Quantization of crack speeds in dynamic fracture of silicon: Multiparadigm ReaxFF modeling
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0910-A06-07
Quantization of Crack Speeds in Dynamic Fracture of Silicon: Multiparadigm ReaxFF Modeling Harvey Tang1, Janet Rye2, Markus J. Buehler3, Adri van Duin4, and William A. Goddard III4 1 Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, 02139 2 Materials Science and Engrg., Massachusetts Institute of Technology, Cambridge, 02139 3 Civil and Environmental Engrg., Massachusetts Institute of Technology, Cambridge, MA, 02139 4 Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, 91125 Corresponding author, electronic address: [email protected] ABSTRACT We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of crack dynamics (Buehler et al., Phys. Rev. Lett., 2006). In this article, we focus on crack speeds as a function of loading and crack propagation mechanisms. We find that the steady state crack speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of crack speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We observe similar effects in the (110) crack direction. INTRODUCTION Brittle fracture is characterized by breaking of atomic bonds leading to formation of two
Figure 1: Subplot (a): The interpolation method for defining a mixed Hamiltonian in the transition region between two different paradigms, as implemented in the CMDF framework. As an alternative to the linear interpolation, we have also implemented smooth interpolation function based on a sinusoidal function. This enables using slightly smaller handshake regions thus increasing the computational efficiency. Subplot (b): Geometry used for simulating mode I fracture in silicon. The (110) crack surface system contains 28,800 atoms with Lx≈230Å, and Ly≈460Å. The (111) crack surface system contains 86,400 atoms with Lx≈400Å, and Ly≈1130Å. At the tip of the crack, up to 3,000 atoms are modeled with ReaxFF.
new materials surfaces.
Most existing atomistic models of fracture assume an empirical
Crack Speed vs. Loading (110)
Figure 2: Crack speed as a function of reduced load, for a crack in the (110) orientation. For 4000 small loads ( G / GC < 1 ), the 3000 crack speed is zero. Above G / G > 1 we observe a finite 2000 C crack speed, with a sudden jump to 1000 approximately 3,000 m/s. Then 0 the crack speed displays a steady, 0 10 20 30 40 50 linearly incre
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