SOME PROBLEMS ON THEORY OF CREEP

Abstract

Modern technological development h^s resulted In use of materiala over wide ranges of temperature and stresses where creep behaviour becomes algnlfleant. Design considerations* thsrefore, require stress analysis under ©reap. Study of aome problems on the theory of creep is presented in this thesis, the analyals Is developed under both time-hardening and atrain-hardening laws. Interpretatioa of results has been based, Whenever possible, on the experimental values of material constants. She mathematical analysis has also been extended to include anisotropy. The first chapter Is introductory and deals with fundamental concepts of 9tm^m V rieua empirical laws relating to strain-rate and stresa have been discussed to represent tension creep data. Second chapter discusses the large deformntions of circular membranes under creep. The problem has been studied on the basis of a non-linear creep law and the solutions are obtained la terras of infinite series,These solutions are much more general than the ones which were previously obtained by Prof. Odqvlst. This work has been published in Journal of Physical Society of Japan vol*£2, $0*t* February (1947). u; In the third chapter creep in rotating disks been discussed under strain-hardening laws with (1) Treeca-Mieas criterion and (11) Miaes-Mlses criterion. The resulting equations are solved by using a method of successive approxlmatlone and the aolutlons are discussed graphically. This work waa presented at the Xth Congress on Theoretical and Applied Isehaaies, Hadraa, India, Dec* 19€S* Fourth chapter is devoted to the study of torsion of Cylindrical Bare of arbitrary cross sections using non-linear oreep laws. A basic differential equation in terms of stress function la obtained. A solution of this equation consistent with boundary conditions for the particular ease of circular boundary has also been discussed. In chapter five the constitutive equations of the orthotropic theory of creep have bean formulated for the multi-axial state of stress based on an invariant proposed by Hill for the theory of plasticity. Sixth chapter deals with some problems on the orthotropic theory of creep. As an example ia which principal axes of stress do not coincide with the asms of anisotropy, tension of a prismatic bar la discussed* Another example that of compression under conditions of plane strain,illus trates variation of stress with time when load Is kept cons tant* The orthotropic theory of plane-strain has also been (J.li) developed* Chapter 6 and a part of chapter 4 has been published together in Wood Science and Technology, Jspringer-Verlag lew York Iac*l Vol.1, Wo *S(1947).