A state variable description of mechanical properties

--A state variable approach based on Hart’s [1] formulation for describing nonelastic deformation of crystalline solids is reviewed. It is shown to describe commonly observed deformation phenomena, such as creep. Presently, deformation phenomena such as inhomogeneous flow and those involving strong dislocation-solute interactions are not within the scope of this approach. Revue Phys. Appl. 23 (1988) 639-647 AVRIL 1988, Classification Physics Abstracts 81.40L 62.20F 62.20H 62.205 61.70L The nonelastic properties of a crystalline solid depend upon prior deformation and thermal history. To fully account for the history effects can be a cumbersome task in stress analysis and mechanical testing. If the deformation properties can be demonstrated to be uniquely characterized by state variables, and if the manner in which the properties evolve along an arbitrary thermal or mechanical path can be shown to depend upon the state variables as well, time dependent stress analysis and materials testing can be greatly simplified. The appropriate state variables are not easily identified based solely on theoretical arguments. The experimental effort required to establish them can also be difficult. In part this is because a variety of mechanisms contribute to nonelastic deformation, and the delineation of these mechanisms requires extensive experimental effort. For example, the separation of the grain boundary sliding contribution from grain matrix deformation during creep at elevated temperatures is an important but difficult task. This paper reviews a phenomenological approach, originally proposed by E.W. Hart designed to establish state variable flow relationships based on direct experimental measurements without first resorting to a microscopic t"heory of deformation [1]. Many of the state variables involved in this approach have been given physical significance, but no general theory based on microscopic processes has been developed. REVUE DE PHYSIQUE APPLIQUÉE. T. 23, N° 4, AVRIL 1988 The existence of state variables characterizing the structural state of a material is a fundamental basis of Hart’s formulation. In this approach the load relaxation test has been used extensively to determine flow relations at a constant (or nearly constant) structure. It has been found that the logarithmic plots of stress versus strain rate, obtained from load relaxation tests of specimens with different degrees of workhardening, can be translated along a linear path to overlap each other. This is the so-called scaling relationship, not hitherto predicted by dislocation based theories [1]. Mathematically it means that the plots belong to a one-parameter family of curves, a concept first proposed by E.W. Hart. This parameter is called the hardness, a*, and is a state variable. It is uniquely defined by the current value of stress, strain rate, and temperature, which are other state variables. In practice, it is not only important to know the existence of a*, but also to be able to experimentally measure this parameter. In contrast, often-used flow laws relating minimum creep rate to applied stress are obtained experimentally without the assurance that the stress dependence of the creep rate corresponds to that of a constant structural state. In fact, such a correspondence is highly unlikely. To interpret the minimum creep rate data additional information on the structural state of the material and its variation during creep are required. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:01988002304063900