[1] M. A.Meyers, C.T. Aimone. Dynamic fracture (spalling) of metals. Prog. Mater. Sci., 28, 1-96(1983).
[2] G. I.Kanel. Spall fracture: Methodological aspects, mechanisms and governing factors. Int. J. Fract., 163, 173-191(2010).
[3] A. A.Benzerga, J.-B.Leblond, A.Needleman, V.Tvergaard. Ductile failure modeling. Int. J. Fract., 201, 29-80(2016).
[4] A. A.Benzerga, T.Pardoen, A.Pineau. Failure of metals I: Brittle and ductile fracture. Acta Mater., 107, 424-483(2016).
[5] Y.Cui, X.Pei, Q.Wu, S.Yao, J.Yu, Y.Yu. Revisiting the power law characteristics of the plastic shock front under shock loading. Phys. Rev. Lett., 126, 085503(2021).
[6] A.Bakaeva, H.Duan, A.Dubinko, D.Terentyev, X.Xiao. Dislocation-mediated strain hardening in tungsten: Thermo-mechanical plasticity theory and experimental validation. J. Mech. Phys. Solids, 85, 1-15(2015).
[7] L.Chen, H.Chu, H.Duan, X.Xiao, L.Yu. A micromechanical model for nano-metallic-multilayers with helium irradiation. Int. J. Solids Struct., 102–103, 267-274(2016).
[8] Y.Cui, N.Ghoniem, G.Po. Does irradiation enhance or inhibit strain bursts at the submicron scale?. Acta Mater., 132, 285-297(2017).
[9] Y.Chen, K.Hattar, J.Li, N.Li, M.Nastasi, L.Shao, C.Sun, M. L.Taheri, H.Wang, J.Wang, K.Yu, X.Zhang. Radiation damage in nanostructured materials. Prog. Mater. Sci., 96, 217-321(2018).
[10] H.Chu, H.Duan, D.Terentyev, X.Xiao. Theoretical models for irradiation hardening and embrittlement in nuclear structural materials: A review and perspective. Acta Mech. Sin., 36, 397-411(2020).
[11] L.Chen, Y.Cheng, H.Duan, W.Liu, K.Ren, H.Sui, X.Yi, L.Yu. Probabilistic and constitutive models for ductile-to-brittle transition in steels: A competition between cleavage and ductile fracture. J. Mech. Phys. Solids, 135, 103809(2020).
[12] X.Chen, Y.Cui, P.Du, W.Feng, S.Fu, Y.Gao, Y.Hua, X.Huang, L.Ji, F.Li, X.Li, D.Liu, J.Liu, J.Liu, W.Ma, W.Pei, D.Rao, C.Shan, H.Shi, Z.Sui, X.Sun, T.Wang, L.Xia, T.Zhang, X.Zhao, J.Zhu. Development of low-coherence high-power laser drivers for inertial confinement fusion. Matter Radiat. Extremes, 5, 065201(2020).
[13] Z.Cao, Y.Ding, X.Hu, T.Huang, S.Jiang, L.Kuang, S.Li, Y.Li, Z.Li, S.Liu, W.Miao, X.Peng, K.Ren, Q.Tang, F.Wang, Z.Wang, D.Yang, G.Yang, J.Yang, Z.Yang, R.Yi, B.Zhang, J.Zhang. Recent diagnostic developments at the 100 kJ-level laser facility in China. Matter Radiat. Extremes, 5, 035201(2020).
[14] P. A.Gruber, O.Kraft, R.M?nig, D.Weygand. Plasticity in confined dimensions. Annu. Rev. Mater. Res., 40, 293-317(2010).
[15] L.Chen, Y.Cheng, H.Duan, W.Liu, Y.Liu, X.Yi, L.Yu. Unified model for size-dependent to size-independent transition in yield strength of crystalline metallic materials. Phys. Rev. Lett., 124, 235501(2020).
[16] T.Antoun, D.Curran, G.Kanel, S.Razorenov, L.Seaman, A.Utkin. Spall Fracture(2003).
