Application of modified Ritchie-Knott-Rice criterion to cellular automata
More details
Hide details
Kielce University of Technology, Kielce, Poland
Submission date: 2018-06-26
Acceptance date: 2019-02-05
Online publication date: 2019-07-15
Publication date: 2019-07-15
Journal of Theoretical and Applied Mechanics 2019;57(3):577-590
In this paper, the cellular automata model is applied to analyse cleavage and ductile fracture, in front of a crack in three-point-bend specimens made of Hardox-400 steel. The research, programme was composed of experiments followed by fractographic and numerical analyses, On the basis of microscopic observations, the sizes of cells used in the automata were determined, The algorithm enabled mapping of the two-dimensional crack surface as well as, a simulation of temperature-dependent failure mechanisms by defining transition rules based, on the modified Ritchie-Knott-Rice cleavage fracture criterion. The critical stress values, were estimated and verified by the cellular automata model
Achenbach J.D., 1974, Dynamic effects in brittle fracture, [In:] Mechanics Today, S. Nemat-Nasser (Edit.), Pergamon Press, 1-57.
Achenbach J.D., 1976, Wave Propagation in Elastic Solids, North-Holland/American Elsevier.
Achenbach J.D., Neimitz A., 1981, Fast fracture and arrest according to the Dugdale model, Engineering Fracture Mechanics, 14, 385-395.
Besson J., edit., 2004, Local Approach to Fracture, Ecole des Mines de Paris.
Dighe M.D., Gokhale A.M., Horstemeyer M.F., 2002, Effect of loading condition and stress state on damage evolution of silicon particles in an Al-Si-Mg-base case alloy, Metallurgical and Materials Transactions A, 33, 555–565.
Freund L.B., 1972, Energy flux into the tip of an extending crack in an elastic solid, Journal Elasticity, 2, 341-349.
Freund L.B., 1990, Dynamic Fracture Mechanics, Cambridge University Press.
Gałkiewicz J., Graba J., 2006, Algorithm for determination of , , , , functions in Hutchinson-Rice-Rosengren solution and its 3D generalization, Journal of Theoretical and Applied Mechanics, 44, 1, 19-30.
Gullerud A.S., Gao X., Dodds R.H. Jr., Haj-Ali R., 2000, Simulation of ductile crack growth using computational cells: numerical aspects, Engineering Fracture Mechanics, 66, 65-92.
Gurland J., 1972, Observations on the fracture of cementite particles in a spheroidised 1.05%C steel deformed at room temperature, Acta Metallurgica, 20, 735-741.
Halberg H., 2011, Approaches to modeling of recrystallization, Metals, 16-48.
Horstemeyer M. F., Ramaswamy S., Negrete M., 2003, Using a micromechanical finite element parametric study to motivative a phenomenological macroscale model for void/crack nucleation in aluminum with a hard second phase, Mechanics of Materials, 35, 7, 675-687.
Hutchinson J.W., 1968, Singular behaviour at the end of a tensile crack in a hardening material, Journal of the Mechanics and Physics of Solids, 16, 13-31.
Janssens K., 2003, Random grid, three dimensional, space-time coupled cellular automata for the simulation of recrystallization and grain growth, Modelling and Simulation in Materials Science and Engineering, 11, 157-171.
Kozioł P., Perzyński K., Madej Ł., 2010, The cellular automata based modeling of crack propagation (in Polish), Materiały XVII Konferencji Informatyka w Technologii Metali.
Neimitz A., 2008, The jump-like crack growth model, the estimation of fracture energy and JR curve, Engineering Fracture Mechanics, 75, 236-252.
Neimitz A., Dzioba I., 2017, Fracture toughness of the high-strength steel within the ductile to cleavage transition temperature range – master curves, Physicochemical Mechanics of Materials, 2, 16-23.
Neimitz A., Dzioba I., Janus U., 2014, Cleavage fracture of ultra-high-strength steels. Microscopic observations. Numerical analysis. Local fracture criterion, Key Engineering Materials, 598, 168-177.
Neimitz A., Graba, M., Gałkiewicz J., 2007, An alternative formulation of the Ritchie-Knott-Rice local fracture criterion, Engineering Fracture Mechanics, 74, 8, 1308-1322.
Neimitz A., Janus U., 2016a, Analysis of stress and strain fields in and around inclusions of various shapes in a cylindrical specimen loaded in tension, Archives of Metallurgy and Materials, 61, 2, 569-576.
Neimitz A., Janus U., 2016b, Voids nucleation at inclusions of various shapes in front of the crack in plane strain, Archives of Metallurgy and Materials, 61, 3, 1241-1246.
Pineau A., 2006, Development of the local approach to fracture over the past 25 years: theory and applications, International of Fracture, 139-166.
Pineau A., Pardoen T., 2007, Failure of metals, [In:] Comprehensive Structural Integrity. Vol. 2 – Fundamental Theories and Mechanisms of Failure, I. Milne, R.O. Ritchie and B. Karihaloo (Edit.), 684-783.
Rice J.R., Rosengren G.F., 1968, Plane strain deformation near crack tip in a power-law hardening material, Journal of the Mechanics and Physics of Solids, 16, 1-12.
Wolfram S., 1983, Statistical mechanics of cellular automata, Reviews of Modern Physics, 55, 3, 601-644.
Wolfram S., 2002, A New Kind of science, Wolfram Media, US.
Yamamoto Y., Shibanuma K., Yanagimoto F., Suzuki K., Aihara S., Shirahata H., 2016, Multiscale modeling to clarify the relationship between microstructures of steel and microscopic brittle crack propagation/arrest behavior, Procedia Structural Integrity, 2, 2389-2396.
Journals System - logo
Scroll to top