o 3 1 o θ = 850 C ε = 10 s 001 ε [%] 001 001 V = 0.68 f V = 0.58 f Data [MPa] Figure 1: Effect of precipitate volume fraction on the <001 >monotonic response of CMSX4 at 850◦C and 10−3 1/s. Symbols represent experimental data for the Vf =0.68 case V = 0.68 f V = 0.58 f S S B B Time [s] [MPa] a a a a Figure 2: Predicted effect of the evolutionary behaviour of the {111} <011 >internal slip system variables for the monotonic stress-strain curves shown in Fig. 1 associated with pure slip, and an elastic component, Fe, which accounts for the elastic stretching and rigidbody rotations. Thus, F=FeFp. For details, refer to [4],[5]. The model calibration was carried out with the twelve octahedral ({111} < 011 >) and six cubic ({100} < 011 >) slip systems considered to be potentially active. The reference data to calibrate the model for vf =0.68 were obtained from uniaxial monotonic, cyclic and creep tests, and, the data for vf <68% from periodic unit cell analyses (see [3],[4]). Typical predictions of the monotonic uniaxial behaviour of CMSX4 at 850◦Cand 10−3 1/s are shown in Fig. 1 for two different γ’ volume fractions, namely 58 and 68%, together with experimental data for the latter case. Figure 1 shows that a 10% reduction in volume fraction results in a 40% decrease in the superalloy steady state flow stress at this temperature and strain rate. The corresponding evolutionary behaviour of the internal slip system variables for each of the eight active (and equally stressed) {111} < 011 > systems is shown in Fig. 2. The correspondence between the macroscopic softening and hardening behaviour and the steady state values of the slip resistance and the back stress can be clearly inferred from Figs. 1 and 2. For instance, the macroscopic softening observed for vf =0.68 is associated with a large decrease in the slip resistance, from its initial value of 338 MPa to its steady state value of 201 MPa. Even though a similar Sα softening trend is seen for vf =0.58, the macroscopic effect is negligible (see Fig. 1). 3
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