A generalized model for dynamic mixed-mode fracture via state-based peridynamics
Corresponding Author
Mirmilad Mirsayar
Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, Florida, USA
Correspondence
Mirmilad Mirsayar, Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, Florida 32901, USA.
Email: [email protected]
Search for more papers by this authorCorresponding Author
Mirmilad Mirsayar
Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, Florida, USA
Correspondence
Mirmilad Mirsayar, Department of Aerospace, Physics, and Space Sciences, Florida Institute of Technology, Melbourne, Florida 32901, USA.
Email: [email protected]
Search for more papers by this authorFunding information: Florida Institute of Technology
Abstract
A generalized model is developed to investigate dynamic crack propagation in isotropic solids under mixed-mode I/II conditions using state-based peridynamics. The critical stretch and the critical strain energy release rate (ERR) are related within the state-based peridynamic framework to construct a computational model capable of capturing fracture energy of the kinked cracks. A novel formulation is presented to predict crack growth trajectory and pattern by combining the traditional expression of ERR and the peridynamic states of the crack opening and sliding displacements. The proposed model is used to predict dynamic fracture behavior in polymethyl methacrylate (PMMA) and soda-lime glass using various test specimens, including cracked semi-circular bending (SCB), cracked rectangular plate, and single edge-notched tensile (SENT) specimens, and under different dynamic loading conditions. The developed model is examined against the numerical and experimental data available in the literature, and a very good agreement is observed.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study maybe available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.
REFERENCES
- 1Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids. 2000; 48(1): 175-209.
- 2Silling SA, Epton M, Weckner O, Xu J, Askari E. Peridynamic states and constitutive modeling. J Elast. 2007; 88(2): 151-184.
- 3Silling SA. Linearized theory of peridynamic states. J Elast. 2010; 99(1): 85-111.
- 4Silling SA, Askari E. A meshfree method based on the peridynamic model of solid mechanics. Comput Struct. 2005; 83(17-18): 1526-1535.
- 5Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng. 1999; 45(5): 601-620.
- 6Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Methods Eng. 1999; 46(1): 131-150.
- 7Belytschko T, Gracie R. On XFEM applications to dislocations and interfaces. Int J Plast. 2007; 23(10-11): 1721-1738.
- 8Stazi FL, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements for curved cracks. Comput Mech. 2003; 31(1): 38-48.
- 9Sukumar N, Moës N, Moran B, Belytschko T. Extended finite element method for three-dimensional crack modelling. Int J Numer Methods Eng. 2000; 48(11): 1549-1570.
- 10Krysl P, Belytschko T. The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks. Int J Numer Methods Eng. 1999; 44(6): 767-800.
- 11Carpinteri A, Ferro G, Ventura G. An augmented Lagrangian element-free (ALEF) approach for crack discontinuities. Comput Methods Appl Mech Eng. 2001; 191(8-10): 941-957.
- 12Chen YP, Lee JD, Eskandarian A. Dynamic meshless method applied to nonlocal crack problems. Theor Appl Fract Mech. 2002; 38(3): 293-300.
- 13Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids. 1998; 46(8): 1319-1342.
- 14Bleyer J, Alessi R. Phase-field modeling of anisotropic brittle fracture including several damage mechanisms. Comput Methods Appl Mech Eng. 2018; 336: 213-236.
- 15Hu YL, Madenci E. Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence. Compos Struct. 2016; 153: 139-175.
- 16Mengesha T, Du Q. The bond-based peridynamic system with Dirichlet-type volume constraint. Proc R Soc Edinb A: Math. 2014; 144(1): 161-186.
- 17Prudhomme S, Diehl P. On the treatment of boundary conditions for bond-based peridynamic models. Comput Methods Appl Mech Eng. 2020; 372: 113391.
- 18Carrara P, Ambati M, Alessi R, De Lorenzis L. A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach. Comput Methods Appl Mech Eng. 2020; 361:112731.
- 19Salvati E. Residual stress as a fracture toughening mechanism: a phase-field study on a brittle material. Theor Appl Fract Mech. 2021; 114:103021.
- 20Carlsson J, Isaksson P. Crack dynamics and crack tip shielding in a material containing pores analysed by a phase field method. Eng Fract Mech. 2019; 206: 526-540.
- 21Cheng Z, Liu Y, Zhao J, Feng H, Wu Y. Numerical simulation of crack propagation and branching in functionally graded materials using peridynamic modeling. Eng Fract Mech. 2018; 191: 13-32.
- 22Wu L, Wang L, Huang D, Xu Y. An ordinary state-based peridynamic modeling for dynamic fracture of laminated glass under low-velocity impact. Compos Struct. 2020; 234:111722.
