PSI - Issue 28

Rhys Jones et al. / Procedia Structural Integrity 28 (2020) 26–38 Author name / Structural Integrity Procedia 00 (2019) 000–000

33

8

1.0E-04

1.0E-05

1.0E-06

1.0E-07

1.0E-09 da/dN (m/cycle) 1.0E-08

y = 1.73E-08x 2.22E+00 R² = 9.94E-01

0.1

1

10

100

(  √ G -  √ G thr )/ √ (1- √ G max / √ A) (√(J/m 2 ))

48 ply 3.1 mm 48 ply 69.6 mm 24 ply 1.3 mm 24 ply 58.3 mm Test 3 58.1 mm

48 ply 12.5 mm 48 ply 83.9 mm 24 ply 10.4 mm Test 3 2.65 mm Test 3 85.2 mm

48 ply 20.4 mm

48 ply 31 mm

48 ply 39.8 mm Mode II R = 0.3 24 ply 35.5 mm Test 3 49.6 mm

48 ply 54.4 mm Mode II R = 0.1 24 plies 48.9 mm Test 3 37.2 mm

48 ply 101.2 mm Mode II R = 0.5

24 ply 20.9 mm Test 3 11.6 mm

24ply 27.7 mm Test 3 24.6 mm

45 Interface 3.3 mm 45 Interface 9 mm 45 Interface 20.9 mm 45 Interface 29 mm 45 Interface 38 mm 45 Interface 51.3 mm 45 Interface 62.8 mm Test 1 2.7 mm R = 0.1 Test 1 14.8 mm R = 0.1 Test 1 28 mm R = 0.1 Test 1 40 mm R = 0.1 Test 1 53.6 mm R = 0.1 Test 2 4.1 mm R = 0.1 Test 2 16.5 mm R = 0.1 Test 2 43.8 mm R = 0.1 Test 2 60.3 mm R = 0.1 Test 2 79.6 mm R = 0.1 Test 1 3.4 R = 0.5 Test 1 11.6 R = 0.5 Test 1 19.5 R = 0.5 Test 1 26.6 mm R = 0.5 Test 1 37.2 mm Test 1 47.5 mm Test 1 59.8 mm Test 1 68.1 mm Test 2 4.1 mm Test 2 12.7 mm Test 2 20.5 mm Test 2 27.7 mm Test 2 39.5 mm Test 2 51.3 mm Test 2 63.4 mm Test 2 79.5 mm Yao Test 1 9.9 mm Yao Test 1 20.9 mm Yao Test 1 29.3 mm Yao Test 1 38.0 mm Yao Test 1 51.3 mm Yao Test 1 62.9 mm Yao Test 2 11.4 mm Yao Test 2 20.5 mm Yao Test 2 28.4 mm Yao Test 2 37.4 mm Yao Test 2 59.9 mm Yao Test 2 70.6 mm Yao Test 3 12.8 mm Yao Test 3 22.6 mm Yao Test 3 33.7 mm Yao Test 3 46.7 mm Yao Test 3 58.8 mm Yao Test 3 88.4 mm

Fig. 3. The single, linear, ‘master’ relationship obtained for all the seventy-seven tests from Yao et al. (2014, 2017, 2017a, 2018, 2018a) calculated using the Hartman-Schijve approach, i.e. Equation (2).

3.4 The ‘upper-bound’ FCG rate curve As explained above, the concept of an ‘upper-bound’ curve for the FCG of the delamination is that such a curve is intended to give the ‘worst-case’ for the fatigue behaviour of the composite, since it excludes any retardation effects on the FCG rate, e.g. from fibre-bridging effects in the DCB test. Furthermore, it also should take into account the inherent experimental scatter typically observed in fatigue tests. This FCG curve will therefore act as an ‘upper-bound’ curve to all the experimentally-measured data for a composite and gives a curve which can be used with confidence for industrial applications. Now, firstly, from the Mode I results shown in Fig. 2, then from plotting the single, linear, ‘master’ Hartman-Schijve relationship, see Fig. 3, a mean value of ∆� ��� of 8.40  (J/m 2 ), with a standard deviation (sd) of 1.90  (J/m 2 ), is required to obtain the ‘master’ Hartman-Schijve relationship. Obviously, the statistical nature of the test data needs to be considered and, clearly, the test data should encompass a relatively wide range of the test variable which is influencing the extent of fibre-bridging. Since such a test variable will control the degree of retardation of the FCG rate that is observed in the measured results. It is difficult to be rigorous in this respect but employing a wide range of values of the initial pre-crack extension length, a p - a o , used for the fatigue test is a clear route to achieving this goal. The work of Yao et al. (e.g. 2014, 2017, 2017a, 2018, 2018a) does cover a very wide range of values of the pre extension crack length, a p - a o , and represents an excellent example of how it can be assured that the measured FCG rate data does indeed encompass a wide range of fibre-bridging effects, i.e. going from very little FCG retardation to significant FCG retardation in the measured data as the value of a p - a o is steadily increased. However, it should be noted that if no test data are determined when relatively limited fibre-bridging, and hence little FCG rate retardation,