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Meshfree simulations of spall fracture. (English) Zbl 1225.74125

Summary: Shock wave induced spall fracture is a complex multiscale phenomenon, and it is a challenge to build a constitutive and computational model that can capture essential features of the spall fracture. In this work, we present a computational micro-mechanics model to simulate spall fracture by utilizing the multiscale micro-mechanics theory proposed by T.W. Wright and K. T. Ramesh [J. Mech. Phys. Solids 9, 297–335 (2008)] and a RKPM meshfree method. The focus of this work is to develop and demonstrate a simulation tool that is capable of simulations of spall fracture in engineering application. First, based on a well-known empirical formula,we relate the macroscale spall strength to the kinematics of micro void growth in a Representative Volume Element (RVE). The connection between micro void growth and overall kinematics of the RVE is made through the conservation of mass in the micro to macro transition process. Second, we develop a set of meshfree void growth algorithms that is tailored to represent kinematics of void nucleation, growth and coalescence, and these algorithms retain the conservation of mass, momentum, and energy during simulations of ductile spall fracture. Third, based on the Johnson – Cook model, we developed a meshfree computational formulation, and we have carried out simulations of the spall fracture of a Ti – 6Al plate under impact loads to validate the model. From the simulation, we find that the interaction between the first two inelastic wave pulses plays an important role in the mechanism of spall fracture. The numerical results show that the proposed method can capture some features of the spall fracture, and it may be used to simulate the spall fracture in engineering applications.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74R20 Anelastic fracture and damage
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[1] Armero, F.; Simo, J.C., A priori stability estimate and unconditionally stable product formula algorithm for nonlinear coupled thermoplasticity, Int. J. plast., 9, 749-782, (1993) · Zbl 0791.73026
[2] Antoun, T.; Seaman, L.; Curran, D.R.; Kane, G.I.; Razorenov, S.V.; Utkin, A.V., Spall fracture, (2003), Springer New York
[3] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods for static and dynamic fracture, Int. J. solids struct., 32, 2547-2570, (1995) · Zbl 0918.73268
[4] Belytschko, T.; Lu, Y.Y.; Gu, L., Crack propagation by element-free Galerkin methods, Engrg. fract. mech., 51, 295-315, (1995)
[5] Clayton, J.D., Modeling dynamic plasticity and spall fracture in high density polycrystalline alloys, Int. J. solids struct., 42, 4613-4640, (2005) · Zbl 1119.74572
[6] Davison, L.; Stevens, A.L.; Kipp, M.E., Theory of spall damage accumulation in ductile metals, J. mech. phys. solids, 9, 11-28, (1977)
[7] Dorogoy, A.; Rittel, D., Determination of the johnsonccook material parameters using the SCS specimen, Exp. mech., 9, 881-885, (2009)
[8] Duarte, C.A.; Oden, J.T., Hp clouds – an hp meshless method, Numer. meth. partial differ. equat., 9, 673-705, (1996) · Zbl 0869.65069
[9] Gluzman, V.D.; Kanel, G.I., Resistance to deformation and fracture of 35kh3NM steel under conditions of shock loading, Strength mater., 17, 8, (1985), (Translated from Problemy Prochnosti 17(8) 52-57)
[10] Hao, S.; Liu, W.K., Moving particle finite element method with superconvergence: nodal integration formulation and applications, Comput. meth. appl. mech. engrg., 195, 6059-6072, (2006) · Zbl 1120.74051
[11] Hao, S.; Liu, W.K.; Chang, C.T., Computer implementation of damage models by finite element and meshfree methods, Comput. meth. appl. mech. engrg., 187, 401-440, (2000) · Zbl 0980.74063
[12] Hopkinson, B., A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets, Phil. trans. R. soc. lond. A, 213, 437-456, (1914)
[13] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperature, in: Proceedings of the Seventh International Symposium on Ballistics, 1983, pp. 1-7.
