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1.
A. Kazberuk 《Materials Science》2009,45(5):676-687
The method of singular integral equations was applied to determine the stress intensity factors for a system of cracks emanating
from the vertex of an infinite rounded V-notch subjected to symmetric loading. The numerical values were obtained for two
cases—the case of a single crack and the case of a system of two cracks of equal length. The influence of the rounding radius
of the vertex of the notch and its opening angle on the stress intensity factors at the crack tips was analyzed. The solution
obtained as a result has a general nature—the stress intensity factors at the crack tip are expressed as a function of the
V-notch stress intensity factor and, hence, this solution could be treated as an asymptotic relation for finite bodies with
deep V-notches subjected to symmetric loads. 相似文献
2.
H. Yuan 《Acta Mechanica》1996,118(1-4):151-170
Summary Elastoplastic solutions with the higher-order terms for V-notches in materials exhibiting pressure-sensitive yielding and plastic volumetric deformations are presented. It is shown that under plane strain conditions the variable-separable solution exists within some limited pressure-sensitivities. The limit values grow significantly with increasing notch angle. The leading singularity is a decreasing function of notch angle. The small notch angle can hardly affect the singularity. The plane stress fields are generally more singular than the plane strain ones under the same conditions. The pressure-sensitivity does not affect the plane strain field singularity, but the angular stress distributions. The plane stress singularity is slightly increased by the high pressure-sensitivities at the large notch angles. The second-order exponent grows significantly with increasing notch angle. At a notch angle greater than 60°, the elasticity enters the second-order terms in all materials under plane strain conditions, while the plane stress second-order solutions contain the elasticity effects for all notches. It implies that the second-order terms in the notch analysis may not give a significant improvement in characterising the full stress fields. For an apex notch bounded to a rigid substrate, the leading-order singularity falls with increasing notch angle more slowly than that in the homogeneous pressure-sensitive materials. It vanishes at a notch angle of about 125° for all strain-hardening exponents. The elasticity affects the second-order solutions when notch angle becomes large. Whereas the stress fields are dominated by the hoop stress under assumptions of the traction-free crack surfaces, the shear stress is significant for large angle notches. 相似文献
3.
The method of singular integral equations is used to find the solution of the plane problem of the theory of elasticity for
a plane containing an infinite V-shaped rounded notch. This enables us to establish the relationship between the stress intensity
factor at the tip of the sharp V-shaped notch, the stress concentration factor for the corresponding rounded notch, and the
radius of curvature at the notch tip. It is shown that the indicated relationship is not unique. Indeed, for the same curvature
at the notch tip, we get different dependences for different shapes of its vicinity.
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 17–26, November–December, 2006. 相似文献
4.
The solution of crack problems in plane or antiplane elasticity can be reduced to the solution of a singular integral equation along the cracks. In this paper the Radau-Chebyshev method of numerical integration and solution of singular integral equations is modified, through a variable transformation, so as to become applicable to the numerical solution of singular integral equations along semi-infinite intervals, as happens in the case of semi-infinite cracks, and the direct determination of stress intensity factors at the crack tips. This technique presents considerable advantages over the analogous technique based on the Gauss-Hermite numerical integration rule. Finally, the method is applied to the problems of (i) a periodic array of parallel semi-infinite straight cracks in plane elasticity, (ii) a similar array of curvilinear cracks, (iii) a straight semi-infinite crack normal to a bimaterial interface in antiplane elasticity and (iv) a similar crack in plane elasticity; in all four applications appropriate geometry and loading conditions have been assumed. The convergence of the numerical results obtained for the stress intensity factors is seen to be very good. 相似文献
5.
The paper deals with the determination of analytical expressions for the mode III notch stress intensity factors for circumferentially-sharply-notched rounded bars under torsion loading, starting from the theoretical stress concentration factors of the corresponding notch problem.An exact, closed-form solution for the NSIFs is obtained for deep notches; subsequently the solution is extended also to finite notched components taking advantage of a shape function determined by a numerical best fitting procedure. 相似文献
6.
