DOI: https://doi.org/10.15587/1729-4061.2018.119727

### Numerical simulation of two-dimensional problems of creep crack growth with material damage consideration

Dmytro Breslavsky, Alyona Kozlyuk, Oksana Tatarinova

#### Abstract

Approach for numerical simulation of the process of the creep crack growth taking into account the hidden material damage is proposed. The approach is based on the application of finite element creep modeling, accompanied by damage. For calculations, the FEM Creep software package is used. Using the proposed algorithm for rebuilding the grid with the removal of the destroyed elements, the current picture of deformation and fracture is analyzed. This takes into account the growing level of damage during the crack motion in each element. Numerical fracture simulation data are used to determine the constants in the differential creep fracture propagation equation. As an example, the creep fracture of planar specimens with sharp notches in their plane is considered. The material of the specimens is a high-temperature nickel-based alloy EI 867 at a temperature of 950 °C. Calculations are carried out for different values of the load. For different times, finite element grids with remote elements are shown. Graphs of the dependence of crack length on time are built. Comparison of numerical and calculated data obtained with the motion equation of a crack shows their acceptable coincidence. The possibility of using the proposed approach for obtaining constants in the equation of crack motion as an alternative to the existing experimental one is discussed.

#### Keywords

creep; damage; creep crack growth; finite element calculation model

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#### References

Erdogan, F. (2000). Fracture mechanics. International Journal of Solids and Structures, 37 (1-2), 171–183. doi: 10.1016/s0020-7683(99)00086-4

Rice, J. R. (1968). A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks. Journal of Applied Mechanics, 35 (2), 379. doi: 10.1115/1.3601206

Webster, G. A., Nikbin, K. M. (1981). History of Loading Effects on Creep Crack Growth in ½% Cr, ½% Mo, ¼% V Steel. Creep in Structures, 576–591. doi: 10.1007/978-3-642-81598-0_38

Riedel, H. (1981). The Extension of a Macroscopic Crack at Elevated Temperature by the Growth and Coalescence of Microvoids. Creep in Structures, 504–519. doi: 10.1007/978-3-642-81598-0_33

Hayhurst, D. R., Morrison, C. J., Brown, P. R. (1981). Creep Crack Growth. Creep in Structures, 564–575. doi: 10.1007/978-3-642-81598-0_37

Moës, N., Dolbow, J., Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46 (1), 131–150. doi: 10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.3.co;2-a

Hayhurst, D. R., Brown, P. R., Morrison, C. J. (1984). The Role of Continuum Damage in Creep Crack Growth. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 311 (1516), 131–158. doi: 10.1098/rsta.1984.0022

Ohtani, R. (1981). Finite Element Analysis and Experimental Investigation on Creep Crack Propagation. Creep in Structures, 542–563. doi: 10.1007/978-3-642-81598-0_36

Chaboche, J. L. (2003). Damage Mechanics. Comprehensive Structural Integrity, 213–284. doi: 10.1016/b0-08-043749-4/02085-1

Riedel, H. (1989). Creep Crack Growth. Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), 101–101-26. doi: 10.1520/stp18822s

Perrin, I. J., Hayhurst, D. R. (1999). Continuum damage mechanics analyses of type IV creep failure in ferritic steel crossweld specimens. International Journal of Pressure Vessels and Piping, 76 (9), 599–617. doi: 10.1016/s0308-0161(99)00051-4

Yatomi, M., Nikbin, K. M., O’Dowd, N. P. (2003). Creep crack growth prediction using a damage based approach. International Journal of Pressure Vessels and Piping, 80 (7-8), 573–583. doi: 10.1016/s0308-0161(03)00110-8

Cuvillez, S., Feyel, F., Lorentz, E., Michel-Ponnele, S. (2012). Transition from a gradient damage model to a cohesive zone model within the framework of quasi-brittle failure. Proc. of First Int. Conf. on Damage Mechanics ICDM1. Belgrade, 97–100.

Astaf’ev, V. I., Radaev, Yu. N., Stepanova, L. V. (2004). Nonlinear fracture mechanics. Samara: Samarskiy universitet, 562.

Xu, M., Chen, J., Lu, H., Xu, J., Yu, C., Wei, X. (2016). Effects of residual stress and grain boundary character on creep cracking in 2.25Cr-1.6W steel. Materials Science and Engineering: A, 659, 188–197. doi: 10.1016/j.msea.2016.02.025

Breslavskii, D. V., Morachkovskii, O. K. (1998). Nonlinear creep and the collapse of flat bodies. International Applied Mechanics, 34 (3), 287–292.

Breslavsky, D. V., Korytko, Yu. M. (2017). Design and development of Finite Element Method software. Kharkiv: KhPi, 232.

