Engineering Physics of High-Temperature Materials. Nirmal K. Sinha

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СКАЧАТЬ alt="ModifyingAbove epsilon With ampersand c period dotab semicolon"/> _v = ε _v/t _SR for the period t = 0⁺ to t _SR. How does ε _d vary with time? How does _v vary with time, stress, temperature, and initial (constant) microstructure?

      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 the rise time of less than 1 s is also expected to minimize the scatter in the stress dependency of mcr as discussed by Bressers et al. (1981).

Figure 1.4 Short‐term (200 s) and longer‐term (2341 s) tensile SRRTs on a single specimen of polycrystalline nickel‐base superalloy Waspaloy at 1005 K (732 °C) for 650 MPa using linear timescale.

      Source: N. K. Sinha.

      There are innumerable sets of creep curves for a wide variety of manufactured and natural materials illustrating transient and tertiary creep stages, but the recovery on full unloading is rarely reported. There are, however, examples of stress‐dip tests in which creep continues after a short recovery on partial unloading during the steady state or actually at mcr that occurs at evolved microstructure corresponding to this state. Unfortunately, stress‐dip tests do not provide useful information on transient creep at the beginning of a creep test and the characteristics of neither the delayed elastic deformation nor the viscous flow corresponding to the original, undeformed and undamaged microstructure.

      Figure 1.4 exemplifies a unique set of results for a complex nickel‐based aerospace alloy. It brings out the fact that the delayed elastic strain, ε _d, recovered on full unloading well within the tertiary stage of creep, after mcr, was not negligible and not “absorbed” within the viscous component. The long‐term test (2341 s) is noticeably larger than that of the 200 s test. Hence, ε _d increases with time. This raises the question as to the mechanism(s) responsible for generating delayed elasticity in polycrystalline materials that may have far‐reaching consequences, presented in Chapter 5, in developing physically based creep models.

Conventionally, a typical (often called normal) creep curve is described in terms of three stages: a primary regime during which the creep rate continuously decreases, a secondary regime where the creep rate is at a minimum, and a tertiary regime where the creep rate continuously increases, leading to rupture. All these three stages (except for the rupture) can be seen in the long‐term creep curve in Figure 1.5. The slope of the curve at a given time gives the creep rate at that time. It varies with time. However, the creep rate at a given time provides “total strain rate” or the rate of the “sum of reversible and irreversible strain” at that time. If the creep rate is plotted against time on a log–log scale, a typical creep response can be described by only two regimes: primary and tertiary. The minimum creep rate represents only the transition point between these two regimes. From the physics point of view, its numerical value provides no information either during the primary regime or the tertiary stage – the regimes important for engineering designs and life cycle management.

The use of the linear scale for time obscures the initial conditions of CL creep tests. Moreover, traditional methods of using a dead‐load lever system, although very simple and ideal for conducting very long‐term creep‐rupture tests with durations of 10 000 hours or more (e.g. Holdsworth et al. 2005; Yagi 2005; Kimura et al. 2009), do not allow the load to be applied as quickly as possible to satisfy the common assumption of “instantaneous” load application. Consequently, the materials science literature СКАЧАТЬ