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
Why not stop the test, unload the specimens completely (unlike partial unloading used in “strain‐ or stress‐transient dip tests”) during the creep test, as well as during other tests, such as constant‐strain‐rate strength tests and constant‐strain SRTs, and monitor the strain–time response for extended periods and evolution of strain trinity? This is like looking backward (hindsight) at the growth history of elastic, delayed elastic, and viscous characteristics.
This book revolves around the concept of opening up the door for hindsight and using the opportunity it offers for developing both experimental and theoretical approaches. This is a recurring theme of various chapters. Experimental procedures were developed to examine not only total deformation, but also the three strain components: elastic, recoverable delayed elastic, and permanent viscous strain. Most importantly, theoretical developments can also be judged not only by how well they predict the total deformation under specific external conditions, but also how well they predict the strain components.
It is well known that viscous flow (dislocation creep creep) exhibits stress‐wise highly nonlinear response, with stress exponent, n v, varying from a value of 4 for pure metals to significantly higher values for complex alloys. It is shown in Chapters 5 and 6 that delayed elastic response could exhibit nearly linear to highly nonlinear response, with stress exponent, s, varying from 1 to 4 for complex nickel‐base superalloys, so far examined experimentally. However, the ratio, n v/s, may not vary significantly for different materials examined so far. The n v/s (n v = 11.8 and s = 4.0) ratio of ≈3 for the nickel‐base superalloy IN‐738LC is similar to that of 4.3 for another nickel‐base superalloy – Waspaloy is also very close to that of 3.3 for titanium‐base alloy Ti‐6246 (n v = 4 and s = 1.2) and is exactly like that of polycrystalline ice with n v/s = 3 (n v = 3 and s = 1); however, ice is not a metal!
1.8.3 Exemplification of the Novel Approach
Let us very briefly look at the essence of the technique of looking backward. The principle of the use of hindsight for a creep test is illustrated in Figure 1.4 using the traditional presentation of linear timescale. In this case of a popular nickel‐base superalloy (Waspaloy), a tensile specimen is first loaded fully and rapidly (rise time <1 s) and unloaded completely (also in <1 s) after a creep time of 200 s, well within the transient or primary creep range, in comparison with 800 s for the time to reach the minimum creep rate for this level of stress. The axial strain recovery, after rapid removal of the load, was monitored for a relatively long time until a permanent or a viscous strain could be evaluated. Then, the same specimen was loaded for a long time to the accelerating tertiary stage and then fully unloaded, and strain recovery was recorded. For clarity, the strain level and time for the mcr for the longer‐term test are also shown. The mcr was determined from the strain rate versus time curve. The differences in the amount of permanent or viscous strain for the two tests are clearly noticeable. As expected, the permanent or viscous strain that occurred during the long test (duration of 2341 s) is significantly greater than that of the short test (for 200 s). Note the amount of elastic strain, delayed elastic strain, and viscous strain, shown for the longer‐term test. The delayed elastic strain is small, but not negligible. Similar observations were also noticed for the short‐time test. These observations provide clear indication that delayed elasticity, mostly ignored so far in high‐temperature rheological models emphasizing only mcr or steady‐state creep rate, should be given due consideration in order to get a better understanding of the mechanics of high‐temperature creep and failure. It should be mentioned here that the time span for full load application or