A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates
The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, "The Damage Mechanics of Brittle Solids in Compression," Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, "Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model," J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ~10^(−6) to 10^3s^(−1). Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent.
© 2012 American Society of Mechanical Engineers. Received 19 July 2011; revised 18 January 2012; accepted manuscript posted 13 February 2012; published 4 April 2012. The authors would like to acknowledge the constructive reviews provided by Professor Mark Kachanov and one anonymous reviewer. HSB wishes to acknowledge the singular influence of Professor James R. Rice in his intellectual and personal development. HSB and CGS also wish to thank Professors Vikram Deshpande and Robert McMeeking for the help and guidance provided in implementing the micromechanical constitutive law into ABAQUS. This research was funded through the National Science Foundation collaborative Grant No. EAR-0711171 to the University of Southern California and the California Institute of Technology, the National Science Foundation for the research grant (Award No. EAR-0911723), provided under the American Recovery and Reinvestment Act of 2009 (ARRA) (Public Law 111-5), the Department of the Air Force though Grant No. FA8718-08-C- 0026, and the Southern California Earthquake Center (SCEC). The SCEC contribution number for this paper is 1598.
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