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Simulations of Fractures
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Supersonic Crack Propagation In Brittle Fracture
The computer experiments setup
We consider a strongly nonlinear elastic solid described by a tethered Lennard-Jones potential where the compressive part of this potential is identical to that of the usual Lennard-Jones 12;6 function and the tensile part is the reflection of the compressive part with respect to the potential minimum. An fcc crystal formed by this potential exhibits a strongly nonlinear stress-strain behavior resulting in elastic stiffening and an increase of the elastic modulus with strain. The elastic modulus increases by a factor of 10 at 13% of elastic strain, indicating that the material properties of such a solid is strongly nonlinear in the hyperelastic regime.
We have perform three dimensional MD simulations of two face-center-cubic (fcc) crystals joined by a weak interface. In this study, we used system sizes of about twenty million atoms. For comparison, we consider the anharmonic tethered potential together with the harmonic potential where the spring constant is equal to the tethered potential at equilibrium. The interatomic force bonding the two crystals is given by the Lennard-Jones 12:6 potential. The simulation results are expressed in reduced units: lengths are scaled by the value of the interatomic separation where the LJ potential is zero and energies are scaled by the depth of the minimum of the LJ potential. Atoms bond only with their original nearest neighbors. Hence, rebonding of displaced atoms due to applied loading does not occur. For the adjoining two crystal slabs, we consider the following three simulation cases: (1) Harmonic case: both crystal slabs are characterized by the harmonic potential. This is used as a control for the anharmonic studies; (2) Anharmonic case: both crystal slabs are characterized by the anharmonic potential; (3) Mixed case: one crystal slab is characterized by the anharmonic potential, and the other is characterized by the harmonic potential. In each case, a shear crack lies along the (110) plane and oriented toward the [110] direction. The crack front is parallel to the [001] direction. The applied loading is dominated by shear.
The computer simulations descriptions
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