Dynamic fracture analysis for the crack arrest phenomenon is performed by ordinary state-based peridynamics formulation and discretization employing transition bond concept. Double cantilever beam specimen is chosen for our numerical evidence purpose. The analysis consists of two main phases namely, generation and application (prediction) phases. In the generation phase, the dynamic stress intensity factors of propagating and arrested cracks are estimated by the present formulation for given crack path histories, and a good agreement is achieved. As for the application phase, dynamic stress intensity factors as well as total crack lengths after crack arrests are in good agreement with the experiments. Moreover, the influence of transition bond concept on the crack arrest behavior is investigated and it is found that the transition bond is very efficient in the simulation of the crack arrest problem such that premature arrests of cracks are observed without transition bond cases.
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Anderson TL (2005) Fracture mechanics: fundamentals and applications. Taylor & Francis, Milton Park
Aoki S, Kishimoto K, Sakata M (1987) Finite element computation of dynamic stress intensity factor for a rapidly propagating crack using J-integral. Comput Mech 2:54–62
Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45:601–620
Cheng Z, Zhang G, Wang Y, Bobaru F (2015) A peridynamic model for dynamic fracture in functionally graded materials. Compos Struct 133:529–546
Coré A, Kopp JB, Girardot J, Viot P (2018) Dynamic energy release rate evaluation of rapid crack propagation in discrete element analysis. Int J Fract 214:17–28
Crosley PB, Ripling EJ (1969) Dynamic fracture toughness of A533 steel. ASME J Basic Eng 91:525–534
Crosley PB, Ripling EJ (1971) Crack arrest toughness of pressure vessel steels. Nuclear Eng Des 17:32–45
Dipasquale D, Sarego G, Zaccariotto M, Galvanetto U (2017) A discussion on failure criteria for ordinary state-based peridynamics. Eng Fract Mech 186:378–398
Freund LB (1990) Dynamic fracture mechanics. Cambridge University Press, Cambridge
Hahn GT, Hoagland RG, Kanninen MF, Rosenfield AR (1973) The characterization of fracture arrest in structural steel. In: Proceedings of the second international conference on pressure vessel technology, pp 981–994
Imachi M, Tanaka S (2016) Dynamic stress intensity factors evaluation employing ordinary state-based peridynamics. Trans JSCES 2016:20160017 (in Japanese)
Imachi M, Tanaka S, Bui TQ (2018) Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics. Theor Appl Fract Mech 93:97–104
Imachi M, Tanaka S, Bui TQ, Oterkus S, Oterkus E (2019) A computational approach based on ordinary state-based peridynamics with new transition bond for dynamic fracture analysis. Eng Fract Mech 206:359–374
Kalthoff JF, Beinert J, Winkler S (1976) Measurements of dynamic stress intensity factors for fast running and arresting cracks in double-cantilever-beam specimens. In: Hahn GT, Kanninen MF (eds) Fast fracture and crack arrest. American Society for Testing and Materials, Philadelphia, pp 161–176
Kanninen MF (1978) A critical appraisal of solution techniques in dynamic fracture mechanics. In: Luxmoore AR, Owen DRJ (eds) Numerical methods in fracture mechanics. Pineridge Press, Swansea, pp 612–634
Kanninen MF, Popelar CH (1985) Advanced fracture mechanics. Oxford University Press, Oxford
Kilic B, Madenci E (2009) Prediction of crack paths in a quenched glass plate by using peridynamic theory. Int J Fracture 156:165–177
Kobayashi A (1979) Dynamic fracture analysis by dynamic finite element method-generation and propagation anlyses. In: Perrone N, Atluri SN (eds) Nonlinear and dynamic fracture mechanics, vol 35. ASME, New York, pp 19–37
Kopp JB, Fond C, Hochstetter G (2018) Rapid crack propagation in PA11: an application to pipe structure. Eng Fract Mech 202:445–457
Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37:141–158
Le QV, Chan WK, Schwartz J (2014) A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int J Numer Meth Eng 98:547–561
Liu ZL, Menouillard T, Belytschko T (2011) An XFEM/spectral element method for dynamic crack propagation. Int J Fract 169:183–198
Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, Berlin
Menouillard T, Réthoré J, Combescure A, Bung H (2006) Efficient explicit time stepping for the eXtended Finite Element Method (X-FEM). Int J Numer Meth Eng 68:911–939
Nishioka T, Atluri SN (1982) Numerical analysis of dynamic crack propagation: generation and prediction studies. Eng Fract Mech 16:303–332
Nishioka T, Stonesifer RB, Atluri SN (1981) An evaluation of several moving singularity finite element models for fast fracture analysis. Eng Fract Mech 15:205–218
Oterkus E, Madenci E (2012) Peridynamic analysis of fiber-reinforced composite materials. J Mech Mater Struct 7:45–84
Prabel B, Combescure A, Gravouil A, Marie S (2007) Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media. Int J Numer Meth Eng 69:1553–1569
Ravi-Chandar K (2004) Dynamic fracture. Elsevier, Amsterdam
Réthoré J, Gravouil A, Combescure A (2005) An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. Int J Numer Meth Eng 63:631–659
Shibanuma K, Yanagimoto F, Namegawa T, Suzuki K, Aihara S (2016a) Brittle crack propagation/arrest behavior in steel plate—Part I: model formulation. Eng Fract Mech 162:324–340
Shibanuma K, Yanagimoto F, Namegawa T, Suzuki K, Aihara S (2016b) Brittle crack propagation/arrest behavior in steel plate—Part II: experiments and model validation. Eng Fract Mech 162:341–360
Shibanuma K, Yanagimoto F, Suzuki K, Aihara S (2018) Brittle crack propagation/arrest behavior in steel plate—Part III: discussions on arrest design. Eng Fract Mech 190:104–119
Shojaei A, Mossaiby F, Zaccariotto M, Galvanetto U (2018) An adaptive multi-grid peridynamic method for dynamic fracture analysis. Int J Mech Sci 144:600–617
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209
Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535
Silling SA, Lehoucq RB (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93:13–37
Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88:151–184
Zhang Y, Qiao P (2019) A new bond failure criterion for ordinary state-based peridynamic mode II fracture analysis. Int J Fract 215:105–128
Zhao J, Tang H, Xue S (2018) A new fracture criterion for peridynamic and dual-horizon peridynamics. Front Struct Civ Eng 12:629–641
Zhou X, Wang Y, Qian Q (2016) Numerical simulation of crack curving and branching in brittle materials under dynamic loads using the extended non-ordinary state-based peridynamics. Eur J Mech Solid 60:277–299
Zhou W, Liu D, Liu N (2017) Analyzing dynamic fracture process in fiber-reinforced composite materials with a peridynamic model. Eng Fract Mech 178:60–76
Zienkiewicz O, Taylor R, Zhu JZ (2005) The finite element method: its basis and fundamentals, 6th edn. Elsevier and Butterworth-Heinemann, Oxford
This research was partially supported by Sasakawa Scientific Research Grant from the Japan Science Society and the JSPS Grants-in-Aid for Scientific Research (C)(18K04582), Grant-in-Aid for JSPS Fellows (19J14053).
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Imachi, M., Tanaka, S., Ozdemir, M. et al. Dynamic crack arrest analysis by ordinary state-based peridynamics. Int J Fract 221, 155–169 (2020). https://doi.org/10.1007/s10704-019-00416-3