for example the inapplicability of the empirical power‐law relation between t f and σ f or between ε f and strain rate. It is shown that strain‐rate sensitivity of volumetric dilatation can also be reasonably predicted.
The EDEV model has been extended to stress relaxation tests (SRTs) at elevated temperatures in Chapter 9 and applied successfully to nickel‐base superalloys, like In‐738LC, titanium‐base alloys, like Ti‐6246, and polycrystalline ice (especially the grain‐size effects on stress relaxation). Theoretical predictions on total strain as well as the components of elastic, delayed elastic, and viscous strain at any time during creep and SRTs can be examined and compared with experimental observations. EDEV model is based on observations that the viscous strain rate (for dislocation creep) is constant throughout the primary creep under constant stress (for conditions of no microcracking activities) and the shape of the primary creep is governed by delayed elastic deformation that is recoverable on unloading. The acid tests of the developed model are provided by the comparisons between the predicted permanent strain and the recovered elastic and delayed elastic strain components with the corresponding experimental observations of both SRRTs and SRTs. Since delayed elastic response in single‐crystal materials may be neglected, the EDEV model reduces to a simple nonlinear elasto–viscous relation, as presented in Chapter 5, for most of the deformation of engineering design purposes.
But why does the viscous strain rate, associated with dislocation creep, appear to be constant during normal primary or transient creep? This SRRT‐based experimental observation in single‐phase crystalline materials and complex crystalline materials, including at least one rock type, ice, and complex alloys, goes against the dislocation theories developed over many decades. Theoreticians have to modify some of the classical assumptions and start working on the development of some new ideas.
1.8 Paradigm Shifts
The Oxford English Dictionary defines paradigm (pær&ip.schwa;da&ip.iscp;m) as “example or pattern, esp., of inflexions of noun, verb, etc.” (Simpson and Weiner 1989). In science and philosophy, a paradigm may be considered as a distinct set of concepts or thought patterns that have developed to guide workers in a specific area. In his book, The Structure of Scientific Revolutions, Kuhn (1996; first published in 1962) defines a scientific paradigm as: “universally recognized scientific achievements that, for a time, provide model problems and solutions for a community of practitioners.”
1.8.1 Paradigm Shift in Experimental Approach
The history of cultures and nations, including various economic and political aspects of the inhabitants, provides opportunities to look back and make judgments that can, eventually, influence and improve our understanding of the global society. Looking back is always healthy as long as the approach is rational and forward looking. This approach has been the key to success for the development of science and technology and building bonds between diverse societies and linguistic groups of the world using a more‐or‐less common multidisciplinary scientific and technical language and jargon. A thorough and critical, but unbiased (hopefully), review of literature is therefore essential for embarking on any scientific work. It is said, “Hindsight 20‐20.” Why not apply this approach with a fresh outlook to high‐temperature materials science? But then, what would be that approach?
Materials exhibit elastic and inelastic deformation on application of a load. Inelastic deformation is commonly known as plastic. The paradigm of plasticity theories was developed on the basis of engineering experience with materials at low homologous temperatures. Plastic deformation is thought to occur when stress exceeds a specific range. The thoughts of practitioners in several engineering disciplines are molded by theories of plasticity proven to be very successful in explaining failures. Plastic deformation is traditionally assumed to be independent of time and hence independent of strain rate or stress rate. As a consequence, failure processes of geological materials have continued to be presented/discussed in terms of yield functions, yield surfaces, yield diagrams, envelops, etc. As the operational temperature rises, complex issues related to time–temperature effects complicate matters.
Inadvertently, plasticity theories have created confusion for many aspects of engineering materials science in general at elevated temperatures. Yield strength is, for example, very subjective and depends on the user of the information and materials. For example, “yield strength” in mechanical metallurgy and materials engineering, in general, is used to mean the stress corresponding to a specific strain, such as 0.2% offset strain on stress‐strain diagrams. Strength of engineering materials, especially at elevated temperatures, is known to be rate dependent, and inelastic deformation leading to permanent changes in a solid depends on time, among other parameters. Consequently, a small shift in paradigm occurred. Yield strengths had to be defined with respect to a specific range of loading rates. Nowadays, measurement of 0.2% yield is undertaken through uniaxial constant strain rate or more often constant crosshead or displacement rates with respect to “tensile tests” or “compressive tests” (mainly for ceramics, rocks, and ice) at some specific strain rate between 5 × 10−5 s−1 and 1.2 × 10−4 s−1 (ASTM 1998). These considerations led us to the use of the word “viscous” for any permanent deformation, irrespective of the micromechanisms (dislocation or diffusion) involved in inducing the changes in the shape of a body. By looking back at the history of the theoretical front and engineering practices, we will try (as mentioned earlier in several places) to avoid the use of the term “plastic strain” in this book. However, we recognize that the terms like plastic deformation and plastic strain continue to be used strongly for describing inelastic strain even for high temperatures, such as creep strain. We recognize that paradigm shifts take time. For this reason, we will often remind the reader about the equivalency of the two terms: viscous and plastic.
1.8.2 Breaking Tradition for Creep Testing
On the experimental front, constant‐load or constant‐stress creep tests are customarily performed at elevated temperatures. Room temperature creep tests are also performed on certain materials exhibiting low‐temperature ductility. The uniaxial tension test or compression creep test is the simplest and fundamentally most important test for the evaluation of material properties. The tradition is to load a specimen and monitor the evolution of strain. No specific efforts are made to determine the elastic modulus, such as Young's modulus (E), corresponding to the initial microstructure of the test specimen. At some stage, either the load is removed intentionally or by rupture. The post‐test analysis concentrates typically on stress–time–temperature dependence of strain and strain rate, and sometimes on microstructural examinations at room temperature. Almost invariably, the characteristics of the minimum creep rate (mcr), often considered as the steady‐state flow rate, are discussed. It is trendy to report only the mcr, time to rupture (t f), and elongation (engineering strain) at failure, ε f. Efforts are also sometimes made, but not necessarily as a normal practice, in fitting the creep curves for the transient creep, especially, for example, in the case of rocks.
High‐temperature deformation processes are continuous, and each regime depends on earlier deformation and microstructural history. Materials remember their thermomechanical history! What happens if the load is applied (rise time) in fractions of second and if the creep (strain relaxation) test is terminated by unloading in fractions of second after a short creep or strain relaxation time of t SR and the strain ε (recovery) is monitored continuously for a long time? It should provide a historical record of strain that recovers immediately (elastic, ε e), strain that recovers with time (delayed elastic, ε d), the permanent or viscous strain, ε v, accumulated during t SR, and an average viscous strain rate
