A new computational method for treating the elastic interaction between dislocations and precipitates was developed and applied to problems which involved dislocation cutting and looping around precipitates. On the basis of the superposition principle, the solution to the dislocation–precipitate interaction problem was obtained as the sum of two solutions . One was a dislocation problem, with image stresses from interfaces between the dislocation and the precipitate, and the other was a solution for the elastic problem of a precipitate with an initial strain distribution. The current development was based upon a combination of parametric dislocation dynamics and boundary element methods with volume integrals. The method permitted the calculation of the stress field both inside and outside of precipitates having elastic moduli which were different to those of the matrix, and which might have initial coherency strain fields. The present numerical results exhibited good convergence and high accuracy, when compared with a known analytical solution, and were also in good agreement with molecular dynamics simulations. Sheared copper precipitates (2.5nm in diameter) were shown to lose some of their resistance to dislocation motion after they were cut by the leading dislocations in a pile-up. Successive cutting of precipitates by the passage of a dislocation pile-up reduced the resistance by about 50% when the number of dislocations in the pile-up exceeded about 10. The transition, from the shearable precipitate regime to the Orowan looping regime, occurred for precipitate/matrix elastic modulus ratios above 3 to 4; with some dependence upon the precipitate size. The effects of precipitate size, spacing and elastic modulus mismatch with the host matrix upon the critical shear stress for dislocation motion were determined.

A Computational Method for Dislocation-Precipitate Interaction. A.Takahashi, N.M.Ghoniem: Journal of the Mechanics and Physics of Solids, 2008, 56[4], 1534-53