A critical examination of the long-range stress theory of work-hardening

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Abstract
The stress distributions from piled up groups of discrete dislocations in various configurations are evaluated. It turns out that the back stress from the pile-ups is considerably smaller than had been inferred previously using the continuum approximation. The new calculations are used to assess how far Seeger's model could explain the experimental results on work-hardening and the slip line lengths in stage II of the work-hardening curve. It is concluded that if Seeger's general interpretation of the parameter β in the theory is retained, the back stress can account at most for about 55% of the flow stress, and is more likely to contribute rather less. A larger contribution is possible only if the parameter β is reinterpreted so as to allow the dislocations to be more concentrated at the tips of the slip lines if all the dislocation pile-ups were to occur in the configurations most effective as obstacles, the back stress could contribute as much as 70% of the flow stress, but if other less effective configurations were equally probable, the contribution would be unlikely to exceed about 59% for the types of arrangements observed by electron microscopy the contribution would be even smaller. It is concluded that even if the back stress from primary pile-ups contributes appreciably to the flow stress, another hardening mechanism is essential to explain the experimental work-hardening rates and slip line lengths, and is likely to contribute 50% or more to the flow stress.

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