STRESS DISTRIBUTION ANALYSIS UNDER CREEP CONDITIONS

Abstract

Many materials-metals at elevated temperatures and wood, concrete, rubber, plastics etc. at the room temperatureare known to have the characteristics of deforming with time under constant external loading. This time-dependent deform ation is designated as 'CREEP'. In the last fifty years creep deformations have attracted intensive investigations due to their importance in the design of various structuralparts and machine-components for use at high temperatures such as nuclear power generating equipments, nuclear reactors, high speed aeroplanes, jet engines and missiles etc. Other structures such as gas turbines, oil refineries and chemical plants etc. are also required to work at high temperatures where creep is prevalent. Creep not only causes the stress to redistribute with time but also affects the strength and stability of the structure. These pose a great problem before the designer and it becomes essential for him to make use of the theory of creep for a rational design of structures. Thus the calculation of stresses, strains and strength of structural parts with due consideration being given to creep is of the utmost importance for present-day engineering and technology. In the present thesis some creep problems of technical importance for isotropic or anisotropic materials under steady or non-steady stage of creep have been analyzed. The thesis runs into seven chapters, and the chapterwise details are as follows; -iv- The first chapter is introductory. Creep phenomenon and brief history of the development of creep theory has been presented. Various types of empirical relationships between the strain-rate, stress, time and temperature have been discussed. The concept of anisotropy in the theory of creep has been explained. A method for estimating the numerical values of the ratios of constants occurring in the anisotropic laws has been developed. The numerical values of ratios of anisotropic constants for a number of actual materials having different creep indices have been obtained and depicted in Table 1.1. These values have been used in subsequent chapters of the thesis. The second chapter presents a study pertaining to the creep of pin-jointed frame-works, which are commonly used in air-frames or in missile structures, where the duration of creeping is small. The analysis is based on the assumption that the total strain-rate is composed of the following three components s (i) Elastic strain-rate, (ii) Non-steady state creep strain-rate and (iii) Steady-state creep strain-rate. The differential equations governing the problem have been solved by Runge.-Kutta method. The stress is found to get re distributed with time due to creep and the ultimate stress distribution is found to be very much different from the -vinitial distribution. The results obtained are presented graphically. This work has been published in Indian Journal of Technology, 15,518(1977). A creep analysis for an anisotropic spherical vessel using Norton's power law has been carried out in the third chapter. The analysis is based on the assumption that the strains are large which necessitates the use of the finitestrain theory for obtaining the stresses, creep strains and creep strain-rates in the vessel. It is found that the creep strain varies with the varying anisotropy of the material.The results obtained for the anisotropic cases have been compared with those obtained for the isotropic case. It is observed that the stress and the strain distributions in the wall of the vessel are strikingly different for the isotropic and anisotropic materials. The paper based on this investigation has been presented at the 46th Symposium of National Academy of Sciences, India held at New Delhi in February 1977. f*^sU iU^WioT^ crourmovJ 0% Nan-L^tVl^iAa*^, fc^am** pr«.s-aw;. In the fourth chapter the problem of creep of an orthotropic thin circular cylindrical shell has been analyzed. The analysis, based on a time-hardening creep law, is an attempt to study the effect of material anisotropy in the shell. The differential equations obtained are converted into linear simultaneous equations with the help of finite-difference relations. The equations thus obtained are then solved by the method of successive approximation. It is found that the stresses and deflections (strains) are significantly affected -viby the anisotropy of the material.The results have been compared with those for the isotropic case. The results indicate that the anisotropy of the material can be exploited for a better design of the shell. For example, the use of an anisotropic material of the type as discussed in Case II will result in lower values of deflections than those for a shell of isotropic material and will thus ensure a longer service-life for the shell.