13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3. Free temperature model Pressure vessel components are normally designed for a long service time such as 200 000 h. Since creep is a very slow process, creep data for such a time are not available for design. They are therefore calculated by an extrapolation from the creep data of shorter time tests. One recently proposed procedure for extended extrapolation of creep rupture data is the free temperature model that allows for extrapolation by more than a factor of three in time [6, 7]. The procedure is based on a time-temperature parameter (TTP) which has the general mathematical form: ) ( ) ( )log(t wT P v T r TTP + = (1) where PTTP is the time-temperature parameter, tr is the time to rupture, and v(T) and w(T) are the functions of temperature. In the proposed procedure these functions are assumed to be polynomials in T. The TTP in Eq. 1 is referred as the free temperature model (FTM). The free temperature model is well suited for austenitic stainless steels where the temperature dependence of the creep rupture curve is non-monotonous [7]. The master curve is expressed by the creep stress as a function of polynomial in the TTP: j n j j a TTP P = ∑ =0 ) log( σ (2) The coefficients aj are fitted to the creep rupture data and the stress – rupture time relations are derived. The reason for using a polynomial in log (tr) rather than log (σ) which is the more common approach, is that it has been shown that this improves the accuracy in extended extrapolated values [7]. The extrapolation was performed in a Matlab program. The coefficients to the polynomials are derived by a non-linear least squares fit to the creep data. To extrapolate the creep rupture data, the polynomials in Eq. 1 were both set to order 3 and the master curve, Eq. 2, was set to a second order polynomial. Figure 3 shows the master curve for the free temperature model of the austenitic stainless steel grade, UNS S31035, which is based on creep data at 550°C, 600°C, 650°C, 700°C and 800°C.
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