  A generalized line tension model has been developed to estimate the critical
resolved shear stress in precipitation hardened alloys. The model is based in
previous line tension models for regular arrays of either impenetrable or
shearable spherical precipitates that were expanded to take into account the
effect of the elastic mismatch between the matrix and the precipitates. The
model parameters are calibrated from dislocation dynamics simulations that
covered a wide range of precipitate diameters and spacing as well as of the
mismatch in elastic constants. This model is extended to deal with random
arrays of monodisperse spherical precipitates by changing the geometrical
parameters of the model by the averaged ones corresponding to the random
distributions. The model predictions were in good agreement with the critical
resolved shear stresses obtained from dislocation dynamics simulations of
random spherical precipitates distributions for both impenetrable and shearable
precipitates, providing a fast and accurate tool to predict precipitate
strengthening in metallic alloys.
