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Research Papers

Contours for Planar Cracks Growing in Three Dimensions: Influence of Kinetic Energy

[+] Author and Article Information
L. M. Brock

Fellow ASME
College of Engineering,
University of Kentucky,
Lexington, KY 40506
e-mail: louis.brock@uky.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 6, 2015; final manuscript received September 12, 2015; published online September 28, 2015. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 82(11), 111011 (Sep 28, 2015) (6 pages) Paper No: JAM-15-1303; doi: 10.1115/1.4031585 History: Received June 06, 2015; Revised September 12, 2015

Dynamic steady-state growth in 3D of a semi-infinite plane brittle crack in isotropic elastic solids is considered. Loads cause growth by translating on the crack surfaces at constant, subcritical speed. An analytical solution is obtained and subjected to a criterion for brittle crack growth based on dynamic energy release rate, with kinetic energy included. The result is a nonlinear differential equation for the crack contour, i.e., the curve formed by the crack edge in the crack plane. The equation is studied for the case of compression loading by translating point forces. At large distances from the forces, the crack edge asymptotically approaches the rectilinear and kinetic energy effects can be negligible. A bulge forms around the forces, however, the effect of kinetic energy on its size can be pronounced.

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References

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Brock, L. M. , 2012, “ Two Cases of Rapid Contact on an Elastic Half-Space: Sliding Ellipsoidal Die, Rolling Sphere,” J. Mech. Mater. Struct., 7(5), pp. 469–483. [CrossRef]
Brock, L. M. , 2013, “ Rapid Contact on a Prestressed Highly Elastic Half-Space: The Sliding Ellipsoid and Rolling Sphere,” ASME J. Appl. Mech., 80(2), pp. 1–8. [CrossRef]
Brock, L. M. , 2014, “ The Rigid Die on a Half-Space With Thermal Relaxation and Convection: Influence of Sliding Speed, Die Temperature and Geometry,” J. Therm. Stresses, 37(7), pp. 832–851. [CrossRef]
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Freund, L. B. , 1972, “ Energy Flux Into the Tip of an Extending Crack in an Elastic Solid,” J. Elasticity, 2(4), pp. 341–349. [CrossRef]
Achenbach, J. D. , and Brock, L. M. , 1973, “ On Quasistatic and Dynamic Fracture,” Dynamic Crack Propagation, G. C. Sih , ed., Noordhoff, Leyden, The Netherlands, pp. 529–542.
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Bazant, Z. P. , and Caner, F. C. , 2013, “ Comminution of Solids Caused by Kinetic Energy of High Shear Strain Rate, With Implications for Impact, Shock and Shale Fracturing,” Proc. Natl. Acad. Sci., 110(48), pp. 19291–19294. [CrossRef]

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