SOME PROBLEMS IN THE ORTHOTROPIC THEORY OF CREEP

Abstract

fcodem technology haa demanded the use of materials In machine parte end structures at high temperetures where creep deform tions are significant, for example in hyperaonie planes* Jet enginea, missiles, gas turbines* nuele r reactors etc. many investigators have w«*rked out problems of ttrets an iyeia under creep for isotropic medium. However, some of the materiala are initially anisotropic and tome become eo during continuing deformation. In other words as the deformation continues material develops preferred orientations. Stress analysis for such meterialt It thus of con aidarable importance, street distributions in anisotropic materiel may differ considerably from the isotropic cate. In this thesis* an attempt haa been made to study some problem« in the orthotopic theory of creep. The thesis is divided into seven chapters* The flret chapter Is introductory* £reep phenomenon and creep lama have been described briefly* The concept of anlsotropy in creep theory is explained and relationships between strein retee end stress state proposed by many investigates have been compared. The fundamental consti tutive equation a have been derived from the equations for the CTthetrmpie creep theory given by Bhatnegar and tfupta<a>? s»eond chapter deals with the analysis of the torsion problem. The analysis is booed on Norton*s lew for a mulUaxial email i iwawwa— • —ai -iriiarirr"TT—i———— •.,«..• ..»••••. —-.. •>«« n«a m **aw#aiM •*•'•*.•>.. mm* nm iwawn « «««•* '«•«• •l"»l1* www* * Numbers within parenthesis < > indicate references given in the end of the thesis* -iiiatete of strata for an orthotopic medium* An exprettion giving twist at a function of time hat also been derived* The effect of anltotropy it discussed graphically (published In the Journal of *o*d Science end Technology* Vel.3*(l9d») pmaiT-iyaj* In third chapter, a method for enelyelng distribution of stress and creep rotes for a thin walled tubular specimen under combined tension-tortion hat been developed. It ie shewn thet axes of an1sotropy change orientation with the angle of twitt of the tube during ttralning* and if the principal axea of enisotropy are not allowed to change orien tation* the analysis reduces to the isotropic cast which has been discussed by Bailey* Tapsell and Johnson. This agree ment seems to confirm the accuracy of the analytit (presented in the Convention of Physical Beeeareh Committee at Nelnltai, India* SO-29 ApriitiafO)* Pourth chapter deals «?lth the analysis of thickmelled orthotropic cylinder in the theory of creep. Exprestions for ttrettet end creep rates ere obtained under the eteumptlona of (l) plane ttraln* (11) generalised plane atrain and (iU) plane stress. The rceilte for plane ttraln ctte are compared with thoae obtained by Pal* It la shown that his conclusion that etrets distribution w»e independent of anisotropic constants is not correct. The error eppeert to be due to elmplified conttitutivt equation t which have only one anisotropic constant used by him. The reaulta indicate thet creep enisotropy has a algnlficant effect on -ivthe cylinder behaviour (published In Journal of the Physical society of Japan* Vol.87, N©*6* Dee. 1967, pp*l66o- 1661). In chapter fifth* equations are obtained for stresses and creep rotea, for a thick walled cylinder of an orthotropic material under combined axial lead and internal press ure. Analytical solution of the equations* in closed form is not passible* but numerical solution to the equation* ere tabulated. The results illustrate thet the maximum stres* la not always at the surface (presented In the Convention of Phytieal Beeeareh Committee at Neinltel* India* April 80-83, 1970)* In chapter sixth* a theoretic el analysis of creep deformation and etrese distrl utlon In rotating disk it presented. It la found that better agreement with available creep teat data for the rotating disk la obtained if the constitutive equations of creep for an orthotopic material are used. On comparison with the modified Belley equation a obtained by *.ahi for the planer anieotrepy caee* It it teen that the equation* used in this chapter for planar enisotropy are simpler end gave the results at obtained by walla Seventh ehepter deelt with creep deformation of eymmetrlcally leaded shells of revolution* Analysis is based en Norton's creep law* generalised for a multlaxlal state of etrese for an orthotopic material. The numerical calculat ions have been carried out for ellipsoidal and spherical shells. The effect of an i sotropy is discussed graphically.