The tables describing the geometry of the yield surface are derived. They concern only fcc metals which undergo isotropic hardening, and which glide on the 24 {111} slip systems. The tables list all five dimensional vertices, and edges of the fourth, third and second order limiting the yield surface as well as the slip systems with which they are associated. A direct method for calculating the yield vectors for any orientation, in five dimensional stress space is established, which enables the user to obtain the yield surface without need of knowing the six deviator stress components. / The relaxed constraint theory, which, by contrast to the classical theory, prescribes only part of the strain increment tensor, is applied to the case of the fixed end torsion test. By taking account of the deformed shape of the grains, three strain components are prescribed; axisymmetry of the sample, which is assumed for every grain, leads to the prescription of another strain component. A further equilibrium condition on the stress associated with the absence of surface tractions leads to an additional constraint. The Yield Subsurface Analysis, which consists of cutting the five dimensional yield surface by the planes of the prescribed stresses, and selecting the p dimensional vertices (p being the number of prescribed strains) that provide maximum work, is carried out. The results are compared with the ones of the classical theory where all the strain components are known. / The simulations are carried out to shear strains of 10, and the orientation changes are calculated incrementally assuming the shear plane and shear direction to be fixed in space. / The texture results are similar up to shear strains of about 3, but differ significantly at larger strains. The relaxed constraint theory predicts the strengthening of the {100} texture component and the development of an equally strong {hk1} fiber component at the expense of the {111} fiber component, whereas the classical theory predicts a very strong {111} fiber component. At large strains, the experimental results agree better with the relaxed constraint predictions. / The average Taylor factors do not exhibit the same trends, since the Bishop and Hill theory predicts a continuous decrease and the RC theory a slight decrease followed by a continuous increase. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.68682 |
| Date | January 1982 |
| Creators | Canova, Gilles R. |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mining and Metallurgical Engineering) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000150761, proquestno: AAINK61090, Theses scanned by UMI/ProQuest. |
Page generated in 0.002 seconds