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Research Papers

An Analytical Theory for Radial Crack Propagation: Application to Spherical Indentation

[+] Author and Article Information
Andrew N. Seagraves

Department of Mechanical Engineering,
Institute for Soldier Nanotechnologies,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: aseagrav@mit.edu

Raúl A. Radovitzky

Department of Aeronautics and Astronautics,
Institute for Soldier Nanotechnologies,
Massachusetts Institute of Technology,
Cambridge, MA 02139
e-mail: rapa@mit.edu

Vargas-Gonzalez and Speyer [22] reported average fracture toughness values of Kc~ 2.5–4.5 MPam for several grades of SiC measured from four-point bend tests.

1Corresponding author.

Manuscript received July 26, 2012; final manuscript received September 12, 2012; accepted manuscript posted October 10, 2012; published online May 16, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 041018 (May 16, 2013) (5 pages) Paper No: JAM-12-1350; doi: 10.1115/1.4007795 History: Received July 26, 2012; Revised September 12, 2012; Accepted October 10, 2012

A simple analytical theory is proposed for estimating the number of radial cracks which will propagate in brittle materials subjected to axisymmetric transverse surface loads. First, an expression is obtained for the stress intensity factor of a traction-free star-shaped crack in an infinite elastic membrane subjected to axisymmetric transverse loads. Combining this relation with the critical stress intensity factor criterion for fracture, an implicit expression is obtained which defines the number of cracks as a function of the applied loading, initial flaw size, and fracture toughness. Based on the form of this expression, we argue that if the initial flaw size is sufficiently small compared to the length scale associated with the loading, then the number of cracks can be determined approximately in closed-form from the analysis of a traction-free star-shaped crack in a thin body subjected to uniform equibiaxial in-plane tension. In an attempt to validate the theory, comparisons are made with spherical micro-indentation experiments of silicon carbide (Wereszczak and Johanns, 2008, “Spherical Indentation of SiC,” Advances in Ceramic Armor II, Wiley, NY, Chap. 4) and good agreement is obtained for the number of radial cracks as a function of indentation load.

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References

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Vargas-Gonzalez, L., and Speyer, R. F., 2010, “Flexural Strength, Fracture Toughness, and Hardness of Silicon Carbide and Boron Carbide Armor Ceramics,” Int. J. Appl. Ceram. Tech., 7(5), pp. 643–651. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic depiction of the star-shaped and hypocycloidal crack geometries for n=6

Grahic Jump Location
Fig. 2

Snapshots of the final deformation and failure pattern as a function of the indentation load for diamond micro-indentation experiments on SiC-SC-1R from [1]

Grahic Jump Location
Fig. 3

Comparison of the number of radial cracks predicted by the theory with experimental results [1] as a function of indentation load

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