The Notch Stress Intensity Factors (NSIFs) quantify the intensities of the asymptotic linear elastic stress distributions
of sharp (zero radius) V-shaped notches. When the notch tip radius is different from zero, the singular sharp-notch field
diverges from the rounded-notch solution in the close neighborhood of the notch tip. Nevertheless the NSIFs might continue
to be parameters governing fracture if the notch root radius is small enough. Otherwise they can be seen simply as stress
field parameters useful in quantifying the stress distributions ahead of the specific notch. Taking advantage of some analytical
formulations which are able to describe stress distributions ahead of parabolic, hyperbolic and V-shaped notches with end
holes, the paper discusses the form and the significance of the NSIFs with reference to in-plane shear loading, considering
explicitly the role played by the notch opening angle and the notch tip radius. These parameters quantify the stress redistribution
due to the root radius with respect to the sharp notch case to which they should naturally tend for decreasing values of the
notch radius. 相似文献
7.
N. I. Ioakimidis 《International journal for numerical methods in engineering》1982,18(9):1416-1419
A numerical method for the direct determination of stress intensity factors at crack tips from the numerical solution of the corresponding singular integral equations is proposed. This method is based on the Gauss-Chebyshev method for the numerical solution of singular integral equations and is shown to be equivalent to the Lobatto-Chebyshev method for the numerical solution of the same class of equations. 相似文献
8.
The method of reflected caustics was used to determine the complex stress intensity factors at the tips of cracks having any shape, which lie at the interface of two dissimilar elastic media. For the evaluation of complex S.I.Fs two measurements of appropriate lengths have to be made on the caustic formed at the crack tip. These measurements allow the determination of both the absolute value and the argument of the respective stress intensity factor. The method was applied for the solution of problems which are referred to cracks at interfaces between two elastic dissimilar media. The experimental results show a good agreement between the experimental and theoretical methods of evaluating SIFs. 相似文献
9.
《Engineering Fracture Mechanics》2004,71(9-10):1235-1254
Laboratory test and in-service experience shows fatigue cracks at holes exhibit unsymmetric growth; thus, the need for the new solutions is paramount. Stress intensity factor, K, solutions for symmetric and unsymmetric corner cracks at a hole subject to general loading were determined using a hp-version of the finite element method (FEM) in conjunction with a mathematical splitting scheme to enable efficient, accurate calculations. In traditional applications of the FEM, mesh generation is labor intensive; however, using the splitting scheme, stress intensity functions are obtained without explicitly including the crack in the FE mesh of the global structure. By using the hp-version of FEM, a set of K-solutions converging exponentially fast to the exact solution is obtained. The crack is analyzed in the local domain with easily generated FE meshes. All structurally significant crack shapes were considered; specifically, crack depth to crack length ratios (a/c) of 0.1–10.0, crack depth to sheet thickness ratios (a/t) of 0.10–0.99, and hole radius to sheet thickness ratios (r/t)=1.0. The loading conditions were remote tension, remote bending, and pin loading (bearing). In addition, all combinations of a/c and a/t are analyzed at each side of the hole; thus 226,875 solutions were developed with control of the error in the computed K solutions. Calculated relative error is generally much smaller than 1% along the entire crack front including the vertex regions. Comparisons are made to solutions in the open literature. The new K solutions show the literature solutions are, in general, accurate for all three load conditions; however, for the extreme cases of a/c, a/t, and r/t; the literature solutions differ by as much as 26%. 相似文献
10.
11.
The steady-state vibration of an infinite plate with collinear cracks is considered for low frequency cyclic loading. The formulation of the mixed boundary value problem leads to a dual trigonometric series. The Schwinger's method gives an automatic perturbation scheme. The dynamic stress intensity factor is found to be higher than the corresponding static one. The inertial effect on the stress intensity factor becomes significant only when the frequency of the external load is close to that of the shear wave. 相似文献
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14.
