Parametric analysis of the stress-strain and continuity fields at the crack tip under creep regime taking into account the processes of damage accumulation using UMAT

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Abstract

The subject of this study is the analysis of the stress-strain and continuity fields in the proximal nearness of the crack tip, which is in creep regime conditions with due regard for the accumulation of damage. The aim of the work is to conduct computer finite element modeling of uniaxial stretching of a two-dimensional plate with a central crack under creep conditions and to analyze the continuity field around the crack tip. The Bailey–Norton power law of creep is used in numerical modeling. The simulation was performed in the software multifunctional complex SIMULIA Abaqus. The analysis of the circumferential apportionment of stresses, creep deformations and continuity in the direct of the crack tip is carried out.
The power law of creep with the help of the user procedure UMAT (User Material) of the SIMULIA Abaqus package was supplemented by the kinetic equation of damage accumulation of Kachanov–Rabotnov in a related formulation. The UMAT subroutine has many advantages in predicting material damage and allows you to work with materials that are not in the Abaqus materials library. The UMAT subroutine is called at all points of the material calculation and updates the stresses and state variables depending on the solution to their values at the end of the increment. After that, the updated elements of the Jacobi matrix are calculated.
Stress, strain and continuity distributions under creep conditions are gained, considering the damage accumulation of over time. Angular distributions of continuity, stresses and deformations are constructed using the Matplotlib library over time at various distances from the crack tip. The obtained angular distributions of the stress and strain tensor components are compared when modeling without taking into account damage and when taking into account damage accumulation. It is shown that the presence of damage leads to large values of creep deformations and lower stresses.

About the authors

Dmitriy V. Chapliy

Samara National Research University

Email: Dch300189@yandex.ru
ORCID iD: 0000-0001-9510-3659
SPIN-code: 3262-0330
ResearcherId: GSI-6114-2022

Postgraduate Student, Dept. of Mathematical Modelling in Mechanics

Russian Federation, 443086, Samara, Moskovskoye shosse, 34

Larisa V. Stepanova

Samara National Research University

Author for correspondence.
Email: Stepanova.lv@ssau.ru
ORCID iD: 0000-0002-6693-3132
SPIN-code: 7564-6513
Scopus Author ID: 7102960155

Dr. Phys. & Math. Sci., Associate Professor, Head of Department, Dept. of Mathematical Modelling in Mechanics

Russian Federation, 443086, Samara, Moskovskoye shosse, 34

Oksana N. Belova

Samara National Research University

Email: belova.on@ssau.ru
ORCID iD: 0000-0002-4492-223X

Assistant, Dept. of Mathematical Modelling in Mechanics

Russian Federation, 443086, Samara, Moskovskoye shosse, 34

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Supplementary files

Supplementary Files
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1. JATS XML
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2. Figure 1. Distributions of the stress tensor components \(\sigma_{11}\) (a–d) and \(\sigma_{22}\) (e–h) under creep conditions at 0.2, 103, 1003 and 5000 hours

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3. Figure 2. Distributions of the stress tensor components \(\sigma_{11}\) (a–d) and \(\sigma_{22}\) (e–h) under creep conditions taking into account damage accumulation processes at 0.2, 103, 1003 and 5000 hours

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4. Figure 3. Continuity distributions at 103 and 1003 hours

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5. Figure 4. Comparison of angular distributions of stress tensor components (a–с) and creep strains (d–f) under creep conditions without taking into account damage (solid curves) and taking into account damage accumulation processes (dotted curves) over time

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6. Figure 5. Comparison of angular distributions of stress tensor components (a–с) and creep strains (d–f) under creep conditions without taking into account damage (solid curves) and taking into account damage accumulation processes (dotted curves) at 5000 hours at different distances from the crack tip

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7. Figure 6. Angular distributions of the continuity parameter \(\psi\)

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8. Figure 7. Continuity distributions near the tip of an inclined crack: a) when \(m=1.5\) at 53 hours; b) when \(m=4\) after 5000 hours

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9. Figure 8. Continuity distributions near the tip of an inclined crack (\(\gamma=45^\circ\)) at 103 and 1003 hours

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10. Figure 9. Continuity distributions near the tip of an inclined crack (\(\gamma=60^\circ\)) at 103 and 1003 hours

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11. Figure 10. Distributions of the Mises stress intensity (a–d) and creep strain tensor component \(\varepsilon_{11}\) (e–h) under creep conditions taking into account damage accumulation processes in the neighborhood of the tip of the inclined crack (\(\gamma=45^\circ\)) at 0.2, 103, 1003 and 5000 hours

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12. Figure 11. Distributions of the Mises stress intensity (a–d) and creep strain tensor component \(\varepsilon_{11}\) (e–h) under creep conditions taking into account damage accumulation processes in the neighborhood of the tip of the inclined crack (\(\gamma=60^\circ\)) at 0.2, 103, 1003 and 5000 hours

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13. Figure 12. Comparison of angular distributions of stress tensor components (a–c) and creep strains (d–f) under creep conditions without taking into account damage (solid curves) and taking into account damage accumulation processes (dotted curves) at 5000 hours at different distances from the inclined crack tip (\(\gamma=45^\circ\))

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14. Figure 13. Angular distributions of the continuity parameter \(\psi\) in the neighborhood of the tip of the inclined crack (\(\gamma=45^\circ\))

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15. Figure 14. Comparison of angular distributions of stress tensor components (a–c) and creep strains (d–f) under creep conditions without taking into account damage (solid curves) and taking into account damage accumulation processes (dotted curves) at 5000 hours at different distances from the inclined crack tip (\(\gamma=60^\circ\))

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16. Figure 15. Angular distributions of the continuity parameter \(\psi\) in the neighborhood of the tip of the inclined crack (\(\gamma=60^\circ\))

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