Parametric analysis of the stress-strain and continuity fields

D. V. Chapliy ; L. V. Stepanova ; O. N. Belova

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 3, pp. 509-529.

Résumé

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.

Détail

Keywords: creep, damage, user procedure UMAT, SIMULIA Abaqus, stress fields, strain fields, crack.

Bibliographie

[1] Kachanov L. M., “Time of the rupture process under creep conditions”, Izv. Akad. Nauk. SSSR, Otd. Tekhn. Nauk, 1958, no. 8, 26–31 (In Russian)

[2] Rabotnov Yu. N., “On a mechanism of delayed failure”, Voprosy prochnosti materialov i konstruktsii [Questions of Strength of Materials and Construction], USSR Academy of Sci., Moscow, 1959, 5–7 (In Russian)

[3] Kachanov L. M., Teoriia plastichnosti [Creep Theory], Fizmatlit, Moscow, 1960, 455 pp. (In Russian)

[4] Rabotnov Yu. N., Creep Problems in Structural Members, North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publ., Amsterdam, London, 1969, ix+822 pp.

[5] Lokoshchenko A. M., Fomin L. V., Teraud W. V., et al., “Creep and long-term strength of metals under unsteady complex stress states (Review)”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:2 (2020), 275–318 (In Russian) | DOI

[6] Meng Q., Zhenqing H., “Creep damage models and their applications for crack growth analysis in pipes: A review”, Eng. Fract. Mech., 205 (2019), 547–576 | DOI

[7] Meng L., Chen W., Yan Y., et al., “Modelling of creep and plasticity deformation considering creep damage and kinematic hardening”, Eng. Fract. Mech., 218 (2019), 106582 | DOI

[8] Murakami S., Continuum Damage Mechanics. A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer, Dordrecht, 2012, xxx+402 pp. | DOI

[9] Riedel H., Fracture at High Temperatures, Springer-Verlag, Berlin, Heidelberg, 1987, 418 pp.

[10] Wen J.-F., Tu S.-T., Gao X.-L., Reddy J. N., “Simulations of creep crack growth in 316 stainless steel using a novel creep-damage model”, Eng. Fract. Mech., 98 (2012), 169–184 | DOI

[11] Rabotnov Yu. N., Vvedenie v mekhaniku razrusheniia [Introduction to the Mechanics of Destruction], Nauka, Moscow, 1987, 80 pp.

[12] Boyle J. T., Spence J., Stress Analysis for Creep, Butterworth-Heinemann, Glasgow, Scotland, 1983, viii+283 pp. | DOI

[13] Shlyannikov V. N., Tumanov A. V., “Force and deformation models of damage and fracture during creep”, Phys. Mesomech., 21:3 (2018), 70–85 (In Russian) | DOI

[14] Shlyannikov V. N., Tumanov A. V., “Creep damage and stress intensity factor assessment for plane multi-axial and three-dimensional problems”, Int. J. Solids Structures, 150 (2018), 166–183 | DOI

[15] Stepanova L. V., “Computational simulation of the damage accumulation processes in cracked solids by the user procedure UMAT of Simulia Abaqus.”, PNRPU Mechanics Bulletin, 2018, no. 3, 71–86 (In Russian) | DOI

[16] Astaf'ev V. I., Radaev Iu. N., Stepanova L. V., Nelineinaia mekhanika razrusheniia [Nonlinear Fracture Mecahics], Samara Univ., Samara, 2001, 632 pp. (In Russian)

[17] Wu Y., Li G., Tan F., et al., “Research on creep damage model of high alumina bricks”, Ceramics Int., 48:19, Part A (2022), 27758–27764 | DOI

[18] Stewart C. M., A Hybrid Constitutive Model for Creep, Fatigue, and Creep-Fatigue Damage, Ph.D. Dissertation, University of Central Florida, Orlando, Florida, 2013 https://stars.library.ucf.edu/etd/2789/

[19] Liu L. Y., Murakami S., “Damage localization of conventional creep damage models and proposition of a new model for creep damage analysis”, Eng. Fract. Mech., 41:1 (1998), 57–65 | DOI

[20] Vanaja J., Laha K., Mathew M. D., “Effect of tungsten on primary creep deformation and minimum creep rate of reduced activation ferritic-martensitic steel”, Metall. Mater. Trans. A, 45:11 (2014), 5076–5084 | DOI

[21] Ro U., Kim S., Kim Y., Kim M. K., “Creep-fatigue damage analysis of modified 9Cr–1Mo steel based on a Voronoi crystalline model”, Int. J. Pressure Vessels Piping, 194, Part B (2021), 104541 | DOI

[22] Dyson B., “Use of CDM in materials modeling and component creep life prediction”, J. Pressure Vessel Technol., 122:3 (2000), 281–296 | DOI

[23] Abdel Wahab M. M., Ashcroft I. A., Crocombe A. D., Shaw S. J., “Prediction of fatigue thresholds in adhesively bonded joints using damage mechanics and fracture mechanics”, J. Adh. Sci. Techn., 15:7 (2001), 763–781 | DOI

[24] He Q., Wu F., Gao R., “Nonlinear creep-damage constitutive model of surrounding rock in salt cavern reservoir”, J. Energy Storage, 55, Part B (2022), 105520 | DOI

[25] Dummer A., Neuner M., Hofstetter G., “An extended gradient-enhanced damage-plasticity model for concrete considering nonlinear creep and failure due to creep”, Int. J. Solids Struct., 243 (2022), 111541 | DOI

[26] Belova O. N., Chapliy D. V., Stepanova L. V., “Application of the UMAT subroutine for solving continuum mechanics problems (Review)”, Vestn. Samar. Univ., Estestvennonauchn. Ser., 27:3 (2021), 46–73 (In Russian) | DOI

[27] Ilin V. N., Mordashov S. V., Pusach S.V., “Laws of creep for computation of fire resisance for steel equipment”, Technology of Technosphere Safety, 2008, no. 6, 10 (In Russian)