PSI - Issue 28

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

32

7

1.0E‐04

1.0E‐05

1.0E‐06

1.0E‐08 da/dN (m/cycle) 1.0E‐07

1.0E‐09

18

 √ G (√(J/m 2 ))

2

48 ply 3.1 mm 48 ply 39.8 mm 48 ply 101.2 mm 24 ply 27.7 mm 32 plies 2.7 mm 32 plies 37.2 mm 45 Interface 9.0 mm 45 Interface 51.3 mm Test 1 19.5 mm Test 1 58.9 mm Test 2 20.5 mm Test 2 64.3 mm Yao Test 1 29.3 mm Yao Test 2 11.4 mm Yao Test 2 75.6 mm Yao Test 3 46.7 mm

48 ply 12.5 mm 48 ply 54.4 mm 24 ply 1.3 mm 24 ply 35.5 mm 32 plies 11.7 mm 32 plies 58.2 mm

48 ply 20.4 mm 48 ply 69.6 mm 24 ply 10.4 mm 24 plies 48.9 mm 32 plies 24.6 mm 32 plies 85.2 mm Test 1 3.4 mm Test 1 37.2 mm Test 2 4.1 mm Test 2 39.5 mm Yao Test 1 9.9 mm Yao Test 1 51.3 mm Yao Test 2 28.4 mm Yao Test 3 22.6 mm Yao Test 3 88.4 mm 45 Interface 29.0 mm

48 ply 31.0 mm 48 ply 83.9 mm 24 ply 20.9 mm 24 ply 58.3 mm 32 plies 49.6 mm 45 Interface 3.3 mm 45 Interface 38.0 mm Test 1 11.6 mm Test 1 47.5 mm Test 2 12.7 mm Test 2 51.3 mm Yao Test 1 20.9 mm Yao Test 1 62.9 mm Yao Test 2 37.4 mm Yao Test 3 33.7 mm

45 Interface 20.9 mm 45 Interface 62.8 mm Test 1 26.6 mm Test 1 68.1 mm Test 2 27.7 mm Test 2 79.5 mm Yao Test 1 38.0 mm Yao Test 2 20.5 mm Yao Test 3 12.8 mm Yao Test 3 58.8 mm

Prior upper‐bound FCG curve

Predicted upper bound curve

Fig. 2. Values of logarithmic da/dN versus logarithmic ∆√ replotted from many different test programs using the DCB Mode I specimen, as reported in Yao et al. (e.g. 2014, 2017, 2017a, 2018). Added to this figure are the values from Fig. 1. Values are given in the legend for the pre crack extension length, a p - a o , prior to the start of measurements from a DCB fatigue test. The ‘upper-bound’ curves for the FCG rate using the ‘mean-3sd’ values for ∆� ��� , as determined using the prior, see Yao et al. (2108), and the present prediction methodologies are shown. 3.3 The Hartman-Schijve ‘master’ relationship The next step is to explore whether the data shown in Fig. 2 can all be brought together to give a single, linear, ‘master’ relationship by replotting the data in the form of the Hartman-Schijve relationship, i.e. Equation (2), as previously proposed by Jones et al. (2015, 2016, 2017) and Yao et al. (2018).To achieve this, a value of the fatigue threshold, ∆� ��� , for each test, and the values of the other constants A , D and n , are chosen so as to give a linear relationship with the lowest value of the coefficient of determination to fit Equation (2), as explained in Appendix B. Fig. 3 clearly demonstrates that a single, linear, ‘master’ relationship can be obtained from all the seventy-seven test results shown in Fig. 2. Therefore, by allowing for small changes in the threshold term, ∆� ��� , all the experimental results may be collapsed to give a unique, linear, ‘master’ Hartman-Schijve relationship. This ‘master’ representation captures all the results the many tests and includes: (a) the effect of the pre-crack extension length, a p - a 0 , used, (b) the scatter observed in the test programs employing (nominally) replicate composite specimens, (c) the results from the different stress ratios used, i.e. the R -ratio, (d) the results from the different lay-ups and thicknesses of the composite specimens employed, and (e) even the results from the different modes of loading, i.e. Modes I and II. This unique, ‘master’ relationship has a coefficient of determination, R 2 , of 0.994 and a slope, n , which has a relatively low value of about two.