Research Papers

Hypervelocity Cavity Expansion in Porous Elastoplastic Solids

[+] Author and Article Information
Tal Cohen

e-mail address: btal@tx.technion.ac.il

Faculty of Aerospace Engineering,
Technion, Haifa 32000, Israel

1This work is based on part of a Ph.D. thesis to be submitted to the Technion.

2Correspond author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received April 6, 2011; final manuscript received July 8, 2012; accepted manuscript posted July 25, 2012; published online November 19, 2012. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(1), 011017 (Nov 19, 2012) (7 pages) Paper No: JAM-11-1114; doi: 10.1115/1.4007224 History: Received April 06, 2011; Revised July 08, 2012; Accepted July 25, 2012

Dynamic steady-state spherical cavitation fields are examined with emphasis on material porosity at large strain. Cavity expansion is driven by constant internal pressure in presence of remote tension or compression. The plastic branch of constitutive relations is described by the Gurson model, with arbitrary strain hardening. The mathematical model is reduced to a system of four ordinary nonlinear coupled differential equations. Numerical examples show that a plastic shock wave builds up as expansion velocity approaches a critical value and jump conditions across the shock are accounted for. At critical levels of remote tension, quasi-static cavitation of all internal voids is induced before dynamic cavity expansion occurs.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Masri, R., and Durban, D., 2005, “Dynamic Spherical Cavity Expansion in an Elastoplastic Compressible Mises Solid,” J. Appl. Mech., 72, pp. 887–898. [CrossRef]
Masri, R., and Durban, D., 2009, “Deep Penetration Analysis With Dynamic Cylindrical Cavitation Fields,” Int. J. Impact Eng., 86, pp. 830–841. [CrossRef]
Cohen, T., Masri, R., and Durban, D., 2010, “Shock Waves in Dynamic Cavity Expansion,” J. Appl. Mech., 77, p. 041009. [CrossRef]
Durban, D., and Fleck, N. A., 1997, “Spherical Cavity Expansion in a Drucker-Prager Solid,” J. Appl. Mech., 64, pp. 743–750. [CrossRef]
Durban, D., and Masri, R., 2004, “Dynamic Spherical Cavity Expansion in a Pressure Sensitive Elastoplastic Medium,” Int. J. Solids Struct., 41, pp. 5697–5716. [CrossRef]
Ashby, M. F., Blunt, F. J., and Bannister, M., 1989, “Flow Characteristics of Highly Constrained Metal Wires,” Acta Metall., 37, pp. 1847–1875. [CrossRef]
Tvergaard, V., and Vadillo, G., 2007, “Influence of Porosity on Cavitation Instability Predictions for Elastic-Plastic Solids,” Int. J. Mech. Sci., 49, pp. 210–216. [CrossRef]
Bishop, R. F., Hill, R., and Mott, N. F., 1945, “The Theory of Indentation and Hardness Tests,” Proc. Phys. Soc., 57, pp. 147–159. [CrossRef]
Gurson, A. L., 1977, “Continuum Theory of Ductile Rapture by Void Nucliation and Growth: Part 1—Yield Criteria and Flow Rules for Porous Ductile Media,” J. Eng. Mat. Tech., 99, pp. 2–15. [CrossRef]
Tvergaard, V., 1981, “Influence of Voids on Shear Band Instabilities Under Plane Strain Conditions,” Int. J. Fract., 17, pp. 389–407. [CrossRef]
Nahson, K., and Hutchinson, J. W., 2008, “Modification of the Gurson Model for Shear Failure,” Eur. J. Mech. A/Solids, 27, pp. 1–17. [CrossRef]
Durban, D., Cohen, T., and Hollander, Y., 2010, “Plastic Response of Porous Solids With Pressure Sensitive Matrix,” Mech. Res. Commun., 37, pp. 636–641. [CrossRef]
Goodier, J. N., 1965, “On the Mechanics of Indentation and Cratering in the Solid Targets of Strain Hardening Metal by Impact of Hard and Soft Spheres,” Proceedings of the 7th Symposium on Hypervelocity Impact, Vol. III, pp. 215–259.
Durban, D., and Baruch, M., 1977, “Analysis of an Elasto-Plastic Sphere Loaded by Internal and External Pressure,” Int. J. Nonlinear Mech., 12, pp. 9–21. [CrossRef]
Durban, D., and Baruch, M., 1976, “On the Problem of a Spherical Cavity in an Infinite Elasto-Plastic Medium,” J. Appl. Mech., 43, pp. 633–638. [CrossRef]
Ball, J. M., 1982, “Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity,” Philos. Trans. R. Soc. London, 306, pp. 557–611. [CrossRef]


Grahic Jump Location
Fig. 1

Scheme of the self-similar field induced by expansion of a spherical cavity in an unbounded medium, in the presence of an elastoplastic shock wave at ξ=ξp

Grahic Jump Location
Fig. 2

(a) Hydrostatic field–applied tension versus volume ratio J=ρo/ρ for varying values of initial porosity fo, (b) elemental spherical cell–quasi-static expansion. All curves are for material with Σy=0.003,n=0.1 and v=0.3.

Grahic Jump Location
Fig. 3

The elemental spherical cell on the right is a representative volume element of the parent material on the left. Both the elemental spherical cell and the parent material have identical initial porosity ratio fo.

Grahic Jump Location
Fig. 4

Variation of effective stress along radial coordinate ξ with various values of m(m=0.1,0.2,...,0.6)

Grahic Jump Location
Fig. 5

Variation of porosity along radial coordinate ξ with various values of m(m=0.1,0.2,...,0.6)

Grahic Jump Location
Fig. 6

Variation of density along radial coordinate ξ with various values of m(m=0.1,0.2,...,0.6)

Grahic Jump Location
Fig. 7

Variation of radial stress along radial coordinate ξ with various values of m(m=0.1,0.2,...,0.6)

Grahic Jump Location
Fig. 8

Variation of applied pressure P with cavity expansion velocity m

Grahic Jump Location
Fig. 9

Radial profiles of porosity ratio for increasing values of applied remote tension. Material with Σy=0.001,n=0.1,v=0.3,fo=0.001,and m=0.1.

Grahic Jump Location
Fig. 10

Pressure-tension interaction curves at cavitation for material with Σy=0.001,v=0.3, and fo=0.001. In (a) varying expansion velocities m with n=0.3 and in (b) varying hardening index n with m=0.1.

Grahic Jump Location
Fig. 11

Pressure-tension interaction curves at cavitation for material with Σy=0.001,n=0.3,v=0.3, and m=0.1 with varying initial porosity fo



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In