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

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      SECONDARY (steady state)

      TERTIARY

Evans and Wilshire (1985, p. 72) eloquently pointed out that the now standard terminology of primary, secondary, and tertiary creep, the main features of normal creep curve in metals, originated in Andrade's work on steel. We will call this the “creep trinity.”

      Creep curves for polycrystalline materials (also ordinary glass) drawn between axial strain and time for a constant load typically (called normal) consist of three stages: a decelerating primary or transient stage, a secondary or steady‐state stage, and an accelerating tertiary stage.

      Experimentally, it is simpler to concentrate on the secondary creep during which the strain rate does not vary with time and tends to a minimum value. The minimum creep rate is thus subjected to minimal error of measurement. Constitutive equations for high‐temperature deformation of metals, alloys, rocks, and ceramics are thus largely based on the concept of “steady‐state” conditions. Tertiary or accelerating stages were associated with damage‐enhanced creep and were of no interests until the aeroengine usage of nickel‐base single‐crystal superalloys in gas turbine engines became a reality (see Chapter 5 for details). Tertiary creep under constant tensile load in nickel‐base single‐crystal superalloys has been shown to represent a “dynamic steady state” for the dependence of engineering strain rate on the corresponding actual or true stress (Sinha 2006).

      For temperatures less than 0.3 T _m, time‐dependent deformation is characterized by asymptotically decreasing creep rate, known as logarithmic creep. At elevated temperatures, higher than 0.4 T _m, trinity aspects of creep are readily noticeable, but the shape of the primary creep in polycrystalline materials varies on the texture and structure of the material. Primary creep is called “normal” when it exhibits decelerating creep rate with time. Steady‐state or secondary creep rate is quantified experimentally from the measurements of minimum creep rate (mcr). It takes a long time to reach steady state for stresses less than about 1 × 10⁻⁵E (where E is the Young's modulus) known to initiate microcracking activities at high temperatures. Consequently, to reduce test durations, relatively high loads are chosen to attain the mcr as quickly as possible followed by the tertiary stage of accelerating creep rate. No doubt, higher loads cause more structural damage during creep in shorter times. The onset of tertiary stage is known to be linked with microstructural damages. The range of mcr is a transitory stage providing only a “snapshot” of the strain rate during the transition period from primary creep to tertiary creep for an evolved microstructure depending on stress, temperature, initial structure, and texture (Evans and Wilshire 1985). Nonetheless, both fundamental theories and engineering applications are based on the concept of steady state and have been strengthened by the success of the MG rule (Monkman and Grant 1956), relating failure time with mcr. We address this issue in Chapter 6.

      The above phenomenological categorization of creep‐rupture characteristics is known to apply for levels of stresses relevant to engineering structures or components. For such operational conditions, contributions due to elasticity and delayed elasticity (or anelasticity) are assumed to be negligible and thus considered unimportant. This presumption of the role of delayed elastic effect as negligible for mechanical response relevant to practical engineering applications is not correct. This topic will be dealt with in various chapters in this book, and particularly, while presenting strain‐rate dependence of yield (0.02% strain) strength, stress relaxation, and nucleation kinetics of grain‐boundary cracks at elevated temperatures.

      The inelastic or the creep component of deformation has been “recognized” to be primarily controlled by the mobility of intracrystalline (or intragranular) lattice defects, called dislocations. This regime is called “dislocation creep.” An introduction to dislocations in crystals is given by Weertman and Weertman (1964), Nabarro (1967, 1987), and Hull and Bacon (1984), to name a few books. Significant progress has been made in mapping the regime of dislocation creep on the basis of experimental observations on the stress–temperature–grain size dependence of the secondary or actually minimum creep rate (Ashby 1972; Frost and Ashby 1982). While this was convenient for a working‐model kind of description, minimum creep rates, as pointed out by Evans and Wilshire (1985) and shown in Chapter 8, represent evolved characteristics, not fundamental properties of polycrystalline materials. The deformation maps also describe the conditions for diffusional creep, which is extremely important for the processing industry. Burton (1977) has given a brief, but comprehensive, introduction to diffusion creep of polycrystalline materials.

For metallic alloys, it is customary to use significantly high temperatures for processing during which high‐level strains are involved. Diffusion processes within the grains and along the grain boundaries are activated vigorously during this type of deformation. Three types of diffusion creep have been identified for polycrystalline materials. They are known as Nabarro (1948)–Herring (1950), Coble (1963), and Ashby–Verrall (1973) diffusional creep (presented in detail in Chapter 5). Ashby–Verrall (A–V) described a model that differs fundamentally from Nabarro–Herring (N–V) creep and Coble creep in a topological sense. They called their model as, “diffusion‐accommodated flow.” According to the A–V model, grains switch with their neighbors and do not elongate significantly. At large strains, A–V flow proceeds faster than N–H creep or Coble creep. Such high‐strain flow conditions are popularly known as “superplastic.” This is certainly a misnomer and often misleading because classical theories of plasticity do not recognize rate effects and hence “time” as a parameter. To avoid contradiction, is it appropriate to described this as “superviscous”? For this same reason, the term “plastic” will not be used in this book, except for as a reminder or cue. We will use “viscous flow” in a general sense for describing permanent or nonreversible flow, irrespective of its dependence on stress. Thereby, the terms viscoelastic response and viscous flow will be applied universally. It should also be emphasized that “viscous strain rate,” used frequently in this book, is not a synonym for a minimum or steady‐state flow rate.

1.7 Strength of Materials

      The concept of “strength” implies a specific material property. Methods have been developed to quantify tensile, compressive, bending, shear, etc. strength and standard procedures have been developed for conducting appropriate tests (see Chapter 4). At ordinary temperatures, strength is taken for granted to be independent of the rate of loading. However, the rate effects are recognized, especially for materials with pores and microcracks, and standard tests are recommended to perform in a specific range of loading rate. Stress–strain (σ–ε) diagrams are used to characterize the yield and ultimate strengths. These diagrams have no room for time. Traditionally, the initial linear part of σ–ε curves implies elastic regime, and deviation from the linearity is considered as plastic flow. At elevated temperatures, the linear σ–ε response does not necessarily mean pure elastic response. Material strength, defined by yield, is thus a low‐temperature concept. This low‐temperature concept does not apply at the elevated temperatures relevant to many engineering applications. Nonetheless, the concept prevailed and was extended to elevated temperatures. It has retarded growth in the understanding of failure processes involving inelastic deformation or creep and hence microstructure–property relationship in engineering components subjected to high temperatures. Application of this concept has misleading implications, drawing away from one basic fact: Transient or primary creep stage, involving the initial periods of damage accumulation, plays a dominant and perhaps decisive role in many engineering design problems. At high temperatures, strength, creep, and relaxation СКАЧАТЬ