Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

Jeong, Won−Cheol; Alexandrov, Sergei; Lang, Lihui

doi:10.3390/sym10090420

Cited by 6 publications

(9 citation statements)

References 36 publications

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“…The condition (1) and the first equation in (8) are then automatically satisfied for any choice of the function g(ϕ). Equations (9) and (26) combine to give:…”

Section: General Velocity Solutionmentioning

confidence: 99%

“…In total, there are five unknowns (three components of the stress tensor and two components of the velocity vector). The equations to solve are (6), (8) and (10). It is understood here that the components of the strain rate tensor in (8) should be eliminated by means of (9).…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…It is assumed that the principal axes of anisotropy are straight lines through the apex of the wedge and orthogonal curves, which are of course circular arcs. This type of orthotropy is of practical interest [5][6][7][8] among many others. The paper focuses on qualitative features of the solution such as non-existence of the solution, singularity in the stress and velocity fields, appearance of a rigid region near the plates and transition between the regimes of sticking and sliding.…”

Section: Introductionmentioning

confidence: 98%

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Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution

et al. 2019

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An infinite wedge of orthotropic material is confined between two rotating planar rough plates, which are inclined at an angle 2α. An instantaneous boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, the solution being in closed form. The solution may exhibit the regimes of sliding or sticking at the plates. It is shown that the overall structure of the solution significantly depends on the friction stress at sliding. This stress is postulated by the friction law. Solutions, which exhibit sticking, may exist only if the postulated friction stress at sliding satisfies a certain condition. These solutions have a rigid rotating zone in the region adjacent to the plates, unless the angle α is equal to a certain critical value. Solutions which exhibit sliding may be singular. In particular, some space stress and velocity derivatives approach infinity in the vicinity of the friction surface.

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“…The condition (1) and the first equation in (8) are then automatically satisfied for any choice of the function g(ϕ). Equations (9) and (26) combine to give:…”

Section: General Velocity Solutionmentioning

confidence: 99%

Section: Statement Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution

et al. 2019

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“…For example, the residual stresses and, hence, the elastic springing are very sensitive to plastic anisotropy [3,4]. The effect of plastic anisotropy on the solution behavior for thin rotating disks has been revealed in [5][6][7]. However, for simplifying theoretical calculations, the real orthotropic yield criterion is often replaced with a transversely isotropic yield criterion (i.e., it is assumed that the material properties are independent of the direction within the transverse plane).…”

Section: Introductionmentioning

confidence: 99%

Influence of the Replacement of the Actual Plastic Orthotropy with Various Approximations of Normal Anisotropy on Residual Stresses and Strains in a Thin Disk Subjected to External Pressure

et al. 2020

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Plastic anisotropy is very common to metallic materials. This property may significantly affect the performance of structures. However, the actual orthotropic yield criterion is often replaced with a criterion based on the assumption of normal anisotropy. The present paper aims to reveal the influence of this replacement on the distribution of strains and residual strains in a thin hollow disk under plane stress conditions. The boundary-value problem is intentionally formulated such that it is possible to obtain an exact semi-analytical solution without relaxing the boundary conditions. It is assumed that the disk is loaded by external pressure, followed by elastic unloading. The comparative analysis of the distributions of residual strains shows a significant deviation of the distribution resulting from the solutions based on the assumption of normal anisotropy from the distribution found using the actual orthotropic yield criterion. This finding shows that replacing the actual orthotropic yield criterion with the assumption of normal anisotropy may result in very inaccurate predictions. The type of anisotropy accepted is of practical importance because it usually results from such processes as drawing end extrusion with an axis of symmetry.

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“…In the case of circular discs and cylinders, a common type of anisotropy is polar orthotropy. In particular, the effect of plastic anisotropy on stress and strain fields in rotating discs has been studied in [34][35][36][37][38][39], using different material models and boundary conditions. Various boundary value problems for orthotropic cylinders have been solved in [40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

2019

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Autofrettage is a widely used process to enhance the fatigue life of holes. In the theoretical investigation presented in this article, a semi-analytic solution is derived for a polar, orthotropic, open-ended cylinder subjected to internal pressure, followed by unloading. Numerical techniques are only necessary to solve a linear differential equation and evaluate ordinary integrals. The generalized Hooke’s law connects the elastic portion of strain and stress. The flow theory of plasticity is employed. Plastic yielding is controlled by the Tsai–Hill yield criterion and its associated flow rule. It is shown that using the strain rate compatibility equation facilitates the solution. The general solution takes into account that elastic and plastic properties can be anisotropic. An illustrative example demonstrates the effect of plastic anisotropy on the distribution of stresses and strains, including residual stresses and strain, for elastically isotropic materials.

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Effect of Plastic Anisotropy on the Distribution of Residual Stresses and Strains in Rotating Annular Disks

Cited by 6 publications

References 36 publications

Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution

Compression of a Polar Orthotropic Wedge between Rotating Plates: Distinguished Features of the Solution

Influence of the Replacement of the Actual Plastic Orthotropy with Various Approximations of Normal Anisotropy on Residual Stresses and Strains in a Thin Disk Subjected to External Pressure

A Theory of Autofrettage for Open-Ended, Polar Orthotropic Cylinders

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