PSI - Issue 28

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

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The recent introduction by the Federal Aviation Administration, FAA (2009), of a ‘slow growth’ approach to the certification of composites has focused attention on the experimental data and the analytical tools needed to assess the growth of delaminations in composites under fatigue loads. Of direct relevance is the fact that fatigue tests on aircraft components and structures manufactured using composites reveal no, or only little, retardation (i.e. slowing) of the fatigue crack growth (FCG) rate occurs as delaminations grow, e.g. from impact damage, see Jones et al. (2017). Therefore, of course, the FCG data that are ascertained in laboratory tests must also exhibit no, or only minimal, retardation if they are to be of relevance and of use in such industrial applications. Now, the most common method for determining the FCG rate data for composites, such as continuous carbon-fibre reinforced-plastics (CFRPs), is to use a linear-elastic fracture-mechanics (LEFM) approach, see for example Brunner et al. (2009), Murri (2014) and Stelzer et al. (2012, 2014). Typically the double-cantilever beam (DCB) test is employed to determine the FCG rate, da/dN , for the delamination as a function of an energy-release rate, G , term, where a is the crack (i.e. delamination) length and N is the number of fatigue cycles. However, recent work has highlighted two major problems that arise when adopting this test method. Firstly, following the work of Paris et al. (1961), Paris and Erdogan (1963) and Paris (2014) on the fatigue of metals, a common method for plotting the experimentally-measured data for composites (and adhesives) has been in the form of the logarithmic (log) FCG rate, da / dN , versus the logarithmic (log) ∆ , where ∆ is the range of the applied energy release-rate in the fatigue cycle. Here, the term �∆ � ��� � ��� , where ��� and ��� are the maximum and minimum values of the applied energy release-rate, , in the fatigue cycle, respectively. However, such plots are not equivalent to the Paris Equation, see for example Sih et al. (1965) and Rans et al. (2011), and indeed can often give very misleading results, as shown by Jones et al. (2016). Secondly, the LEFM DCB test has for many years been reported to give a relatively large scatter in the measured test data, see for example the work of Jones et al. (2017), Stelzer et al. (2012, 2014) and Yao et al. (2014, 2017, 2018), and the main reason for this observation has only recently been clearly identified, for example see Jones et al. (2017) and Yao et al. (2014, 2017, 2017a, 2018, 2018a). These workers have shown that the main cause of the large scatter observed when using the DCB test arises from the fibre-bridging that develops behind the advancing crack tip. This fibre-bridging is generally present behind the tip of the pre-crack (i.e. pre-delamination) of extension length, a p -a o , in the DCB test specimen (i.e. prior to any cyclic-fatigue fracture measurements being taken for the test) and may develop further as the delamination propagates under the fatigue loading. This fibre-bridging carries stresses across the faces of the crack behind the tip and, hence, the presence of fibre-bridging leads to a retardation of the FCG rate. Unless this important aspect of the DCB test is taken into account this effect will lead to (a) the experimentally-measured DCB test data giving very misleading, and over-optimistic, results and (b) very large scatter being observed in the measured fatigue behaviour of a polymer-matrix fibre composite. In previous work by Jones et al. (2017) and Yao et al. (2018) a methodology for calculating an ‘upper-bound’ FCG rate curve from such typical DCB test data has been proposed. Such an ‘upper-bound’ curve for the FCG rate of the delamination is intended to give the ‘worst-case’ FCG rate curve for the fatigue behaviour of the composites, since it excludes any retardation effects on the FCG rate, e.g. from fibre-bridging occurring in the DCB test. Furthermore, the proposed methodology also takes into account the inherent experimental scatter that is typically observed in fatigue tests for all types of materials. This FCG rate curve would, therefore, act as an ‘upper-bound’ curve for (a) material development, characterisation and comparison studies, and (b) design and lifing studies. Now, in a previous paper by Yao et al. (2018) a route for obtaining this ‘upper-bound’ FCG rate curve was suggested that involved a rather extensive extrapolation of the measured data, which is not always feasible and is somewhat cumbersome. Thus, in the present paper a very much simplified methodology to determine the ‘upper-bound’ FCG rate curve is proposed and its validity is then established. 2. Background Due to the inhomogeneity and anisotropy of continuous-fibre composites, the energy release-rate, G , approach, rather than the stress-intensity factor approach, is generally used to study delamination growth in such materials. Now, following the work of Paris et al. (1961, 1963, 2014) on metals, where the range, ∆ , of the applied stress-intensity factor is invariably employed to analyse the data, then at first sight the most obvious and corresponding parameter