Research Papers

Proof of the Splitting Mode of Compressive Brittle Failure and Integration With General Failure Theory

[+] Author and Article Information
Richard M. Christensen

Professor Research Emeritus
Department of Aeronautics and Astronautics,
Stanford University,
Stanford, CA 94305
e-mail: christensen@stanford.edu

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received June 3, 2019; final manuscript received June 4, 2019; published online June 27, 2019. Assoc. Editor: Yonggang Huang.

J. Appl. Mech 86(9), 091011 (Jun 27, 2019) (5 pages) Paper No: JAM-19-1282; doi: 10.1115/1.4044016 History: Received June 03, 2019; Accepted June 05, 2019

The problem of special interest is the nature of the mode of failure in uniaxial compression at the brittle limit. This problem is known by observation to undergo a splitting mode of failure. The present work gives a full theoretical treatment and proof for this mode of failure. The general failure theory of Christensen for isotropic materials provides the basis for the derivation. The solution demonstrates the depth of technical capability that is required from the failure theory to treat such a classically difficult problem.

Copyright © 2019 by ASME
Topics: Brittleness , Failure
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Christensen, R. M., 2013, The Theory of Materials Failure, Oxford University Press, Oxford, UK.
Christensen, R. M., 2019, “The Ductility Number Nd Provides a Rigorous Measure for the Ductility of Material Failure,” ASME J. Appl. Mech., 86, p. 041001. [CrossRef]
Christensen, R. M., 2018, “The Ductile/Brittle Transition Provides the Critical Test for Materials Failure Theory,” Proc. Roy. Soc. A, 474(2210), p. 20170817. [CrossRef]
Fairhurst, C., and Cook, N. G. W., 1966, “The Phenomenon of Rock Splitting Parallel to the Direction of Maximum Compression in the Neighborhood of a Surface,” Proceedings 1st Congress, International Society for Rock Mechanics, Lisbon, Sept. 25–Oct. 1, Laboratory Nacional de Engenharia Civil, Lisbon, Portugal, pp. 687–692.
Jaeger, J., Cook, N. G., and Zimmerman, R., 2007, Fundamentals of Rock Mechanics, 4th ed., Wiley, New York.
Chen, W., and Ravichandran, G., 1997, “Dynamic Compressive Failure of a Glass Ceramic Under Lateral Constraint,” J. Mech. Phys. Solids, 45, pp. 1303–1328. [CrossRef]
Christensen, R. M., Li, Z., and Gao, H., 2018, “An Evaluation of the Failure Modes Transition and the Christensen Ductile/Brittle Failure Theory Using Molecular Dynamics,” Proc. Roy. Soc. A, 474, p. 20180361. [CrossRef]
Christensen, R. M., Li, Z., and Gao, H., 2019, “An Independent Derivation and Verification of the Voids Nucleation Failure Mechanism: Significance for Materials Failure,” Proc. Roy. Soc. A, 475, p. 20180755. [CrossRef]


Grahic Jump Location
Fig. 1

The plane of failure in uniaxial stress

Grahic Jump Location
Fig. 2

Failure angles in uniaxial stress including only the shear band mode of compressive failure

Grahic Jump Location
Fig. 3

Failure angles in uniaxial stress including the splitting mode of compressive failure



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