Scaling of Dislocation Strengthening by Multiple Obstacle Types
Strengthening of dislocations by multiple obstacle types occurs in many engineering alloys. Theories have rationalized two different scaling laws for the total strength, tau(alpha)(t) = tau(alpha)(1) + tau(alpha)(2) with alpha = 1 or 2, where tau(1) and tau(2) are the strengths of the two individual obstacle types. Simulations have clearly demonstrated alpha = 2, while "friction'' strengthening must correspond to alpha = 1. Here, line-tension simulations of dislocation glide through two types of point obstacles are performed to examine the friction limit. One obstacle type is weak (critical angle approaching 180 deg) but with very high density, approximately corresponding to solute strengthening; and the second obstacle type is stronger (smaller critical angle) but with lower density, approximately corresponding to forest or precipitate strengthening. Additive strengthening alpha = 1 is obtained when the densities of the two obstacle types differ by more than a factor of similar to 67, while a transition to alpha = 2 occurs with increasing density of the second obstacle. These simulations confirm the long-held metallurgical wisdom regarding additivity of solute or friction strengthening with other strengthening mechanisms and also demonstrate that apparent intermediate scaling laws with 1 textless alpha textless 2 can arise for a range of relative obstacle densities. Investigation of several literature experimental studies shows some agreement with the model here but quantitative comparisons remain difficult.