The Mechanism of Plastic Deformation of Crystals. Part II. Comparison with Observations
Proceedings of the Royal Society A
Comparison with Observed Plastic Stress-strain Relationships. According to the theory given in P art I the strain-hardening or plastic stressstrain curve for a pure metal should be a parabola. In figs. 1, 2, and 3, Part I, parabolas are drawn, the parameters being chosen so that they lie as close as possible to the points which represent actual observations. It will be seen that for aluminium and gold the agreement is good. For a single crystal of copper the agreement is not good, but, on the
... good, but, on the other hand, the plastic stress-strain curve for polycrystalline specimens of copper which is shown in fig. 1 is very nearly parabolic over a large range. The observations for iron seem to show that there is a small finite elastic limit, i.e., ST may be finite. Parabolas corresponding with the existence of a small elastic limit and with no elastic limit have been drawn. It seems that the observed points lie rather closer to the former curve. In any case, the observed curves have the essential characteristic of the theoretical ones that they are very steep at small strains, but get less and less steep as the strain increases. In some branches of physics the measure of agreement between theory and observation which is shown in figs. 1, 2, and 3, Part I, would perhaps not be considered encouraging. I t must be remembered, however, that up to the present no theory of the strength of metals has been devised which is capable of being expressed in an analysable form. Also the plastic stress-strain curves of similar metals vary so much in detail that it would be impossible to devise any general theory which w^ould account so accurately for the behaviour of every metal crystal that good agreement with actual individual observations could be attained. Another difficulty is that the large changes which very small amounts of impurity can cause in the stress-strain curves make it difficult to be certain that the observed curves are really those which would be found if the test were made with a perfect crystal of a metal containing no impurities.