1975
DOI: 10.1115/1.3423579
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Elastic-Plastic Analysis of an Infinite Sheet Having a Circular Hole Under Pressure

Abstract: An exact elastic-plastic solution for the stresses in an infinite sheet having a circular hole subject to pressure is obtained on the basis of J2 deformation theory together with a modified Ramberg-Osgood law. The sheet is orthotropic but isotropic in its plane. The results are assessed on the basis of Budiansky’s criterion for the acceptability of J2 deformation theory. By using exact elastic-plastic stresses, the function connecting the pressure at the hole with the radial enlargement is obtained. Upon relea… Show more

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Cited by 116 publications
(67 citation statements)
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“…This analytical solution, such as all other analytical models (Nadai, 1943;Hsu and Forman, 1975;Rich and Impellizzeri, 1977), does not provide the stress differences through the thickness. Guo's model, which is rather complex (Guo, 1993), represents fine the real residual stress distribution at mid-thickness without considering the split of the sleeve.…”
Section: Comparison With Analytical Theorymentioning
confidence: 99%
See 1 more Smart Citation
“…This analytical solution, such as all other analytical models (Nadai, 1943;Hsu and Forman, 1975;Rich and Impellizzeri, 1977), does not provide the stress differences through the thickness. Guo's model, which is rather complex (Guo, 1993), represents fine the real residual stress distribution at mid-thickness without considering the split of the sleeve.…”
Section: Comparison With Analytical Theorymentioning
confidence: 99%
“…Analytical studies have determined the closed-form solution of the residual stress for considering the material's yield limit on unloading step (Guo, 1993;Nadai, 1943;Hsu and Forman, 1975;Rich and Impellizzeri, 1977). However, many solutions are based on two-dimensional approximations, and theories are not able to predict the through-thickness residual stress field.…”
Section: Introductionmentioning
confidence: 99%
“…The literature presents several representative theories to evaluate the residual stress field, and these analytical models are perhaps an example of the historical development of plasticity theory [3][4][5][6][7]. However, these solutions are based on assumptions that neglect the through-thickness changes of residual stresses along the hole bore.…”
Section: Introductionmentioning
confidence: 99%
“…Extensive literature covers so many results of analytical, numerical and experimental methods [1,2,7,[11][12][13][14][15][16]19,[25][26][27][28][29][30][31][32][33][34][36][37][38][39][40][41][42][43][44][45][46][47][48][55][56][57][58][59], which they do not entirely match each other.…”
Section: Introductionmentioning
confidence: 99%
“…Mathematical derivations mostly employ closed form solutions adopting already existing solutions of thin walled [11][12][13][14][15] and thick walled [16][17][18][19][20] tubes subjected to an internal pressure. Further, strain hardening behavior [13,14,[16][17][18], elastic unloading [11] and non linear elastic-plastic behavior on both loading and unloading [15,20] of the material after cold expansion were considered. Serious deficiencies of the mathematical models mostly arise from the limitations of small deformation theory for strains (5%).…”
Section: Introductionmentioning
confidence: 99%