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Maec.19 70 (University of London) London COMPLEX & INCREMENTAL STRESS CREEP OF A HIGH STRENGTH ALUMINIUM ALLOY AT ELEVATED TEMPERATURES (ALLOY: HIDUMINIUM RR58 SPECIFICATION DTD 731) by SURINDAR BAHADUR MATHUR Thesis presented in the Department of Mechanical Engineering for the Award of the Doctor of Philosphy in Mechanical Engineering of the University of London. Mechanical Engineering Department Imperial College of Science and Technology mAec.19 70 (University of London) London. ABSTRACT A theory for creep rates under complex and incremental stresses is deduced from experimental data concerning complex creep at elevated temperatures for the test material HIDUMINIUM RR 58 - Specification DID 731. The most important results are for tubular specimens tested at 150°C and 250°C under incremental loads. The analysis of results relates to steady state creep only. Modified relationships in stress equivalence and strain equivalence are proposed to account for thermal softening, polygonization, recrystallization and the resulting exaggerated flow in the direction of the applied shear. (The original equations are based on the hypothesis of Von Mises). A further relationship is suggested between the immediate total energy of distortion and the subsequent creep work rate. Results of the static tests and the results of the tests for creep behaviour under complex loading are presented and compared with the results of static torsion and simple incremental torsion creep tests on the basis of the proposed equations. An appendix describes the complex creep testing machine, furnace, extensometers and ancillary equipment which were designed for this programme and later modified to suit the behaviour of the test material. CONTENTS Page No. ABSTRACT 1 NOMENCLATURE 5 INTRODUCTION 7 LITERATURE SURVEY 11 (a) Simple creep theory (11) (b) Metallurgical aspects (13) (i) Behaviour of polycrystalline materials (13) (ii) Effect of solute atoms (15) (iii) Effect of excessive temperature at high stresses (i5) (iv) Effect of precipitation on strength (16) (v) Effect of precipitation during creep (17) (vi) Crack initiation and rupture (18) (c) Mathematical theory of steady static creep under complex stresses (0 Complex stress equivalence (19) (ii) Total effects of ageing, anisotropy and precipitation on theories of equivalence (22) (iii) Effect of pre-strain on subsequent creep (24) (iv) Effect of rotating principal axes (24) (v) Mathematicl equivalence and the mode of creep behaviour in HIDUMINIUM RR 58 at varying stresses and elevated temperatures (25) DESCRIPTION OF TEST EQUIPMENT 34 (a) Den n creep tester and test specimen (34) (W Complex creep testing machine (35) (i) Extensometer No. 1 (Modified) (36) (ii) Furnace modification and recalibration (37) (c) Instrumentation, Control and strain calibration (38) SELECTION OF TEST MATERIAL 39 (a) Manufacture of tubular specimens (41) (b) Selection Tests — analysis and conclusion (41) (c) Test material specification and requirements (43) PRELIMINARY TESTS 44 (a) Manufacture of 1.00 inch gauge length specimens (44) (b) Static tests — tensile and torsion (45) (c) Isotropy tests (46) (d)' Incremental stress tensile creep (47) MAIN TEST PROGRAMME 49 (a) Nature of tests (49) (b) Test procedUre (50) ANALYSIS OF TEST RESULTS 52 (a) Selection tests (52) (b) Static tests (52) (c) Preliminary tests (55) (d) Main test programme (57) METALLURGICAL EXAMINATION, RELEVANT SURVEYS AND DISCUSSION 60 DISCUSSION 66 (a) Complex creep machine (66) (b) Material selection (67) (c) Static tests (67) (d) Isotropic compatibility (69) (e) Preliminary tensile creep (69) (f) Main tests (71) CONCLUSIONS AND SUGGESTIONS FOR FURTHER WORK 74 ACKNOWLEDGEMENTS 78 BIBLIOGRAPHY 79 APPENDIX 1 85 Instrumentation and specimen details APPENDIX 2 89 Experimental data, calculated results and curves APPENDIX 3 171 (0 Theoretical calculations — current stress (ii) Complex creep Machine — published work NOMENCLATURE Original and final lengths of test specimen t Time Direct stresses Engineer's direct strain Engineer's shear strain , C y , 17 Suffixes x, y and z define directions in terms of 6'5 lo; 4z Cartesian coordinates Direct secondary creep rate T Absolute test temperature "ro Absolute equicohesive temperature Strain and strain rate tensors Stress tensor JZ Second invariant of the stress equation Principal stresses ri 21 or3 62 Principal strains El ) 63 . , Principal strain rates E 62 , 63 - in the planes defined by the Cartesian coordinates Z'ry,ZY2, "tzx Shear stresses Direct strain rates in the direction of the Cartesian coordinates 6xi e Y planes defined by the Cartesian coordinates 1(KYI x Shear strain rates in the Plastic strain tensor e Equivalent strain and equivalent strain rate V'Jp Work expended during plastic and creep strains NOMENCLATURE (contd) UsN