PSI - Issue 28

Slobodanka Boljanović et al. / Procedia Structural Integrity 28 (2020) 2370 – 2377 Slobodanka Boljanović et al. / Procedia Structural Integrity 00 (2020) 000 – 000

2373

4

Fig. 1. Geometrical sizes: (a) the dog bone specimen/plate; (b) the finite plate.

Since the part-through corner cracks pose a threat to plate-type structural components serving in aggressive load/environment conditions, the impact of the load is theoretically analyzed through the fracture mechanics parameter M expressed as follows:

    



1 

 (1 ) (1 ) R R 

   5 R

0

0

0.5





M

  R



(10)

  (1.05 1.4 0.6 ) 2 R R

0.5

1





  R

where R is stress ratio,  and  1 are experimental parameters related to material type and environmental conditions. Moreover, by integrating relevant equations for the crack growth rate, the failure strength may be estimated in terms of number N of loading cycles through depth and surface crack growth directions:

a

b

 A C M K da (

 B C M K db (

f

f





N

N





,

(11)

m

m

)

)

A

B

A

B

a

b

0

0

where (a 0 , b 0 ) and ( a f , b f ) are initial and final crack length in depth and surface direction, respectively. In designing against fatigue, the novel numerical- analysis software based on the Euler’s algorithm is developed in the present research work to solve the above complex-valued functions and to analyze the driving mode progression associated with stress-raiser and stress-ratio effects under cyclic loading. 4. Applications of the developed computational algorithm 4.1. Failure stability evaluation Firstly, the fatigue strength of the plate with a quarter-elliptical corner crack (Fig. 1a) is estimated under constant amplitude cyclic loading, in the case of stress ratios equal to R = -1 and 0. In such a residual life analysis, the dog bone plate, whose width and thickness are equal to w = 25.4 mm and t = 2.3 mm, respectively, is made of 2024 T3 aluminium alloy ( C A = 3.3 10 -10 , m A = m B =3.02). Further, the initial corner crack-like flaw is characterized by the crack length a 0 = b 0 = 20  m in depth and surface directions, respectively, whereas relevant maximum stresses applied are shown in Table 1. The interaction between flaw/crack effects and load-environmental effects, which can have devastating impact on the bearing capacity of plate-type components, is herein examined through Eqs. (1) to (11). The fatigue performance in terms of the number of loading cycles versus crack length in depth and surface direction are shown in Fig. 2a, 2b