| Title | On the transformation of the passive deformation area in a nonlinear elastic anisotropic body with crack |
| Publication Type | Journal Article |
| Year of Publication | 2019 |
| Authors | Kaminsky, AA, Kurchakov, EE |
| Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
| DOI | 10.15407/dopovidi2019.09.020 |
| Issue | 9 |
| Section | Mechanics |
| Pagination | 20-33 |
| Date Published | 09/2019 |
| Language | Russian |
| Abstract | The deformation of a nonlinear elastic orthotropic thin plate with a crack of normal separation is considered. It is assumed that there is a prefracture zone in the crack tip. It is assumed that the plane stress conditions are applicable. The boundary-value problem for the plate is stated in terms of the displacement vector. Governing equations are stated to describe the dependence between the stress and the strain tensors. Constitutive equations are used as an interlink between components of the stress vector at the points on the opposite faces of the prefracture zone and components of the mutual displacement vector for these points. The partial derivatives in the equations are transformed into the finite differences using the mesh discretization. Terms “active” and “passive” are introduced for the deformation according to its action on the nonlinear elastic anisotropic body. The problem is solved using the additional stress method that was earlier proposed by the authors of this work. The boundary-value problem solution allows concluding that a passive deformation area appears around the prefracture zone. Stresses in this area diminish, as the loading parameter grows. An analysis is given for the extents of the passive deformation area. In particular, it is investigated how it changes its dimensions and form depending on the loading parameter. A comparison is made between the passive deformation area and the nonlinearity area around the crack tip. It is shown that there are some differences between them. |
| Keywords | constitutive equations, crack of normal separation, nonlinear elastic orthotropic body, passive deformation area, prefracture zone |
1. Каminsky, А. А. & Кurchakov, Е. Е. (2018). On Evolution of Fracture Process Zone near the Crack Tip in Nonlinear Anisotropic Body. Dopov. Nac. akad. nauk Ukr., No. 10, pp. 44-55 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.10.044
2. Selivanov, M. F. & Chornoivan, Y. O. (2018). A Semi-Analytical Solution Method for Problems of Cohesive Fracture and Some of Its Applications. Int. J. of Fracture, 212, No. 1, pp. 113-121. doi: https://doi.org/10.1007/s10704-018-0295-6
3. Selivanov, M. F., Chornoivan, Y. O. & Kononchuk, O. P. (2019). Determination of Crack Opening Displacement and Critical Load Parameter within a Cohesive Zone Model. Cont. Mech. and Thermodynamics, 31, No. 2, pp. 569-586. doi: https://doi.org/10.1007/s00161-018-0712-0
4. Bogdanova, O. S., Kaminsky, A. A. & Kurchakov, E. E. (2017). On the Fracture Process Zone near the Front of an Arbitrary Crack in a Solid. Dopov. Nac. akad. nauk Ukr., No. 5, pp. 25-33 (in Russian). doi: https://doi.org/10.15407/dopovidi2017.05.025
5. Kaminsky, A. A. & Kurchakov, E. E. (2019). Fracture Process Zone at the Tip of a Mode I Crack in a Nonlinear Elastic Orthotropic Material. Int. Appl. Mech., 55, No. 1, pp. 23-40. doi: https://doi.org/10.1007/s10778-019-00931-9
6. Kurchakov, E. E. (1979). Stress-Strain Relation for Nonlinear Anisotropic Medium. Sov. Appl. Mech., 15, No. 9, pp. 803-807. doi: https://doi.org/10.1007/BF00885391
7. Kaminsky, A. A., Kurchakov, E. E. & Gavrilov, G. V. (2006). Study of the Plastic Zone near a Crack in an Anisotropic Body. Int. Appl. Mech., 42, No. 7, pp. 749-764. doi: https://doi.org/10.1007/s10778-006-0143-7
8. Hencky, H. (1940). Development and Present State of the Theory of Plasticity. Prikl. Mat. i Mekh., 4, No. 3, pp. 31-36 (in Russian).
9. Kurchakov, E. E. & Gavrilov, G. V. (2008). Formation of the Plastic Zone in an Anisotropic Body with a Crack. Int. Appl. Mech., 44, No. 9, pp. 982-997. doi: https://doi.org/10.1007/s10778-009-0120-z
10. Hencky, H. (1924). Zur Theorie plastische Deformationen. Proc. 1-st Int. Congress Appl. Mech. Delft.
11. Nadai, A. (1931). Plasticity. New York—London: McGraw–Hill.
12. Kurchakov, E. E. (2015). Thermodynamic Verification of Constitutive Equations for a Nonlinear Anisotropic Body. Dopov. Nac. akad. nauk Ukr., No. 9, pp. 46-53 (in Russian). doi: https://doi.org/10.15407/dopovidi2015.09.046
13. Love, A. (1927). Treatise on the Mathematical Theory of Elasticity. Cambridge: Univ. Press.
14. Ilyushin, А. А. (1948). Plasticity. Moscow—Leningrad: OGIZ (in Russian).
