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1.
An interface crack of finite length is considered between two semi-infinite planes with an artificial contact zone at one
of the two crack tips. A transcendental equation and certain simple asymptotic formulas are established for the real contact
zone (in the Comninou-Dundurs sense) in terms of the stress intensity factors (SIFs) of the considered model. In these terms analytical expressions are also provided for the energy release rate and for the
SIF of the classical interface crack model with an oscillating singularity at the crack tip. The appropriate length of the artifical
contact zone is shown to be attainable on the basis of the analysis of the stresses at the crack tip. The use of the proposed
model is suggested for integrity assessment of inhomogeneous structural elements of composites containing interface cracks.
Received 26 March 1997; accepted for publication 12 September 1997 相似文献
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载流薄板中裂纹形成瞬间尖端附近的应力场 总被引:2,自引:0,他引:2
利用电磁场的热效应对带有裂纹的载流导体进行裂纹止裂,是为了达到延长其工作寿命,提高安全性、可靠性的一种行之有效的方法。本文在文献[1]的基础上,以导电弹性体的麦克斯威尔方程为出发点,借助于边界条件和初始条件,推得了载流无限大薄板在形成裂纹的瞬间,裂纹尖端附近电流密度、温度和应力的具体表达式。通过算例分析证实了:在给定参数的情况下,通入适当强度的电流时,在电流所产生的焦耳热源的作用下,裂尖区域处的温度将瞬时升高,同时伴有压应力的产生,从而可达到阻止裂纹扩展的目的。 相似文献
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Summary An interface crack with an artificial contact zone at the right-hand side crack tip between two piezoelectric semi-infinite
half-planes is considered under remote mixed-mode loading. Assuming the stresses, strains and displacements are independent
of the coordinate x
2, the expression for the displacement jumps and stresses along the interface are found via a sectionally holomorphic vector
function. For piezoceramics of the symmetry class 6 mm and for electrically permeable crack faces, the problem is reduced
to a combined Dirichlet-Riemann boundary value problem which can be solved analytically. Further, analytical expressions for
the stresses, electrical displacements, derivatives of elastic displacement jumps, stress and electrical intensity factors
are found at the interface. Real contact zone lengths and the well-known oscillating solution are derived from the obtained
solution as well. Analytical relationships between the fracture-mechanical parameters of various models are found, and recommendations
are suggested concerning the application of numerical methods to the problem of an interface crack in the discontinuity area
of a piezoelectric bimaterial.
Received 16 March 1999; accepted for publication 31 May 1999 相似文献
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孔边裂纹对SH波的散射及其动应力强度因子 总被引:14,自引:1,他引:14
采用Green函数法研究任意有限长度的孔边裂纹对SH波的散射和裂纹尖端场动应力强度因子的求解.取含有半圆形缺口的弹性半空间水平表面上任意一点承受时间谐和的出平面线源荷载作用时位移函数的基本解作为Green函数,采用裂纹“切割”方法并根据连接条件建立起问题的定解积分方程,得到动应力强度因子的封闭解答.最后给出了孔边裂纹动应力强度因子的算例和结果,并讨论了圆孔的存在对动应力强度因子的影响 相似文献
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本文提出用裂尖附近2点或3点的应力和位移计算应力强度因子K_I的杂交方法.这种方法充分利用了边界单元法的计算结果,考虑了裂尖应力场和位移场渐近展开式的高阶项,使用远离裂尖的点算出的K_I也有较好的精度,拟合线十分平坦.用算例的结果将杂交法与一般的位移法和应力法进行了比较,同时,对常量单元和线性单元也进行了比较. 相似文献
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R. I. Kadiev V. M. Mirsalimov 《Journal of Applied Mechanics and Technical Physics》2005,46(1):108-116
