Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 10, 2008, Pages 3077-3100

  Deshpande, V S ^a   Evans, A G ^a  

^a University of California   (United States)

Author keywords

Ballistics; Cavity expansion; Ceramic; Damage mechanics; Micro cracking

Indexed keywords

BALLISTICS; CERAMIC MATERIALS; CONCRETE AGGREGATES; CONSTITUTIVE MODELS; CRACK CLOSURE; CRACK PROPAGATION; DYNAMIC LOADS; ELASTIC WAVES; ENERGY DISSIPATION; GRAIN GROWTH; GRAIN SIZE AND SHAPE; SPALLING;

CAVITY EXPANSIONS; CERAMIC; DAMAGE MECHANICS; ESSENTIAL FEATURES; HIGH CONFINING PRESSURE; INELASTIC DEFORMATION; INTERMEDIATE VELOCITIES; QUASI-STATIC CONDITIONS;

CRACKS;

EID: 55349095762     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.05.002     Document Type: Article

References (48)

1. Adams, M., Sines, G., 1976. Determination of biaxial compressive strength of a sintered alumina ceramic. J. Am. Ceram. Soc. 59, 300-304.
2. Aeberli, K.E., Rawlings, R.D., 1983. Effect of simulated body environments on crack propagation in alumina. J. Mater. Sci. Lett. 2, 215-220.
3. Ashby, M.F., Hallam, S.D., 1986. The failure of brittle solids containing small cracks under compressive stress states. Acta Metall. 34. 497-510.
4. Ashby, M.F., Sammis, C.G., 1990. The damage mechanics of brittle solids in compression. PAGOEPH 133, 489-521.
5. Brannon, R.M., Wells, J.M., Strack, O.E., 2007. Validating theories for brittle damage. Metall. Mater. Trans. A.
6. Bristow, J.R., 1960. Microcracks, and the static and dynamic elastic constants of annealed and heavily cold-worked metals. Br. J. Appl. Phys. 11, 81-85.
7. Budiansky, B., O'Connell, R.J., 1976. Elastic moduli of a cracked solid. Int. J. Solids Struct. 12, 81-97.
8. Chen, W.W., Rajendran, A.M., Song, B., Nie, X., 2007. Dynamic fracture of ceramics in armor applications. J. Am. Ceram. Soc. 90, 1005-1018.
9. Drucker, D.C., Prager, W., 1952. Soil mechanics and plastic analysis or limit design. Q. Appl. Math. 10, 157-165.
10. Durban, D., Masri, R., 2004. Dynamic spherical cavity expansion in a pressure sensitive elastoplastic medium. Int. J. Solids Struct. 41, 5697-5716.
11. Espinosa, H.D., Raiser, G., Clifton, R.J., Ortiz, M., 1992. Experimental observations and numerical modeling of inelasticity in dynamically loaded ceramics. J. Hard Mater. 3, 285-313.
12. Espinosa, H.D., Zavattieri, P.D., Dwivedi, S.K., 1998. A finite deformation continuum/discrete model for the description of fragmentation and damage in brittle materials. J. Mech. Phys. Solids 46, 1909-1942.
13. Evans, A.G., 1974. Slow crack growth in brittle materials under dynamic loading conditions. Int. J. Fract. 10, 251-259.
14. Evans, A.G., 1978a. Microfracture from thermal expansion anisotropy. Acta Metallurg. 26, 1845-1853.
15. Evans, A.C., 1978b. A general approach for the statistical analysis of multiaxial fracture, J. Am. Ceram. Soc. 61, 302-308.
16. Evans, A.C., Meyer, M.E., Fertig, K.W., Davis, B.I., Baumgartner, H.R., 1980. Probabilistic models for defect initiated fracture in ceramics. J. Nondestr. Eval. 1, 111-122.
17. Forrestal, M.J., Tzou, D.Y., 1997. A spherical cavity expansion penetration model for concrete targets. Int. J. Solids Struct. 34, 4127-4146.
18. Forrestal, M.J., Tzou, D.Y., Askari, E., Longcope, D.B., 1995. Penetration into ductile metal targets with rigid spherical-node rods. Int. J. Impact Eng. 16, 699-710.
19. Frost, H.J., Ashby. M.F., 1982. Deformation-Mechanism Maps. Pergamon Press. Oxford.
20. Fu, Y., Evans, A.C., 1982. Microcrack zone formation in single phase polycrystals. Acta Metallurg. 30, 1619-1625.
21. Guiberteau, F., Padture, N.P., Lawn, B.R., 1994. Effect of grain size on Hertzian contact in alumina. J. Am. Ceram. Soc. 77, 1825-1831.
22. Hinton, E., Rock, T., Zienkiewicz, O.C., 1976. A note on mass lumping and related processes in the finite element method. Earthquake Eng. Struct. Dyn. 4, 245-249.
23. Hockey, B.J., 1971. Plastic deformation of aluminum oxide by indentation and abrasion. J. Am. Ceram. Soc. 54, 223-231.