Breslavs’kyi, D. V., Korytko, Y. M., Morachkovs’kyi, O. K. (2011). Cyclic thermal creep model for the bodies of revolution. Strength of Materials, 43 (2), 134–143. doi: 10.1007/s11223-011-9279-8

Lemaitre, J., Chaboche, J. L. (1994). Mechanics of solid materials. Cambridge University Press, 556.

Golub, V. P. (1983). Cyclic Creep of Refractory Nickel Alloys. Kyiv: Naukova dumka, 224.

Taira, S., Otani, R. (1986). Theory of High-Temperature Strength of Materials. Moscow: Metallurgiya, 280.

#### GOST Style Citations

Erdogan F. Fracture mechanics // International Journal of Solids and Structures. 2000. Vol. 37, Issue 1-2. P. 171–183. doi: 10.1016/s0020-7683(99)00086-4

Rice J. R. A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks // Journal of Applied Mechanics. 1968. Vol. 35, Issue 2. P. 379. doi: 10.1115/1.3601206

Webster G. A., Nikbin K. M. History of Loading Effects on Creep Crack Growth in ½% Cr, ½% Mo, ¼% V Steel // Creep in Structures. 1981. P. 576–591. doi: 10.1007/978-3-642-81598-0_38

Riedel H. The Extension of a Macroscopic Crack at Elevated Temperature by the Growth and Coalescence of Microvoids // Creep in Structures. 1981. P. 504–519. doi: 10.1007/978-3-642-81598-0_33

Hayhurst D. R., Morrison C. J., Brown P. R. Creep Crack Growth // Creep in Structures. 1981. P. 564–575. doi: 10.1007/978-3-642-81598-0_37

Moës N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing // International Journal for Numerical Methods in Engineering. 1999. Vol. 46, Issue 1. P. 131–150. doi: 10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.3.co;2-a

Hayhurst D. R., Brown P. R., Morrison C. J. The Role of Continuum Damage in Creep Crack Growth // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 1984. Vol. 311, Issue 1516. P. 131–158. doi: 10.1098/rsta.1984.0022

Ohtani R. Finite Element Analysis and Experimental Investigation on Creep Crack Propagation // Creep in Structures. 1981. P. 542–563. doi: 10.1007/978-3-642-81598-0_36

Chaboche J. L. Damage Mechanics // Comprehensive Structural Integrity. 2003. P. 213–284. doi: 10.1016/b0-08-043749-4/02085-1

Riedel H. Creep Crack Growth // Fracture Mechanics: Perspectives and Directions (Twentieth Symposium). 1989. P. 101–101-26. doi: 10.1520/stp18822s

Perrin I. J., Hayhurst D. R. Continuum damage mechanics analyses of type IV creep failure in ferritic steel crossweld specimens // International Journal of Pressure Vessels and Piping. 1999. Vol. 76, Issue 9. P. 599–617. doi: 10.1016/s0308-0161(99)00051-4

Yatomi M., Nikbin K. M., O'Dowd N. P. Creep crack growth prediction using a damage based approach // International Journal of Pressure Vessels and Piping. 2003. Vol. 80, Issue 7-8. P. 573–583. doi: 10.1016/s0308-0161(03)00110-8

Transition from a gradient damage model to a cohesive zone model within the framework of quasi-brittle failure / Cuvillez S., Feyel F., Lorentz E., Michel-Ponnele S. // Proc. of First Int. Conf. on Damage Mechanics ICDM1. Belgrade, 2012. P. 97–100.

Astaf’ev V. I., Radaev Yu. N., Stepanova L. V. Nonlinear fracture mechanics. Samara: Samarskiy universitet, 2004. 562 р.

Effects of residual stress and grain boundary character on creep cracking in 2.25Cr-1.6W steel / Xu M., Chen J., Lu H., Xu J., Yu C., Wei X. // Materials Science and Engineering: A. 2016. Vol. 659. P. 188–197. doi: 10.1016/j.msea.2016.02.025

Breslavskii D. V., Morachkovskii O. K. Nonlinear creep and the collapse of flat bodies // International Applied Mechanics. 1998. Vol. 34, Issue 3. P. 287–292.

Breslavsky D. V., Korytko Yu. M. Design and development of Finite Element Method software. Kharkiv: KhPi, 2017. 232 р.

Breslavs’kyi, D. V., Korytko Yu. M., Morachkovs’kyi O. K. Cyclic thermal creep model for the bodies of revolution // Strength of Materials. 2011. Vol. 43, Issue 2. – P. 134–143. doi: 10.1007/s11223-011-9279-8

Lemaitre J., Chaboche J. L. Mechanics of solid materials. Cambridge University Press, 1994. 556 p.

Golub V. P. Cyclic Creep of Refractory Nickel Alloys. Kyiv: Naukova dumka, 1983. 224 p.

Taira S., Otani R. Theory of High-Temperature Strength of Materials. Moscow: Metallurgiya, 1986. 280 p.

Copyright (c) 2018 Dmytro Breslavsky, Alyona Kozlyuk, Oksana Tatarinova