Radiation interaction with materials results in the production oflattice defects. The motion and interac­tion between radiation-induced lattice defects among
themselves and the existing microstructure have direct consequences to the macroscopic response of the material to the radiation environment. We present in this section several applications of computational DD to modeling of radiation-induced defects and their effects on mechanical properties.

1.16.3.1 Dislocation Interaction with Radiation-Induced Defects

Using an infinitesimal loop approximation, Kroupa found the stress tensor of a prismatic loop to be of the form s j = kjm bR2/2p, where kjis an orientation factor of order unity, R is the loop radius, and p the distance from the loop center. The total force and its moment on an SIA cluster can be expressed respectively as

Fi = — nj Ojk, ib’k dA

Mi Eijknj bisikdA

where nl, b’k, dA1 refer to the Cartesian components of the normal vector, the Burgers vector, and the habit plane area of the cluster, respectively. As a mobile SIA dislocation loop moves closer to the core of the slip loop, the turning moment on its habit plane increases. When the mechanical work of rotation exceeds a criti­cal value of ~0.1 eV per crowdion, we assume that the cluster changes its Burgers vector and habit plane, and moves to be absorbed into the dislocation core. Thus, the mechanical work for cluster rotation is equated to a critical value (i. e., dW = Jy2 Mddj = A Uerit) and used as a criterion to establish the stand-off distance.35

The two main aspects of dislocation interaction with defect clusters that affect both hardening and ensuing plastic flow localization are (1) dislocation unlocking from defect cluster atmospheres; and (2) destruction of SFTs on nearby slip planes by gliding dislocations. The interaction between grown-in dislo­cations and trapped defect clusters has been shown to lead to unfaulting of vacancy clusters in the form of vacancy loops. It can also result in rotation of the habit plane of mobile SIA clusters. Once either of these possibilities is realized for a vacancy or SIA cluster, it is readily absorbed into the dislocation core. Ghoniem etal3 used these conditions to determine an appropri­ate stand-off distance from the dislocation core, which is free of irradiation-induced defect clusters. It is esti­mated that clusters within a distance of 3-9 nm from the dislocation core in Cu will be absorbed, either by rotation of their Burgers vector or by unfaulting. We will use this estimate as a guide to calculations of long-range interactions of dislocations with sessile
prismatic SIA clusters situated outside the stand-off distance. While the experimentally observed average SFT size is 2.5 nm for oxygen free high conductivity (OFHC) copper, the radius of a sessile interstitial clus­ter, which results from coalescence of smaller mobile clusters, is assumed to be in the range ^4—20 nm. The local density of interstitial defect clusters at the stand­off distance is taken to be in the range 0.6-4 x 1024 m~3, giving an average intercluster spacing of ~18-35й. In subsequent computer simulations, we use the fol­lowing set of material data for Cu: lattice constant a = 0.3615nm, shear modulus m = 45.5 GPa, Poisson’s ratio n = 0.35, and F-R source length L = 1500-2000a.

Consider now the more complex interaction between an expanding Frank-Read (F—R) dislocation source, and the full field of multiple sessile SIA clusters (loops) present in a region of decoration. As the F—R source expands in the elastic field of SIA clusters, each point on the dislocation line will experience a resistive (or attractive) force, which must be overcome for the dislocation to move further. The dislocation line curvature and, hence, the local self-force also change dynamically. To determine the magnitude of collective cluster resistance, systematic calculations for the dynamics of interaction between

SIA clusters are presented (Figure 3). When the SIA clusters are all attractive, the dislocation line is imme­diately pulled into their atmosphere, but as the applied stress is increased, the dislocation remains trapped by the force field of SIA clusters. When the stress is increased to 200 MPa, the line develops an asymmetric configuration as a result of its Burgers vector orienta­tion, and an unzipping instability eventually unlocks the F—R source from the collective cluster atmosphere. This asymmetric unlocking mode is characteristic of a high linear cluster density on smaller sections of the F—R source decoration, where the linear density of SIA clusters is 50 (cluster/lattice constant).

Figure 3 shows the detailed dynamics of the col­lective cluster interaction with an expanding F—R source. A fluctuation in the line shape is amplified by the combined effects of the applied and self-forces on the middle section of the F—R source, and the disloca­tion succeeds in penetrating through the collective cluster field at a critical tensile stress of s11 = 180 MPa (or equivalently at CRSS of t/m = 0.0015). The critical shear stress (in units of the shear modulus) to unlock the F—R source is shown in Figure 4 as a function of the stand-off distance for a fixed intercluster dis­tance of 50a. The results of current calculations are

compared with the analytical estimates of Trinkaus eta/.23 For larger stand-off distances, the current results show a larger critical stress as compared to the analyti­cal estimates, while for stand-offdistances smaller than ^60a, a smaller critical stress is required to unlock the F—R source. When the stand-off distance is large, the applied stress must overcome the self-force, which results from the finite length of the F—R source, in addition to the collective cluster elastic field. At smaller stand-off distances, however, the dislocation easily unlocks by one of the two unzipping instability modes discussed earlier, and the predicted CRSS is smaller than analytical estimates. At intercluster dis­tances smaller than 70a, the dislocation shape instabil­ity results in a CRSS value that is smaller than the corresponding analytical result. It is estimated that the required CRSS is ^0.001m (^50 MPa for copper), for an average intercluster distance of / ~ 50a, and a stand­off distance of ^40a. It is experimentally difficult to determine the local value of / in the decoration region of dislocations, which is likely to vary considerably, depending on the character of the dislocation Burgers vector. However, /~ 50a is an upper bound, while /~ 20-30a is more likely. Since the CRSS is roughly inversely proportional to /, the most likely value of the CRSS to unlock dislocations and start the operation of F—R sources would be TcRss ^100-150 MPa. Depend­ing on the local value of the Schmidt factor, the corresponding uniaxial applied stress is thus likely to be on the order of 200-300 MPa, under conditions of heavy decoration (i. e., at a displacement damage dose of >0.1 dpa).

The current estimates for the unlocking stress are thus consistent with the experimental data, and indi­cate that the operation of F-R sources from deco­rated dislocations can be initiated by one (or both) of the following possibilities:

1. Activated F-R sources are decorated with a statis­tically low linear defect cluster density;

2. Dislocation sources are initiated at stress singula­rities in regions of internal stress concentration.