Unified Constitutive Equations for Creep and Plasticity

herausgegeben von: Alan K. Miller

Verlag: Springer Netherlands

Enthalten in: Professional Book Archive

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Constitutive equations refer to 'the equations that constitute the material response' at any point within an object. They are one of the ingredients necessary to predict the deformation and fracture response of solid bodies (among other ingredients such as the equations of equilibrium and compatibility and mathematical descriptions of the configuration and loading history). These ingredients are generally combined together in complicated computer programs, such as finite element analyses, which serve to both codify the pertinent knowledge and to provide convenient tools for making predictions of peak stresses, plastic strain ranges, crack growth rates, and other quantities of interest. Such predictions fall largely into two classes: structural analysis and manufacturing analysis. In the first category, the usual purpose is life prediction, for assessment of safety, reliability, durability, and/or operational strategies. Some high-technology systems limited by mechanical behavior, and therefore requiring accurate life assess ments, include rocket engines (the space-shuttle main engine being a prominent example), piping and pressure vessels in nuclear and non-nuclear power plants (for example, heat exchanger tubes in solar central receivers and reformer tubes in high-temperature gas-cooled reactors used for process heat applications), and the ubiquitous example of the jet engine turbine blade. In structural analysis, one is sometimes concerned with predicting distortion per se, but more often, one is concerned with predicting fracture; in these cases the informa tion about deformation is an intermediate result en route to the final goal of a life prediction.

Inhaltsverzeichnis

Frontmatter

1. Constitutive Behavior Based on Crystal Plasticity

Abstract

Constitutive equations are the vehicle by which our knowledge of material behavior enters into engineering design. At the very least, they should be sufficiently accurate. This could be—and frequently is—achieved by an empirical description based on data obtained under conditions that essentially duplicate those of the specific application. Of more general usefulness are relations that can be applied under a wide range of conditions and for many materials, containing a number of materials parameters (the fewer the better), which can be measured in simple tests. Such general relations can be expected to be found only if they fulfill two conditions: they must be phenomenologically sound; and they should be based on as much of the underlying physics as can be ascertained with some confidence. The closer the phenomenological description reflects the actual physical processes involved, the further it can be extrapolated beyond the range of variables for which it was measured.

U. F. Kocks

2. State Variable Theories Based on Hart’s Formulation

Abstract

Constitutive equations based on state variables are very attractive in stress analysis because of their ability to characterize the consequences of mechanical history by current values of state variables. By virtue of this a state variable theory can organize and rationalize a wealth of accumulated data, and the ensuing economy in thought will automatically lead to economy in experiment.¹ Moreover, with the aid of state equations, material behavior under difficult or even unmanageable conditions may be predicted by more readily performable tests; for example, long-term creep behavior at high temperatures might be estimated based on combined short-term tensile and relaxation testing at a lower temperature.

M. A. Korhonen, S.-P. Hannula, Che-Yu Li

3. The MATMOD Equations

Abstract

Among the several sets of unified constitutive equations described in this volume, the MATMOD (standing simply for MATerials MODel) equations probably attempt to cover the broadest set of phenomena. These are enumerated in Table 1. Like many of the other unified approaches, the MATMOD equations treat most of the phenomena within the categories of ‘creep’ and ‘plasticity’; however, the equations are also designed to predict many aspects of cyclic deformation and, more generally, multiaxial non-proportional straining. The manner in which the equations represent solute drag effects (dynamic strain aging) is unique. This breadth does come at the expense of accuracy, given our present incomplete knowledge of the ‘first principles’ physical laws governing dislocation-controlled straining.

Alan K. Miller

4. The Mechanical Equation of State

Abstract

The mechanical equation of state (MEOS) must relate to the full strain and stress tensor and it must predict not only the steady-state creep contribution (if any) but also the transient creep which follows every change in the stress system. In this chapter we indicate the progress that is being made to arrive at such an equation and the resultant equation that has been developed.

J. H. Gittus

5. A Physically Based Internal Variable Model for Rate Dependent Plasticity

Abstract

In 1978 Krieg et al. published a ‘unified creep-plasticity’ model for rate-dependent deformation of metals, incorporating a power-law relationship between inelastic strain rate, applied stress, and instantaneous value of two internal variables.¹ The internal variables were permitted to evolve by a Bailey—Orowan process, including strain hardening and recovery. Hardening was taken to be linear and to increase the internal variables rather than the flow stress directly; recovery was treated as thermal (as opposed to dynamic strain-activated) only, where the kinetics were derived from dislocation mechanics for the process in question. The physical basis was established because (a) the power-law flow rule was taken to be a mathematically convenient approximation to rate-process theory at fixed microstructural state, (b) linear strain hardening in polycrystals is usually viewed as an aggregate manifestation of the linear (stage II) hardening behavior of fcc single crystals oriented initially for single slip and in the absence of dynamic recovery,^2,3 and (c) the recovery kinetics were derived from dislocation models. The value of physical bases follows, of course, from the confidence (indeed the meaning) that is given to extrapolation of the relationship beyond the range of measured data.

R. D. Krieg, J. C. Swearengen, W. B. Jones

6. Review of a Unified Elastic—Viscoplastic Theory

Abstract

Although inelastic response of solid materials at low stress levels has been observed and measured for over a century and a half (an account of the early work is given by Bell¹), engineering thinking on material behavior has been dominated by the considerable success of the classical elastic and plastic theories. In contrast, the work on ‘dislocation dynamics’ in the 1950s and early 1960s by Johnston and Gilman^2,3 and by Hahn⁴ and others was based on the concept of considering both elastic and plastic deformations to be generally non-zero at all stages of loading. Those formulations were one-dimensional and restricted to simple loading histories such as uniaxial extension and creep. One of the main interests in those studies was to obtain the form of the equations and the material constants from measurements of microstructural quantities.

S. R. Bodner

7. Summary and Critique

Abstract

Unified creep-plasticity (UCP) models have many facets. Because there is no clear demarcation between plastic and creeping behavior, a good model should mimic both behaviors and should pass from one behavior to the other in a continuous manner. Furthermore, since plasticity and creep are both caused by similar physical processes, there should be no specific separation of the processes in the constitutive model. It appears that all of the models examined here have accomplished these basic objectives and in that sense qualify as unified creep-plasticity models. But constitutive modeling is multifaceted as stated above. Some authors have made a great effort to model time-dependent monotonic mechanical loading, others cyclic mechanical loading, and others multiaxial or temperature effects. Each author has also identified microstructural processes which he is modeling, and these are not the same in every case.

D. Bammann, R. D. Krieg

Backmatter

Titel: Unified Constitutive Equations for Creep and Plasticity
herausgegeben von: Alan K. Miller
Verlag: Springer Netherlands
Electronic ISBN: 978-94-009-3439-9
Print ISBN: 978-94-010-8039-2
DOI: https://doi.org/10.1007/978-94-009-3439-9

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Inhaltsverzeichnis

Frontmatter

1. Constitutive Behavior Based on Crystal Plasticity

2. State Variable Theories Based on Hart’s Formulation

3. The MATMOD Equations

4. The Mechanical Equation of State

5. A Physically Based Internal Variable Model for Rate Dependent Plasticity

6. Review of a Unified Elastic—Viscoplastic Theory

7. Summary and Critique

Backmatter