Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue
Spontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shape...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1028 |
| _version_ | 1797598213982650368 |
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| author | Hiroyuki Shima Yoshitaka Umeno Takashi Sumigawa |
| author_facet | Hiroyuki Shima Yoshitaka Umeno Takashi Sumigawa |
| author_sort | Hiroyuki Shima |
| collection | DOAJ |
| description | Spontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern as the amplitude of external shear strain increases. However, the physical mechanism that causes the crossover between different dislocation patterns remains unclear. In this study, we theorized a bifurcation diagram that explains the crossover between the two dislocation patterns. The proposed theory is based on a weakly nonlinear stability analysis that considers the mutual interaction of dislocations as a nonlinearity. It was found that the selection rule among the two dislocation patterns, “spotted” and “ladder-shaped”, can be described by inequalities with respect to nonlinearity parameters contained in the governing equations. |
| first_indexed | 2024-03-11T03:16:11Z |
| format | Article |
| id | doaj.art-32433964892048c0847f023e00090094 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:11Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-32433964892048c0847f023e000900942023-11-18T03:29:54ZengMDPI AGSymmetry2073-89942023-05-01155102810.3390/sym15051028Spot–Ladder Selection of Dislocation Patterns in Metal FatigueHiroyuki Shima0Yoshitaka Umeno1Takashi Sumigawa2Department of Environmental Sciences, University of Yamanashi, Kofu 400-8510, JapanInstitute of Industrial Science, The University of Tokyo, Tokyo 153-8505, JapanDepartment of Energy Conversion Science, Graduate School of Energy Science, Kyoto University, Kyoto 606-8501, JapanSpontaneous pattern formation by a large number of dislocations is commonly observed during the initial stages of metal fatigue under cyclic straining. It was experimentally found that the geometry of the dislocation pattern undergoes a crossover from a 2D spot-scattered pattern to a 1D ladder-shaped pattern as the amplitude of external shear strain increases. However, the physical mechanism that causes the crossover between different dislocation patterns remains unclear. In this study, we theorized a bifurcation diagram that explains the crossover between the two dislocation patterns. The proposed theory is based on a weakly nonlinear stability analysis that considers the mutual interaction of dislocations as a nonlinearity. It was found that the selection rule among the two dislocation patterns, “spotted” and “ladder-shaped”, can be described by inequalities with respect to nonlinearity parameters contained in the governing equations.https://www.mdpi.com/2073-8994/15/5/1028pattern formationmetal fatiguebifurcation theoryturing instabilityreaction–diffusion dynamics |
| spellingShingle | Hiroyuki Shima Yoshitaka Umeno Takashi Sumigawa Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue Symmetry pattern formation metal fatigue bifurcation theory turing instability reaction–diffusion dynamics |
| title | Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue |
| title_full | Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue |
| title_fullStr | Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue |
| title_full_unstemmed | Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue |
| title_short | Spot–Ladder Selection of Dislocation Patterns in Metal Fatigue |
| title_sort | spot ladder selection of dislocation patterns in metal fatigue |
| topic | pattern formation metal fatigue bifurcation theory turing instability reaction–diffusion dynamics |
| url | https://www.mdpi.com/2073-8994/15/5/1028 |
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