Analysis of creep ductility in a ferritic martensitic steel using a hybrid strain energy technique

The energy density exhaustion method for assessing the creep-fatigue lives of specimens and components

“…i.e., the fit is less good than that given by Eqn (16) in the present instance. Before proceeding, it may be noted that (i) very few investigators have quoted separate energy-expenditure values in the mode of Bicego et al [6] and equally, (ii), the number of continuous-cycling LCF tests that have been undertaken at low strain rates at elevated temperatures is severely limited.…”

“…Substituting Eqns (4), (15) and (16) into Eqn (18), the required SNOR integral is: Table 2 Values of constants for energy-density-strain-rate relations, Eqns (16) and (17) Material…”

“…It would be tempting to suggest that the value of critical strain rate, c ε , in Eqn (16), which effectively describes a 'pivot point' for the S-shaped curve, occurs at an equal mixture of trans-and intergranular cracking, see Figures 8,9 and 10. From these, it is evident that there is a strain-rate zone in the range 10 -8 s -1 -10 -6 s -1 which technically belongs to both the continuous-cycling LCF range and to the forward creep range.…”

“…As part of a sensitivity analysis, we thus re-work the SFEL example of Section 6.1, taking the fatigue damage 1/N o to be exactly as before but reducing the value of W U to 200 MPa, i.e., at the highest level of the creep failure data in Figure 8. The value of W L is retained at 2.5 MPa and the new curve fit according to Eqn (16) gives c ε = 6.39 × 10 -8 s -1 , a = 0.669 with a fit of R = 0.918, cf. Table 2.…”

“…In this regard, the energy method may be considered similar in principle, since both stress and strain are employed [5][6][7][8][9] Modern energy methods as a form of damage summation descend from Miner's [10] original proposal, which took the 'net work absorbed at failure' Sw j /W fj as an alternative parameter to the now more familiar cycle quantity SN j //N fj where the subscript 'f' denotes a failure criterion, defined further in the Nomenclature, and the subscript 'j' here denotes a cycle of type j. Ostergren [11] applied the principle to laboratory creepfatigue studies while Charkaluk [12] employed the method on a cast iron for assessing the life of exhaust manifolds. For a wide range of high temperature alloys, Takahashi et al [13] have shown how the energy method, when creep damage is taken into account, compares more favourably with other methods described above, as have Payten et al [14,15] for CrMoV steels at 550°C and a 9Cr1Mo alloy in the temperature range 500-650°C [16].…”