On the Plasticity of Crystals

In the following, a theory is given with the purpose of establishing a mathematical relation between the stress and the strain in a crystal when plastically deformed. The existence of a "secondary structure" in crystals is adopted as a basic hypothesis. This structure was pointed out by Professor F. Zwicky to be a consequence of what he calls "cooperative phenomena." The assumption that gliding in crystals takes place between the blocks of the secondary structure is the starting point of the following theory. The additional hypothesis of assuming a statistical distribution of the different forces which produce gliding between the blocks, gives us the means for going further in the calculations. The final result which is the stress strain curve of a crystal, is an exponential law containing three constants, i.e., the torsional modulus $G$, the elastic limit, (${\gamma }_s,{\tau }_s$) and the maximum applicable stress ${\tau }_m$. The form of the hysteresis cycles is deduced from the same considerations and moreover a formula is obtained for the areas of the cycles. Experimental verifications were made on a single crystal of copper, and also on ordinary microcrystalline copper.