24. Hopkins, H.G., 1960. Dynamic expansion of spherical cavities in metal. In: Sneddon, I.N., Hill, R. (Eds.), Progress in Solid Mechanics, vol. 1. North-Holland, Amsterdam.
25. James, B., 1995. The influence of the material properties of alumina on ballistic performance. 15th International Symposium on Ballistics, Jerusalem, Israel, pp. 3-10.
26. Johnson, K.L., 1985. Contact Mechanics. Cambridge University Press, Cambridge, UK.
27. Johnson, G.R., Cook, W.H., 1985. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng. Fract. Mech. 21, 31-48.
28. Johnson, G.R., Holmquist, T.J., 1999. Response of boron carbide subjected to large strains, high strain rates, and high pressures. J. Appl. Phys. 85, 8060-8073.
29. Ku, R., Johnston, T.L., 1964. Fracture strength of MgO bicrystals. Philos. Mag. 9, 231-247.
30. Lagerlof, K.P.D., Heuer, A.H., Castaing, J., Riviere, J.P., Mitchell, T.E., 1994. Slip and twining in sapphire. J. Am. Ceram. Soc. 77, 385-397.
31. Laugier, M.T., 1984. Hertzian fracture of sintered alumina. J. Mater. Sci. 19, 254-258.
32. Lawn, B.R., 1998. Indentation of ceramics with spheres: a century after hertz. J. Am. Ceram. Soc. 81, 1977-1994.
33. Macek, R.W., Duffey, T.A., 2000. Finite cavity expansion method for near-surface effects and layering during earth penetration. Int. J. Impact Eng. 24, 239-258.
34. Nemat-Nasser, S., Horii, H., 1982. Compression-induced nonplanar crack extension with application to splitting, exfoliation, and rockburst. J. Geophys. Res. 87, 6805-6821.
35. Paliwal, B., Ramesh, K.T., 2007. An interacting micro-crack damage model for the failure of brittle materials under compression, J. Mech. Phys. Solids 1.
36. Rajendran, A.M., 1994. Modeling the impact behavior of AD85 ceramic under multi-axial loading. Int. J. Impact Eng. 15, 749-768.
37. Rajendran, A.M., 2001. Historical perspective on ceramic materials damage models. In: Proceedings of the Ceramic Armor by Design Symposium, Pacific Rim IV International Conference on Advanced Class and Ceramics, Wailea, Maui, Hawaii, pp. 281-297.
38. Rajendran, A.M., Grove, D.J., 1996. Modeling the shock response of silicon carbide, boron carbide and titanium diboride. Int. J. Impact Eng, 18, 611-631.
39. Rice, R.W., 1977. Microstructural Dependence of Mechanical Behavior of Ceramics. Treatise on Materials Science and Technology: Properties and Microstructure, vol. 11. Academic Press, New York, pp. 199-381.
40. Satapathy, S., 2001. Dynamic spherical cavity expansion in brittle ceramics. Int. J. Solids Struct. 38, 5833-5845.
41. Tada, H., Paris, P.C., Irwin, C.R., 1985. The Stress Analysis of Cracks Handbook. Del Res.. St. Louis, MO.
42. Templeton, D.W., Holmquist, T.J., Meyer, H.W., Grove, DJ., Leavy, B., 2001. A comparison of ceramic material models. In: Proceedings of the Ceramic Armor by Design Symposium, Pacific Rim IV International Conference on Advanced Glass and Ceramics, Wailea, Maui, Hawaii, pp. 299-308.
43. Walker, J.D., 2001. Analytic model for penetration of thick ceramic targets. In: Proceedings of the Ceramic Armor by Design Symposium, Pacific Rim IV International Conference on Advanced Glass and Ceramics. Wailea, Maui. Hawaii, pp. 337-348.
44. Wei, Z., Evans, A.C., Deshpande, V.S., 2008. Simulation of the dynamic penetration of alumina by hard spheres. J. Appl. Mech., to appear.
45. Weibull, W., 1951. A statistical distribution function of wide applicability, J. Appl. Mech. 18, 293-297.
46. Wiederhorn, S.M., Bolz, L.H., 1970. Stress corrosion and static failure of glass. J. Am. Ceram. Soc. 53, 543-548.
47. Zavatieri, P.D., Raghuram, P.V., Espinosa, H.D., 2000. A computational model of ceramic microstructures subjected to multi-axial dynamic loading, J. Mech. Phys. Solids 49, 27-68.
48. Zhou, F., Molinari, J.F., 2001. 3D finite element analysis of impact damage in metallic and ceramic targets. In: Proceedings of the Ceramic Armor by Design Symposium, Pacific Rim IV International Conference on Advanced Glass and Ceramics, Wailea, Maui, Hawaii, pp. 317-327.