PSI - Issue 5

G. Lesiuk et al. / Procedia Structural Integrity 5 (2017) 904–911 Lesiuk et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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Based on the (13), the possibility of construction the energy fatigue crack growth rate model depends on the theoretical crack model, plastic zone model etc. So, there is no one, but hundreds possibilities modelling of fatigue crack growth in term of the energy approach. In present paper, the detailed determination of the last form of the kinetic equation, will be not presented here. Details of the existing models are available in works of Szata (2002), Szata and Lesiuk (2009) based on phenomenological approach as well as based on Dimensional Analysis Approach (Szata 2002, Lesiuk 2017). According to Szata (2002) and using Dudgale model, the new kinetic energy formula is presented (Szata 2002, Szata and Lesiuk 2009) = (∆ ) . (14) In (14), D and m are Paris’ law -like constants, but the  H represents a new “ crack driving force ” called as an energy parameter:

c

 B K H W 1

(15)

 

   

   

2 Im

ax

2

K

fc

where: W c – energy per thickness dissipated in each cycle of loading, K Imax – maximal value of stress intensity factor, K fc – critical value of cyclic stress intensity factor, B – thickness of component (specimen).

Of course, the energy concept can involve more than one energy parameter - W c or its part. This problem was considered by the Ostash (2007) in conjunction with the different regions of FCGR diagram. The authors’ suggested to use different part of energy for different crack growth rates – see Fig. 3.

Fig. 3. Schematic diagrams of the dependences of crack-tip opening displacement on the process of loading and unloading of the specimen for low (left), medium (middle), and high (right) growth rates of the fatigue macrocrack, Ostash (2007)

2.2. Cyclic J-integral description of FCGR

The  J parameter range for mode I is calculated by using the following relationship (Rozumek, 2009, Rozumek, Macha, 2009)     / n J 1 K / E Y a p 2 1 2 I 2 I          , (16) where the first term of (16) concerns the linear-elastic range, and the other term refers to the elasto-plastic range, a – crack length, E – Young’s modulus,  - Poisson’s ratio,  - ranges of stresses under bending in the near crack tip (notch),  p – range of plastic strain under bending in the near crack tip (notch). The stress intensity factors ranges  K l for mode I is calculated from (Rozumek, Marciniak, 2011)   0 1 n I a a K Y      , (17)