PSI - Issue 48

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

24

6

=  1 + 2   2 + 3   4 

(6) where  1 = 1.13 − 0.09  /  ,  2 =− 0.54 + 0.89/ ( 0.2 + / ) ,  3 = 0.5 − 0.6 1 5 +   + 14 ( 1 − / ) 24 and = 1 + 1.466 ( /  ) 1.65 . The parameter "a" refers to the depth of the crack, or the distance between the inner surface of the barrel and the deepest point of the crack. The parameter "c" is defined as half of the crack width. To determine the critical crack length for fracture under a given maximum pressure, experimentally obtained values of the fracture toughness (KIC) are taken into account, which defines the maximum stress intensity factor that can be applied. Doing the maximum K value given by Eq. 6 equal to the KIC of the material, the critical crack length can be estimated for a given maximum pressure. The critical crack length ranged from 5.1 mm to 10.5 mm for a maximum pressure (pmax) ranged from 420 to 300 MPa, respectively. Fatigue crack propagation occurs only if the applied crack driving force DK is greater than the crack propagation threshold DKth for a given load ratio  . Then the minimum crack length that is allowed to propagate can be estimated for a given maximum pressure. Literature indicates that for howitzer cannon barrels with an inside diameter of 155 mm, maximum pressure values typically range from 300 MPa to 420 MPa. Among these values, 380 MPa is the most frequently cited pressure. Fig. 3(a) shows the threshold curve DKth (a) estimated by Eq. (3) for the material A and the applied DK estimated by Eq. (5) for a maximum pressure equal to 420 MPa, which represents the most unfavourable condition (minimum threshold for long crack and maximum pressure). For this case, the minimum crack length to allow crack propagation is equal to 130 mm. If the maximum applied pressure decreases, the minimum crack length allowed to propagate increases. Fig. 3(a) shows that for the analysed crack length range the threshold for crack growth is already developed and only the threshold for long crack is needed (Eq. 1 is fulfilled). In other words, the results obtained show that for the analysed pressures the sizes of the minimum cracks that could propagate to generate the failure of the barrel substantially exceed the values that correspond to the end of the short cracks range estimated by the Eq. (4), of approximately 100-120 mm. Besides, since the minimum crack length for crack propagation at the maximum considered pressure is equal to 130 µm, it can be said that the size of the biggest non-metallic inclusions observed in Materials A and B (21.9 and 16.9 mm, respectively), are not large enough to cause fatigue crack propagation.

(a) (b) Fig. 4. (a) Threshold for crack growth for material B and applied  Kfor p max =420 MPa. (b) Crack fatigue and safe domains for howitzer cannon barrel made of materials A or B. Figure 4(b) illustrates the relationship between the maximum pressure and the minimum crack length allowed to propagate for both materials in the pressure range of 200 MPa to 900 MPa. The curves for each material delineate a