[17] D.Curran, L.Seaman, D. A.Shockey. Dynamic failure of solids. Phys. Rep., 147, 253-388(1987).
[18] M. F.Ashby, R.Raj. Intergranular fracture at elevated-temperature. Acta Metall., 23, 653-666(1975).
[19] J.Marian, M.Ortiz, C.Reina. Nanovoid nucleation by vacancy aggregation and vacancy-cluster coarsening in high-purity metallic single crystals. Phys. Rev. B, 84, 104117(2011).
[20] D. H.Kalantar, V. A.Lubarda, M. A.Meyers, B. A.Remington, M. S.Schneider. Void growth by dislocation emission. Acta Mater., 52, 1397-1408(2004).
[21] K. T.Ramesh, J. W.Wilkerson. A closed-form criterion for dislocation emission in nano-porous materials under arbitrary thermomechanical loading. J. Mech. Phys. Solids, 86, 94-116(2016).
[22] D. R.Curran, R.Rohde, L.Seaman, D. A.Shockey, R.Rohde, B.Butcher, J.Holland, C.Karnes and, B.Butcher, R.Rohde, B.Butcher, J.Holland, C.Karnes and, J.Holland, R.Rohde, B.Butcher, J.Holland, C.Karnes and, C.Karnes. The influence of microstructural features on dynamic fracture. Metallurgical Effects at High Strain Rates, 473-499(1973).
[23] T.-J.Chuang, K. I.Kagawa, J. R.Rice, L. B.Sills. Non-equilibrium models for diffusive cavitation of grain interfaces. Acta Metall., 27, 265-284(1979).
[24] M. F.Ashby. Work hardening of dispersion-hardened crystals. Philos. Mag., 14, 1157-1178(1966).
[25] A. C.Bernstein, D. A.Dalton, T.Ditmire, N. A.Pedrazas, H. J.Quevedo, P. A.Sherek, S. P.Steuck, E. M.Taleff, D. L.Worthington. Effects of microstructure and composition on spall fracture in aluminum. Mater. Sci. Eng., A, 536, 117-123(2012).
[26] T.Mori, T.Nakamura, K.Tanaka. Cavity formation at interface of a spherical inclusion in a plastically deformed matrix. Philos. Mag., 21, 267-279(1970).
[27] L. M.Brown, S. H.Goods. Overview No. 1: The nucleation of cavities by plastic deformation. Acta Metall., 27, 1-15(1979).
[28] J.Atkinson. Fatigue and the Bauschinger effect in dispersion-hardened copper single crystals(1973).
[29] A. S.Argon, J.Im. Separation of second-phase particles in spheroidized 1045 steel, Cu-0.6pct Cr alloy, and maraging-steel in plastic straining. Metall. Trans. A, 6, 839-851(1975).
[30] T.Inoue, S.Kinoshita. Three stages of ductile fracture process and criteria of void initiation in spheroidized and ferrite/pearlite steels. Trans. Iron Steel Inst. Jpn., 17, 523-531(1977).
[31] N. J.Long. Deformation behaviour of particle strengthened copper alloys(1977).
[32] L. M.Brown, W. M.Stobbs. The work-hardening of copper-silica V. Equilibrium plastic relaxation by secondary dislocations. Philos. Mag., 34, 351-372(1976).
[33] J. Z.Cui, X. G.Jiang, L. X.Ma. A cavity nucleation model during high temperature creep deformation of metals. Acta Metall. Mater., 41, 539-542(1993).
[34] J. C.Earthman, X.-G.Jiang, F. A.Mohamed. Cavitation and cavity-induced fracture during superplastic deformation. J. Mater. Sci., 29, 5499-5514(1994).
[35] D.Byler, R.Dickerson, S.DiGiacomo, S.Greenfield, A.Koskelo, N.Kovvali, K.Krishnan, S. N.Luo, K. J.McClellan, D.Paisley, P.Peralta, L.Wayne. Statistics of weak grain boundaries for spall damage in polycrystalline copper. Scr. Mater., 63, 1065-1068(2010).
