Penetration of activated F-R sources into a 3D field of destructible SFTs can be viewed as a per­colation problem, first considered by Foreman19 on a single glide plane, and extended here to complex 3D climb/glide motion. The critical stress above which an equilibrium dislocation configuration is unsustain­able corresponds to the percolation threshold, and is considered here to represent the flow stress of the radiation-hardened material. Since activated F-R sources may encounter nearby dislocations, such interactions should be considered in estimates of the flow stress. The effects of interplanar F-R source interactions on the flow stress in copper irradiated and tested at 100°C are shown in Figure 7. A plastic stress-strain curve is constructed from the computer

simulation data, where the local strain is measured in terms of the fractional area swept by expanding F—R sources on the glide plane. It is shown that, while the majority of the increase in applied stress of irradiated copper can be rationalized in terms of dislocation interaction with SFTs on a single glide plane, dislocation-dislocation dipole hardening can have an additional small component on the order of 15% for very close dislocation encounters on neighboring slip planes (e. g., separated by ~20й). For larger sepa­ration (e. g., ^500й) the additional effects of dipole hardening is negligible. Dislocation forest hardening does not seem to play a significant role in determina­tion of the flow stress, as implicitly assumed in earlier treatments of radiation hardening (e. g., Seeger eta/40 and Foreman19).

The influence of the irradiation dose on the local stress-strain behavior of copper irradiated and tested at 100oC is shown in Figure 8. In the present calculations, we do not consider strain hardening by dislocation — dislocation interactions, and make no attempt to reproduce the global stress-strain curve of irradiated copper. Computed values of the flow stress are in general agreement with the experimental measure­ments of Singh et a/.38 as can be seen from Figure 9. A more precise correspondence with experimental data depends on the value of the critical interaction angle Fc, which is the only relevant adjustable param­eter in the present calculations. In Figure 8, Fc = 165°. Determination of the two adjustable parameters (Fc and B) requires atomistic computer simulations
beyond the scope of the present investigation. Addi­tional calculations for the flow stress for OFHC copper, irradiated at 47 °С and tested at 22 °С, are given in Table 1 and compared with the experimental data of Singh et a/.38 The flow stress value at a dose of 0.001 dpa has been extrapolated from the experimental results of Dai39 for single-crystal copper irradiated with 600-MeV protons. It is noted that, while the general agreement between the computer simulations and the experimental data of irradiated Cu is reason­able at both 22 and 100 °С, the dose dependence of radiation hardening indicates that some other mechan­isms may be absent from the current simulations.

Investigations of dislocation interactions with full or truncated SFTs considered by Sun et a/.37 indi­cated that local heating may be responsible for the dissolution of SFTs by interacting dislocations, and that their vacancy contents are likely to be absorbed by rapid pipe diffusion into the dislocation core. The consequence of this event is that the dislocation climbs out of its glide plane by the formation of atomic jogs, followed by subsequent glide motion of jogged dislocation segments on a neighboring plane. In Figure 10, we present results of computer simulations of this glide/climb mechanism of jogged F-R source dislocations. Figure 11 shows a side view of the glide/climb motion of a dislocation loop pileup, consisting of three successive loops, by projecting dislocation lines on the plane formed by the vectors [111] and [ТІ2]. SFTs have been removed for visualization clarity. It is noted that

for this simulated three-dislocation pileup, the first loop reaches the boundary and is held there, while the second and third loops expand on different slip planes. We assume that the simulation boundary is rigid, and no attempt is made to simulate slip trans­mission to neighboring grains. However, the force field of the first loop stops the motion of the second and third loop, even though the stress is sufficient to penetrate through the field of SFTs. This glide/ climb mechanism of jogged dislocations in a pileup can be used to explain two aspects of dislocation channel formation.

As the group of emitted dislocations expands by glide, their climb motion is clearly determined by the size of an individual SFT. For the densities consid­ered here, a climb step of nearly one atomic plane results from the destruction of a single SFT. The climb distance is computed from the number of vacancies in an SFT and the length of contacting dislocation segments. The jog height is thus variable, but is generally of atomic dimensions for the condi­tions considered here. The width of the channel is a result of two length scales: (1) the average size of an SFT (^2.5 nm); and (2) the F-R source-to-boundary distance (^1-10 pm). Secondary channels, which are activated from a primary channel (i. e., source point), and which end up in a nearby primary channel (i. e., boundary) are thinner than primary channels. Fur­ther detailed experimental observations of the chan­nel width dependencies are necessary before final conclusions can be drawn. The second aspect of experimental observations, and which can also be explained by the present mechanism, is that a small degree of hardening occurs once dislocation channels
have been formed. Dislocation-dislocation interac­tion within the noncoplanar jogged pile up requires a higher level of applied stress to propagate the pileup into neighboring grains.

