Accession Number : AD0011838
Title : EXPERIMENTAL EVIDENCE OF NON-LINEARITY IN PLASTIC STRESS-STRAIN RELATIONS. PART 1. THEORETICAL CONSIDERATIONS. PART 2. EXPERIMENTAL EVIDENCE
Descriptive Note : Technical rept.
Corporate Author : BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
Personal Author(s) : Stockton, F D
Report Date : May 1953
Pagination or Media Count : 59
Abstract : The mathematical theory of stress-strain laws of plasticity is discussed for elastic-plastic materials whose properties are independent of time and temperature effects. The material is assumed to be work-hardening in the sense of Drucker (Qaurt. Appl. Math. 1:411-418, 1950). The most general stress- strain law is described as a functional relation between (1) the components of delta ij and epsilon ij and (2) the entire stress and strain history. The only restrictions are those implied by : (1) positive work being done by the external agency B during the application of the Delta delta to the power of B subscript ij; (2) positive work being done by the external agency B over the entire cycle if plastic deformations have occurred; and (3) zero work being done by B for purely elastic strains. This is considered to be unsatisfactory from the engineering viewpoint, and the problem of determining the stress-strain law for a given material is made more useful by assuming the existence of a loading function. A variety of loading functions are discussed, as well as Prager's criteria (J. Appl. Phys. 20:235-241, 1949) which a useful mathematical stress- strain relation should satisfy. Experimental data for 2 Al-alloy thin-walled tubes were compared with the implications of linearity for the incremental theories of plasticity for work-hardening materials. The linearity assumption was considered to be justified for 1 tube, but not for the other. The second tube possessed a definite corner.
Descriptors : *PLASTIC DEFORMATION , *STRESS STRAIN RELATIONS , TIME DEPENDENCE , THEORY , ELASTIC PROPERTIES , PLASTIC PROPERTIES , FUNCTIONS , EXPERIMENTAL DATA
Subject Categories : Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE