Читать книгу Engineering Physics of High-Temperature Materials - Nirmal K. Sinha - Страница 38

Creep theories for polycrystals are essentially based on idealized microstructures. This is essential to keep the number of material parameters as low as possible. To check the theoretical predictions, ideally experiments should be performed on specimens with exactly the same microstructure and chemical characteristics. In reality, it is impossible to have polycrystalline samples with exactly the same microstructure, i.e. the same number of grains, sizes, distribution, orientations, etc. CL creep tests are mostly carried out. Tests aimed at exploring the stress exponent (n _min or n _m) characterizing the dependence of steady state or minimum creep rate (mcr) on stress and temperature are therefore performed on different specimens with similar physical qualities. However, mcr may occur at a relatively large strain with evolved microstructure depending on the initial structures, stress, temperature, and test environment (air, gas, or vacuum). All the tests are different even though performed under similar conditions. Is it possible to use one specimen (i.e. constant microstructure) to perform a number of very short‐term creep tests and determine n _v for viscous flow (dislocation creep)? The answer will be a quick “no,” “impossible.” This quick answer is based on classical approaches that have been taken for many decades. This is where a change in paradigm is required; Figures 1.4–1.7 are illustrations of this possibility using SRRT – a stylized name for a simple creep and recovery test originally developed for ice (Sinha 1978a), later coined by Sinha (2001), and used extensively for advanced aerospace alloys.

Figure 1.8 Stress dependence of average viscous strain rate during primary creep and the corresponding minimum creep rate from short‐term and long‐term SRRTs on five different specimens of Waspaloy at 1005 K.

Source: N. K. Sinha.

The numerical equivalency of n _v and n _min, for stress levels of engineering importance, has far‐reaching consequences. Since failure and fractures in metals and alloys at high temperatures are traditionally linked to n _min, does it mean that SRRTs requiring “a single specimen” can be used for the characterization of failures? Sounds incredible! One of the primary goals for writing this book is to convince metallurgists, ceramicists, and rock mechanics researchers to use SRRTs and explore certain important aspects of materials (delayed elasticity and crack nucleation and multiplication during primary creep stages) neglected so far in the general field of materials science and engineering.

One approach of utilizing the methodology of “hindsight” is to perform a series of creep and recovery tests (SRRTs) on one specimen. For each test, the full load is applied as quickly as possible and, at the end of the creep time, completely unloaded from the specimen very quickly. The strain is continuously monitored during the recovery. This approach allows one to explore the “trinity of creep” in a quantitative manner at different stages of creep. It is by no means a novel approach, but improvements can be made by decreasing the durations of loading and unloading, and by increasing the observation time during recovery. The initial strain, ε _i, on full loading provides an “effective” elastic modulus, E_i, which can be compared with Young's modulus, E, obtained from seismic or resonance technique. The difference ΔE = E−E_i provides a measure of the weakness in the loading sequence and can be improved and optimized by decreasing ΔE. The residual strain after full recovery provides a measure of the “viscous” strain, ε _v, and the “average viscous strain” rate, (defined by Equation 1.1), for the load‐duration time, t (shown in Figure 1.5). This “pseudo” strain rate () can be numerically compared with the “secondary” creep rate.

An example of the above approach is illustrated in Figure 1.5. It shows that the “pseudo” or the average strain rate () during the first 200 s during the primary creep of the short test is 3.05 × 10⁻⁶ s⁻¹. It may be safely assumed that “negligible” structural damage occurred in the specimen during this test. Now compare this with the slightly lower of 2.68 × 10⁻⁶ s⁻¹ for the entire 2342 s of the long test performed on the same specimen. The difference is small, but may be linked to the expected structurally damaged state of the specimen undergoing tertiary creep. These two estimations are subjected to least experimental errors in comparison with the estimation of the minimum creep rate (mcr), as all experimentalists can understand. The mcr was estimated to be 2.8 × 10⁻⁶ s⁻¹ that occurred at about 800 s as shown in Figure 1.5. No importance can be given to the fact that this value lies in between the other two values, but why is this numerically comparable to the average viscous strain rate during the primary creep? This similarity opens a floodgate of experimental possibilities and potentials of SRRT (presented in Chapters 4–9) and theoretical nightmares for materials scientists, in general, concentrating on numerous hypothesis on the generations, multiplications, annihilations, climb, etc. and hence interactions of matrix dislocations with grain boundaries during primary creep leading to steady‐state creep rate.

Most fundamental studies have concentrated exclusively on “steady‐state” behavior and ignored the primary or the transient creep – which are of high importance for the engineering design of various components. These fundamental studies shaped the materials world, including the rock mechanics people, even though it is well known that earthquakes are linked to transient creep, which are known to depend on materials characteristics, temperatures, strain/stress rate, etc. As a consequence, most experimental investigations, undertaken to understand dependence of creep and failure on materials variables, reported only the characteristics of the mcr.

