Observaciones

A mapping of obstacle strength of defects based on results obtained in past stud- ies is depicted in fig. 7.1, which shows a comparison of_τc obtained under the same

simulation conditions (T=300 K, ˙=10×106s−1) for interaction of a 1/2[111](1¯10) edge dislocation with a row of obstacles consisting of either100or 1/2111in- terstitial dislocation loops or spherical voids, with periodic spacing L=41 nm. All simulations but one used the A04 IAP (37 SIAs 1/2[1¯11] loop used A97, as indicated in the figure). The 100 loops are those treated in chapter 6 of this thesis, obtained by Dr. D. Terentyev. As shown in table 6.3, _τc obtained for

most of these loops was similar to that of loops reproduced by the A97 potential. This will be more explicitly demonstrated in figure 7.2, below. The results for 1/2111 loops are taken from [140], for loops placed initially about 5 nm below the dislocation glide plane withb equal to either 1/2[1¯11] or 1/2[¯111]. The voids were placed with their equators coinciding with the dislocation glide plane (cor- responding to what was referred to as configuration 0 in chapter 5, as indicated in the figure) [115].

The range of_τc values for the loops withb=100is large. Those withb=[001]

proved to be the strongest obstacles, irrespective of the directions of the loop sides (in figure 7.1 loops with sides along 110 directions are marked as squares with white interior, in contrast to those with sides lying along 100 directions marked as squares with green interior). Among the inclined loops with b=[100] or [010], configurations C4 and C5 with 100 sides are relatively strong, but C2 and C3 with 110 sides are the weakest of all. Of the four orientations of loops with b=1/2111, those with b inclined to the (1¯10) glide plane, i.e. 1/2[1¯11 or 1/2[¯111], are relatively strong obstacles. The void of 169 vacancies is a weaker obstacle than the 1/2111loops and some of the100loops containing the same number of SIAs.

Obstacle size dependence of _τc is also presented in figure 7.1 for 1/2[1¯11] SIA

loops and voids, at the same temperature. The number of point defects in each obstacle is indicated against the data points. The size-range for loops is between 1.6 and 4.9 nm (37-361 SIAs) and for voids between 1.0 and 2.0 nm (59-339 vacancies). A strong size dependence of obstacle strength of 1/2[111] loops is clear from the figure. In contrast, void obstacle strength has a much weaker

Figure 7.1: Comparison of τc for the 100 loops, 1/2111 loops and voids obtained

with the A04 potential under the same simulation conditions. The number of SIAs in the 1/2111 loops and vacancies in the voids are indicated against the data points. Also depicted are continuum modelling results. Reproduced from Terentyevet al. [99].

variation with number of vacancies (a result commented on in chapter 5). Figure 7.1 also presents continuum modelling results represented by the pur- ple triangles. For these, the obstacle diameter, D, that appears in equation (7) of [35], has been calculated for a loop or spherical void that contains 169 SIAs or vacancies, respectively. Continuum modelling with dislocation self-stress in- cluded has shown that for ‘strong’ obstacles, the edge dislocation bows out so that its branches at the obstacle form a screw dipole, i.e. they adopt the shape associated with the Orowan process for impenetrable obstacles and the critical stress corresponds to that to draw out the dipole. Indeed, _τc values obtained for

100loops, 1/2111loops and voids are 266, 239 and 207 MPa, respectively, sig- nificantly higher than atomistic results for defects of the same size. This happens because the continuum approximation mimics a crystal atT=0 K, i.e. no kinetic effects are considered. An almost screw-dipole configuration was obtained for all the defects that were strong obstacles, such as C1, C4, C6D, C6, resembling

Figure 7.2: Comparison of τc for the 100 loops, 1/2111 loop, voids and Cu-

precipitates obtained with the A97 potential under the same simulation conditions.

the continuum results. However, temperature (and possibly applied strain rate) affected the dislocation release mechanism and dislocation breakaway occurred before a stable dipole was drawn out, thus reducing the value of_τc. More details

on the continuum approximation results can be found in [99].

Results obtained within the framework of research presented in this thesis are compared in figure 7.2. The simulation conditions are as similar to the ones in fig. 7.1 as possible, to assist comparison. The potential used was A97, the tem- perature was 300 K and the strain rate the highest available from the simulations run (5 or 10×106 s−1). On the left-hand side of this figure, there are data for 100 loops, as presented in section 6.3. Next, one configuration was selected from section 6.2: the one run at 300 K under applied strain rate of 10×106 s−1. One set of results for all configurations of voids and precipitates is shown in the right-hand side, simulated at strain rate of 5×106 s−1. Small and big circles in the figure represent 2 and 4 nm defects, respectively.

Once again, like the results presented in the previous figure, configuration C1 of the 100 loops is the strongest obstacle, followed by configuration 0 of voids

4 nm in diameter. The range of values of_τc for the 100 loops is similar to the

ones for the A04 potential. So is the order of obstacle strength, with the obvious exception of configuration C4 which is a very weak obstacle for the A97 potential unlike the case of A04. The 1/2[1¯11] SIA loop is a stronger obstacle for A97 than for A04 (200 MPa compared to 170 MPa). In contrast, configuration 0 for the 339 vacancy void for A97 is a slightly weaker obstacle than that of A04 (156 MPa compared to 164 MPa).

It is clear from both figures 7.1 and 7.2 that the size-dependence of the strength of the loops, voids and precipitates is different. The loops withb=1/2[1¯11] exhibit a 10-fold increase in _τc as the number of interstitials increases from 37 to 331,

i.e. as the diameter changes from 1.6 to 4.9 nm. This stems from the fact that, as mentioned in chapter 6, bL of small loops is spontaneously transformed by

reaction with a gliding dislocation to 1/2[111] and so they are readily absorbed on it as a pair of superjogs. When large loops react with a gliding dislocation, a segment on the line with bL=[010] is formed, which is sessile on the (1¯10) plane

and stalls the dislocation motion, which manages to break away either by glide of the [010] segment over the loop surface or by cross-slip of the screw side-arms created on the dislocation line (or by a combination of both mechanisms). Hence, large loops are strong obstacles.

No data is available within this study about the size dependence of obstacle strength of 100 SIA loops. Since the mechanisms of their interaction with a gliding edge dislocation are similar to those of 111 loops, though, a similar dependence on size is expected.

Voids have a smaller dependence on size, as mentioned in section 5.3, since the mechanism of edge dislocation cutting and unpinning is not dependent on diameter. Precipitate obstacle strength increases more rapidly with increasing diameter, due to the fact that precipitates are weak obstacles in the first place, and that, in the diameter range studied, the extra mechanism of the bcc-to-fcc transition occurred only for the big precipitates, increasing their strength.