Engineering Transactions, 45, 3-4, pp. 505-531, 1997

Modeling of Spall Fracture in Brittle Solids

M. Basista
Institute of Fundamental Technological Research, Warszawa

This is a synthetic and critical review of the selected theories of brittle spall fracture. Since the main body of research clone on spalling can actually be credited to a few research institutions, the papers selected for this overview are classified according to their place of origin with some effort to maintain their order of appearance. Emphasis is placed on those models which were instrumental in the development of spall fracture modeling in brittle solids. Consequently, early models based on the critical stress criterion are merely recalled whereas micromechanical and phenomenological damage models of brittle spalling are discussed in more detail. The methods developed in the physics of critical phenomena (e.g. percolation theory), so far relatively unexplored in the modeling of dynamic fracture processes, are also outlined.

Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


A. ZUREK and M.A. MEYERS, Microstructural aspects of dynamic failure, [in]: High­ Pressure Shock Compression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

B. HOPKINSON, Scientific papers, Cambridge University Press, London 1910.

J.S. RINEHART, Some quantitative data bearing on the scabbing of metals under explosive attack, J. Appl. Phys., 22, 555-560, 1951.

J.S. RINEHART, Scabbing of metals under explosive attack: Multiple scabbing, J. Appl. Phys., 23, 1229-1233, 1952.

J.H. SMITH, Three low pressure spall thresholds in copper, [in]: Dynamic Behavior of Materials, 264-282, ASTM, Philadelphia 1963.

F.R. TULER and B.M. BUTCHER, A criterion for the time dependence of dynamic fracture, Int. J. Fract. Mech., 4, 431-437, 1968.

D.E. GRADY and M.E. KIPP, Dynamic rock fragmentation, [in]: Fracture Mechanics of Rocks, B.K. ATKINSON [Ed.], Academic Press, 429-475, 1987.

M.A. MEYERS, Dynamic behavior of materials, J. Wiley and Sans, New York 1995.

J. EFTIS, Constitutive modeling of spall fracture, [in]: High-Pressure Shock Compression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

L. DAVISON and A.L. STEVENS, Continuum measures of spall damage, J. Appl. Phys., 43, 988-994, 1972.

L. DAVISON and A.L. STEVENS, Thermomechanical constitution of spalling elastic bodies, J. Appl. Phys., 44, 668-674, 1973.

L. DAVISON, A.L. STEVENS and M.E. KIPP, Theory of spall damage accumulation in ductile metals, J. Mech. Phys. Solids, 25, 11-28, 1977.

L. SEAMAN, T.W, BARBEE and D.R. CURRAN, U.S. Air Force Weapons Laboratory Report, AFWL-TR-71-156, 1971.

D.E. GRADY and M.E. KIPP, Continuum modeling of explosive fracture in oil shale, Int. Rock. Mech. Min. Sci. & Geomech. Abstr., 17, 147-157, 1980.

D.E. GRADY, Local inertial effects in dynamic fragmentation, J. Appl. Phys., 53, 322-325, 1982.

D.E. GRADY, The spall strength of condensed matter, J. Mech. Phys. Solids, 36, 353-384, 1988.

J.B. WALSH, The effect of cracks on the compressibility of rocks, J. Geophys. Res., 70, 381-389, 1965.

J. LEMAITRE and J.-L. CHABOCHE, Mécanique des Materiaux Solides, Dunod, Paris 1985.

B. BUDIANSKY and R.J. O'CONNELL, Elastic moduli of cracked solid, Int. J. Solids Struct., 12, 81-97, 1976.

A.L. GURSON, Continuum theory of ductile rupture by void nucleation and growth, J. Engng. Mater. Tech., 99, 2-15, 1977.

V. TVERGAARD and A. NEEDLEMAN, Analysis of the cup-cone fracture in a round tensile bar, Acta Metali., 32, 157-169, 1984.

D.E. GRADY, Spall and fragmentation in high-temperature metals, [in:] High-Pressure Shock Compression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

L. SEAMAN, D.R. CURRAN and D.A. SHOCKEY, Computational models for ductile and brittle fracture, J. Appl. Phys., 47, 4814-4826, 1976.

D.A. SHOCKEY, D.R. CURRAN, L. SEAMAN, J.T. ROSENBERG and C.F. PETERSEN, Fragmentation of rock under dynamic loads, Int. J. Rock Mech. Sci. & Geomech. Abstr., 11, 303-317, 1974.

P. PERZYNA, Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures, 22, 797-818, 1986.

D.R. CURRAN and L. SEAMAN, Simplified models of fracture and fragmentation, [in]: High-Pressure Shock Compression of Solids Il, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

D.R. CURRAN, L. SEAMAN and D.A. SHOCKEY, Dynamic failure of solids, Phys. Reports, 147, 253-388, 1987.

D.R. CURRAN, L. SEAMAN, T. COOPER and D.A. SHOCKEY, Int. J. Impact Engng., 13, 53-83, 1993.

S.J. BLESS and A.M. RAJENDRAN, Initiation and propagation of damage caused by im­pact on brittle materials, [in]: High-Pressure Shock compression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

A.M. RAJENDRAN, Modeling of impact behavior of AD85 ceramic under multiaxial load­ing, Int. J. Impact Engng., 15, 749-768, 1994.

