PSI - Issue 48

Gašper Fašun et al. / Procedia Structural Integrity 48 (2023) 19–26 Fašun et al/ Structural Integrity Procedia 00 (2023) 000–000

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stress range  are shown in Fig. 3. The number of cycles in each step in the thermographic procedure (each  ) was limited to 15000 cycles. For the initial value of the loading stress, a stress range of 600 MPa was chosen. Using the results shown in Table 3 and the procedure described in chapter 3.1. the value of the fatigue limits,  eR , are estimated: 605 MPa for the material A, and 548 MPa for material B.

Fig. 3. ∆ as a function of stress range  in thermographic testing method for fatigue limit estimation.

3. Fracture mechanic’s approach A fracture mechanics approach based on fatigue resistance curve concepts was used in order estimate the fatigue resistance of the analysed howitzer cannon. In this approach the total applied  K is compared with the threshold curve  K th between the initial crack length given by the biggest defect size, a i , and the final crack length that produces the failure of the component, a crit . In order for the crack to grow between these two limits ( a i and a crit ), the applied ΔK has to exceed the ΔK th threshold at any crack length. The fatigue endurance of the configuration will be given by the applied nominal stress for which ΔK equals ΔK th at any crack length in the integration interval. In order to include the short crack stage in the analysis, it is necessary to estimate the development of the fatigue propagation threshold. For this, the model proposed by Chapetti is used here [15]. The Chapetti model estimates the threshold for crack growth in terms of the stress intensity factor range for a given stress ratio, as follows: ∆ ℎ =∆ ℎ  = ∆  + ∆ ℎ − ∆  1 −  − − (3) ∆  =∆   = 4 1  ∆  ∆ ℎ −∆  (4) , where Y is taken conservatively as 0.65 (semi-circular crack). The  K dR parameter, a microstructural threshold, represents the minimum driving force that can be applied to propagate a crack of size d . From this value, the threshold develops until reaching the maximum value defined by the long crack threshold,  K thR . Further details of this model can be found in references [15] and [16]. The applied stress intensity factor is estimated using the following expression [17]: =  =   ∙ 0,97   2 +݅ 2   2 −݅ 2 + 1 − 0,5   ݅  (5) where =  −݅ is the wall thickness,   = /  ∙ (  −݅ ) /2 is the hoop stress and  is a factor expressed by the following equation [32]: