The brittle—ductile behaviour of materials: Modelling the effect of interatomic force laws

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Abstract
We present a model for brittle—ductile behaviour of materials containing interfaces based on the idea that the criteria for fracture can be couched as a balance between elastic driving forces and lattice resistance terms. This approach leads to a simple block construction for the lattice resistance term for blunting dislocation emission, which can be generalized to apply to first-principles quantum-mechanical bonding calculations for the crack. We have tested the model with a generic two-dimensional hexagonal lattice with universal binding energy relation (UBER) pair force laws and shown that the model gives quantitative results. The only exception is when the bonding relations at the crack tip lead to significant lattice trapping, for which the material is more ductile than predicted. With the generic system (which should be useful in a qualitative way for more realistic materials), we find that firstly the cross-over between ductile and brittle behaviour is determined by the local bonding at the interface atoms, secondly the cross-over occurs at λ ≈ 0·17 (in units of the lattice spacing), where λ is the range parameter in the UBER force law for a system emitting at an angle of about 60[ddot] to the cleavage plane and thirdly the cross-over is independent of the spring constants in the interface but depends on the crystallography of the crack—emission system and on the elastic mismatch between the two sublattices at the interface. Consequences for chemical embrittlement are discussed.

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