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

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Figure 1.5 Results of Figure 1.4 shown in a logarithmic timescale, illustrating load‐application times (<1 s) and similarities between the minimum creep rate of 2.85 × 10⁻⁶ s⁻¹ and the average viscous strain rates of 3.05 × 10⁻⁶ s⁻¹ and 2.68 × 10⁻⁶ s⁻¹, respectively, for 200 s and 2432 s from the corresponding, ε_v, at the end of recovery.

      Source: N. K. Sinha.

      Figure 1.5 also shows the “average viscous strain rate”, , during the creep time or the “strain relaxation” time, t _SR, of 200 s and 2432 s, respectively, given by

(1.1)

      where ε_v is the “measured permanent or viscous strain” after full recovery, as shown in Figure 1.5.

A set of five long‐term SRRT curves for Waspaloy is presented in Figure 1.6. All of these tests were carried out to periods well within the tertiary stages, but unloaded completely and extremely rapidly before fracturing and the strains were monitored for a long period to explore strain recoveries. Since the total strain even at unloading times was less than 1.2%, the true stress increased only slightly even at the time of unloading. These results are consistent with numerous published creep data in the literature, but with two important differences. These results present, for the first time to the authors’ knowledge, the systematic observations on creep recovery after full unloading during the tertiary stages and specimen response during “rise times” to apply the full load. Figure 1.6 clearly illustrates the strain–time response during the “rise time” (from which elastic modulus E can be determined for each of the specimens). It also shows the creep curves with the corresponding minimum creep rates, and most importantly the permanent viscous strains, ε _v, and the corresponding recovered delayed elastic strains, ε _d (des), at the end of the tests. Analysis of the short‐term and long‐term SRRT data (Figure 1.6) indicated that the creep strain at minimum creep rate consists of a significant amount of recoverable delayed elastic strain (32% at 450 MPa and 38% at 650 MPa).

Figure 1.6 Strain–time curves, showing rise time to apply full load (<1 s), during creep for five SRRTs, including the longer duration results of Figure 1.4, on a polycrystalline nickel‐base superalloy Waspaloy at 1005 K (732 °C) for initial stresses 450–650 MPa. Note the delayed elastic recovery and viscous strains after unloading.

      Source: N. K. Sinha.

      Figure 1.6 points out that the time to mcr, t _m , decreased significantly, over an order of magnitude, with increase in engineering stress from 450 to 650 MPa. The dependence of t _m on stress, σ, may be expressed by the following relationship:

      (1.2)

      where M = 1.61 × 10²⁹ and p = 9.36. Such a relationship has commonly been seen for the dependence of rupture or fracture time on stress, leading to popular ideas on relating mcr to failures at high temperatures (see Chapter 6). Note that the total strain, ε _min (which includes the elastic strain, ε _e), corresponding to mcr increased only from 0.38% for 450 MPa to about 0.64% for 650 MPa. The corresponding values of the creep strain (ε _min−ε _e) increased from 0.12 to 0.27%. This type of diminished stress dependency of ε _min agrees with general observations available in the literature on the relatively small increase in strain at mcr with increase in stress. In fact, the elongation at fracture hardly varies with stress. However, note the increase in the permanent or viscous strain, ε _v, at unloading time of the tests, with increase in stress. Viscous strain thus provides a measure of the permanent change in the structure.

The analysis in Figure 1.7 clearly demonstrates that (i) the amount of delayed elastic strain, des, accumulated during the tests is not negligible and that (ii) it is not consumed within the mass and is recoverable at the end of the tests even well within the tertiary stages. The set of these types of creep and recovery curves illustrates the potentials of the SRRTs.

Figure 1.7 Stress–strain diagram. (a) Two values of elastic modulus, E, and strain trinity (elastic, delayed elastic, and viscous) for loading and unloading the 200 s SRRT of Figure 1.5 on Waspaloy at 1005 K and 650 MPa. (b) Stress–strain diagram, and the strain components for the longer‐term (2341 s) test in Figures 1.4 and 1.5 on Waspaloy at 732 °C (1005 K) and 650 MPa; the lower value of E (168 GPa) during unloading compared to 178 GPa during loading indicates structural damage during tertiary creep with slight increase in true stress.

      Source: N. K. Sinha.

      Stress–strain (σ–ε) diagrams for engineering materials are commonly “reserved” for constant displacement (nominally constant strain rate) tests from which some sort СКАЧАТЬ