PSI - Issue 2_B

Andreas J. Brunner et al. / Procedia Structural Integrity 2 (2016) 088–095 Author name / Structural Integrity Procedia 00 (2016) 000–000

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1. Introduction

CFRP epoxy composites are increasingly used in structures, especially where low specific weight and simultaneously high specific strength and stiffness offer advantages, e.g., in the aerospace and automotive sectors. Use of these composites is still limited by their comparatively weak interlaminar delamination resistance and shear strength. Therefore, test methods for quasi-static and fatigue delamination resistance are developed. For a long time, analysis of fatigue fracture test data for composites has been based on so-called Paris-plots, i.e., double logarithmic presentation of the (average) delamination length per cycle (da/dN) versus a quantity relating to the critical energy release rate G C for the respective fracture mode, e.g., mode I for tensile opening loads based on an analysis by Paris and Erdogan 1963. Literature (e.g., Hojo et al. 1987, Brunner et al. 2009, Stelzer et al. 2012) chooses either the maximum applied G-value (G Imax in case of mode I) or the difference between the maximum and minimum applied G-value defined by the so-called R-ratio (  G = G Imax – G Imin ) for the Paris-plot. From the graphical presentation of the data in this form, a so-called threshold value of G is defined (labelled G thr ), below which no delamination propagation is expected. This threshold value, with appropriate safety factors, can then be used in design of composite structures in the so-called “no growth” approach (see, e.g., Jones et al. 2014 for details). Recently, as discussed by Jones et al. 2014 also, this design criterion has been reconsidered in view of the so-called “short crack effects” observed in metal alloys (see, e.g, Smith 1977) and it has been realized that a controlled amount of crack propagation may have to be allowed in structures (the so-called “damage-tolerant design approach) requiring periodic non-destructive inspection for cracks and their propagation throughout the service life. It is not fully clear yet, whether short crack effects analogous to those observed in metals exist in CFRP or polymer composites in general as well, but there is accumulating evidence that this may be the case (Jones et al. 2014 discuss one example). This requires experimental testing and analysis methods for determining the delamination propagation behavior of structural CFRP composites to be used in structural design. Analysis of polymer composite fatigue fracture data is currently discussed in literature in great detail and various effects have been pointed out that will affect the Paris type curves, and hence, also their interpretation. One aspect is that the original Paris-type analysis is based on critical stress intensity factors and that these are replaced by critical energy release rates for polymer composites. As discussed by, e.g., Pascoe et al. 2013a, a double-logarithmic relation between da/dN and the square-root of the critical energy release rate G C (or analogous quantities like  G) seems better suited to describe the fatigue fracture behavior of CFRP than the Paris-type equation. Pascoe et al. 2015 also point out that both, maximum strain energy release rate and stress energy release rate range may have limitations in capturing the fatigue fracture behavior of CFRP, and interference from additional defects, e.g., multiple delaminations are discussed by Pascoe et al. 2013b. Another aspect is the effect of fiber bridging that is likely to occur in unidirectional CFRP laminates, and that is discussed in detail, e.g., by Yao et al. 2014 and 2016. The present contribution looks into a modified Hartman Schijve fitting approach for analyzing CFRP fatigue fracture data under different loading modes. As discussed by Jones et al. 2012 and 2014 and detailed in section 2 below, this approach is based on a double-logarithmic plot of da/dN versus a quantity with square-root dependence on energy release rate G on one side (e.g., discussed by Pascoe et al. 2013a), and, on the other, includes a threshold G thr as explicit fit parameter. As further advantage, Hartman Schijve fitting might be suitable to accommodate the short-crack effects that possibly occur in CFRP, analogous to the data shown for metal alloys in Fig. 3 in Jones et al. 2014. In spite of these advantages for analysis of fatigue fracture data, the question remains how accurately Hartman-Schijve fitting can quantify the fatigue fracture behavior of CFRP, in particular the value of G thr for the no-growth design and also with respect to stable delamination propagation for damage tolerant designs in view of experimental scatter that, based on round robin testing (Stelzer et al. 2012, 2014), can amount to up to a decade on the double logarithmic scales of the data plots. 2. Material, testing, and analysis approach

2.1. Material and testing

The material for the fatigue test data is a CFRP epoxy composite (type IM7/8552) with double cantilever beam (DCB) specimens manufactured by two different suppliers from the same type of prepreg (see Murri 2013 for details). The DCB specimens were tested for quasi-static mode I toughness (ASTM D5528) at a rate of 0.02