Thermo elastic-plastic transition in a thin rotating disc with inclusion

Abstract

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that the rotating disc with inclusion and made of compressible material requires lesser angular speed to yield at the internal surface and higher percentage increase in angular speed to become fully plastic as compare to disc made of incompressible material. With the introduction of thermal effect the rotating disc with inclusion required lesser angular speed to yield at the internal surface. Rotating disc made of compressible material with inclusion requires higher percentage increase in angular speed to become fully-plastic as compare to disc made of incompressible material. Thermal effect also increases the values of radial and circumferential stresses at the internal surface for fully-plastic state. .

Mathematical model in a thin non-homogeneous rotating disc for isotropic material with rigid shaft by using Seth's transition theory

“…Substituting equation (4) in equation (1), the generalized components of strain are: The stress -strain relations for isotropic material are given by [13]:…”

“…[4,[10][11][12], SHUKLA [8,9 ] , THAKUR [14 -42]) at the transition point P → ±∞ . We take the transition function T is defined as:…”

“…Substituting the value of / dP dβ from equation (11) in equation (14) and taking the asymptotic value as ±∞ → P , we get after integration:…”

“…GHOSH [2] on the problem involving the study of elastic-plastic stress in a spherically pressure vessel of non-homogeneous material and MUKHOPADHYAY [3 ] studied the effect of non-homogeneity on yields stress in a thick walled cylinder tube under pressure. Gupta et al [4] solved the problems effect of non-homogeneity on elastic-plastic transition in a thin rotating disc by using Seth's transition theory and plane stress condition. This theory [5] does not required any assumptions like an yield condition, incompressibility condition and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out.…”

“…This theory [5] does not required any assumptions like an yield condition, incompressibility condition and thus poses and solves a more general problem from which cases pertaining to the above assumptions can be worked out. It utilizes the concept of generalized strain measure and asymptotic solution at critical points or turning points of the differential equations defining the deformed field and has been successfully applied to a large number of problems [7][8][9][10][11][12]. SETH [5] has defined the generalized principal strain measure as:…”