high temperatures.
There are a number of excellent reviews and innumerable books and monograms on strength of materials, including response at high temperatures on physics and mechanics of creep and strength of metals and alloys. The situation has improved significantly over the last century in extending this knowledge to other materials, such as rocks and ceramics. Investigators in the field of mechanics of nonmetallic materials looked toward the knowledge gained and concepts developed in metallic materials. Theories on diffusion and dislocation creep in metals, concentrated on explaining the steady‐state flow, dominated the minds of innumerable experimentalists irrespective of materials. The main reason, of course, includes the technical difficulties in performing experiments at high temperatures together with in situ measurements and in‐depth microstructural analysis at experimental temperatures. While presenting a damage mechanics treatment of creep failure in rock salt, Chan et al. (1997) remarked that it is not difficult to give a rational explanation for the deficiency, but the fact admits of no doubt of experimental difficulties and limitations, but also challenging traditional approaches. The transient creep, although recognized, is given only a passing importance and practically no importance is given to the delayed elastic phenomenon even though delayed elastic strain can be measured and analyzed. The contribution of transient creep, particularly the recoverable part, is assumed to be negligible without any serious challenge to this belief. Fortunately, the situation has improved considerably over the last 40 years in engineering physics of ice, a material that naturally exists at extremely high homologous temperatures. In situ measurements can be made and microstructural investigations can be made at experimental temperatures. Engineering physics of ice emphasized the importance of micromechanics of transient creep and its role in developing grain‐boundary microvoids, kinetics of void formation, void‐enhanced creep, etc. The transparency of pure polycrystalline ice and relatively large grain sizes has also been proved to be most important, in fact unique, in making in situ observations on grain‐facet‐sized void formation.
There was a need to overhaul the basic experimental techniques. Classical use of the dead‐load creep test procedures, ideal for long‐term tests, was complemented with the introduction of closed‐loop‐controlled constant‐stress “strain relaxation and recovery tests” (SRRTs) for short‐term tests (Chapter 4). Dead‐load systems cannot provide the necessary data for the initial and early part of creep curves, necessary for the interpretation of engineering (say 0.2% offset) yield strengths or low‐cycle fatigue or dwell‐fatigue properties. SRRTs can generate a significant amount of data on reversible elastic and delayed elastic strain and the irreversible (permanent) viscous strain components in a short time using only one specimen, if necessary, to avoid specimen‐to‐specimen microstructural variations and thus keep the structure fixed. Three basic components of strain (elastic, delayed elastic, and viscous) during primary creep over a wide range of stresses and temperatures can be examined. SRRT is more powerful than any mechanical tests popular today for investigating “constant stress” and “constant microstructure” creep properties at high temperatures.
As described in Chapter 5, SRRT methodology was based on experimental observations on glass, an amorphous material. It was extended to ice that is crystalline. Eventually, SRRTs were performed on a titanium‐base alloy, Ti‐6246, a wrought nickel‐base alloy, Waspaloy forgings, nickel‐base precipitation hardened superalloys, IN‐738LC, and single‐crystal superalloys. Minimum creep rates were also examined using SRRTs. Both viscous strain rate and the minimum creep rate were shown to obey the same power‐law dependence on stress with equivalent stress exponents. SRRTs also allowed investigations of the stress sensitivity of the delayed elastic strain. Similar to the viscous flow, varying from a linear to a highly nonlinear response, delayed elasticity was also shown to vary from linear to nonlinear, though to a lesser extent. In Chapter 5, we have also discussed SRRTs performed on a [001]‐oriented nickel‐base single‐crystal, CMSX‐10, in the temperature range 1073–1273 K for conditions where rafting of γ′ did not play a major role. Long‐term creep recovery, over several months, allowed examination of reversible delayed elastic strain. For a total strain of 15%, the delayed elastic strain was found to be about 0.15 or 25% of the elastic strain. A possible relationship has been proposed between the delayed elastic strain measured at 15% strain and area fraction of γ′ facet‐sized cracks for the onset of ultimate fracture. Nonetheless, delayed elastic effect in the single‐crystal material could not be detected during the primary creep period of small strain of engineering importance.
The lack of a reliable, simple – with a limited number of material constants or parameters – microstructurally sensitive, three‐dimensional constitutive model of polycrystalline materials at high homologous temperatures is the stumbling block against the use of sophisticated computer modeling and numerical simulations available today. A successful constitutive equation should have a physical basis and be able to describe the features that can be readily seen in the real field conditions. Such a model for inelastic deformation must be able to predict the usual empirically derived relations and be adequate for extrapolation to account for the effects of microstructural altercations or loading conditions. Moreover, such a model must be capable of predicting delayed elastic phenomena that can be quantified on the removal of the external driving forces. This means, predictability of the rebound of the structure on partial or full unloading should be built in the model. To date, most constitutive equations are highly empirical in nature and are useful for interpretation in the range investigated, but inadequate for extrapolation.
The chronology of the development of the three‐term rheological model, called EDEV model, is described in Chapter 5. This model relies on the incorporation of grain‐boundary shearing processes to relate with the delayed elastic phenomenon. A review of the phenomenological aspects of the failure processes at elevated temperatures is presented in Chapter 6. The crucial roles played by the phenomenon of delayed elasticity are examined in depth. Delayed elasticity can be linked to the predictability of the conditions necessary for the onset of grain‐facet‐sized crack formation and the kinetics of microcracking (Chapter 7). This leads to the development of the crack‐enhanced EDEV model that can handle, for example, the strain‐rate sensitivity of strength of polycrystalline solids at high temperatures (Chapter 8). EDEV is a nonlinear constitutive equation for high‐temperature applications. It consists of elastic, delayed elastic, and viscous components corresponding to three micromechanisms: lattice deformation, intergranular shearing/sliding, and intragranular dislocation motion. The model incorporates the predictability of the onset of cracking activity and damage accumulation due to the mechanism(s) of high‐temperature grain‐boundary embrittlement.
Grain facet long cracks develop when a critical grain‐boundary sliding or shearing (gbs) displacement or an equivalent delayed elastic strain is reached. Further damage is given in terms of the excess gbs, displacement over its critical value. As cracks form, they enhance the deformation matrix affecting the overall creep rate, leading to a minimum rate and then tertiary creep. Formulations have been developed in Chapter 8, using this model, for predicting the deformation and cracking activity for conditions of constant strain‐rate strength tests. The theory was tested with published experimental data on the strain‐rate sensitivity of the compressive strength of transversely isotropic, columnar‐grained, pure polycrystalline ice with a load applied in the plane of isotropy. Calculations using material constants were obtained from constant‐stress creep and recovery (SRRT) experiments totally independent of the strength tests. One‐to‐one correspondence of theory and experiments was noted for the dependence of strength, failure strain, and failure time on strain rate. The theory has the capabilities for predicting the popular empirically obtained relations between these quantities, such