[36] F.Cao, E. K.Cerreta, G. T. Gray, A. G.Perez-Bergquist, C. P.Trujillo. Orientation dependence of void formation and substructure deformation in a spalled copper bicrystal. Scr. Mater., 65, 1069-1072(2011).
[37] C.Brandl, E. K.Cerreta, J. P.Escobedo, T. C.Germann, G. T. Gray, D. D.Koller, A.Perez-Bergquist, C. P.Trujillo. Early stage dynamic damage and the role of grain boundary type. Scr. Mater., 66, 638-641(2012).
[38] E. K.Cerreta, S. J.Fensin, G. T. Gray, S. M.Valone. Why are some interfaces in materials stronger than others?. Sci. Rep., 4, 5461(2014).
[39] J.Chen, A. M.Dongare, S. J.Fensin, E. N.Hahn. Understanding and predicting damage and failure at grain boundaries in BCC Ta. J. Appl. Phys., 126, 165902(2019).
[40] J.Chen, S. J.Fensin. Associating damage nucleation and distribution with grain boundary characteristics in Ta. Scr. Mater., 187, 329-334(2020).
[41] C.Brandl, E. K.Cerreta, J. P.Escobedo-Diaz, S. J.Fensin, T. C.Germann, G. T. Gray, S. M.Valone. Effect of loading direction on grain boundary failure under shock loading. Acta Mater., 64, 113-122(2014).
[42] J.Belak, R. E.Rudd, E. T.Sepp?l?. Effect of stress triaxiality on void growth in dynamic fracture of metals: A molecular dynamics study. Phys. Rev. B, 69, 134101(2004).
[43] D. J.Benson, E. M.Bringa, M. A.Meyers, S.Traiviratana. Void growth in metals: Atomistic calculations. Acta Mater., 56, 3874-3886(2008).
[44] R. E.Rudd. Void growth in bcc metals simulated with molecular dynamics using the Finnis–Sinclair potential. Philos. Mag., 89, 3133-3161(2009).
[45] Y.Liu, L.Wang, Y.Wang, W.Xing, S.Zhang, J.Zhou. Nanovoid growth in nanocrystalline metal by dislocation shear loop emission. Mater. Sci. Eng., A, 528, 5428-5434(2011).
[46] V. S.Krasnikov, A. E.Mayer. Plasticity driven growth of nanovoids and strength of aluminum at high rate tension: Molecular dynamics simulations and continuum modeling. Int. J. Plast., 74, 75-91(2015).
[47] Z.Chen, Y.Cui. Material transport via the emission of shear loops during void growth: A molecular dynamics study. J. Appl. Phys., 119, 225102(2016).
[48] S.Chandra, V. M.Chavan, S.Raghunathan, M. K.Samal. Void growth in single crystal copper-an atomistic modeling and statistical analysis study. Philos. Mag., 98, 577-604(2017).
[49] Z.Chen, Y.Cui, Y.Ju. Fundamental insights into the mass transfer via full dislocation loops due to alternative surface cuts. Int. J. Solids Struct., 161, 42-54(2019).
[50] A. M.Cuiti?o, M.Ortiz. Ductile fracture by vacancy condensation in f.c.c. single crystals. Acta Mater., 44, 427-436(1996).
[51] E. M.Bringa, M. A.Meyers, S.Traiviratana. Void initiation in fcc metals: Effect of loading orientation and nanocrystalline effects. Acta Mater., 58, 4458-4477(2010).
[52] V. A.Lubarda. Emission of dislocations from nanovoids under combined loading. Int. J. Plast., 27, 181-200(2011).
[53] L.Chen, H.Duan, W.Liu, H.Sui, L.Yu. Three dimensional dislocation-loop emission criterion for void growth of ductile metals. Int. J. Plast., 131, 102746(2020).
[54] D. J.Bacon, D.Hull. Introduction to Dislocations(1964).
[55] Y.Shibutani, T.Tsuru. Initial yield process around a spherical inclusion in single-crystalline aluminium. J. Phys. D: Appl. Phys., 40, 2183-2188(2007).