This paper considers local temperature variations near the tip of a crack in the presence of regions in which the crack faces interact. It is assumed that these regions are adjacent to the crack tip and are comparable in size to the crack size. The problem of local temperature variations consists of delay or retardation of crack growth. For a crack with connections between the crack faces subjected to external tensile loads, an induced thermoelastic stress field, and the stresses at the connections preventing crack opening, the boundary-value problem of the equilibrium of the crack reduces to a system of nonlinear singular integrodifferential equations with a Cauchy kernel. The normal and tangential stresses at the connections are found by solving this system of equations. The stress intensity factors are calculated. The energy characteristics of cracks with tip regions are considered. The limiting equilibrium condition for cracks with tip regions is formulated using the criterion of limiting stretching of the connections.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 133–143, January–February, 2005 相似文献
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基于数字散斑相关方法测定Ⅰ型裂纹应力强度因子 总被引:1,自引:0,他引:1
提出了一种通过数字散斑相关方法测定金属材料Ⅰ型裂纹尖端位置和应力强度因子的实验方法.实验采用疲劳试验机对含Ⅰ型缺口的Cr12MoV钢试件预制裂纹,通过数字散斑相关方法测试试件在三点弯曲加载条件下裂纹的扩展过程及裂尖区域的位移场.将位移场数据代入裂尖位移场方程组,采用牛顿-拉普森方法求解含未知参量的裂尖非线性位移场方程组,计算裂尖位置和应力强度因子.实验结果表明,采用该方法可以准确地测定金属材料Ⅰ型裂纹应力强度因子、裂尖位置及裂纹扩展长度,解决了以往研究中因不能准确测定裂纹尖端位置,而无法准确计算Ⅰ型裂纹裂尖断裂参数的难题,揭示了金属材料裂纹扩展过程中应力强度因子演化特征. 相似文献
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Fracture toughness of metals depends strongly on the state of stress near the crack tip. The existing standards (like R-6, SINTAP) are being modified to account for the influence of stress triaxiality in the flaw assessment procedures. These modifications are based on the ability of so-called ‘constraint parameters’ to describe near tip stresses. Crack tip stresses in homogeneous fracture specimens are successfully described in terms of two parameters like J–Q or J–T. For fracture specimens having a weld center crack, strength mismatch ratio between base and weld material and weld width are the additional variables, along with the magnitude of applied loading, type of loading, and geometry of specimen that affect the crack tip stresses. In this work, a novel three-parameter scheme was proposed to estimate the crack tip opening stress accounting for the above-mentioned variables. The first and second parameters represent the crack tip opening stress in a homogeneous fracture specimen under small-scale yielding and are well known. The third parameter accounts for the effect of constraint developed due to weld strength mismatch. It comprises of weld strength mismatch ratio (M, i.e. ratio of yield strength of weld material to that of base material), and a plastic interaction factor (Ip) that scales the size of the plastic zone with the width of the weld material. The plastic interaction factor represents the degree of influence of weld strength mismatch on crack tip constraint for a given mismatch ratio. The proposed scheme was validated with detailed FE analysis using the Modified Boundary Layer formulation. 相似文献
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缺口根部和裂纹尖端残余应力的X射线法测定 总被引:1,自引:0,他引:1
X射线法用于缺口根部和裂纹尖端等徽区的残余应力测试的先决条件是解决缩小光束直径、提高衍射束的强度和准确设置试样等技术问题.在X射线衍射仪上借助于自行设计制造的限束对光装置和侧倾对中附件,成功地测定了缺口根部半径为1mm的喷丸残余应力场和板形试样压-压周期载荷下裂纹尖端的残余拉应力场. 相似文献
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本文应用复变函数解法,等出复合型中心裂纹板弹性应力场的精确解及主应力和与主应力差的精确表达式。通过与各自的奇异表达式比较,得到了主应力和与主应力差的远近场关系图谱。利用这些图谱以及全息光弹性试验所获得的远场等和线与等差线条纹,就能确定裂纹尖端的应力强度因子 K_Ⅰ,K_Ⅱ。实例表明:本法概念清晰、演算简便、精度较高。 相似文献
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首先,采用特征函数渐近展开法,推导了Reissner板弯曲界面裂纹尖端附近位移场渐近展开的前两阶显式表达式,并利用所获得的位移场渐近表达式构造了一种可用于Reissner板弯曲界面裂纹分析的奇异单元。然后,将该奇异单元与外部的常规有限单元相结合,开展了含界面裂纹Reissner板弯曲断裂问题的数值分析。奇异单元可以较好地描述裂纹尖端附近的内力场与位移场,其优势是它与常规单元进行连接时不需要使用过渡单元,并且可以直接给出应力强度因子等断裂参数的高精度数值结果。最后,通过两个数值算例验证了本文方法的有效性。 相似文献
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圆弧形裂纹问题中的应力对数奇异性 总被引:2,自引:1,他引:1
研究了无限大板上的一条圆孤形裂纹, 又在裂纹表面作用有反对称载荷. 换言之,
裂纹两侧表面的载荷是大小相等方向相同的.