While the initiation of a dislocation channel is simulated here, full evolution of the channel requires successive activation of F-R sources within the vol­ume weakened by the first F-R source, as well as forest hardening within the channels themselves. The possibility of dislocation channel initiation on the basis of the climb/glide mechanism is further investigated by computer simulation of OFHC cop­per, irradiated to 0.01 dpa and tested at 100 °C, is shown in Figure 12. Formation of clear channels is experimentally observed at this dose level (Singh eta/.38). The figure is a 3D representation for the initial stages of multiple dislocation channel for­mation. For clarity of visualization, the apparent SFT density has been reduced by a factor of 100, since the total number of SFTs in the simulation volume is 3.125 x 10[20] [21] [22] [23] [24] [25] [26] [27]. The initial dislocation den­sity is taken as p = 1013m~ . To show the impor­tance of spatial SFT density variations, a statistical spatial distribution within the simulation volume has
been introduced such that lower SFT densities are assigned near ten glide planes. All dislocation seg­ments are inactive as a result of high density of surrounding SFTs, except for those on the specified glide planes. Search for nearby SFTs is performed only close to active channel volumes, which in this case totals 174 846. It is observed that within a 5-pm volume, the number of loops within a pileup does not exceed 5. It is expected that if the pileup continues across an entire grain (size ~10 pm), a higher number of loops would be contained in a jogged dislocation pileup, and that the corresponding channel would be wider than in the present calculations. We have not attempted to initiate multiple F-R sources within the volume swept by the dislocation pileup to simu­late the full evolution of channel formation. As a result, the channel shape created by a single active F-R source is of a wedge nature. In future simula­tions, we plan to investigate the full evolution of dislocation channels.

The present investigations have shown that two possible mechanisms of dislocation unlocking have been identified: (1) an asymmetric unzipping-type instability caused by partial decoration of dislocations; (2) a fluctuation-induced morphological instability, when the dislocation line is extensively decorated by defect clusters. Estimated unlocking stress values are in general agreement with experimental observa­tions, which show a yield drop behavior. It appears that unlocking of heavily decorated dislocations will be most prevalent in areas of stress concentration (e. g., precipitate, grain boundary, triple point junc­tion, or surface irregularity). Computer simulations of the interaction between unlocked F-R sources and a 3D random field of SFTs have been used to esti­mate the magnitude of radiation hardening and to demonstrate a possible mechanism for the initiation of localized plastic flow deformation and cleared channels. Reasonable agreement with experimental hardening data has been obtained with the critical angle Fc in the limited range of 158-165°. Both the magnitude and dose dependence of the increase in flow stress by neutron irradiation at 50 and 100 °C are reasonably well predicted. In spatial regions of inter­nal high stress, or on glide planes of statistically low SFT densities, unlocked dislocation sources can expand and interact with SFTs. Dislocations drag atomic-size jogs and/or small glissile SIAs when an external stress is applied. High externally applied stress can trigger point-defect recombination within SFT volumes resulting in local high temperatures. A fraction of the vacancies contained in SFTs can
therefore be absorbed into the core of a gliding dis­location segment, producing atomic-size jogs and segment climb. The climb height is a natural length scale dictated by the near-constant size of the SFT in irradiated copper. It is shown by the present com­puter simulations that the width of a dislocation channel is on the order of 200-500 atomic planes, as observed experimentally and is a result of a stress — triggered climb/glide mechanism. The atomic details of the proposed dislocation-SFT interaction and ensuing absorption of vacancies into dislocations need further investigation by atomistic simulations. Finally, it should be pointed out that at relatively high neutron doses, dense decorations of dislocations with SIA loops and a high density of defect clusters/ loops in the matrix are most likely to occur. As shown here, these conditions can lead to the phenomena of yield drop and flow localization.