCAB试件进行了冲击实验,并采用裂纹扩展计(crack propagation gauge,CPG)监测裂纹起裂和扩展时间,从而获得裂纹扩展速度。采用有限差分软件AUTODYN对落锤冲击设备和试件进行数值模拟,研究了裂纹的动态扩展过程及止裂规律。还基于实验和数值方法,计算了裂纹的临界动态应力强度因子。实验和数值结果均表明：3种弧度的TOCAB试件都可以实现运动裂纹止裂,该构型可用于研究动态裂纹止裂问题;数值计算的裂纹扩展路径与实验结果基本一致,验证了数值模型的有效性;裂纹起裂和止裂时刻的临界动态应力强度因子大于裂纹动态扩展过程中的临界动态应力强度因子。

     

冲击载荷下两裂纹间的连通规律

脆性材料内部含有大量裂纹,当某一裂纹扩展时,其他裂纹会对扩展裂纹产生影响。为了研究冲击载荷下,脆性材料内两裂纹的相互影响、连通规律及裂纹尖端应力强度因子的变化规律,利用有机玻璃板制作了含非平行双裂纹的实验试件,利用落板冲击设备进行了中低速冲击实验,结合有限元分析软件ABAQUS计算出裂纹尖端应力强度因子,利用有限差分软件AUTODYN进行了动态数值模拟研究,并将其模拟结果与实验结果进行对比分析。实验及模拟结果表明：裂纹破坏形态与AUTODYN数值模拟破坏形态基本一致;试件的断裂形态随着两裂纹间距不同而不同;裂纹间的相互影响程度随着裂纹间间距增大而减小;裂纹尖端应力强度因子K_I随着裂纹间距的增大而减小,而K_II随着裂纹间距增大而增大。

     

Thermostressed state of a piezoelectric bodywith a plane crack under symmetric thermal load

The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 96–108, March 2008.     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.     

Stress state of a transversely isotropic magnetoelectroelastic body with a plane crack under antisymmetric loads

The static equilibrium of a transversely isotropic magnetoelectroelastic body with a plane crack of arbitrary shape in the isotropy plane under antisymmetric mechanical loading is studied. The relationships between the stress intensity factors (SIFs) for an infinite magnetoelectroelastic body and the SIFs for a purely elastic body with the same crack and under the same antisymmetric loading are established. This enables the SIFs for a magnetoelectroelastic body to be found directly from the analogous problem of elasticity. As an example of using this result, the SIFs for penny-shaped, elliptic, and parabolic cracks in a magnetoelectroelastic body under antisymmetric mechanical loading are found Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 37–51, October 2008.     

The dynamic stress intensity factor analysis of adhesively bonded material interface crack with damage under shear loading

This paper studies the dynamic stress intensity factor (DSIF) at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.     

Stress state of an orthotropic material with an elliptic crack under linearly varying pressure

The static equilibrium of an elastic orthotropic medium with an elliptic crack subject, on its surface, to linearly varying pressure is studied. The stress state of the elastic medium is represented as a superposition of the principal and perturbed states. Use is made of Willis’ approach based on the triple Fourier transform in spatial variables, the Fourier-transformed Green’s function for an anisotropic material, and Cauchy’s residue theorem. The contour integrals are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of orthotropy on the stress intensity factors is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 73–81, July 2006.     

空心车轴不同深度表面裂纹应力强度因子研究

分析了空心车轴的旋转弯曲载荷的特点,建立了空心轴表面周向半椭圆裂纹的模型,给出了半椭圆裂纹的构形参数定义,即形状比、深度比和裂纹前缘相对位置。采用四分之一20节点等参退化奇异单元,通过有限元计算,模拟裂纹前沿的应力奇异性。在此基础上,计算了裂纹前缘表面点和中心点的应力强度因子随着裂纹扩展深度和旋转角度的变化。计算结果表明,对于给定的裂纹构形,在车轴的一个载荷循环中,裂纹前缘同一相对位置的应力强度因子是不断变化的,不同位置的应力强度因子在达到最大值的角度也是不同的,这就导致了裂纹前缘表面点在一些角度下的扩展是不对称的。这些结果为进一步研究空心轴表面裂纹的扩展路径和寿命提供了参考。     

冲击载荷下含表面裂纹圆柱壳体的动态断裂

动态载荷下含表面裂纹的有限尺寸构件的断裂问题在工程实践中有着重要意义,但由于此类问题非常复杂,目前还不能求得解析解。本文针对含轴向半椭圆盘状表面裂纹的圆柱壳体,应用有限元法研究了动态载荷下其断裂问题,计算了动态应力强度因子与静态应力强度因子的比值KdIyn(t)/KsIta。从计算结果可以得出,比值KdIyn(t)/KsIta与结构和裂纹的尺寸有关,而与冲击载荷的大小无关。本文所得结果在一定程度上揭示了圆柱壳体表面、裂纹面、物质惯性和弹性波的相互作用及其对动态断裂的影响。     

SEMI-ELLIPTIC SURFACE CRACK IN AN ELASTIC SOLID WITH FINITE SIZE UNDER IMPACT LOADING

In this paper a semi-elliptic surface crack problem in an elastic solid of finite size under impact loading is investigated. An analysis is performed by means of fracture dynamics and the finite element method, and a three-dimensional finite element program is developed to compute the dynamic stress intensity factor. The results reveal that the effects of the solid's boundary surface, crack surface, material inertia and stress wave interactions play significant roles in dynamic fracture.     

不同倾角预制裂纹缺陷与运动裂纹的相互作用

为了研究运动裂纹与不同倾角预制裂纹缺陷之间的作用机制,采用数字激光动态焦散线方法对含不同倾角预制裂纹缺陷的三点弯曲梁进行冲击实验。研究结果表明,在冲击载荷作用下,预制裂纹缺陷尖端均产生了次生裂纹;当运动主裂纹与预制裂纹缺陷贯通时,次生裂纹不会立即起裂,而是经过0~10 μs的能量积蓄后,次生裂纹才起裂;运动主裂纹应力强度因子峰值与次裂纹起裂时的应力强度因子值均随预制裂纹倾角的增大而增大。     

Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008.