[56] V. V.Bulatov, M.Kumar, W. G.Wolfer. Shear impossibility: Comments on ‘Void growth by dislocation emission’ and ‘Void growth in metals: Atomistic calculations. Scr. Mater., 63, 144-147(2010).
[57] B.Appolaire, A.Finel, P.-A.Geslin. Investigation of coherency loss by prismatic punching with a nonlinear elastic model. Acta Mater., 71, 80-88(2014).
[58] J. C.Crone, J.Knap, L. B.Munday. The role of free surfaces on the formation of prismatic dislocation loops. Scr. Mater., 103, 65-68(2015).
[59] J. C.Crone, J.Knap, L. B.Munday. Prismatic and helical dislocation loop generation from defects. Acta Mater., 103, 217-228(2016).
[60] R.Bullough, S.Pugh, J.Willis, S.Pugh, M.Loretto, D.Norris and, M.Loretto, S.Pugh, M.Loretto, D.Norris and, D.Norris. The interaction between a void and a dislocation loop, 133-147(1971).
[61] D. C.Ahn, R.Minich, P.Sofronis. On the micromechanics of void growth by prismatic-dislocation loop emission. J. Mech. Phys. Solids, 54, 735-755(2006).
[62] D. C.Ahn, J.Belak, M.Kumar, R.Minich, P.Sofronis. Void growth by dislocation-loop emission. J. Appl. Phys., 101, 063514(2007).
[63] F. A.McClintock. A criterion for ductile fracture by the growth of holes. J. Appl. Mech., 35, 363-371(1968).
[64] J. R.Rice, D. M.Tracey. On the ductile enlargement of voids in triaxial stress fields. J. Mech. Phys. Solids, 17, 201-217(1969).
[65] J. M.Ball. Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Philos. Trans. R. Soc. London, Ser. A, 306, 557-611(1982).
[66] Y.Huang, J. W.Hutchinson, V.Tvergaard. Cavitation instabilities in elastic plastic solids. J. Mech. Phys. Solids, 39, 223-241(1991).
[67] Y.Huang, J. W.Hutchinson, V.Tvergaard. Cavitation instabilities in a power hardening elastic-plastic solid. Eur. J. Mech.: A/Solids, 11, 215-231(1992).
[68] Z. P.Huang, J.Wang. Nonlinear mechanics of solids containing isolated voids. Appl. Mech. Rev., 59, 210-229(2006).
[69] A. L.Gurson. Continuum theory of ductile rupture by void nucleation and growth: Part I-yield criteria and flow rules for porous ductile media. J. Eng. Mater. Technol., 99, 2-15(1977).
[70] A.Molinari, M.Ortiz. Effect of strain-hardening and rate sensitivity on the dynamic growth of a void in a plastic material. J. Appl. Mech., 59, 48-53(1992).
[71] K. T.Ramesh, T. W.Wright, X. Y.Wu. The dynamic growth of a single void in a viscoplastic material under transient hydrostatic loading. J. Mech. Phys. Solids, 51, 1-26(2003).
[72] K. T.Ramesh, T. W.Wright, X. Y.Wu. The effects of thermal softening and heat conduction on the dynamic growth of voids. Int. J. Solids Struct., 40, 4461-4478(2003).
[73] K. T.Ramesh, T. W.Wright, X. Y.Wu. The coupled effects of plastic strain gradient and thermal softening on the dynamic growth of voids. J. Mech. Phys. Solids, 40, 6633-6651(2003).
[74] A.Molinari, T. W.Wright. A physical model for nucleation and early growth of voids in ductile materials under dynamic loading. J. Mech. Phys. Solids, 53, 1476-1504(2005).
[75] C.Czarnota, S.Mercier, A.Molinari. Modelling of nucleation and void growth in dynamic pressure loading, application to spall test on tantalum. Int. J. Fract., 141, 177-194(2006).
