© copyright FACULTY of ENGINEERING ‐ HUNEDOARA, ROMANIA 225 1. Sanjeev SHARMA, 2. Pankaj THAKUR, 3. Manoj SAHNI ELASTIC‐PLASTIC DEFORMATION OF A THIN ROTATING DISK OF EXPONENTIALLY VARYING THICKNESS WITH EDGE LOAD AND INCLUSION 1,3. DEPARTMENT OF MATHEMATICS,JAYPEE INSTITUTE OF INFORMATION TECHNOLOGY,A‐10, NOIDA‐201307, INDIA 2. DEPARTMENT OF APPLIED SCIENCE, MIT COLLEGE OF ENGINEERING &MANAGEMENT,BANI,HAMIRPUR, H.P. ‐ 174304, INDIA ABSTRACT: Transition theory has been used to derive the elastic‐plastic and transitional stresses. Results obtained have been discussed numerically and depicted graphically. It is observed that the rotating disc made of incompressible material with inclusion require higher angular speed to yield at the internal surface as compared to disc made of compressible material. It is seen that the radial and circumferential stresses are maximum at the internal surface with and without edge load (for flat disc). With the increase in thickness parameter (k = 2, 4), the circumferential stress is maximum at the external surface while the radial stress is maximum at the internal surface. From the figures drawn the disc with exponentially varying thickness (k = 2), high angular speed is required for initial yielding at internal surface as compared to flat disc and exponentially varying thickness for k = 4 onwards. It is concluded that the disk made of isotropic compressible material is on the safer side of the design as compared to disk made of isotropic incompressible material as it requires higher percentage increase in an angular speed to become fully plastic from its initial yielding. KEYWORDS: elastic, plastic, compressibility, transitional stresses, isotropic, rotating disk INTRODUCTION This paper is concerned with the analysis of a rotating disk made of isotropic material with exponentially varying thickness. There are many applications of such type of rotating disks, such as in turbines, rotors, flywheels and with the advent of computers, disk drives. The use of rotating disk in machinery and structural applications has generated considerable interest in many problems in domain of solid mechanics. The analysis of stress distribution in circular disk rotating at high speed is important for a better understanding of the behavior and optimum design of structures. The analysis of thin rotating discs made of isotropic material has been discussed extensively by Timoshenko and Goodier [1]. In the classical theory, solutions for such type of discs made of isotropic material can be found in most of standard text books [1‐5]. Chakrabarty [2] and Heyman [6] solved the problem for the plastic state by utilizing the solution in the elastic range and considering the plastic state with the help of Tresca’s, Von‐Mises or any other classical yield condition. Han [7] has investigated elastic and plastic stresses for isotropic materials with variable thickness. Eraslan [8] has calculated elastic and plastic stresses having variable thickness using Tresca’s yield criterion, its associated flow rule and linear strain hardening. Wang [9] has investigated deformation of elastic half rings. Transition is a natural phenomenon and there is hardly any branch of science or technology in which we do not come across transition from one state to another. At transition, the fundamental structure of the medium undergoes a change. The particles constituting a medium rearrange themselves and give rise to spin, rotation, vorticity and other non‐linear effects. This suggests that at transition, non‐linear terms are very important and neglection of which may not represent the real physical phenomenon. Therefore transition fields are non‐linear, non‐conservative and irreversible in nature. Elasticity‐plasticity, visco‐elastic, creep, fatigue, relaxation are some of the examples of transition in which non‐linear terms are very important. At present, such problems like elastic‐plastic, creep and fatigue are treated by assuming ad‐hoc, semi‐empirical laws with the result that discontinuities, singular surfaces, non‐differentiable regions have to be introduced over which two successive states of a medium are matched together. In a series of papers, Seth [1962‐64] has given an entirely different orientation to this interesting problem of transition. He has developed a new ‘transition theory’ [10‐12] of elastic‐plastic and creep deformation. The transition theory utilizes the concept of generalized principal strain measure and asymptotic solution at critical points or turning points of the differential system defining the deformed field and has been successfully applied to a large number of problems [13‐19]. The generalized principal strain measure [19] is defined as,