Derivation of the antiphase-boundary energy of L1 2 long-range-ordered precipitates from measurements of the minimum size of stable dislocation loops

Abstract

In an alloy that is strengthened by long-range-ordered particles, a matrix dislocation generates an antiphase boundary (APB) when it cuts through such a particle. The speci®c energy ® APB of this APB has been measured for two fcc alloys with spherical coherent L1 2 ordered particles: an Al±7.5 at.% Li-alloy and the commercial Ni-base superalloy Nimonic PE16. Peak-aged specimens have been deformed and Orowan loops searched for using transmission electron microscopy. ® APB has been derived from the radii of the smallest dislocation loops which have been left behind around particles. Such an approach had been used previously, for example, by Raynor and Silcock and by Nembach et al. Here an improved evaluation method has been applied; it is based on the results of computer simulations of the equilibrium con®gurations of dislocation loops.} 1. Introduction A dislocation in a disordered matrix cutting through a coherent L1 2 long-rangeordered precipitate generates an antiphase boundary (APB) inside this particle. This causes a stress which tends to drive the dislocation back out of the particle. Hence dislocation glide is impeded and the material is strengthened. Such a hardening mechanism is e ective for instance in Al-rich Al±Li alloys and in the commercial nickel-base superalloy Nimonic PE16 (Nembach and Neite 1985, Nembach 1996, 2000.The strengthening contribution of these L1 2 long-range ordered precipitates strongly depends on the energy density ® APB of the APB. To measure this important strengthening parameter ® APB , several approaches have been used in the past. For spherical particles, one method is to measure the minimum radius r min of Orowan loops found around the L1 2 -ordered precipitates in a specimen that has been deformed up to the external resolved stress ½ ext (Raynor andSilcock 1970, Nembach et al. 1992). To derive ® APB from r min , a model for the interaction of the Orowan loop with itself is required. Nembach et al. (1992) based their derivation of the function ® APB (r min ) on the mean self-stress ½ self;mean of a circular loop as calculated by Brown (1964):

The critical resolved shear stress of single crystals with long-range ordered precipitates calculated by dislocation dynamics simulations

“…But the cause of the difference can already be seen in Fig. 1: it is always the dislocation parts of D1 k with predominant screw character that penetrate the particles first [13] because screw dislocations are stiffer than edge dislocations [9]. Hence, D2 k can follow and touch the inside of the same particle as D1 k .…”

“…The peak in τ p will always be in the transition from particle shearing to circumventing. As long as the CRSS is significantly lower than |τ obst | = γ APB /b [13,22], this transition is governed by the particle strength 2ω rr γ APB , which is independent of f.…”