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

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СКАЧАТЬ is assumed (by default) to be time independent and is commonly referred to as “plastic.” However, experimental evidence tends to indicate that the classically described inelastic part actually includes a time‐dependent recoverable portion, called anelastic or delayed elastic strain. This portion is more observable as temperature increases.

      Experimental and theoretical concepts of time‐independent plastic deformation and the large volume of associated literature involving various yield functions, yield surfaces, envelopes, etc. have become the backbone for many engineering practices. These developments occurred before our knowledge of crystalline defects, particularly lattice vacancies (point defects) and dislocations (line defects) and their dynamics, broadened our understanding of microstructure‐sensitive micromechanical processes of failure in engineering materials. For historical reasons, the literature is still not clear about the exact definition of the term “plastic.” There are confusions between the classical “rate‐insensitive” or “time‐independent” plasticity (which is physically impossible because crystalline defects take time to move) and time‐dependent, rate‐sensitive flow, called “creep,” often treated as independent mechanisms. Moreover, the term “plastic” usually lumps together the permanent and the time‐dependent and hence rate‐sensitive recoverable anelastic or delayed elastic component of deformation readily observed at temperatures >0.3 T _m.

      In this book, we try to avoid the term “plastic” and associated terms, like “viscoplasticity,” and others. We will use the term “viscous” for any permanent deformation. Viscous deformation provides a measure of irreversible changes in the structure of the material. This name is consistent with the term “viscoelastic,” irrespective of stress‐wise “linear” or “nonlinear” viscoelasticity (known as power‐law creep). Unfortunately, the use of the term “viscoelasticity,” because of historical usage in association with classical plasticity, may lead one to think of only linear stress dependency. We realize that the use of this term may therefore cause some uneasiness among the investigators accustomed to the characteristics often associated with this terminology in classical theories of plasticity. Of course, metallurgists liberally use plastic deformation for creep strain in metals. We will return to this topic in Section 1.7.

      

1.6.2 Elastic, Delayed Elastic, and Viscous Deformation

Mechanically or thermodynamically induced stress deforms a material from its original shape. Stress‐induced deformation in a material, whether it is stated clearly or not, is historically assumed to be divided into two major parts – an elastic part and an inelastic part. Instantaneously occurring deformation of the lattice structure on the rapid application of a load or instantaneously recoverable deformation on the rapid removal of a load is known as an elastic response. Perhaps the latter description is more appropriate, because inelastic deformation may occur during loading, but any inelastic deformation is “not expected” to recover on unloading. The use of the words “not expected” is associated with the idea that it is rather complicated and sounds vague. This is because the term “inelastic” in the multidisciplinary field of classical engineering, as mentioned earlier, is associated with part of the deformation that is “really a deviation” from the elastic behavior.

      Trinity of Strain

      ELASTIC

      DELAYED ELASTIC

      VISCOUS

      It is recognized that inelastic or permanent viscous deformation is always accompanied by small, but recognized, elastic deformation. But, what about the strain component that is elastic, but develops with time and is recoverable on unloading? Naturally, the preferred term for this is “delayed elastic.”

      The use of the term “delayed elasticity,” as an integral part of the field of rheology, needs some explanations. Briefly, the term “rheology” was defined as “the science of the deformation and flow of matter” at the inaugural meeting of the (American) Society of Rheology in Washington, DC, in 1929. Rheology is a broad field, and consequently different technical terms are used for the same or similar experimental observations. The rheological terms adopted by the British Standards Institution (BSI 1975) are used in this book. The term “anelasticity,” although popular in the field of metallic materials and rock mechanics, will be avoided. In Section 6.2 of Chapter 6, we have clarified this in detail.

      The delayed response is not given importance in mechanics unless seismic frequencies or short‐term loadings are involved. It is also not universally recognized (rather ignored) unless high temperatures are involved, that inelastic deformation is always time dependent, and that “time” could be very short, but indeed sufficiently long to stretch the lattice bonds between the constituent atoms, as well as moving the lattice defects (point and line). Time dependency arises because inelastic deformation involves the movement of lattice defects within the solid material. Perhaps because of this nonrecognition, inelastic deformation is often called “plastic” deformation, when the time dependency involved is not obvious, and “creep” when time becomes a major factor. The concept of time‐independent plasticity and its broad application in many engineering fields simply ignores the physics of materials science. Since time‐dependent deformation is readily observed at high temperatures, creep is always, or readily, associated with high temperatures. This leads to the widespread misconception that creep is a high‐temperature phenomenon. The often not recognized fact is that creep can also occur at low temperatures. Sagging in glass windows of old buildings is an example. It has been seen that windows reveal measurable differences in their thickness between thinner upper and thicker lower parts. Of course, early manufacturing of glass sheets using rollers was also not optimized and the installer of the plate would naturally choose the thicker end for the bottom. Sagging in steel beams due to creep, beyond elastic response, with age in buildings is also commonly seen. Short‐term creep can occur in certain modern metals and alloys at low temperatures as well, for example, in aerospace materials, like titanium‐base alloys at room temperature (Wapniarsky et al. 1991).

      Historically systematic studies on “creep and recovery” aspects of engineered materials at elevated temperatures became popular since the publication of Andrade (1910) on steel (see Chapter 6 on fundamentals of high‐temperature deformation). During the last hundred years, the phenomenological and micromechanical aspects of creep and failure properties obtained from simple isothermal constant‐load (CL) “creep and creep‐rupture tests” drew the attention of most materials scientists. Creep tests at a constant temperature are performed by applying a load as quickly as possible, using a dead‐load system, and the increase in strain with time is monitored while maintaining the load constant. As mentioned earlier, several books have been published on high‐temperature creep and failure of materials, but these books mostly covered progress made primarily on metallic materials. Many crucial aspects of the “physics of creep,” however, have remained unanswered and vigorous attempts are being continued in materials science laboratories all over the world. As mentioned earlier, Holdsworth et al. (2005) have provided an up‐to‐date list of wide‐ranging creep model equations being used today for ascertaining high‐temperature rheological properties of engineering materials. Most of these equations are based on classical empirically derived representation of primary, secondary, and/or tertiary creep deformation in pure metals and alloys as functions of stress, time, and temperature. Creep responses of single‐crystal and polycrystalline alloys used at high temperatures have been covered. Surprisingly, none of the empirically based models address the grain‐size effects of transient, secondary, or tertiary creep. Moreover, none address microstructure‐dependent, experimentally verifiable, delayed elastic phenomena in engineering materials.

      Creep СКАЧАТЬ