Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics
The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strai...
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MDPI AG
2023-05-01
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| Online Access: | https://www.mdpi.com/2076-3417/13/10/6333 |
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| author | Yury Solyaev |
| author_facet | Yury Solyaev |
| author_sort | Yury Solyaev |
| collection | DOAJ |
| description | The elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown. |
| first_indexed | 2024-03-11T03:57:40Z |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T03:57:40Z |
| publishDate | 2023-05-01 |
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| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-69afce368f084c2baa5fe249b2592c7c2023-11-18T00:24:05ZengMDPI AGApplied Sciences2076-34172023-05-011310633310.3390/app13106333Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient ElastodynamicsYury Solyaev0Moscow Aviation Institute, Volokolamskoe Ave., 4, 125993 Moscow, RussiaThe elastodynamic stress field near a crack tip propagating at a constant speed in isotropic quasi-brittle material was investigated, taking into account the strain gradient and inertia gradient effects. An asymptotic solution for a steady-state Mode-I crack was developed within the simplified strain gradient elasticity by using a representation of the general solution in terms of Lamé potentials in the moving framework. It was shown that the derived solution predicts the nonsingular stress state and smooth opening profile for the growing cracks that can be related to the presence of the fracture process zone in the micro-/nanostructured quasi-brittle materials. Note that similar asymptotic solutions have been derived previously only for Mode-III cracks (under antiplane shear loading). Thus, the aim of this study is to show the possibility of analytical assessments on the elastodynamic crack tip fields for in-plane loading within gradient theories. By using the derived solution, we also performed analysis of the angular distribution of stresses and tractions for the moderate speed of cracks. It was shown that the usage of the maximum principal stress criterion within second gradient elastodynamics allows us to describe a directional stability of Mode-I crack growth and an increase in the dynamic fracture toughness with the crack propagation speed that were observed in the experiments with quasi-brittle materials. Therefore, the possibility of the effective application of regularized solutions of strain gradient elasticity for the refined analysis of dynamic fracture processes in the quasi-brittle materials with phenomenological assessments on the cohesive zone effects is shown.https://www.mdpi.com/2076-3417/13/10/6333quasi-brittle fracturesteady-state crack growthasymptotic solutionstrain gradient effectsdynamic toughness |
| spellingShingle | Yury Solyaev Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics Applied Sciences quasi-brittle fracture steady-state crack growth asymptotic solution strain gradient effects dynamic toughness |
| title | Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics |
| title_full | Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics |
| title_fullStr | Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics |
| title_full_unstemmed | Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics |
| title_short | Steady-State Crack Growth in Nanostructured Quasi-Brittle Materials Governed by Second Gradient Elastodynamics |
| title_sort | steady state crack growth in nanostructured quasi brittle materials governed by second gradient elastodynamics |
| topic | quasi-brittle fracture steady-state crack growth asymptotic solution strain gradient effects dynamic toughness |
| url | https://www.mdpi.com/2076-3417/13/10/6333 |
| work_keys_str_mv | AT yurysolyaev steadystatecrackgrowthinnanostructuredquasibrittlematerialsgovernedbysecondgradientelastodynamics |