Application of analytical techniques to stress relaxation experiments in commercial zinc
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I.
INTRODUCTION
THE primary
focal point in the study of the mechanical properties of materials is understanding the relation between stress and strain at various rates of deformation, temperatures, internal structures, e t c . , IL2} and stress relaxation experiments have contributed greatly to this understanding3 L4,51 The principal advantage of a stress relaxation test is that it scans a broad range of strain rates while straining the specimen by only a small amount. Therefore, it is usual, and at low homologous temperature seems reasonable, to assume that the substructure of the material remains approximately constant during the test. Thus, the stress is obtained as a function of the strain rate at constant structure, t3'61 T w o of the most common stress relaxation methods used are the continuous relaxation of Gupta and Li TM and the incremental unloading technique of Gibbs. t81 The stress relaxation technique would be very useful hut, as indicated by Guiu [91 and Reed-Hill e t a l . , ~51 the relaxation inherent in a tensile testing machine can be large enough to influence the tests. Most of the stress relaxation tests that have been reported in the scientific literature were conducted using screw-driven testing machines. I3-~2~ These machines deform significantly under load, leading to difficulties concerning the effects of the machines on test results. The main problem is that the deformation of the machine has a nonelastic component that has not been quantitatively related to any test variables, t7,~3] Nonelastic means deformation that depends not only on load but also on time, which is usually called the "relaxation" of the machine. There are two solutions to this problem. One is to employ a so-called closedloop testing machine which does not have a nonelastic response component, It4'151 The other is to measure the actual change of strain in the specimen as a function of time during the relaxation, i~Sl RICARDO ENRIQUE MEDRANO, Professor, is with the Instituto de Fisica, UNICAMP, Campinas, SP, Brazil. PETER P. GILLIS, Professor, is with the Department of Materials Science and Engineering, University of Kentucky, Lexington, KY 40506-0046. Manuscript submitted February 8, 1991. METALLURGICAL TRANSACTIONS A
The objective of many researchers is to find a mechanical equation of the state for plastic deformation, in which stress is related to deformation variables, without any explicit dependence upon time. Changes in substructure can only be obtained by a change in strain, but this variable is not a proper state variable, because the stress depends on previous deformation history. Hart [61 and Hart and Solomon 116Jmade a phenomenological description of the plastic deformation of materials through a state equation. Hart showed that it was possible to replace the prior deformation history of the material by a knowledge of its current structure, which was presumed to be a measurable quantity. Using this approach, the behavior of the material can be predicted from its current defect structure without any knowle
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