- 23Breitenfeld MS, Geubelle PH, Weckner O, Silling SA. Non-ordinary state-based peridynamic analysis of stationary crack problems. Comput Methods Appl Mech Eng. 2014; 272: 233-250.
- 24Li P, Hao ZM, Zhen WQ. A stabilized non-ordinary state-based peridynamic model. Comput Methods Appl Mech Eng. 2018; 339: 262-280.
- 25Le QV, Chan W, Schwartz J. A two-dimensional ordinary, state-based peridynamic model for linearly elastic solids. Int J Numer Methods Eng. 2014; 98(8): 547-561.
- 26Yang D, Dong W, Liu X, Yi S, He X. Investigation on mode-I crack propagation in concrete using bond-based peridynamics with a new damage model. Eng Fract Mech. 2018; 199: 567-581.
- 27Liu S, Fang G, Liang J, Lv D. A coupling model of XFEM/peridynamics for 2D dynamic crack propagation and branching problems. Theor Appl Fract Mech. 2020; 108:102573.
- 28Chen B, Yu T, Natarajan S, Zhang Q, Bui TQ. Three-dimensional dynamic and quasi-static crack growth by a hybrid XFEM-peridynamics approach. Eng Fract Mech. 2022; 261:108205.
- 29Diana V, Ballarini R. Crack kinking in isotropic and orthotropic micropolar peridynamic solids. Int J Solids Struct. 2020; 196: 76-98.
- 30Yu H, Chen X, Sun Y. A generalized bond-based peridynamic model for quasi-brittle materials enriched with bond tension–rotation–shear coupling effects. Comput Methods Appl Mech Eng. 2020; 372:113405.
- 31Ozdemir M, Kefal A, Imachi M, Tanaka S, Oterkus E. Dynamic fracture analysis of functionally graded materials using ordinary state-based peridynamics. Compos Struct. 2020; 244:112296.
- 32Panchadhara R, Gordon PA. Application of peridynamic stress intensity factors to dynamic fracture initiation and propagation. Int J Fract. 2016; 201(1): 81-96.
- 33Askari E, Bobaru F, Lehoucq RB, Parks ML, Silling SA, Weckner O. Peridynamics for multiscale materials modeling. J Phys: Conf Ser 2008; 125(1): 012078. IOP Publishing.
10.1088/1742-6596/125/1/012078 Google Scholar
- 34Tupek MR, Rimoli JJ, Radovitzky R. An approach for incorporating classical continuum damage models in state-based peridynamics. Comput Methods Appl Mech Eng. 2013; 263: 20-26.
- 35Mousavi F, Jafarzadeh S, Bobaru F. An ordinary state-based peridynamic elastoplastic 2D model consistent with J2 plasticity. Int J Solids Struct. 2021; 229:111146.
- 36Gu X, Zhang Q, Madenci E. Non-ordinary state-based peridynamic simulation of elastoplastic deformation and dynamic cracking of polycrystal. Eng Fract Mech. 2019; 218:106568.
- 37Zhang H, Qiao P. A state-based peridynamic model for quantitative elastic and fracture analysis of orthotropic materials. Eng Fract Mech. 2019; 206: 147-171.
- 38Gao Y, Oterkus S. Fully coupled thermomechanical analysis of laminated composites by using ordinary state based peridynamic theory. Compos Struct. 2019; 207: 397-424.
- 39Rokkam S, Gunzburger M, Brothers M, Phan N, Goel K. A nonlocal peridynamics modeling approach for corrosion damage and crack propagation. Theor Appl Fract Mech. 2019; 101: 373-387.
- 40Kulkarni SS, Tabarraei A. An ordinary state based peridynamic correspondence model for metal creep. Eng Fract Mech. 2020; 233:107042.
- 41Li H, Hao Z, Li P, Li X, Zhang D. A low cycle fatigue cracking simulation method of non-ordinary state-based peridynamics. Int J Fatigue. 2022; 156:106638.
- 42Freund BL. Dynamic Fracture Mechanics. Cambridge University Press; 1998.
- 43Zhang H, Qiao P. A state-based peridynamic model for quantitative fracture analysis. Int J Fract. 2018; 211(1): 217-235.
- 44Imachi M, Tanaka S, Bui TQ. Mixed-mode dynamic stress intensity factors evaluation using ordinary state-based peridynamics. Theor Appl Fract Mech. 2018; 93: 97-104.
- 45Silling SA, Lehoucq RB. Convergence of peridynamics to classical elasticity theory. J Elast. 2008; 93(1): 13-37.
- 46Foster JT, Silling SA, Chen W. An energy-based failure criterion for use with peridynamic states. Int J Mult Comp Eng. 2011; 9(6): 675-688.