[14] Johnson, G.R.; Cook, W.H., Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engrg. fract., 21, 31-48, (1985)
[15] Kanel, G.I.; Razorenov, S.V.; Bogatch, A.; Utkin, A.V.; Grady, Dennis E., Simulation of spall fracture of aluminum and magnesium over a wide range of load duration and temperature, Int. impact engrg., 20, 467-478, (1997)
[16] Kanel, G.I., Spall fracture: methodological aspects, mechanisms and governing factors, Int. J. fract., 163, 173-191, (2010) · Zbl 1425.74431
[17] Krivtsov, A.M.; Mescheryakov, Y.I., Molecular dynamics investigation of spall fracture, Proceedings of SPIE, 3687, 205-212, (1999)
[18] Lee, W.S.; Lin, C.F., Plastic deformation and fracture behaviour of ti-6al-4V alloy loaded with high strain rate under various temperatures, Mater. sci. engrg. A, 6, 48-59, (1998)
[19] Li, S.; Simonsen, B.C., Meshfree simulations of ductile crack propagation, Int. J. comput. meth. engrg. sci. mech., 6, 1-19, (2005)
[20] Li, S.; Qian, D.; Liu, W.K.; Belytschko, T., A meshfree contact-detection algorithm, Comput. meth. appl. mech., 6, 3271-3292, (2001) · Zbl 0998.74081
[21] Simkins, D.C.; Li, S., Meshfree simulations of thermo-mechanical ductile fracture, Comput. mech., 38, 235-249, (2005) · Zbl 1162.74052
[22] Li, S.; Liu, W.K., Meshfree particle method, (2004), Springer-Verlag Berlin, Germany
[23] Liu, W.K.; Jun, S., Reproducing kernel particle method, Int. J. numer. meth. fluids, 6, 1081-1106, (1995) · Zbl 0881.76072
[24] Liu, W.K.; Hao, S.; Belytschko, T.; Li, S.; Chang, C.T., Multiple scale meshfree methods for damage fracture and localization, Comput. mater. sci., 16, 197-205, (1999)
[25] Meyer, H.W.; Kleponis, D.S., Modeling the high strain rate behavior of titanium undergoing ballistic impact and penetration, Int. J. impact engrg., 6, 509-521, (2001)
[26] Monaghan, J.J., An introduction to SHP, Comput. meth. appl. mech. engrg., 6, 247-273, (1988)
[27] Peirce, D.; Shih, C.F.; Needleman, A., A tangent modulus method for the rate dependent solids, Comput. struct., 18, 168-173, (1984) · Zbl 0531.73057
[28] Rajendran, A.M.; Dietenberger, M.A.; Grove, D.J., A void growth-based failure model to describe spallation, J. appl. phys., 65, 1521-1527, (1989)
[29] Ren, B.; Li, S., Meshfree simulation of plugging failure in high-speed impacts, Comput. struct., 88, 909-923, (2010)
[30] Simonsen, B.C.; Li, S., Meshfree modeling of ductile fracture, Int. J. numer. meth. engrg., 60, 1425-1450, (2004) · Zbl 1060.74673
[31] Simkins, D.C.; Li, S., Meshfree simulations of ductile failure under thermal-mechanical loads, Comput. mech., 38, 235-249, (2006) · Zbl 1162.74052
[32] Seo, S.; Min, O.; Yang, H., Constitutive equation for ti-6al-4V at high temperatures measured using the SHPB technique, Int. J. impact engrg., 38, 735-754, (2005)
[33] Taylor, G.; Quinney, H., The latent energy remaining in a metal; after cold working, Proc. R. soc., 143, 307-326, (1934)
[34] Trott, W.M.; Castaneda, J.N.; O’Hare, J.J.; Knudson, M.D.; Chhabildas, L.C.; Baer, M.R.; Asay, J.R., Examination of the mesoscopic scale response of shock compressed heterogenous materials using a line-imaging velocity interferometer, (), 47-645
[35] Vogler, T.J.; Clayton, J.D., Heterogeneous deformation and spall of an extruded tungsten alloy: plate impact experiments and crystal plasticity modeling, J. mech. phys. solids, 9, 297-335, (1993)
[36] Wright, T.W.; Ramesh, K.T., Dynamic void nucleation and growth in solids: a self-consistent statistical theory, J. mech. phys. solids, 9, 297-335, (2008) · Zbl 1171.74313
[37] Wang, Z.P.; Lam, K.Y., Evolution of microcracks in brittle solids under intense dynamic loading, J. appl. phys., 9, 3479-3483, (1995)
[38] Wang, Z.P., Void-containing nonlinear materials subject to high-rate loading, J. appl. phys., 9, 7213-7227, (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.