The strength (both yield and ultimate tensile stress) of metals/alloys increases along with appreciable reduction in ductility coupled with reduction in strain

hardening exponent. For example, strain hardening exponent of Zircaloy-2 has been found to vary between 0.1 to 0.15 in annealed condition. However, after irradiation, the exponent may decrease to 0.02 to 0.01 depending on the extent of radiation damage, thus affecting the uniform elongation of the alloy (as described in Chapter 5.1). Radiation hardening can occur due to the multitude of defect cre­ation in irradiated materials: (i) point defects (vacancies and self-interstitials), (ii) impurity atoms, (iii) small defect clusters, (iv) dislocation loops, (v) dislocation lines, (vi) cavities (voids/bubbles), and (vii) precipitates. Generally, radiation hard­ening effect starts to appear at temperatures less than <0.4Tm (where in situ recov­ery effect is less) and at radiation damage of >0.1 dpa.

Figure 6.23a-c shows tensile stress-strain curves of irradiated (increasing flu — ence) BCC-based alloy (A533B — low-alloy ferritic steel), an FCC-based alloy (316- type stainless steel), and a HCP-based alloy (zircaloy-4), respectively. Generally, FCC — and HCP-based alloys do not show discontinuous behavior in unirradiated state. However, in irradiated state they exhibit yield point-like behavior, as shown in Figure 6.23b and c.

In BCC metals where yield points appear along with Luders strain before expo­sure to high-energy radiation, Luders strain increases following irradiation and at high neutron fluxes (>1019 ncm~2) fracture occurs during Luders strain itself. Figure 6.24 depicts a series of stress-strain curves in mild steel tested at ambient temperature following neutron radiation exposures.

An actual example of the effect of neutron irradiation on tensile strength and ductility properties is shown in Figure 6.25. Here, we describe one example from

9Cr-1MoVNb steel (T91) on the radiation effect in F/M steels. Irradiation exposure dose of 9 dpa resulted in appreciable radiation hardening due to the formation of a wide range of radiation-produced defects in a temperature range of 425-450 °C (Figure 6.25a). Figure 6.25b shows the corresponding ductility as a function of test temperature. Hardening causes a decrease in ductility at the lowest temperature. However, interestingly, the ductility of the irradiated alloy increases at 450 °C com­pared to that of the aged alloy. It is interesting to note that the aged alloy shows a maximum strength at a temperature where the irradiated alloy shows much higher

ductility. However, note that the ductility data of the unirradiated alloy are not avail­able at 450 °C. Radiation hardening saturates by around 10dpa. For irradiation above 425-450 °C, there may be enhanced softening due to increased recovery and coarsening.

Understanding radiation hardening would need our understanding of the dislo­cation theories and strengthening mechanisms. First, we will discuss the two major components of radiation hardening — source hardening and friction harden­ing. As discussed in Chapter 5, yield stress (ty) can be regarded as composed of source hardening (ts) and friction hardening (т;) terms, representing the hardening due to solute atoms locking dislocation sources and due to subsequent dislocation movement through the lattice.

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Figure 6.25 Variation of (a) yield strength and (b) total elongation as a function of test temperature in aT91 steel Ref. [16].

a) Source Hardening (ts) This hardening can increase the stress required to start a dislocation moving on its glide plane. This can be found in irradiated FCC met­als, and in both unirradiated and irradiated BCC metals. In case of FCC metal — s/alloys and most HCP metals/alloys, the unirradiated materials do not show source hardening behavior. This is shown by continuous stress-strain curve without yield point phenomenon (note in Section 5.1). However, the unirradi­ated BCC metals (low-alloy ferritic steels) manifest a source hardening-like phe­nomenon that occurs due to the dislocation-interstitial impurity interaction as seen in the yield point phenomenon (Figure 6.23a). Source hardening observed in irradiated FCC metals is due to the formation of irradiation-produced defect clusters near the Frank-Read sources, consequently raising the stress (tFR = Gb/L) required to activate the loop by decreasing the pinning point dis­tance (L). However, once the loop starts forming, it sweeps away the defect clus­ters and the stress drops.

In a polycrystalline material, majority of the dislocation sources are on or near the grain boundaries and the dislocation pileups create stress concentration at the boundaries to activate dislocation sources and generate dislocations in the other grain. Basically, the Hall-Petch strengthening (fcyd~1/2) effect, discussed in Section 5.1 contributes profusely to the source hardening term in poly­crystalline materials.

b) Friction Hardening (ti) After being generated from the source, the dislocation encounters a number of obstacles that lie on the slip plane or near the slip plane while moving on it. This raises the stress needed to move dislocations on the slip plane and in aggregate is called friction hardening. Friction stress (t) consists of two components: long-range stresses (tLR) and short-range stresses (tSR):

ti = tLR + tSR, (6.3)

The long-range stresses generally arise from the repulsive interaction between a moving dislocation and the dislocation network. This effect is termed as long range as it works over a distance from the gliding dislocation (Taylor Equation).

tLR = aGbg1/2,

where gd is the dislocation density.

The short-range stresses may have two origins — athermal and thermally activated. The short-range stresses may arise out of precipitates, such as precipitate hardening in terms of Orowan bowing and particle cutting, in the presence of voids/bubbles (void hardening) and dislocation loops. One general way of expressing the short-range stresses is the summation of the contributions of precipitation hardening (tp), void hardening (tv), and loop hardening (tl):

tSR — tp + tv + tl.

If it is assumed that these obstacles are dispersed in a random fashion, it can be shown that the average interparticle spacing (l) between the defects characteristics (number density N and average diameter d) can be described as Eq. (6.6):

l = (Nd)~1/2. (6.6)

Thus, the general form of tSR can be given by

rSR = aGb(Nd)1/2. (6.7)

At a very low dose, the irradiated microstructure would contain defect clusters and small loops. With increasing dose, the loop microstructure saturates at a particular number density and size as the loops unfault and become part of the dislocation line network, thus increasing dislocation density. At higher tempera­tures, voids/bubbles would be present and irradiation-induced precipitation can also contribute to the radiation hardening effect.