Influence of crack closure on the stress intensity factor in bending plates ? A classical plate solution

Young, M. J.; Sun, C. T.

doi:10.1007/bf00018034

Cited by 41 publications

(18 citation statements)

References 21 publications

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“…It is noted that Cl is a function of e and is equivalent to H(e) in (9) The resultant crack opening displacement v(~, 0 +, z) can be obtained using (22) and (24) v(~,O+,z) = u,(~,0 +) + z~,,0L 0+),…”

Section: Momentioning

confidence: 99%

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On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Young

Sun

1993

Int J Fract

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For a through-the-thickness crack in an infinite plate subjected to out-of-plane uniform bending moment, the strain energy release rate is determined using the virtual crack extension and the variation of potential energy. It is shown that the strain energy release rate for the Reissner's plate approaches the classical plate solution as the ratio of plate thickness to crack size becomes infinitesimally small. By using this result, the limiting expression of the stress intensity factor can be explicitly obtained. For general problems, the modified crack closure method is shown to be an efficient tool for evaluating the strain energy release rates from which the stress intensity factor can be calculated. Both the classical plate element and the Mindlin plate element are investigated, and the applicability of the classical plate element is evaluated.Because the stress-free conditions along the crack face lead to inter-penetration of the plate, a line contact model is assumed to investigate the closure effect using Reissner plate theory. Closure at the compressive side is shown to reduce crack opening displacement and consequently the stress intensity factors. When closure is considered, the strain energy rate based on the Reissner plate theory converges to the classical plate solution. This is similar to the nonclosure case.

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Section: Momentioning

confidence: 99%

“…In order to gain an understanding of the line contact model [21,22], Young and Sun [24] used classical plate theory to solve an infinite plate analytically. Their solutions show a reduction of 7 to 12 percent for the crack opening displacement and approximately 35 percent for stress intensity factors.…”

Section: Introductionmentioning

confidence: 99%

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Young

Sun

1993

Int J Fract

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“…Some researchers used classical plate theory [1][2][3][4][5][6][7][8], and some employed Reissner/Mindlin plate theory [9][10][11][12][13][14][15][16][17][18][19][20][21] for investigation. One peculiar result from these studies is that the stress intensity factors and near-tip stress distributions associated with classical plate theory are different from Reissner's plate solutions and that Reissner/Mindlin plate solutions do not approach classical plate solutions even as the ratio of plate thickness to crack size (h/a) approaches zero.…”

Section: Introductionmentioning

confidence: 99%

Cracked plates subjected to out-of-plane tearing loads

Young

Sun

1993

Int J Fract

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Cracked plates subjected to out-of-plane tearing loads were investigated using both classical plate theory and Reissner/Mindlin plate theory. It was shown that the total strain energy release rate according to Reissner/Mindlin plate theory converges to that of classical plate theory as the thickness to crack length ratio approaches zero. It was demonstrated that it is not meaningful to separate mode II and mode III strain energy release rates using classical plate theory.

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“…In recent years, crack-face closure in plates and shells has attracted significant attention, and some o f the new solutions have been incorporated into ASME design code. For instance, Young and Sun [16,17]…”

Section: The Crack-closure Theorymentioning

confidence: 99%

“…In their solutions material overlap is allowed at the compressive edges when a bending load is involved, which is physically unrealistic. In reality, crack-face closure on the compressive edges may occur as crack faces rotate when a shell or a plate is subjected to a bending load, as illustrated in Figure 2 Young and Sun [16,17]…”

Section: Crack Closure In Platesmentioning

confidence: 99%

Fracture mechanics analyses of partial crack closure in shell structures

Zhao¹

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Library and Archives Canada Bibliotheque et Archives Canada Published Heritage Branch 395 W ellington Street Ottawa ON K1A 0N4 CanadaY our file Votre referen ce ISBN: 9 7 8 -0 -4 9 4 -3 3 5 1 8 -5 O ur file N otre referen ce ISBN: 9 7 8 -0 -4 9 4 -3 3 5 1 8 -5 ABSTRACT This thesis presents the theoretical and finite element analyses o f crack-face closure behavior in shells and its effect on the stress intensity factor under a bending load condition. Various shell geometries, such as spherical shell, cylindrical shell containing an axial crack, cylindrical shell containing a circumferential crack and shell with double curvatures, are all studied. In addition, the influence o f material orthotropy on the crack closure effect in shells is also considered. The theoretical formulation is developed based on the shallow shell theory o f Delale and Erdogan, incorporating the effect o f crack-face closure at the compressive edges. The line-contact assumption, simulating the crack-face closure at the compressive edges, is employed so that the contact force at the closure edges is introduced, which can be translated to the mid-plane o f the shell, accompanied by an additional distributed bending moment. The unknown contact force is computed by solving a mixed-boundary value problem iteratively, that is, along the crack length, either the normal displacement o f the crack face at the compressive edges is equal to zero or the contact pressure is equal to zero. It is found that due to the curvature effects crack closure may not always occur on the entire length o f the crack, depending on the direction o f the bending load and the geometry o f the shell. The crack-face closure influences significantly the magnitude o f the stress intensity factors; it increases the membrane component but decreases the bending component. The maximum stress intensity factor is reduced by the crack-face closure. The significant influence o f geometry and material orthotropy on rack closure behavior in shells is also predicted based on the analytical solutions.iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.Three-dimensional FEA is performed to validate the theoretical solutions. It demonstrates that the crack face closure occurs actually over an area, not on a line, but the theoretical solutions o f the stress intensity factor and the FEA solutions are in good agreement, because the contact area is very small compared with the shell thickness.iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Influence of crack closure on the stress intensity factor in bending plates ? A classical plate solution

Cited by 41 publications

References 21 publications

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

On the strain energy release rate for a cracked plate subjected to out-of-plane bending moment

Cracked plates subjected to out-of-plane tearing loads

Fracture mechanics analyses of partial crack closure in shell structures

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