On the influence of a longitudinal tensile load on the deformation of a nonlinear elastic anisotropic body with a crack of normal separation

Dmitrieva, EA
1Kaminsky, AA
1Kurchakov, EE
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2020, 5:17-30
https://doi.org/10.15407/dopovidi2020.05.017
Section: Mechanics
Language: Russian
Abstract: 

We study the deformation of a nonlinear elastic orthotropic body with a crack of normal separation. It is assumed that there is a prefracture zone at the crack tip. The plane stress case is considered. The boundary problem is stated in terms of the displacement vector components. It is done using the tensor-linear governing equations which connect the stress tensor components and the strain tensor components and constitutive equations which state the dependence of components of the stress vector at the opposite points on the boundary of prefracture zone on the components of the displacement vector for these points relative to each other. The boundary problem solution is obtained numerically by replacing the partial derivatives with the corresponding finite differences. The supplementary stress method which was proposed in the earlier works by the authors of this paper is used to solve the problem. The results obtained show an influence of the longitudinal tensile loading on the normal components of the strain tensor and the normal components of the stress tensor at the points on the prefracture zone boundary. In particular, it is determined that the longitudinal tensile loading substantially affects the normal components of the stress tensor at the points that initially were at the crack tip.

Keywords: crack of normal separation, nonlinear elastic orthotropic body, prefracture zone
References: 

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. 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
4. 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
5. 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
6. Love, A. (1927). Treatise on the Mathematical Theory of Elasticity. Cambridge: Cambridge Univ. Press.
7. 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