Donald Stone2 Jonathan Puthoff3 Thawatchai Plookphol4 Reid Cooper1

2, University of Wisconsin-Madison, Madison, Wisconsin, United States
3, California Polytechnic State University, Pomona, Pomona, California, United States
4, Prince of Songkla University, Hat Yai, , Thailand
1, Brown University, Providence, Rhode Island, United States

Hart [1] proposed the experimental requirements necessary to establish existance of a mechanical equation of state (MES) with a single internal variable. Hart and Solomon [2] demonstrated that high purity aluminum satisfies this test, at least for limited range of prior deformation and thermal history and under simple (uniaxial) loading. The same observations were later repeated for other crystalline solids including metals, covalently bonded solids, and ionic solids. Key to Hart's demonstration of an MES is the existance of a scaling relationship in which stress-strain rate curves generated from different levels of work hardening, and corresponding to different internal structures, overlap each other when translated on log(stress)-log(strain rate) graphs. Often the translation is a line of slope 1/5, although our own experiments on halite suggest 1/3 is a better fit for high temperatures, in the regime where power-law creep dominates. Furthermore, in the constructed master curves the flow stress, σ, appears to approach a high strain rate limit, σ*, following an exponential form as a function of strain rate that was later called the "Lambda Law."

Here, we discuss how the lambda law can be explained in terms of the statistics of dislocation avalanches, which grow toward a percolation threshold as the stress approaches σ*. Meanwhile, dislocation bursts are coupled with dislocation climb and recovery elsewhere inside the greater dislocation network. Analysis of the coupled process suggests that (strain rate) = k(σ*/σ-1)-(1/λ) where λ≈0.15, and in which the constant of proportionality, k, scales in proportion to (σ*)5 at intermediate homologous temperature and (σ*)3 at high homologous temperature. We provide examples of other materials that behave this way, and we show in experiments on halite how the constant structure load relaxation curves are related to steady state creep.

This research was supported by the National Science Foundation Grant EAR-1620474
[1] Hart, E. W. (1970). A phenomenological theory for plastic deformation of polycrystalline metals. Acta Metall., 18(6), 599–610.
[2] Hart, E. W., & Solomon, H. D. (1973). Load relaxation studies of polycrystalline high purity aluminium. Acta Metallurgica, 21(3), 295–307.