Forensic analyses of microstructure evolution of stage II & III: New assimilated model for work-hardening in FCC metals

From the beginning of crystal plasticity studies, the cause for the small percentage of expended work retained as stored work has been a quandary. From forensic analyses of plastic deformation studies, it was deduced that coplanar annihilation of dislocations occur since slip takes place in small slip-patch areas of mean slip distance squared. A simple model predicts that the athermal annihilation factor A between expended and stored energy is about 20 comparable to the observed 5% for stored work. The derived A ranged from 19 at 20 K to 25 at 300 K for copper. Using the functional constitutive relation which can replicate the stress-strain diagram, analyses invoking the imposed shear strain to assess the height between coplanar slip planes indicate that structure evolution due to monopole dislocations result in the principle of similitude. However, the break-down of this Stage II structure occurs when cross-slip and the accompanying double cross-slip is incurred resulting in increasing height between slip planes. The consequences of these bypass mechanisms are the change of the random array of dislocations to that of clustered patterns with the increase in mean slip distance leading to cell structure formation. This evolution can be examined using the shear flow stress versus the inverse mean slip distance plot. Hence the bases for decoding work-hardening of face-centred cubic metals using constitutive relations have become possible.