PSI - Issue 54

Sjoerd T. Hengeveld et al. / Procedia Structural Integrity 54 (2024) 34–43

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6

S.T. Hengeveld et al. / Structural Integrity Procedia 00 (2023) 000–000

10

10 20 30 40 K II [MPam 0 : 5 ]

Troll 4 e (2014) L e 0 : 080mm L e 0 : 020mm L e 0 : 005mm

-1.5

0 : 5 ]

-2

5

" a 0 : 05mm " a 0 : 10mm " a 0 : 20mm

y [mm]

K I [MPam

-2.5

-6-4-2 0 2 4 6 x/b 0

0

4 4.5 5 5.5 x [mm]

-6 -4 -2 0

2

4

x/b

(a)

(b)

(c)

Fig. 5: SIFs as function of relative loading position; (a) mode I SIF, (b) mode II SIF, (c) Predicted crack paths for di ff erent crack increments ∆ a

(a)

(b)

(c)

2 mm, L

2 mm, L

3 mm

Fig. 6: Element meshes: (a) L e = 8 × 10 −

e = 2 × 10 −

e = 5 × 10 −

tional behaviour is included by changing the assumed friction coe ffi cient in the Mohr-Coulomb friction model. This subsection shows the e ff ect of various friction coe ffi cients on the SIF evolution for an inclined edge crack. All simulations are made with a o = 6mm and α = 15 deg. Two di ff erent traction coe ffi cients are used, namely, µ r − w = 0 . 2and µ r − w = 0 . 4. Figure 7 shows the results in terms of SIF. The influence of µ c on K I appears to be limited. The crack opens when the load reaches the crack mouth, i.e x / b = 0. Due to the crack inclination angle, the crack opening is counteracted by the friction force, so an increase in friction coe ffi cient reduces the max K I .For0 ≤ x / b < 2, a large part of the load patch is above the crack, causing it to close, and therefore K I is zero. For x / b > 2 the crack is fully open causing that there is no e ff ect of the friction coe ffi cient on K I . The e ff ect of the friction coe ffi cient on K II is more profound. Obviously, in the region were the crack is open ( K I > 0), the e ff ect of friction is very limited. K II is reduced with increasing friction coe ffi cient in the interval 0 ≤ x / b < 2. For a high friction coe ffi cient of µ c = 0 . 5, the location of maximum K II shifts from x / b ≈ 0 . 6, with the load above the crack mouth, to x / b > 2 . 0 with the load on the right side of the crack. Figure 7c shows the minimum (crosses) K II and maximum (circles) K II as a function of the friction coe ffi cient. The dashed lines are results of the current research, the solid lines are results for the same geometry obtained by Dubourg and Lamacq (2002). The blue and red curves are results obtained with µ r − w = 0 . 2 and µ r − w = 0 . 4, respectively. The results are in good agreement with the results obtained in Dubourg and Lamacq (2002). The minimum value of K II , K min II is insensitive to µ c , because it occurs when the crack is fully open ( K I > 0). On the other hand, the maximum K II decreases significantly with increasing friction coe ffi cient. Based on these results, it is shown that a good approximation of the friction coe ffi cient is essential in determining the FCGR. Figure 7d shows the predicted crack paths for several friction coe ffi cients, using the previously defined frame work, with a fixed crack increment of ∆ a = 0 . 1mmand µ r − w = 0 . 4. A low friction coe ffi cient results in a large K II component, leading to a sharp angle. However the predicted path of the crack with µ c = 0 . 5 is in between those of µ c = 0 . 1 and µ c = 0 . 3. This is due to the previously mentioned change of location of the maximum K II , from x / b ≈ 0 for µ c ≤ 0 . 3 to x / b ≈ 2 . 5 for µ c = 0 . 5, see Figure 7b. It should be noted that this predicted crack path is strongly dependent on the considered loads and boundary conditions. For future work it is recommended to expand the loads,