Irradiation introduces obstacles to dislocation motion, which results in plastic deformation, in the form of defects resulting from atomic displacement and from transmutation products. Small Frank loops and defect clusters, known as black dots, large Frank loops (about an order of magnitude larger), precipitates, and cavities (either voids or bubbles) contribute to hardening in an irradiated alloy. Frank loops unfault and eventually contribute to the network dislocation density. Precipi­tates are certainly present in the unirradiated alloy, but additional precipitation results from the segrega­tion of elements during irradiation and from the irradiation-induced changes that shift the thermody­namic stability of phases. Transmutation production of new elements in the alloy can also result in the forma­tion of new precipitates. The production of insoluble species, most importantly helium, also results in pre­cipitation, especially in the form of bubbles.

Defects are divided into two classes: long range and short range. Short-range obstacles are defined as those that influence moving dislocations only on the same slip plane as opposed to long-range obstacles, which impede dislocation motion on slip planes not containing the obstacle.1 Coherent precipitates and large loops are long-range obstacles, but for this analysis, only network dislocations will be considered as long-range obstacles, a reasonable simplification from observations. As recommended by Bement,2 the contributions from short-range obstacles are added directly,

AFTs = DFlr + DFsr [1]

where the quantities in eqn [1] are total stress, long — range contribution to stress, and short-range contribu­tion to stress. The contributions from the short-range obstacles are added in quadrature as follows3:

(AFsr)2 = (AFSMloop)2 + (AFlgloop )2

+ (Afprecip)2 + (Afcavity)2 [2]

where the term on the left represents the contribution from all short-range obstacles, and the terms on the right represent the stress contributions from small loops, large loops, precipitates, and cavities, either voids or bubbles.

The contribution to hardening by network dislo­cations may be expressed by

Tnet a Gb / Pd [3]

where tnet is the increment in shear stress, G is the shear modulus, b is the Burgers vector, and pd is the dislocation density. The constant a is dependent upon the geometry of the dislocation configuration and is usually determined experimentally. However, Taylor has calculated a to be between 0.15 and 0.3,4 and Seeger has determined the value to be 0.2, incor­porating the assumption of a random distribution of dislocation directions.5 Short-range defects such as small and large Frank loops and precipitates are treated as hard impenetrable obstacles where disloca­tions bow around them by the Orowan mechanism. The stress increment is expressed by

At = GbJ~NdJJi [4]

where N is the defect density and d is the diameter. The constant b ranges between 2 and 4 as suggested by Bement2 or 6 as suggested by Olander.6 Voids and bubbles are also treated as hard obstacles using the same expression. Precipitates and bubbles have been observed in austenitic stainless steels to nucleate and grow together.7 In this case, the bubbles and precipi­tates are considered as one obstacle where the hard­ening increment is calculated assuming rod geometry using a treatment by Kelly expressed by8:

0.16GbvNd 6d

1 — pVNd n 3b — where the parameters are the same as for eqn [4].

From the previous discussion, it can be inferred that because the nature of the irradiation-induced defects determines the degree of hardening, and because the nature, size, and density ofdefects is a strong function of temperature, radiation strengthening will be a strong function of irradiation temperature. Figure 1 illustrates

1

Temperature (°C)

Figure 1 Relative contribution to strengthening from irradiation-induced defects in the austenitic stainless steel, PCA, irradiated to 7dpa in the Oak Ridge Research Reactor. Reproduced from Grossbeck, M. L.; Maziasz, P. J.; Rowcliffe, A. F. J. Nucl. Mater. 1992, 191-194, 808.

strengthening from individual types of defects as a function of irradiation temperature for the austenitic stainless steel PCA.7

As can be seen from Figure 1, the black dot damage characteristic of low temperatures vanishes at temperatures over 300 °C as Frank loops emerge. Bubbles and precipitates also become major contri­butors to hardening above 200 °C.