Strain gradient plasticity solution for an internally pressurized thick-walled spherical shell of an elastic linear-hardening material

Mechanics of Advanced Materials and Structures

Volumn 13, Issue 1, 2006, Pages 43-49

  Gao, X L ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HARDENING; INDENTATION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PLASTICITY; PRESSURE EFFECTS; SOLUTIONS; STRAIN; STRESS ANALYSIS;

CAVITY MODELS; INDENTATION MECHANICS; LINEAR-HARDENING MATERIAL; STRAIN GRADIENT;

SHELLS (STRUCTURES);

EID: 29644443559     PISSN: 15376494     EISSN: 15376532     Source Type: Journal    
DOI: 10.1080/15376490500343766     Document Type: Article

References (23)

1. Tabor, D., "Indentation hardness: Fifty years on - a personal view," Phil. Mag. 74, 1207-1212 (1996).
2. Cheng, Y.-T., and Cheng, C.-M., "Scaling, dimensional analysis, and indentation measurements," Mater. Sci. Eng. R 44, 91-149 (2004).
3. Johnson, K. L., "The correlation of indentation experiments," J. Mech. Phys. Solids 18, 115-126 (1970).
4. Narasimhan, R., "Analysis of indentation of pressure sensitive plastic solids using the expanding cavity model," Mech. Mater. 36, 633-645 (2004).
5. Hill, R., The Mathematical Theory of Plasticity, 97-106, Clarendon Press, Oxford, 1950.
6. Tabor, D., "Indentation hardness and its measurement: Some cautionary comments," inP.J. Blau andB.R. Lawn (eds.), Microindentation Techniques in Materials Science and Engineering, 129-159, ASTM Press, Philadelphia (1986).
7. Lawn, B. R., "Indentation of ceramics with spheres: A century after Hertz," J. Am. Ceram. Soc. 81, 115-126 (1998).
8. Gao, X.-L., Jing, X. N., and Subhash, G., "Two new expanding cavity models for indentation deformations of elastic strain-hardening materials," Int. J. Solids Struct, (in press) (2005).
9. Hutchinson, J. W., "Plasticity at the micron scale," Int. J. Solids Struct. 37, 225-238 (2000).
10. Swadener, J. G., George, E. P., and Pharr, G. M., "The correlation of the indentation size effect measured with indenters of various shapes," J. Mech. Phys. Solids 50, 681-694 (2002).
11. Mühlhaus, H.-B., and Aifantis, E. C., "A variational principle for gradient plasticity," Int. J. Solids Struct. 28, 845-857 (1991).
12. Fleck, N. A., and Hutchinson, J. W., "A phenomenological theory for strain gradient effects in plasticity," J. Mech. Phys. Solids 41, 1825-1857 (1993).
13. Fleck, N. A., and Hutchinson, J. W., "A reformulation of strain gradient plasticity," J. Mech. Phys. Solids 49, 2245-2271 (2001).
14. Gao, H., Huang, Y., Nix, W. D., and Hutchinson, J. W., "Mechanism-based strain gradient plasticity-I. Theory," J. Mech. Phys. Solids 47, 1239-1263 (1999).
15. Voyiadjis, G. Z., and Abu Al-Rub, R. K., "Gradient plasticity theory with a variable length scale parameter," Int. J. Solids Struct. 42, 3998-4029 (2005).
16. Wei, Y., and Hutchinson, J. W., "Hardness trends in micron scale indentation," J. Mech. Phys. Solids 51, 2037-2056 (2003).
17. Coleman, B. D., and Hodgdon, M. L., "On shear bands in ductile materials," Arch. Rational Mech. Anal 90, 219-247 (1985).
18. Niordson, C. F., and Hutchinson, J. W., "Non-uniform plastic deformation of micron scale objects," Int. J. Numer. Meth. Engng. 56, 961-975 (2003).
19. Tsagrakis, I., and Aifantis, E. C., "Recent developments in gradient plasticity - Parti: Formulation and size effects," ASME J. Eng. Mater. Tech. 124, 352-357 (2002).
20. Gao, X.-L., "An exact elasto-plastic solution for a thick-walled spherical shell of elastic linear-hardening material with finite deformations," Int. J. Pres. Ves. Piping 57, 45-56 (1994).
21. Little, R. W., Elasticity, 316-317, Prentice Hall, Englewood Cliffs, NJ, 1973.
22. Gao, X.-L., "Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory," Int. J. Solids Struct. 40, 6445-6455 (2003).
23. Gao, X.-L., "Expanding cavity model incorporating strain-hardening and indentation size effects," manuscript submitted for publication and orally presented at the 2005 Joint ASCE/ASME/SES Conference on Mechanics and Materials, Baton Rouge, LA (June 1-3, 2005).