A.M. RAJENDRAN, M.A. DIETENBERGER and D.J. GROVE, A void-based failure model to describe spallation, J. Appl. Phys., 65, 1521-1527, 1989.

C.T. AIMONE, M.A. MEYERS and N. MOJTABAI, [in]: Rock Mechanics in Productivity Design, D.H. DOWDING and M.M SINGH [Eds.], Warrendale, PA, 979, 1984.

L.H.L. LOURO and M.A. MEYERS, J. Mater. Sci., 24, 2516, 1989.

H. HORII and S. NEMAT-NASSER, Brittle failure in compression: splitting, faulting and brittle-ductile transition, Phil. Trans. Roy. Soc. London, 319, 337-374, 1986.

J.K. DIENES, A unified theory of flow and fragmentation, [in]: High-Pressure Shock Com­pression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.

J.F. KALTHOFF and S. WINKLER, FAILURE MODE TRANSITION AT HIGH RATES OF SHEAR LOADING, [in]: lmpact Loading and Dynamic Behavior of Materials, Vol. 1, C.Y. CHIEM et al. (Eds.], lnformationsgesellschaft Verlag, 1987.

J.N. JOHNSON, Dynamic fracture and spallation in ductile solids, J. Appl. Phys., 53, 2812-2825, 1981.

J. EFTIS and J.A. NEMES, An evolution equation for the void volume growth rate in a viscoplastic-damage constitutive model, Int. J. Plasticity, 7, 275-293, 1991.

J.R. KLEPACZKO, Dynamic crack initiation: some experimental methods and modelling, [in]: Crack Dynamics in Metallic Materials, J.R. KLEPACZKO [Ed.], Springer, 1990.

H. DENG and S. NEMAT-NASSER, Dynamic damage evolution in brittle solids, Mech. Mater., 14, 83-103, 1992.

M.A. MEYERS, Mech. Mater., 4, 387, 1985.

G.P. CHEREPANOV, Mechanics of brittle fracture, McGraw-Hill, 1979.

V.N. NIKOLAEVSKI, Limit velocity of fracture front and dynamic strength of brittle solids, Int. J. Engng. Sci., 19, 41-56, 1981.

Y.L. ZILBERBRAND, N.A. ZLATIN, A.A KOZUSHKO, V.I. POLOZENKO, G.S. PUGACHEV and A.B. SINANI, Mechanism of interaction of a plastic striker with a brittle solid, Sov. Phys.-Tech. Phys., 34, 1123-1124, 1989.

G.I. KANEL, S.V. RASORENOV and V.E. FORTOV, The failure waves and spallations in homogeneous brittle materials, (in]: Shock Compression of Condensed Matter, Elsevier, 1992.

R. ZALLEN, The physics of amorphous bodies, J. Wiley and Sons, New York 1983.

D. STAUFFER, Introduciton to percolation theory, Taylor & Francis, London, UK 1985.

H.J. HERRMANN and S. ROUX, Statistical models for the fracture of disordered media, North-Holland, The Netherlands 1990.

M. BASISTA and D. KRAJCINOVIC, Brittle deformation of disordered solids, Composites Engng., 1, 103-112, 1991.

D. KRAJCINOVIC, M. BASISTA and D. SUMARAC, Basic principles of damage mechanics, [in]: Damage Mechanics of Composite Materials, R. TALREJA [Ed.], Elsevier, 1994.

D. KRAJCINOVIC, Damage mechanics, Elsevier, The Netherlands 1996.

H. SCHER and R. ZALLEN, Critical density in percolation processes, J. Chem. Phys., 53, 3759-3761, 1970.

V.K.S. SHANTE and S. KIRKPATRICK, An introduction to percolation theory, Adv. Phys., 20, 325-357, 1971.

I. BALBERG, Recent developments in continuum percolation, Phil. Mag. B56, 991-1003, 1987.

G.E. PIKE and C.H. SEAGER, Percolation and conductivity: A computer study, Phys. Rev B, 10, 1421-1446, 1974.

I. BALBERG, C.H. ANDERSON, S. ALEXANDER and N. WAGNER, Excluded volume and its relation to the onset of percolation, Phys. Rev. B, 30, 3933-3943, 1984.

P .C. ROBINSON, Numerical calculations of critical densities for lines and planes, J. Phys. A, 17, 2823-2830, 1984.

E. CHARLAIX, Percolation thresholds of a random array of discs: A numerical simulation, J. Phys. A, 19, L533-L536, 1986.

J .K. DIENES, Permeability, percolation, and statistical crack mechanics, [in:] Issues on Rock Mechanics, R.E. GOODMAN and F.E. HEUZE [Eds.], Proc. 23rd Symp. on Rock Mech., Berkeley, CA., 1982.

D.L. TONKS, Disorder, percolation and wave propagation effects in ductile fracture, [in]: High-Pressure Shock Compression of Solids II, L. DAVISON, D.E. GRADY and M. SHAHINPOOR [Eds.], Springer, 1996.