The approach of opening the door for the “hindsight” described above was taken by the senior author while investigating high‐temperature rheo‐optical behavior of glass in connection with the thermal tempering of structural glass (Sinha 1971). On application of external forces, shearing between ordered (crystal‐like) and disordered zones may develop internal strain (stress) concentrations in silicate glasses with no long‐range orders in the matrices (see Section 2.4.2, “Structure of Real Glass”). These stress concentrations, in absence of any relaxation processes, could become the driving forces on unloading and generate delayed elastic effects in glass. The question is, what happens when the size of the “ordered zones” increases drastically at the cost of “disordered zones”? Do we end up with polycrystalline (ordered) materials with thin layers of grain boundaries (disordered)? Shearing between grain‐boundaries during loading could therefore develop stress concentrations (elastic distortion of the lattice) at triple boundaries because of intragranular lattice distortions near triple‐grain boundaries. The approach used for examining delayed elastic effects in glass was then successfully applied to directionally solidified columnar‐grained pure S‐2 ice (Sinha 1978b) using a conventional dead‐load lever system. However, state‐of‐the‐art, computer‐controlled, servo‐hydraulic technology has provided us with the opportunity to load fully and unload completely in fractions of second for a wide range of stress. Moreover, improvements in measuring specimen strain at high temperatures and controlling it by closed‐loop systems (such as truly constant rate) provide a measure of deformation that was not possible in the past (details are provided in Chapter 4). This is the main reason why the above‐described creep and recovery methodology required a new name – SRRT.

To better understand the need for a new name, let us divert our attention a bit to stress relaxation. Engineering components of nuts and bolts face serious problems at high temperatures, because the bolts lose their grip with time. To understand this issue, Stress Relaxation Tests (SRTs) are performed. An SRT is performed by suddenly applying a strain (constraint) and monitoring the decrease in stress with time. SRT is a universally accepted name. To be consistent, why not use “strain relaxation test” (also SRT) for the test in which a stress is suddenly applied and the increase in strain is monitored thereafter? But that term may create confusion. A clear distinction can be made, however, by adding the “hindsight” or the “recovery” aspect of the new test method to the name. Hence, the name SRRT was chosen for the test approach described above.

As mentioned, the SRRT approach was first applied to soda–lime–silica glass in late 1960. It was extended to natural water ice during the late 1970 and finally to a wide‐ranging nickel‐, titanium‐, and iron‐base complex superalloys in late 1990 and early 2000. The authors have not performed SRRTs on geologic materials and are not aware of any SRRT type of test methodology applied to rocks. However, Chopra (1997) reported two CL creep and recovery tests (on full unloading), essentially SRRTs, on an olivine basalt. Chopra focused on the delayed elastic recovery in order to model transient creep, but inadvertently missed the fact that the permanent strains, he reported, could provide a measure of the average viscous strain rate during loading time, equivalent to the reported steady‐state strain rate. This is presented in Figure 5.5. and discussed further in Section 5.6 in Chapter 5.

Significant progress has been made in physically based holistic modeling of microstructure‐sensitive reversible and irreversible deformation and failure processes based on SRRT. The basic principles of the model can be applied to performance problems of wide‐ranging materials at high temperatures. It includes some very new ideas in the field of gas turbine materials engineering, which could have important practical implications if it stands up to the close scrutiny by others working in the field.

SRRT is a novel approach to the way in which creep and creep‐rupture properties are measured and have been measured for a great many years. This book deals with work that has been done at various homologous temperatures and works well for a number of wide‐ranging materials. What is needed now is to understand if there are any limitations to the technique in terms of the temperatures and stresses that can be used. The SRRT method has a major advantage in that it may now be possible to develop cost‐effective stress rupture properties of alloys at relatively lower homologous temperatures; tests that otherwise take a very long time to complete at great expense.

SRRT‐based test technique for measuring elastic strain, ε _e, delayed elastic strain, ε _d, and viscous strain, ε _v, was developed, as mentioned earlier, first for glass, an amorphous medium without any recognized “grain boundaries.” It was extended to polycrystalline ice, and grain‐size effect was introduced. The transparency of pure polycrystalline ice helped in identifying and quantifying stress and temperature dependence of the initiation and the multiplication of intergranular cavities and cracks, and the role of dislocations in the high‐temperature embrittlement processes. During primary creep period, the pile‐up of dislocations against grain boundaries may not be the major source for the initiation and multiplications of intergranular cracks. At a constant temperature, the first intergranular crack forms during the early primary creep when a critical des, ε _d ^c, corresponding to a critical grain‐boundary shearing (gbs) displacement, x ^c, is reached irrespective of stress. The kinetics of crack multiplication depends exponentially on (ε _d –ε _d ^c ) corresponding to (x–x ^c ). This makes ε _d the Achilles heel for creep activities. Yet, historically, materials scientists in general (metals, ceramics, and rocks) have not paid much attention to the primary creep, and certainly not to delayed elasticity. Traditionally the primary focus has been on minimum creep rate. Even though the rate of ε _d decreases with time leading to a so‐called steady state, cracks are initiated during the primary creep and void density increases rapidly during the later stage of the primary creep, leading to minimum creep rate and ultimately to failure.