Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests
<p>Dislocation channel-veins and persistent slip bands (PSBs) are characteristic dislocation configurations that are of interest to both industry and academia. However, existing mathematical models are not adequate to describe the mechanism of the transition between these two states. In this t...
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| Format: | Thesis |
| Language: | English |
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2012
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| _version_ | 1797088379379122176 |
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| author | Zhu, Y |
| author2 | Chapman, S |
| author_facet | Chapman, S Zhu, Y |
| author_sort | Zhu, Y |
| collection | OXFORD |
| description | <p>Dislocation channel-veins and persistent slip bands (PSBs) are characteristic dislocation configurations that are of interest to both industry and academia. However, existing mathematical models are not adequate to describe the mechanism of the transition between these two states. In this thesis, a series of models are proposed to give a quantitative description to such a transition. The full problem has been considered from two angles.</p> <p>Firstly, the general motion and instabilities of arbitrary curved dislocations have been studied both analytically and numerically. Then the law of motion and local expansions are used to track the shapes of screw segments moving through channels, which are believed to induce dislocation multiplication by cross-slip.</p> <p>The second approach has been to investigate the collective behavior of a large number of dislocations, both geometrically necessary and otherwise. The traditional method of multiple scales does not apply well to describe the pile-up of two arrays of dislocations of opposite signs on a pair of neighbouring glide planes in two dimensional space. Certain quantities have to be more accurately defined under the multiple-scale coordinates to capture the much more localised resultant stress caused by these dislocation pairs. Through detailed calculations, one-dimensional dipoles can be homogenised to obtain some insightful results both on a local scale where the dipole pattern is the key diagnostic and on a macroscopic scale on which density variations are of most interest. Equilibria of dislocation dipoles in a two-dimensional regular lattice have been also studied. Some natural transitions between different patterns can be found as a result of geometrical instabilities.</p> |
| first_indexed | 2024-03-07T02:49:13Z |
| format | Thesis |
| id | oxford-uuid:ad163287-19cc-4318-995a-378df1d80260 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:49:13Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:ad163287-19cc-4318-995a-378df1d802602022-03-27T03:33:13ZModelling the transition from channel-veins to PSBs in the early stage of fatigue testsThesishttp://purl.org/coar/resource_type/c_db06uuid:ad163287-19cc-4318-995a-378df1d80260Approximations and expansionsMathematicsPartial differential equationsEnglishOxford University Research Archive - Valet2012Zhu, YChapman, S<p>Dislocation channel-veins and persistent slip bands (PSBs) are characteristic dislocation configurations that are of interest to both industry and academia. However, existing mathematical models are not adequate to describe the mechanism of the transition between these two states. In this thesis, a series of models are proposed to give a quantitative description to such a transition. The full problem has been considered from two angles.</p> <p>Firstly, the general motion and instabilities of arbitrary curved dislocations have been studied both analytically and numerically. Then the law of motion and local expansions are used to track the shapes of screw segments moving through channels, which are believed to induce dislocation multiplication by cross-slip.</p> <p>The second approach has been to investigate the collective behavior of a large number of dislocations, both geometrically necessary and otherwise. The traditional method of multiple scales does not apply well to describe the pile-up of two arrays of dislocations of opposite signs on a pair of neighbouring glide planes in two dimensional space. Certain quantities have to be more accurately defined under the multiple-scale coordinates to capture the much more localised resultant stress caused by these dislocation pairs. Through detailed calculations, one-dimensional dipoles can be homogenised to obtain some insightful results both on a local scale where the dipole pattern is the key diagnostic and on a macroscopic scale on which density variations are of most interest. Equilibria of dislocation dipoles in a two-dimensional regular lattice have been also studied. Some natural transitions between different patterns can be found as a result of geometrical instabilities.</p> |
| spellingShingle | Approximations and expansions Mathematics Partial differential equations Zhu, Y Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title | Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title_full | Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title_fullStr | Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title_full_unstemmed | Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title_short | Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests |
| title_sort | modelling the transition from channel veins to psbs in the early stage of fatigue tests |
| topic | Approximations and expansions Mathematics Partial differential equations |
| work_keys_str_mv | AT zhuy modellingthetransitionfromchannelveinstopsbsintheearlystageoffatiguetests |