In contrast to the T= 0 K simulations above, mod­eling by MD provides the ability to investigate temperature effects in dislocation-obstacle interac­tion. (The limit on simulation time discussed in

Section 1.12.3.3 prevents study of the creep regime controlled by dislocation climb.) Results on the tem­perature dependence of tc from simulation of inter­action between an edge dislocation and 2 and 6nm voids in Fe,29’30’34 Cu-precipitates in Fe,27,29 and voids in Cu30’34 are presented in Figure 8. In general, the strength of all the obstacles becomes weaker with increasing temperature, although the mechanisms involved are not the same for the different obstacles. The temperature-dependence of void strengthening in Fe has been analyzed by Monnet et a/.44 using a mesoscale thermodynamic treatment of MD data in the point obstacle approximation to estimate activa­tion energy and its temperature dependence. In this way, the obstacle strength found by atomic-scale mod­eling can be converted into a mesoscale parameter to be used in higher level modeling in the multiscale framework. More investigations are required to define mesoscale parameters for more complicated cases such as voids in Cu and Cu-precipitates in Fe. Void strengthening in Cu exhibits specific behavior in which the temperature-dependence is strong at low T< 100 K but rather weak at higher T (for more details see Figure 8 in Osetsky and Bacon34). The reason for this is as yet unclear.

Interestingly, MD simulation has been able to shed light on thermal effects in strengthening due to Cu-precipitates in Fe, as in Figure 8 (for more details see Figure 5 in Bacon and Osetsky2 ). Small precipitates, D < 3 nm, are stabilized in the bcc coherent state by the Fe matrix, as noted above

for T= 0 K, and are weak, shearable obstacles. The resulting temperature-dependence of tc is small.

Larger precipitates were seen to be unstable at T= 0 K with respect to a dislocation-induced trans­formation toward the fcc structure. This transforma­tion is driven by the difference in potential energy of bcc and fcc Cu. The free energy difference between these two phases of Cu decreases with increasing T until a temperature is reached at which the transfor­mation does not occur. Thus, large precipitates are strong obstacles at low T and weak ones at high T. This is reflected in the strong dependence of tc on T shown in Figure 8. More explanation of this effect can be found in Bacon and Osetsky.23 These simula­tion results showing the different behavior of small and large Cu-precipitates suggest that the yield stress of underaged or neutron-irradiated Fe-Cu alloys, which contain small, coherent Cu-precipitates, should have a weak T-dependence, whereas that in an over­aged or electron-irradiated alloy, in which the popu­lation ofcoherent precipitates has a larger size, should be stronger. Some experimental observations support this.45 One is a weak change in the temperature dependence of radiation-induced precipitate harden­ing in ferritic alloys observed after neutron irradiation when only small (<2 nm) precipitates are formed. The other is the experimentally-observed temperature and size dependence of deformation-induced trans­formation of Cu-precipitates in Fe.46

Other obstacles with inclusion properties, such as gas-filled bubbles and other types of precipitates, have been studied less intensively, and we present just a few examples here.

The effect of chromium precipitates on edge dislocation motion in matrices of either pure Fe or Fe-10at.% Cr solid solution was studied by Terentyev et a/47 Cr and Cr-rich precipitates have the bcc structure and are coherent with the matrix. Unlike Cu-precipitates in Fe, G of Cr is higher than that of both matrices and so the dislocation is repelled by Cr precipitates. Under increasing strain, the dislocation moves until it reaches the precipitate- matrix interface where it stops until the stress reaches the maximum, tc, just before the dislocation enters the precipitate (see Figure 2 in Terentyev et a/.47). The t versus e behavior is similar to that for voids in Cu, but without stress drops associated with partial disloca­tions, and no softening effects similar to voids and Cu — precipitates in Fe were observed. At tc, the dislocation shears the obstacle without acquiring a double jog. Only 2.8 and 3.5 nm precipitates in the size range D = 0.6-3.5 nm had tc comparable with values given by eqn [2] (see Figure 4 in Terentyev et al47); the others were much weaker. Separate contributions from the chemical strengthening (CS) and shear mod­ulus difference (SMD) between Fe and Cr were esti­mated and their sum was found to be close to the tc found in simulation. It was also found that tc for the alloy with Cr precipitates in an Fe-Cr solid solution is the sum of tc for the same precipitate in a pure Fe matrix and the maximum stress for glide of the dislo­cation motion in the Fe-Cr solid solution alone.

