Some Observations Regarding Stochasticity of Dynamic Response of 2D Disordered Brittle Lattices

Abstract

It had been long recognized that the tensile strength of brittle materials increases with increase of the loading rate. In the present article, a statistical approach to rupture of a disordered 2D triangular truss lattice consisting of fragile nonlinear springs is attempted in hope to elucidate some generic effects of structural and geometrical disorder on the tensile strength and the (stress-peak and post-peak) damage energy rates. The simulation results reveal increase of the mean and decrease of the standard deviation of the macroscopic tensile strength with increase of the structural and geometrical order till the ‘theoretical strength’ saturation. At the same time, the increase in lattice disorder results in increase of the mean and standard deviation of the stress-peak damage energy rate, followed by the decrease of the same in the softening regime.

Keywords

discrete models brittle systems disorder dynamic strength damage energy rate stochasticity.

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References

Curtin, W.A. , Pamel, M. and Scher, H. ( 1997). Time Dependent Damage Evolution and Failure in Materials. II. Simulations, Physics Review B, 55: 12052-12061.

Dieter, G.E. ( 1986). Mechanical Metallurgy, New York, McGraw-Hill, pp. 189-191.

Espinosa, H.D. and Zavattieri, P.D. ( 2003). A Grain Level Model for the Study of Failure Initiation and Evolution in Polycrystalline Brittle Materials. Part I: Theory and Numerical Implementation, Mechanics of Materials, 35: 333-364.

Field, J.E. , Walley, S.M. , Proud, W.G. , Goldrein, H.T. and Siviour, C.R. ( 2004). Review of Experimental Techniques for High Rate Deformation and Shock Studies, International Journal of Impact Engineering , 30: 725-775.

Grady, D.E. and Hollenbach, R.E. ( 1979). Dynamic Fracture Strength of Rock, Geophysical Research Letters, 7: 73-76.

Hansen, A. , Roux, S. and Herrmann, H.J. ( 1989). Rupture of Central-force Lattices, Journal of Physics, France, 50: 733-744.

Jagota, A. and Bennison, S.J. ( 1994). Spring-network and Finite-element Models for Elasticity and Fracture. In: Bardhan, K.K. , Chakrabarti, B.K. and Hansen, A. (eds), Proceedings of a Workshop on Breakdown and Non-linearity in Soft Condensed Matter, Berlin, Springer-Verlag Lecture Notes in Physics, pp. 186-201.

Kraft, R.H. , Molinari, J.F. , Ramesh, K.T. and Warner, D.H. ( 2008). Computational Micromechanics of Dynamic Compressive Loading of a Brittle Polycrystalline Material Using a Distribution of Grain Boundary Properties, Journal of the Mechanics and Physics of Solids , 56: 2618-2641.

Mastilovic, S. ( 2008). A Note on Short-time Response of Two-dimensional Lattices During Dynamic Loading, International Journal of Damage Mechanics , 17: 357-361.

10.

Mastilovic, S. , Rinaldi, A. and Krajcinovic, D. ( 2008). Ordering Effect of Kinetic Energy on Dynamic Deformation of Brittle Solids, Mechanics of Materials, 40: 407-417.

11.

Ostoja-Starzewski, M. ( 2002). Lattice Models in Micromechanics, Applied Mechanics Reviews, 55: 35-60.

12.

Rinaldi, A. , Krajcinovic, D. and Mastilovic, S. ( 2007). Statistical Damage Mechanics and Extreme Value Theory , International Journal of Damage Mechanics, 16: 57-76.

13.

Rinaldi, A. and Lai, Y.-C. ( 2007). Damage Theory of 2D Disordered Lattices: Energetics and Physical Foundations of Damage Parameter, International Journal of Plasticity, 23: 57-76.

14.

Van Mier, J.G.M. and Man, H. ( 2009). Some Notes on Microcracking, Softening, Localization, and Size Effect, International Journal of Damage Mechanics , 18: 283-309.

15.

Wang, H. and Ramesh, K.T. ( 2004). Dynamic Strength and Fragmentation of Hot-pressed Silicon Carbide Under Uniaxial Compression, Acta Materialia, 52: 355-367.

16.

Zavattieri, P.D. , Raghuram, P.V. and Espinosa, H.D. ( 2001). A Computational Model of Ceramic Microstructures Subjected to Multi-axial Dynamic Loading, Journal of the Mechanics and Physics of Solids, 49: 27-68.

17.

Zhou, F. and Molinari, J.F. ( 2004). Stochastic Fracture of Ceramics Under Dynamic Tensile Loading, International Journal of Solids and Structures, 41: 6573-6596.