Abstract
Hill’s quadratic orthotropic yield criterion is used for revealing the effect of plastic anisotropy on the distribution of stresses and strains within rotating annular polar orthotropic disks of constant thickness under plane stress. The associated flow rule is adopted for connecting the stresses and strain rates. Assuming that unloading is purely elastic, the distribution of residual stresses and strains is determined as well. The solution for strain rates reduces to one nonlinear ordinary differential equation and two linear ordinary differential equations, even though the boundary value problem involves two independent variables. The aforementioned differential equations can be solved one by one. This significantly simplifies the numerical treatment of the general boundary value problem and increases the accuracy of its solution. In particular, comparison with a finite difference solution is made. It is shown that the finite difference solution is not accurate enough for some applications.
Highlights
Thin rotating disks are used in many applications such as energy storage devices; gyroscopic control devices for ships, submarines, aircrafts, rockets, and missiles; high-speed gears; and turbine rotors [1]
Rotational autofrettage has been recently proposed [2] as a new technique for producing compressive residual stresses
The boundary value problem is solved in a cylindrical coordinate system (r, θ, z) whose z axis coincides with the axis of symmetry of a thin annular rotating disk of constant thickness
Summary
Thin rotating disks are used in many applications such as energy storage devices; gyroscopic control devices for ships, submarines, aircrafts, rockets, and missiles; high-speed gears; and turbine rotors [1]. An elastic solution for arbitrarily functionally graded polar orthotropic rotating disks has been recently proposed [5]. A few solutions for the deformation theory of plasticity based on the von Mises yield criterion are available; a review of these solutions has been given [7]. In the case of the flow theory of plasticity, the finite difference method has usually been adopted for determining the distribution of strains [8,9,10]. An efficient method that advances the analytical treatment of elastic/plastic rotating disks has been proposed [11] for the von Mises yield criterion and its associated flow rule. The proposed orthotropic yield criterion [14] is often used to model plastic anisotropy in rotating disks, for example [15,16]. This demonstrates an advantage of using the method [11] as compared with the finite difference method
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