Elastic shear strain energy rec. Current equivalent direct stress suffix L' defines the load stage Current equivalent direct strain rate All other symbols are defined where used. - 7 - INTRODUCTION Up to the turn of the century most engineering components tended to be large because the analysis for estimating nominal dimensions was approximate. Moreoever, generous allowances were made for margins of error. In recent years, however, with more accurate analyses and improvements in the mechanical properties of engineering materials it has been possible to reduce the overall size of components. Amongst the benefits derived from this reduction are smaller inertia and lower material cost, but unfortunately the operating stresses increase. The high stresses produce marked fatigue and creep effects. In post-war years the phenomenon of creep has become increasingly important. The modern use of materials at elevated temperatures has accelerated and magnified creep strains. These are so significant, in particular applications, that they have become major design considerations. High stresses are commonly encountered in high pressure pipes, high pressure vessels, turbine discs, turbine blades, aircraft components and many other major installations and structures. In the past three decades creep behaviour has been investigated by two distinct groups of workers with certain detailed areas of interest. (1) Metallurgists, who are primarily interested in microstructural behaviour with particular reference to grain and atomic structure energies and displacements. (2) Technologists and engineers, who observe the phenomenon as a macrobehaviour. They are generally interested in establishing rules of thumb as well as more sophisticated mathematical analyses which can be suitably employed as design criteria. (This thesis is presented from the viewpoint of the technologists but findings of the metallurgists have been considered). Early investigators tried to establish a law for creep behaviour by a critical study of the parameters involved. Ultimately a mathematical relationship was established by Andrade who proposed an equation for tensile creep in the algebraic form: (.3 t i„) Kt (1) Where p and K are constants for the material at the given temperature. Various theories of elastic failure have been postulated and these have arisen from inconsistent behaviour between predicted and actual results. In general, static tensile data were the yardstick and therefore the corresponding tensile creep data have formed the basis for design. At this point it is worth considering the similarity between static and time - dependent strain behaviours under load, as shown in Figs. 1 and 2. The Aer VA I_ C STRAIN E Constant stress - constant Static Tension temperature creep Fig. 1 Fig. 2 three phases of creep (primary OA, secondary AB and tertiary BC) are comparable with the elastic recoverable phase O'A', the controlled plastic phase A'B' and the phase B'C' respectively in static tension. B'C' is the uncontrolled plastic phase which leads to neck formation and ultimate fracture. The static elastic strain O'A' compares favourably with the primary creep strain CA where unloading of the specimen restores the original physical geometry. Strain A'B' in the controlled plastic deformation is similar to the limiting secondary creep strain AB that can be accepted within the designed working life of a component. The uncontrolled plastic deformation and fracture B'C' is akin to the tertiary creep and rupture strain BC. The strain behaviour of materials under load is a time-dependent or time-independent plastic flow phenomenon. Hence the theories based on time independent flow hold for time dependent conditions as well. The creep phenomenon is a stress dependent flow in solid solution state. If creep occurs, work must be absorbed, therefore any hypothesis formulated for creep behaviour must be based on an energy equation. In constant temperature and constant stress tensile creep too many variables have deliberately been ignored. The basis for design determined on such data is likely to be erroneous and therefore it is important to investigate behaviour under a complex stress pattern. Biaxial loading in creep tests has been extensively used in recent years to obtain complex stress states. A vast amount of work on a number of materials has been carried out in this field at the National Engineering Laboratories by the late Dr. A. E. Johnson and his co-workers. Whereas it has been largely appreciated that a multiaxial load system will produce a comprehensive basis for analysis, very little work on creep under varying and complex stresses has been done. The current research programme was undertaken to investigate this area. It was proposed that tubular test specimens be loaded under
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