[76] C.Czarnota, N.Jacques, S.Mercier, A.Molinari. Modelling of dynamic ductile fracture and application to the simulation of plate impact tests on tantalum. J. Mech. Phys. Solids, 56, 1624-1650(2008).
[77] C.Denoual, F.Hild, Y.-P.Pellegrini, G.Roy, H.Trumel. On probabilistic aspects in the dynamic degradation of ductile materials. J. Mech. Phys. Solids, 57, 1980-1998(2009).
[78] N.Jacques, S.Mercier, A.Molinari. Effects of microscale inertia on dynamic ductile crack growth. J. Mech. Phys. Solids, 60, 665-690(2012).
[79] B.He, T.Hong, J.Hu, J.-L.Shao, F.-G.Zhang, G.-C.Zhang, H.-Q.Zhou. Modelling of spall damage in ductile materials and its application to the simulation of the plate impact on copper. Chin. Phys. B, 21, 094601(2012).
[80] K. T.Ramesh, J. W.Wilkerson. Unraveling the anomalous grain size dependence of cavitation. Phys. Rev. Lett., 117, 215503(2016).
[81] C. A.Bronkhorst, D.Versino. A computationally efficient ductile damage model accounting for nucleation and micro-inertia at high triaxialities. Comput. Methods Appl. Mech. Eng., 333, 395-420(2018).
[82] R. A.Austin, D. L.McDowell. A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates. Int. J. Plast., 27, 1-24(2011).
[83] J. W.Wilkerson. On the micromechanics of void dynamics at extreme rates. Int. J. Plast., 95, 21-42(2017).
[84] O.Cazacu, E.Charkaluk, D.Kondo, V.Monchiet. Macroscopic yield criteria for plastic anisotropic materials containing spheroidal voids. Int. J. Plast., 24, 1158-1189(2008).
[85] A. A.Benzerga, S. M.Keralavarma. A constitutive model for plastically anisotropic solids with non-spherical voids. J. Mech. Phys. Solids, 58, 874-901(2010).
[86] A. A.Benzerga, S.Hoelscher, S. M.Keralavarma. Void growth and coalescence in anisotropic plastic solids. Int. J. Solids Struct., 48, 1696-1710(2011).
[87] J.Besson, S.Bugat, S.Forest, X.Han, B.Tanguy. A yield function for single crystals containing voids. Int. J. Solids Struct., 50, 2115-2131(2013).
[88] R.Brenner, D.Kondo, L.Morin, J.Paux. An approximate yield criterion for porous single crystals. Eur. J. Mech.: A/Solids, 51, 1-10(2015).
[89] J.Devaux, M.Gologanu, J.-B.Leblond, G.Perrin. Recent Extensions of Gurson’s Model for Porous Ductile Metals(1997).
[90] V.Tvergaard. On localization in ductile materials containing spherical voids. Int. J. Fract., 18, 237-252(1982).
[91] A.Needleman, V.Tvergaard. Analysis of the cup-cone fracture in a round tensile bar. Acta Metall., 32, 157-169(1984).
[92] A.Needleman, V.Tvergaard. An analysis of ductile rupture in notched bars. J. Mech. Phys. Solids, 32, 461-490(1984).
[93] I. M.Fyfe, A. M.Rajendran. Inertia effects on the ductile failure of thin rings. J. Appl. Mech., 49, 31-36(1982).
[94] F. L.Addessio, J. N.Johnson. Tensile plasticity and ductile fracture. J. Appl. Phys., 64, 6699-6712(1988).
[95] R. J.Pick, M. J.Worswick. Void growth and coalescence during high-velocity impact. Mech. Mater., 19, 293-309(1995).
[96] A.Needleman, V.Tvergaard. An analysis of dynamic, ductile crack-growth in a double edge cracked specimen. Int. J. Fract., 49, 41-67(1991).
[97] A.Needleman, V.Tvergaard. A numerical study of void distribution effects on dynamic, ductile crack-growth. Eng. Fract. Mech., 38, 157-173(1991).
[98] A.Needleman, V.Tvergaard. Mesh effects in the analysis of dynamic ductile crack-growth. Eng. Fract. Mech., 47, 75-91(1994).
