A coplanar Orowan loops model for dispersion hardening

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Abstract
When an internally oxidized Cu-Al2O3 alloy with Al2O3 particles of diameter <500 Å is plastically deformed, each particle is likely to be intersected by only one or two slip planes. Consequently, at low temperatures, Orowan loops are expected to form coplanar pile-ups rather than the vertical stacks assumed in recent theories of dispersion hardening. The arrangement of concentric Orowan loops is described and the contribution they make to the flow stress of a dispersion-hardened alloy is calculated. To a first approximation, the three principal components, the image stress, the long-range stress and the bowing stress are all proportional to the number of Orowan loops. The flow stress of an alloy has two other components: the interaction stress between gliding dislocations and a further bowing stress from stacks of prismatic loops. The components are combined to describe the stress-strain curve in forward and reverse flow and it is concluded that the experiments are best described by a hybrid model in which small numbers of Orowan loops are first formed at a particle and later interactions give rise to prismatic loops. The work-hardening is controlled by both Orowon and prismatic loops and the Bauschinger effect is due entirely to the Orowan loops. As the number of Orowan loops in the pile-up grows the array becomes unstable and may relax either by cross-slip or by climb of the innermost loop. The values of the stress components acting on the innermost loop at various points on its cross-slip path show that the transfer of the screw dislocation from the primary plane to the cross plane is easily accomplished and that the return to the primary plane is aided by the fact that the partials are constricted in the stress field of the remaining Orowan loops. The climb force on the innermost Orowan loop from the shrinkage of the loop itself and from the collapse of the pile-up during climb is sufficient to reduce the activation energy, and hence to accelerate climb, substantially. Consequently the low-temperature static and dynamic recovery observed in these alloys may be attributed to the annealing of Orowan loops by pipe diffusion with an (unaided) activation energy of 1·1 + 0·2 eV.