Modelling of TMF Crack Initiation in Smooth Single-Crystal Superalloy Specimens

In this paper the TMF crack initiation behaviour of the single-crystal nickel-base superalloy MD2 is investigated and modelled. TMF tests were performed in both IP and OP for varying mechanical strain ranges in the [001] crystallographic direction until TMF crack initiation was obtained. A crystal plasticity-creep model was used in conjunction with a critical-plane approach, to evaluate the number of cycles to TMF crack initiation. The critical-plane model was evaluated and calibrated at a stable TMF cycle, where the effect of the stress relaxation had attenuated. This calibrated criticalplane model is able to describe the TMF crack initiation, taking tension/compression asymmetry as well as stress relaxation anisotropy into account, with good correlation to the real fatigue behaviour. Introduction In the hot sections of gas turbines the components are often made of single-crystal nickel-base superalloys to withstand the high temperatures while still maintaining good mechanical properties, thus achieving a good efficiency of the gas turbine and in turn reducing pollution [1, 2]. During the startup, steady-state operation and shut-down cycle the temperature and load will vary in the gas turbine, hence the components will be exposed to thermomechanical fatigue (TMF). Out-of-phase TMF loading conditions were investigated by Amaro et al. [3] for the single-crystal nickel-base superalloy PWA1484. In this paper a mechanism-based crack initiation model was developed and validated. The model takes crystal orientation, applied strain amplitude and stresses, temperature, cycle time and surface roughness into account and a good estimate of the TMF life is achieved. In the work of Moverare et al. [4], where the deformation and damage mechanisms of the single-crystal superalloy CMSX-4 were investigated under TMF loading, it was concluded that the fracture surfaces were entirely crystallographic (parallel to a (111) slip plane), hence indicating that a crack is preferably to initiate and propagate on one of these crystallographic slip planes. As single-crystal nickel-base superalloys contain an inherent internal structure of discrete slip planes and are deformed in preferred slip directions, it is thus physically motivated that these crystallographic planes may act as potential crack initiation planes. Thus, the critical-plane theory, see e.g. [5], is a useful technique for studying TMF crack initiation in single-crystal material. In the paper by Leidermark et al. [6] a critical-plane model was derived to suit the low-cycle fatigue behaviour of the single-crystal nickel-base superalloy MD2 with good correlation to experimental fatigue crack initiation lives. The objective of this paper is to define and evaluate a critical-plane model, for describing the TMF crack initiation behaviour of the single-crystal nickel-base superalloy MD2 during both in-phase (IP) and out-of-phase (OP) loading conditions for the [001] crystal orientation. Table 1: Experimental test data of the smooth specimens. Specimen S1[001] S2[001] S3[001] S4[001] S5[001] Diameter [mm] 6.0 6.0 6.36 6.0 6.29 ∆εmech [%] 1.1 −1.1 1.25 1.4 −1.4 Ni [cycles] 1102 2158 728 224 156 θ [◦] 9.4 10.2 3.3 9.5 4.5 φ [◦] 31.1 41.3 31.3 22.1 16.5 Experiments In this study the nickel-base single-crystal superalloy MD2 with chemical composition Ni-5.1Co6.0Ta-8.0Cr-8.1W-5.0Al-1.3Ti-2.1Mo-0.1Hf-0.1Si in wt. % was used. The material was first solution heat treated at 1290 ◦C for 8 h. Afterwards, a two-stage ageing process with 3 h at 1100 ◦C and 24 h at 850 ◦C was performed. Smooth specimens in the nominal [001] crystal orientation were investigated, where the deviation (θ, φ, defined as in [7]) from the ideal orientation was determined to be less than∼ 10◦ for all specimens. The test specimens were machined from cast bars to a diameter of approximately 6 mm. An Instron servo-hydraulic TMF machine with induction heating and forced cooling was used for the tests. Both IP and OP strain-controlled TMF cycles were applied in which the temperature was cycled between 100−750 ◦C with a loading rate of 5 ◦C/s, and during which a hold-time of 5 min was applied at maximum temperature, see Fig. 1. Five test specimens were tested at different mechanical strain ranges (∆εmech), two in both IP and OP loading and the last one in only IP loading, where an extensometer with gauge length of 12.5 mm was used. All specimens were cycled until a 60% global load-drop was obtained (defining failure). The number of cycles to TMF crack initiation (Ni) was then determined by a 2% load-drop of the maximum tensile stress obtained in each cycle, see Table 1 for the experimental data and Fig. 2 for the stress responses of the specimens.