Helium-filled bubbles created by vacancies and helium formed in transmutation reactions are com­mon features of the irradiated microstructure of structural materials (see Chapter 1.13, Radiation Damage Theory). However, there is a lack of infor­mation on the properties of He bubbles and their contribution to changes in mechanical properties. The main problem is the uncertainty regarding the equilibrium state of bubbles of different sizes and at different temperatures, that is, their He-to-vacancy ratio (He/Vac). A small (0.5 M-atom) model was used48-50 to simulate interaction between an edge dislocation and a row of 2 nm cavities with He/Vac ratios of up to 5 in Fe at T between 10 and 700 K. It was found that tc has a nonmonotonic dependence on the He/Vac ratio, dislocation climb increases with this ratio, and interstitial defects are formed in the vicinity of the bubble. Recent work to clarify the equation of state of bubbles using a new Fe-He three-body interaction potential51 has shown that the equilibrium concentration of He is much lower than expected; for example the He/Vac ratio is ^0.5 for a 2 nm bubble at 300 K in Fe.52 Simulation of an edge dislocation interacting with 2 nm bubbles using the new potential for He/Vac ratio in the range 0.2-2 and T between 100 and 600 K has now been per- formed53 and preliminary conclusions drawn. The dislocation interaction with underpressurized bub­bles (He/Vac < 0.5) is similar to that with voids described above, that is, the dislocation climbs up by absorbing some vacancies on breakaway and tc increases with increasing values of He/Vac ratio up to 0.5. The interaction with overpressurized bubbles (He/Vac > 0.5) is different. The dislocation climbs down and tc decreases with increasing value of He/Vac ratio. At the highest ratio, the dislocation stress field induces the bubble to emit interstitial Fe atoms from its surface into the matrix toward the dislocation before it makes contact. The bubble pres­sure is reduced in this way and interstitials are absorbed by the dislocation as a double superjog. Equi­librium bubbles are therefore the strongest. Some of these conclusions, such as formation of interstitial clusters around bubbles with high He/Vac ratios, are similar to those observed earlier,48-50 others are not. More modeling is necessary to clarify these issues.

As noted in Section 1.12.2.2, impenetrable obsta­cles such as oxide particles and incoherent pre­cipitates represent another class of inclusion-like features. Although these obstacles are usually preex­isting and not produced by irradiation, they are con­sidered to be of potential importance for the design of nuclear energy structural materials and should be considered here. Atomic-level information on their effect on dislocations is still poor, however, and we can only refer to some recent work on this. The interaction between an edge dislocation and a rigid, impenetrable particle in Cu was simulated by Hatano54 using the Cu-Cu IAP as for the Fe-Cu system36 and a constant strain rate of 7 x 106s-1 at T = 300 K. The particle was created by defining a spherical region in which the atoms were held immo­bile relative to the surrounding crystal. The Hirsch mechanism2 was found to operate. In the sequence shown in Figures 1 and 2 of Hatano,54 several stages can be observed such as (1) the dislocation under stress approaching the obstacle from the left first bows round the obstacle to form a screw dipole; (2) the screw segments cross-slip on inclined {111} planes at tc; (3) they annihilate by double cross-slip, allowing the dislocation, now with a double superjog, to bypass the obstacle; (4) a prismatic loop with the same b is left behind and (5) the dragged superjogs pinch-off as the dislocation glides away, creating a loop of opposite sign to the first on the right of the obstacle. tc varies with D and L as predicted by the continuum modeling that led to eqn [1], but is over 3 times larger in magnitude. Hatano argues that this could arise from either higher stiffness of a dissociated dislocation or a dependence of tc on the initial posi­tion of the dislocation. It is also possible that the requirement for the dislocation to constrict and the absence of a component of applied stress on the cross­slip plane results in a high value of tc.

Simulation of 2 nm impenetrable precipitates in Fe has been carried out by Osetsky (2009, unpub­lished). The method is different from that used by Hatano54 in that the precipitate, constructed from Fe atoms held immobile relative to each other, was trea­ted as a superparticle moving according to the total force on precipitate atoms from matrix atoms. The interaction mechanism observed is quite different from those reported earlier for Cu,54 for the Hirsch mechanism and formation of interstitial clusters does

not occur. Instead, the mechanism observed was close to the Orowan process, with formation of an Orowan loop that either shrinks quickly if the obstacle is small and spherical, or remains around it if D is large (>4nm) or becomes elongated in the direction per­pendicular to the slip plane. It is interesting to note that if the model of a completely immobile precipi­tate in Hatano54 is applied to Fe, the same Hirsh mechanism is observed as that in the earlier study.

Comparison of strengthening due to pinning of a 1/2(111}{110} edge dislocation by 2 nm spherical obstacles of different nature simulated at 300 K is presented in Figure 9. One can see that the coherent Cu precipitate is the weakest whereas a rigid impen­etrable precipitate when Orowan loop is stabilized by its shape is the strongest. A surprising result is that an equilibrium He-bubble is a stronger obstacle than the equivalent void. The reason for this is not clear yet.

Little is known on the interactions between screw dislocations and inclusion-like obstacles. In fact, we are aware of only one published study of screw dislocation-void interaction in fcc Cu.55 It was found that voids are quite strong obstacles and their strength and interaction mechanisms are strongly temperature dependent. Thus at low temperature, the 1/2(110) {111} screw dislocation keeps its original slip plane

when it breaks away from the void. However, at high T> 300 K, cross-slip is activated and plays an im­portant role in dislocation-void interaction. Several depinning mechanisms involving dislocation cross­slip on the void surface were simulated and formation of DLs was observed in some cases. Interestingly, the void strength increases with increasing temperature and the authors explain this by changing interaction mechanisms. Intensive cross-slip was observed54 that propagated through the periodic boundaries along the dislocation line direction, with the result that the void was interacting with its images. Similar effects have been observed in the interaction of a screw dislocation and SIA loops and SFTs, and the possible significance of this for understanding the simulation results has been discussed elsewhere.4