[99] Q.Jiang, Z.-P.Wang. A yield criterion for porous ductile media at high strain rate. J. Appl. Mech., 64, 503-509(1997).
[100] Z.-P.Wang. Void-containing nonlinear materials subject to high-rate loading. J. Appl. Phys., 81, 7213-7227(1997).
[101] S.Mercier, A.Molinari. Micromechanical modelling of porous materials under dynamic loading. J. Mech. Phys. Solids, 49, 1497-1516(2001).
[102] G.Roy. Vers une modélisation approfondie de l’endommagement ductile dynamique. Investigation expérimentale d’une nuance de tantale et développements théoriques(2003).
[103] S.Eliezer, V. E.Fortov, V. V.Kostin. Spallation of metals under laser irradiation. J. Appl. Phys., 70, 4524-4531(1991).
[104] K.Baumung, G. I.Kanel, H. U.Karow, V.Licht, S. V.Razorenov, A. V.Utkin. Spallations near the ultimate strength of solids. AIP Conf. Proc., 309, 1043-1046(1994).
[105] A.Bogatch, V. E.Fortov, D. E.Grady, G. I.Kanel, S. V.Razorenov, A. V.Utkin. Spall fracture properties of aluminum and magnesium at high temperatures. J. Appl. Phys., 79, 8310-8317(1996).
[106] E.Dekel, N.Eliaz, D.Eliezer, S.Eliezer, I. B.Goldberg, Z.Henis, A.Ludmirsky, E.Moshe, M.Werdiger. An increase of the spall strength in aluminum, copper, and Metglas at strain rates larger than 107 s−1. J. Appl. Phys., 83, 4004-4011(1998).
[107] E.Dekel, D.Eliezer, S.Eliezer, I. B.Goldberg, Z.Henis, Y.Horovitz, S.Maman, E.Moshe, M.Werdiger. Experimental measurements of the strength of metals approaching the theoretical limit predicted by the equation of state. Appl. Phys. Lett., 76, 1555-1557(2000).
[108] K.Baumung, G. I.Kanel, S. V.Razorenov, J.Singer. Dynamic yield and tensile strength of aluminum single crystals at temperatures up to the melting point. J. Appl. Phys., 90, 136-143(2001).
[109] R.Adams, A. C.Bernstein, J.Brewer, D. A.Dalton, T.Ditmire, A.Edens, M.Geissel, W.Grigsby, E.Jackson, D.Milathianaki, P.Rambo, J.Schwarz, I.Smith, E.Taleff. Laser-induced spall of aluminum and aluminum alloys at high strain rates. AIP Conf. Proc., 955, 501(2007).
[110] L.Berthe, M.Boustie, A.Claverie, J. P.Colombier, P.Combis, J. P.Cuq-Lelandais, T.de Rességuier, M.Nivard. Spallation generated by femtosecond laser driven shocks in thin metallic targets. J. Phys. D: Appl. Phys., 42, 065402(2009).
[111] K. T.Ramesh, J. W.Wilkerson. A dynamic void growth model governed by dislocation kinetics. J. Mech. Phys. Solids, 70, 262-280(2014).
[112] R.Becker, J. D.Clayton, J. T.Lloyd, D. L.McDowell. Simulation of shock wave propagation in single crystal and polycrystalline aluminum. Int. J. Plast., 60, 118-144(2014).
[113] F. L.Addessio, M. J.Cawkwell, D. J.Luscher, K. J.Ramos. A dislocation density-based continuum model of the anisotropic shock response of single crystal
[114] D. J.Luscher, T.Nguyen, J. W.Wilkerson. A dislocation-based crystal plasticity framework for dynamic ductile failure of single crystals. J. Mech. Phys. Solids, 108, 1-29(2017).
[115] D. J.Luscher, T.Nguyen, J. W.Wilkerson. A physics-based model and simple scaling law to predict the pressure dependence of single crystal spall strength. J. Mech. Phys. Solids, 137, 103875(2020).