A numerical method using a path-independent H-integral based on the Betti reciprocal principle was developed to analyze the stress intensity factors of an interfacial corner between anisotropic bimaterials under thermal stress. According to the theory of linear elasticity, asymptotic stress near the tip of a sharp interfacial corner is generally singular as a result of a mismatch of the materials’ elastic constants. The eigenvalues and the eigenfunctions are obtained using the Williams eigenfunction method, which depends on the materials’ properties and the geometry of an interfacial corner. The order of the singularity related to the eigenvalue is real, complex or power-logarithmic. The amplitudes of the singular stress terms can be calculated using the H-integral. The stress and displacement fields around an interfacial corner for the H-integral are obtained using finite element analysis. A proposed definition of the stress intensity factors of an interfacial corner involves a smooth expansion of the stress intensity factors of an interfacial crack between dissimilar materials. The asymptotic solutions of stress and displacement around an interfacial corner are uniquely obtained using these stress intensity factors. 相似文献
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17.
In this paper, the numerical solution of the hypersingular integral equation using the body force method in curved crack problems is presented. In the body force method, the stress fields induced by two kinds of standard set of force doublets are used as fundamental solutions. Then, the problem is formulated as a system of integral equations with the singularity of the form r
–2. In the numerical calculation, two kinds of unknown functions are approximated by the products of the fundamental density functions and power series. The calculation shows that the present method gives rapidly converging numerical results for curved cracks under various geometrical conditions. In addition, a method of evaluation of the stress intensity factors for arbitrary shaped curved cracks is proposed using the approximate replacement to a simple straight crack. 相似文献
18.
W. B. Fichter 《International Journal of Fracture》1983,22(2):133-143
Fourier transforms and the Wiener-Hopf technique are used in conjunction with plane elastostatics to examine the singular crack tip stress field in the Double Cantilever Beam (DCB) specimen. With terms of orderh 2/a 2 retained in the series expansion, the dimensionless stress intensity factor is found to be \(Kh^{\tfrac{1}{2}} /P = (12)^{\tfrac{1}{2}} (a/h + 0.6728 + 0.0377h^2 /a^2 )\) , in whichP is the magnitude of the concentrated forces per unit thickness, a is the distance from the crack tip to the points of load application, andh is the height of each cantilever beam. This result is quite similar to the expression \(Kh^{\tfrac{1}{2}} /P = 3.46a/h + 2.38\) , which Gross and Srawley obtained by fitting a line to discrete results from their boundary collocation analysis. Still another expression, \(Kh^{\tfrac{1}{2}} /P = [12\{ (a/h + 0.6)^2 + \tfrac{1}{3}\} ]^{\tfrac{1}{2}}\) , obtained by Ripling, Mostovoy and Patrick from a strength of materials approach combined with compliance measurements, although somewhat different in form from the present results, also yields accurate values ofK for thea/h-range of practical interest (2 ?a/h ? 10). The present result serves as both a confirmation and a refinement of the Gross and Srawley formula. For this reason, and because of its simplicity, the present result should be useful in the derivation of other simple and parametrically appropriate equations for the analysis of data from DCB specimen tests. 相似文献
19.
James C. Sobotka R. Craig McClung 《Fatigue & Fracture of Engineering Materials & Structures》2020,43(5):955-964
This work summarizes investigations into stress intensity factor solutions for straight, through cracks at pin‐loaded holes in thin sheets. As shown in this work, several assumptions contribute to the fidelity of a stress intensity factor solution that includes the distribution of contact pressure on the pin‐hole interface, the friction coefficient at the pin‐hole interface, the crack initiation angle, and stiffness mismatch. These assumptions lead to higher or lower stress intensity factor solutions as demonstrated by results generated from advanced finite element analyses of the relevant geometries. Results shown here contribute to the development of a realistic and conservative set of assumptions for stress intensity factor solutions. Conclusions drawn from this work are applicable to cracks originating at pin‐loaded holes in plates and lugs. 相似文献
20.
Zhigen Wu 《Engineering Fracture Mechanics》2008,75(8):2367-2384
On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis. 相似文献