- 47Hussain MA, Pu SL, Underwood J. Strain energy release rate for a crack under combined mode I and mode II. In: Fracture Analysis: Proceedings of the 1973 National Symposium on Fracture Mechanics, Part II. ASTM International.
- 48Kuang JH, Chen LS. A displacement extrapolation method for two-dimensional mixed-mode crack problems. Eng Fract Mech. 1993; 46(5): 735-741.
- 49Vormwald M, Hos Y, Freire JL, Gonzáles GL, Díaz JG. Crack tip displacement fields measured by digital image correlation for evaluating variable mode-mixity during fatigue crack growth. Int J Fatigue. 2018; 115: 53-66.
- 50Murphy N, Ali M, Ivankovic A. Dynamic crack bifurcation in PMMA. Eng Fract Mech. 2006; 73(16): 2569-2587.
- 51Ha YD, Bobaru F. Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract. 2010; 162(1): 229-244.
- 52Ayatollahi MR, Aliha MR, Hassani MM. Mixed mode brittle fracture in PMMA—an experimental study using SCB specimens. Mater Sci Eng A. 2006; 417(1-2): 348-356.
- 53Aliha MR, Samareh-Mousavi SS, Mirsayar MM. Loading rate effect on mixed mode I/II brittle fracture behavior of PMMA using inclined cracked SBB specimen. Int J Solids Struct. 2021; 232:111177.
- 54Kou MM, Lian YJ, Wang YT. Numerical investigations on crack propagation and crack branching in brittle solids under dynamic loading using bond-particle model. Eng Fract Mech. 2019; 212: 41-56.
- 55Hairer E, Lubich C, Wanner G. Geometric numerical integration illustrated by the Störmer–Verlet method. Acta Numer. 2003; 12: 399-450.
10.1017/S0962492902000144 Google Scholar
- 56Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Trans ASME. 1963; 85(4): 519-525.
10.1115/1.3656897 Google Scholar
- 57Sih GC. Strain-energy-density factor applied to mixed mode crack problems. Int J Fract. 1974; 10(3): 305-321.
- 58Smith DJ, Ayatollahi MR, Pavier MJ. The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading. Fatigue Fract Eng Mater Struct. 2001; 24(2): 137-150.
- 59Chang KJ. On the maximum strain criterion—a new approach to the angled crack problem. Eng Fract Mech. 1981; 14(1): 107-124.
- 60Mirsayar MM. Mixed mode fracture analysis using extended maximum tangential strain criterion. Mater Des. 2015; 86: 941-947.
- 61Mirsayar MM, Razmi A, Aliha MR, Berto F. EMTSN criterion for evaluating mixed mode I/II crack propagation in rock materials. Eng Fract Mech. 2018; 190: 186-197.
- 62Mirsayar MM, Berto F, Aliha MR, Park P. Strain-based criteria for mixed-mode fracture of polycrystalline graphite. Eng Fract Mech. 2016; 156: 114-123.
- 63Mirsayar MM, Park P. The role of T-stress on kinking angle of interface cracks. Mater Des. 2015; 80: 12-19.
- 64Mirsayar MM. On fracture of kinked interface cracks–the role of T-stress. Mater Des. 2014; 61: 117-123.
- 65Mirsayar MM. On fracture analysis of dental restorative materials under combined tensile-shear loading. Theor Appl Fract Mech. 2018; 93: 170-176.
- 66Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Methods Eng. 2003; 58(12): 1873-1905.
- 67Bobaru F, Zhang G. Why do cracks branch? A peridynamic investigation of dynamic brittle fracture. Int J Fract. 2015; 196(1-2): 59-98.
- 68Wang X, Kulkarni SS, Tabarraei A. Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems. Comput Methods Appl Mech Eng. 2019; 344: 251-275.
- 69Bowden FP, Brunton JH, Field JE, Heyes AD. Controlled fracture of brittle solids and interruption of electrical current. Nature. 1967; 216(5110): 38-42.
- 70Shojaei A, Mossaiby F, Zaccariotto M, Galvanetto U. An adaptive multi-grid peridynamic method for dynamic fracture analysis. Int J Mech Sci. 2018; 144: 600-617.
- 71Graff KF. Wave Motion in Elastic Solids. New York: Dover; 1975.
- 72Field JE. Brittle fracture: its study and application. Contemp Phys. 1971; 12(1): 1-31.
- 73Ueda Y, Ikeda K, Yao T, Aoki M. Characteristics of brittle fracture under general combined modes including those under bi-axial tensile loads. Eng Fract Mech. 1983; 18(6): 1131-1158.