Theoretical value of the ratio ( K ) of cell diameter to dislocation spacing for a material undergoing dislocation-creep

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Abstract
In many materials undergoing dislocation-creep the dislocations arrange themselves into cells. In the walls of the cells the dislocation density is high whilst within the cell interiors there are very few dislocations. In a previous paper a creep equation was arrived at for specimens exhibiting such structures. It contained a parameter K whose value was arrived at by reference to values that have been measured in experiments. K is the ratio of the cell diameter to the mean (smeared) dislocation spacing. In the present work a theoretical value of K is derived by means of a thermo-dynamic argument. The experimental values of K are typically of order 10. It is shown that such values correspond to a minimum in the free energy of the creeping specimen. In calculating the free energy two components are added together. One is the energy of the dislocations. The other component is the viscoelastic energy stored in the specimen as a result of the recoverable component of strain produced by the applied stress.

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