Effect of damage accumulation on the asymptotic behavior of stresses ahead the crack tip

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

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 29 (2023) no. 1, pp. 47-63

Résumé

The subject of this study is the analysis of mechanical fields associated with a crack tip under creep conditions, taking into account the phenomenon of damage accumulation. The objective of the study is to perform finite element modeling, using the SIMULIA Abaqus software package, of uniaxial tension of a plate with a central horizontal crack under creep conditions, taking into account damage accumulation. For numerical simulation of creep, the Bailey-Norton power law is used. The power law of creep with the help of the user procedure UMAT (User Material) of the SIMULIA Abaqus package was supplemented with the Kachanov-Rabotnov kinetic equation of damage accumulation in a related formulation. In the calculation scheme of finite elements, the crack tip was modeled as a mathematical notch and as a notch with a finite radius of curvature. As a result of the calculations, the distributions of stresses, strains, and continuity under creep conditions were obtained, taking into account the accumulation of damage over time. Radial distributions of continuity, stresses, and strains are plotted over time at various distances from the crack tip. The subject of the study was the consideration of the asymptotic of the stress distribution. As a result of the study, it is shown that in the elastic region the asymptotic corresponds to the distribution under the elastic regime, and in the creep zone the asymptotics of Hutchinson, Rice and Rosengren (HRR-solution) is satisfied for different exponents $n$ of the power law of creep. A comparison is made of the radial stress distributions in modeling without taking into account damage and in the case of taking into account damage accumulation. It is shown that the presence of damage significantly changes the asymptotics of the stress field in the vicinity of the crack tip.

Détail

Keywords: user procedure UMAT, SIMULIA Abaqus, creep, damage, continuity, asymptotic.

Bibliographie

[1] Hayhurst D.R., “Materials Data Bases and Mechanisms-Based Constitutive Equations for Use in Design”, Creep and Damage in Materials and Structures, 399, eds. Altenbach H., Skrzypek J.J., International Centre for Mechanical Sciences, 1999, 167–208 | DOI

[2] Wang X.-Y., Zhang X.-C., Zhu S.-F., “Creep damage characterization of UNS N10003 alloys based on a numerical simulation using the Norton creep law and Kachanov-Rabotnov creep damage model”, Nuclear Science and Techniques, 30 (2019), 65 | DOI

[3] Okereke M., Keates S., “Material Response: Constitutive Models and Their Implementation”, Finite Element Applications, Springer Tracts in Mechanical Engineering, Springer, Cham, 2018, 363–436 | DOI | MR

[4] Ahmad M.I.M, Akbar M., Abdullah N.A., “Development of constitutive creep damage-based modified Robinson-Rousselier (MRR) model with XFEM for void-crack relation in ductile materials”, Mechanics of Time-Dependent Materials, 2022 | DOI

[5] Hosseini-Toudeshky H., Jannnesari M., “An investigation on creep life assessment of welded steam pipeline intersection using classical and progressive damage analyses”, Welding in the World, 66 (2022), 1653–1664 | DOI

[6] 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

[7] Turkova V.A., Stepanova L.V., “Evaluation of damage accumulation zone in the vicinity of the crack tip: FEM analysis via UMAT procedure”, Journal of Physics: Conference Series, 1096 (2018), 012157 | DOI

[8] Shlyannikov V.N., Tumanov A.V., “Force and deformation models of damage and fracture during creep”, Physical Mesomechanics, 21:3 (2018), 70–85 | DOI

[9] Shlyannikov V.N., “Crack tip fields and fracture resistance parameters based on strain gradient plasticity”, International Journal of Solids and Structures, 208–209 (2021), 63–82 | DOI

[10] Shlyannikov V.N., “Solution of nonlinear strain and fracture problems of materials in complex stress states”, Physical Mesomechanics, 15:1 (2012), 57–67 (In Russian)

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

[12] McMeeking R.M., “Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture”, Journal of the Mechancis and Physics of Solids, 25:5 (1977), 357–381 | DOI

[13] Shlyannikov V.N., Kislova S.Y., “Parameters of deformation mixed modes with account of crack tip curvature”, Strength of Materials, 42:6 (2010), 660–674 | DOI

[14] Meng Li., Chen W., Yan Y., Kitamura T., Feng M., “Modelling of creep and plasticity deformation considering creep damage and kinematic hardening”, Engineering Fracture Mechanics, 218 (2019), 106582 | DOI

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

[16] Murakami S., Continuum Damage Mechanics. A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer, Dordrecht, 2012, 423 pp. | DOI

[17] 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”, Engineering Fracture Mechanics, 98 (2012), 169–184 | DOI

[18] Kachanov L.M., “Force and deformation models of damage and fracture during creep”, Physical Mesomechanics, 21:3 (2018), 70–85

[19] Kachanov L.M., Creep theory, Gosudarstvennoe izdatel'stvo fiziko-matematicheskoi literatury, M., 1960, 455 pp. (In Russian)

[20] Rabotnov Yu.N., Creep problems in structural members, Nauka, M., 2014, 752 pp. (In Russian)

[21] Lokoshchenko A.V., Fomin L.V., Teraud W.V., Basalov Y.G., Agababyan V.S., “Creep and long-term strength of metals under unsteady complex stress states (review)”, Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences, 24:2 (2020), 275–318 (In Russian) | DOI

[22] Boyle J.T, Spence J., Stress analysis for creep, Mir, M., 1986, 360 pp. (In Russian)

[23] Riedel H., Fracture at High Temperatures, Springer-Verlag, Berlin–Heidelberg, 1987, 418 pp. | DOI

[24] Rice J.R., Rosengren G.F., “Plane strain deformation near a crack tip in a power-law hardening material”, Journal of The Mechanics and Physics of Solids, 16:1 (1968), 1–12 http://esag.harvard.edu/rice/016_RiceRosengren_CrackSing_JMPS68.pdf | DOI | Zbl

[25] Hutchinson J.W., “Singular behaviour at the end of a tensile crack in a hardening material”, Journal of The Mechanics and Physics of Solids, 16:1 (1968), 13–31 https://groups.seas.harvard.edu/hutchinson/papers/312.pdf | DOI | Zbl

[26] Hutchinson J.W., “Plastic stress and strain fields at a crack tip”, Journal of The Mechanics and Physics of Solids, 16:5 (1968), 337–342 https://groups.seas.harvard.edu/hutchinson/papers/313.pdf | DOI

[27] Naumenko K., Altenbach H., Modelling of Creep for Structural Analysis, Springer, Berlin–Heidelberg, 2007, 220 pp. | DOI

[28] USER MATERIAL IN ABAQUS, , 2017 https://abaqus-docs.mit.edu/2017/English/SIMACAESUBRefMap/simasub-c-umat.htm

[29] Lecture 6. Writing a UMAT or VUMAT, https://imechanica.org/files/Writing