Problem of the stress state in the neck of cylindrical and flat specimens in tensile loading

Vazhentsev, Yu. G.; Isaev, V. V.

doi:10.1007/bf01530861

Cited by 6 publications

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“…The Bridgman factor is somewhat higher than Ñ 2 which in turn exceeds the Vazhentsev-Isaev correction factor [18] for 0 1 0 3 .…”

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confidence: 83%

“…The stress-strain state in a tensile neck has been the subject of numerous experimental and theoretical investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] which are briefly reviewed in [4,8,17]. Tensile tests are widely used for the determination of mechanical properties of materials, metals, steels for engineering applications.…”

Section: A a Ostseminmentioning

confidence: 99%

“…The correction factor Ñ 2 depends only on the ratio h R; therefore, for its calculation we should first determine the radius of curvature R of the neck outer contour. The values of Ñ 2 are presented in Table 2 which, for the sake of comparison, provides also the factors proposed by Bridgman [2], Petrosyan [10], and Vazhentsev-Isaev [18], the latter one being given by…”

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confidence: 96%

“…Expression (4) was derived in [18] on the following assumption made in the Bridgman solution [2]: in the immediate vicinity of the neck smallest cross-section the neck contour can be approximated by a tangent circle of radius R, and one of the stress surfaces by a sphere. Formula (4) was obtained from (1) and expression (5) from (2).…”

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confidence: 99%

“…The Petrosyan solution [10] was obtained without the third assumption, in the form of transcendental equations; however, the formulas for stresses require cumbersome calculations and are really suitable for practical applications [18].…”

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confidence: 99%

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On the analysis of stress state in elliptical tensile neck

Ostsemin

2009

Strength Mater

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A. A. OstseminUDC 539.375The tensile necking in cylindrical and plate specimens is described based on a modification of the Bridgman theory for an isotropic case. A method of determination of principal stress trajectories in an elliptical tensile neck is put forward, which involves transformation of the initial coordinate grid by means of conformal mappings. Expressions are derived for the principal stresses and the radius of curvature of stress trajectories. Based on assumptions that depart from the Bridgman theory, an approximate analytical solution is obtained for the stress distribution in specimens with an elliptical cross-section. The new solution belongs to the one-parameter family of solutions which includes the Bridgman's and Davidenkov-Spiridonova's solutions.Introduction. The stress-strain state in a tensile neck has been the subject of numerous experimental and theoretical investigations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] which are briefly reviewed in [4,8,17]. Tensile tests are widely used for the determination of mechanical properties of materials, metals, steels for engineering applications. One of the main reasons why this type of testing is so widespread is that a simple homogeneous uniaxial stress state is expected to arise during the test. With large strains the process of the specimen tension looses its stability associated with necking. As this takes place, in addition to the obvious correction for the change of the smallest cross-section area one should also introduce a correction factor to allow for the influence of stress triaxiality on the plastic yielding process. In the case of anisotropic materials, the specimens which are initially in the shape of circular cylinder become elliptical in cross-section during the testing [12]. The total (y k ) and uniform (y p ) relative reductions of area are important parameters of plasticity. To judge the mechanism of plastic deformation we should consider the changes in the uniform and concentrated portions of strain rather than limit ourselves to a study of total strains. The proposed theoretical analysis deviates from the Bridgman theory. It will be shown below that this has resulted from new assumptions with respect to the lines of axial principal stresses (LAPS).The objective of the present work has been to determine the stress distribution in an elliptical tensile neck in plate and cylindrical specimens on the basis of conformal mappings.1. Determination of Curvature Radius r of Principal Stress Trajectory and Curvature Radius R in the Specimen Neck. LAPS's were assumed to coincide with the grain flow direction [1]. Also, the radius of curvature of a deformed grain passing through a point with abscissa x was experimentally found to be equal to x -1 . Another approach to the determination of the curvature radius of LAPS in the neck minimum cross-section [2] is based on the concurrent use of equations of the LAPS family and equations of the family orthogonal to the LAPS one. An equation of the neck contour can be const...

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“…The Bridgman factor is somewhat higher than Ñ 2 which in turn exceeds the Vazhentsev-Isaev correction factor [18] for 0 1 0 3 .…”

mentioning

confidence: 83%