PSI - Issue 52

Marie Kvapilova et al. / Procedia Structural Integrity 52 (2024) 89–98 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 4. Different creep curves for the GTD 111 superalloy at 950°C and 125 MPa: (a) standard creep curve, (b) modified creep curve.

The replotted modified curves enable a rigorous determination of the transition between primary and secondary creep region. At the same time, using replotted curves the values of the minimum creep rate, m   , can be rigorously determined in what follows. Significant differences were found in creep behaviour in the tertiary stage at different testing temperatures. Comparison of Figs. 3(b) and 4(b) illustrates sharply increasing the strain rate   in the tertiary creep at 950°C perhaps due to faster development of creep damage (see 3.4).

3.3. Analyses of operating creep mechanisms

The variation of the minimum creep rate m   and the time to fracture t f with stress and temperature could be used to identify the operating mechanisms in creep of the GTD 111 superalloy. Simplified descriptions along with phenomenological and empirical approaches are used for predictive modelling of the creep processes (Čadek (1988), Kassner (2009)). The power-law constitutive equation (Mukherjee et al. (1968), Cui et al. (2017)), which is consistent with Norton´s Law (Norton (1929)) is commonly used as (1) where m   is the minimum creep rate, A being a constant for a given material, σ is the applied stress, Q C is the activation energy for creep, k is Boltzmann constant, T is the testing temperature, and n is the apparent stress exponent of the minimum creep rate which is defined as / ) exp( Q kT − A C n m =   

  .

(2)

( ln

/ ln ) 

n

= 

m

T

The activation energy for creep Q C can be defined as

 (3) Analogously to Eq.(1), the stress dependence of the time to fracture (creep life) t f can be expressed (Maruyama (2008)) as / ) exp( Q kT t B f m f − = −  /kT), (4) where B is a material constant, Q f is the activation energy for creep fracture, and m is the stress exponent of the time to fracture t f which can be described as  / ( / m  −  ) ( ln RT Q C = 

(5)

( ln

/ ln )  

m

f t

=− 

T

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