Abstract
The objective of this paper is to present the study of density parameter in a disk made of orthotropic material and rubber by using Seth’s transition theory. This theory includes classical macroscopic solving problems in plasticity, creep relaxation, and semi-empirical yield conditions. It has been observed that disk made of rubber material requires higher angular speed to yield at the internal surface in comparison to disk made Barytes material at the transition state and for the full-plastic state having density parameter \(m > 0\). The value of circumferential stress is maximum at the internal surface of the rotating disk made of rubber and Barytes materials having density m > 0, whereas the reverse results obtained for \(m \le 0\).
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Abbreviations
- \(v\) :
-
Poisson ratio
- \(A_{0}\) :
-
Constant of integration
- \(c_{ijkl}\) :
-
Elastic constants
- \(a,b\) :
-
Inner and outer radii of the disk
- \(c\) :
-
Compressibility factor
- \(\rho\) :
-
Variable density of material
- \(u,v,w\) :
-
Displacement components
- \(r,\theta ,z\) :
-
Radial, circumferential, and axial directions
- \(\omega\) :
-
Angular velocity of rotation
- \(\rho_{0}\) :
-
Constant density
- \(Y,Y^{*}\) :
-
Yield stress
- \(\lambda ,\mu\) :
-
Lame’s constant
- \(\tau_{ij} ,\varepsilon_{ij}\) :
-
Stress and strain components
- m :
-
Density parameter
- \(\Omega_{1}^{2} ,\Omega_{2}^{2}\) :
-
Angular speed for initial and fully plastic stage (orthotropic material)
- \(\Omega_{3}^{2} ,\Omega_{4}^{2}\) :
-
Angular speed for initial and fully plastic stage (isotropic material)
- \(R = {r \mathord{\left/ {\vphantom {r b}} \right. \kern-\nulldelimiterspace} b},R_{0} = {a \mathord{\left/ {\vphantom {a b}} \right. \kern-\nulldelimiterspace} b}\) :
-
Radii ratio
- \(\sigma_{r}\) :
-
Radial stress component (\({{\tau_{rr} } \mathord{\left/ {\vphantom {{\tau_{rr} } {Y^{*} }}} \right. \kern-\nulldelimiterspace} {Y^{*} }}\))
- \(\sigma_{\theta }\) :
-
Circumferential stress component (\(\tau_{\theta \theta } /Y^{ * }\))
- \(\Omega^{2} = {{\rho_{0} \omega^{2} b^{2} } \mathord{\left/ {\vphantom {{\rho_{0} \omega^{2} b^{2} } {Y^{*} }}} \right. \kern-\nulldelimiterspace} {Y^{*} }}\) :
-
Speed factors
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Thakur, P., Gupta, N., Sethi, M. et al. Effect of density parameter in a disk made of orthotropic material and rubber. J Rubber Res 23, 193–201 (2020). https://doi.org/10.1007/s42464-020-00049-5
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DOI: https://doi.org/10.1007/s42464-020-00049-5