FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES
The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulatio...
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| Format: | Article |
| Language: | Russian |
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Belarusian National Technical University
2014-12-01
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| Series: | Наука и техника |
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| Online Access: | https://sat.bntu.by/jour/article/view/12 |
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| author | Alim. Abed Al-Zobaede Yu. V. Chigareva |
| author_facet | Alim. Abed Al-Zobaede Yu. V. Chigareva |
| author_sort | Alim. Abed Al-Zobaede |
| collection | DOAJ |
| description | The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust) is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase) and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law. |
| format | Article |
| id | doaj-art-5ac06df475014af4b90c96fe38f3c811 |
| institution | OA Journals |
| issn | 2227-1031 2414-0392 |
| language | Russian |
| publishDate | 2014-12-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Наука и техника |
| spelling | doaj-art-5ac06df475014af4b90c96fe38f3c8112025-08-20T02:36:08ZrusBelarusian National Technical UniversityНаука и техника2227-10312414-03922014-12-010642486FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODESAlim. Abed Al-Zobaede0Yu. V. Chigareva1Belarusian National Technical UniversityBelarusian National Technical UniversityThe paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust) is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase) and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law.https://sat.bntu.by/jour/article/view/12structure damagemacdonald functioncantor modeldamage accumulation |
| spellingShingle | Alim. Abed Al-Zobaede Yu. V. Chigareva FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES Наука и техника structure damage macdonald function cantor model damage accumulation |
| title | FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES |
| title_full | FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES |
| title_fullStr | FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES |
| title_full_unstemmed | FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES |
| title_short | FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES |
| title_sort | fractal model of damage accumulation in solid bodes |
| topic | structure damage macdonald function cantor model damage accumulation |
| url | https://sat.bntu.by/jour/article/view/12 |
| work_keys_str_mv | AT alimabedalzobaede fractalmodelofdamageaccumulationinsolidbodes AT yuvchigareva fractalmodelofdamageaccumulationinsolidbodes |