上述问题可用复变函数方法来解决. 应力和位移分量通过两个复位函数来表示.
经过一系列推导, 此问题可归结为复变函数的黎曼-希尔巴德(Riemann-Hilbert)
问题, 并且可用闭合形式得出解答. 裂纹端的应力强度因子用通常方法定出.
在裂纹端邻域, 得到的复位函数中有对数函数部分. 由这个对数函数部分,
可以定义和得出裂纹端的对数奇异性, 此对数奇异性系数用闭合型式得出. 相似文献
15.
Plasticity induced crack closure (PICC) has been widely studied using numerical models. Different numerical parameters can be considered to quantify the opening level, namely one based on the analysis of contact stresses at minimum load. A modified version of this parameter is proposed here, based on nodal contact forces instead of contact stresses. The predictions were found to be similar to those obtained from the contact status of 2nd node behind crack tip. The PICCcontact parameter was also found to be very consistent and adequate for parametric studies of the influence of different physical parameters. The contributions to the opening stress intensity factor of different points along crack flank were found to strongly decrease with distance to crack tip. The cumulative Kopen between the crack tip and a distance of 0.1 mm was found to vary from 30% to 100%, increasing with stress ratio, R. Finally, a K solution was developed for punctual forces applied on crack flank and compared with a literature solution for infinite plates. A good agreement was found for plane strain state but significant differences of about 10% were found for plane stress state. 相似文献
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In this article,a direct stress approach based on finite element analysis to determine the stress intensity fac-tor is improved.Firstly,by comparing the rigorous solution against the asymptotic solution for a problem of an infinite plate embedded a central crack,we found that the stresses in a restrictive interval near the crack tip given by the rigorous solution can be used to determine the stress intensity fac-tor,which is nearly equal to the stress intensity factor given by the asymptotic solution.Secondly,the crack problem is solved numerically by the finite element method.Depending on the modeling capability of the software,we designed an adaptive mesh model to simulate the stress singularity.Thus, the stress result in an appropriate interval near the crack tip is fairly approximated to the rigorous solution of the corre-sponding crack problem.Therefore,the stress intensity factor may be calculated from the stress distribution in the appro-priate interval,with a high accuracy. 相似文献
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The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to
the intrinsic material lengthl, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic
fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that
the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field, the stress asymptotic field
and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular
distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic
field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress
and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic
field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress
and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode
I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic
fields are irrotational and dominated by the stretching gradient.
The project supported by the National Natural Science Foundation of China (19704100), National Natural Science Foundation
of Chinese Academy of Sciences (KJ951-1-20), CAS K.C. Wong Post-doctoral Research Award Fund and Post-doctoral Science Fund
of China 相似文献
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Yonglin Xu Ted Belytschko Dept. of Civil Engineering Northwestern University Evanston IL U. S. A 《Acta Mechanica Solida Sinica》1996,9(2):104-123
The Self-Similar Crack Expansion (SSCE) method is proposed to evaluate stress intensi-ty factors at crack tips, whereby stress intensity factors of a crack can be determined by the crackopening displacement over the crack, not just by the local displacement around the crack tip. The crackexpansion rate is estimated by taking advantage of the crack self-similarity. Therefore, the accuracy ofthe calculation is improved. The singular integrals on crack tip elements are also analyzed and are pre-cisely evaluated in terms of a special integral analysis. Combination of these two techniques greatly in-creases the accuracy in estimating the stress distribution around the crack tip. A variety of two-dimen-sional cracks, such as subsurface cracks, edge cracks, and their interactions are calculated in terms ofthe self-similar expansion rate. Solutions are satisfied with errors less than 0.5% as compared with theanalytical solutions. Based on the calculations of the crack interactions, a theory for crack interactionsis proposed such that for a group of aligned cracks the summation of the square of SIFs at the right tipsof cracks is always equal to that at the left tips of cracks. This theory was proved by the mehtod ofSelf-Similar Crack Expansion in this paper. 相似文献