According to the discussion above, the yield strength increase should be propor­tional to N1/2. In the absence of annihilation mechanisms of obstacles, N is propor­tional to fluence and thus radiation hardening should be proportional to (Wt)1/2. But this is not the case in reality. It has been shown that the radiation hardening does not increase with neutron fluence indefinitely, but seems to saturate as shown in Figure 6.26.

Makin and Minter [23] postulated a theory to explain the observation. According to their model, as the defect concentration increases, it becomes harder to form

new zones because of the reduced volume available for new zone formation. The time rate change of the zone density (N) is given by

dNr = zXsW(1 — VN), (6.8)

where f is the number of zones created per neutron collision (~1), Ss is the macro­scopic scattering cross section, and ф is the fast neutron flux. The term in parenthe­ses represents the fraction of solid volume available for creation of new zones. Radiation saturation takes place because of the dynamic balance reached between creation and annihilation of obstacles.

Studies on mild steel by Murty and Oh [25] revealed that the yield stress increases with fluence raised to 1/3 rather than 1/2; Luders strain also increased correspond­ingly as (ф4)1/3 as expected since in mild steel the Luders strain is proportional to the yield stress (Figure 6.27). They analyzed the results to determine the effect of neutron radiation fluence on friction and source hardening terms and demon­strated that while friction hardening (т;) increases as (ф4)1/2, the source hardening (ts) decreases (Figure 6.28), so the yield stress increases with fluence raised to a power less than 0.5.