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Research Papers

A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates

[+] Author and Article Information
Harsha S. Bhat1

Department of Earth Sciences,  University of Southern California & Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA, 91125bhat@ipgp.fr

Ares J. Rosakis

Graduate Aerospace Laboratories,  California Institute of Technology, Pasadena, CA, 91125arosakis@caltech.edu

Charles G. Sammis

Department of Earth Sciences,  University of Southern California, Los Angeles, CA, 90089sammis@usc.edu

1

Corresponding author. Present address: Institut de Physique du Globe de Paris, France.

J. Appl. Mech 79(3), 031016 (Apr 05, 2012) (12 pages) doi:10.1115/1.4005897 History: Received July 19, 2011; Revised January 18, 2012; Posted February 13, 2012; Published April 04, 2012; Online April 05, 2012

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 103 s− 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.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 2

(a) Normalized dynamic initiation toughness KICDfor fracture initiation as a function of loading rate for several materials (from Ref. 48)

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Figure 3

Normalized dynamic propagation toughness KICdfor fracture propagation as a function of crack-tip velocity for various materials (from Ref. 48)

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Figure 4

Graphical representation of the solution to Eq. 50

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Figure 5

Optical micrographs of the Dionysus-Pentelicon marble

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Figure 6

Stress-strain curves for marble under compressive loading at strain rates differing by more than eight orders of magnitude (from Ref. [48])

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Figure 7

Effect of grid resolution on the temporal evolution of the scalar damage parameter, D. Here Δs is the size of the finite element and a is the size of the penny crack.

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Figure 8

Effect of grid resolution on the temporal evolution of uniaxial stress. Here Δs is the size of the finite element and a is the size of the penny crack.

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Figure 9

Numerically obtained stress-strain curves at different strain-rates for marble based on the constitutive model developed

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Figure 10

Temporal evolution of the scalar damage parameter D for lower strain rate simulations ( ɛ·=1s-1 and 10 s− 1 )

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Figure 11

Temporal evolution of the scalar damage parameter D for higher strain rate simulations ( ɛ·=1600s-1 to 5000 s− 1 )

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Figure 12

Variation of peak or failure stress with strain rate. Experimental results are compared with numerical simulations.

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Figure 13

Snapshot of a bilateral rupture propagating on the boundary between damaged and undamaged rock. Note the generation of dynamic damage in the tensile lobe of the right rupture tip. Rupture tips are denoted by the inverted triangles.

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Figure 1

Geometry in the [12] micromechanical damage mechanics model. Sliding on an array of penny-shaped cracks having volume density of NV and radius a produces a wedging force Fw that drives tensile wing cracks to open in the direction of the smallest principal stress σ3 and propagate parallel to the largest principal stress σ1 . Growth of wing cracks is enhanced by σ1 , retarded by σ3 , and enhanced by a global interaction that produces a mean tensile stress σ3i. The positive feedback provided by this tensile interaction stress leads to a run-away growth of the wing cracks and ultimate macroscopic failure.

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