Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

TL;DR: In this paper, the authors presented a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer-matrix composites, which is based on the identification of the crack tip location using Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates.

About: This article is published in Composites Science and Technology.The article was published on 2010-11-15 and is currently open access. It has received 175 citations till now. The article focuses on the topics: Digital image correlation & Composite laminates.

Summary

1. Introduction

• Sophisticated kinematic representations of failure mechanisms [8,9], and cohesive elements to deal with delamination [10,11], the accurate prediction of intralaminar fracture mechanisms still presents several challenges.
• While this assumption is valid under smallscale bridging conditions, the shape of the cohesive law plays a fundamental role in the prediction of fracture under large-scale bridging conditions [12].
• To account for these different failure mechanisms, a combined linear-exponential softening law for fiber tensile fracture has been proposed [5,6], and it was demonstrated that a simple linear softening law is unable to predict the load–displacement relation obtained in a cross-ply Compact Tension (CT) test specimen, while a bi-linear softening law provides an accurate prediction [13].
• In addition, the experimental determination of the exact location of the tip of a kink-band is even more difficult than for the CT specimens.
• An automatic algorithm that post-processes the full-field data provided by the DIC system during the CT and CC tests is used to detect the crack tip location and to establish the R-curve from the surface measurements of the displacement and strain fields.

2. Identification of the crack tip location

• The algorithm used to identify the crack tip location in the CT and CC test specimens is based on the work of Grégoire [19].
• The contour integral J, which is defined along a region where the material is linear-elastic, is therefore used to calculate the crack resistance curve of the CC and CT test specimens.
• The same happens with the sum of the thicknesses of the all the 90 plies.
• To simplify the calculations, the simple rectangular contour shown in Fig. 6 is selected.
• The differentials dx1 and dx2 are taken as the differences between the centers of adjoining subsets, measured along the corresponding axes.

4.1. Configuration of the test specimens

• The material used in this work is unidirectional carbon-fiber reinforced epoxy Hexcel IM7-8552.
• The elastic properties of IM7-8552, measured in a previous investigation [18], are shown in Table 1. E1 and E2 are the longitudinal and transverse.
• The specimens were finally machined to their final geometry, shown in Fig. 7 (CT specimen), and in Fig. 8 (CC specimen).
• In the set-up, the optical system was positioned perpendicular to the surface of the specimen mounted into the testing machine (Fig. 9).
• The facet step (i.e., the distance between adjacent facets) can also be set either for controlling the total number of measuring points over the region of interest, or for enhancing the spatial resolution by slightly overlapping adjacent facets.

4.2. Compact tension

• The load was measured using the 100 kN load cell, and the displacement was measured using the linear variable differential transformer (LVDT) connected to the hydraulic actuator of the test machine.
• Fig. 12 shows a good correlation between the FEM and DIC data reduction methods.
• This means that the fracture process zone that bridges the crack has a minor effect on the displacement and strain fields in the regions where the Finite Element model computes the J-integral.
• Fig. 13 shows the R-curves obtained from the three CT tests.
• Fig. 13 also shows the mean value of the fracture process zone, 3.4 mm, and the mean values of the initial fracture toughness and that corresponding to steady-state crack propagation, 97.8 kJ/m2 and 133.3 kJ/m2 respectively.

4.3. Compact compression

• A non-linear response is observed in the load–displacement relation before the peak load is attained.
• The reason for this fact is that the FEM-based calculation of the J-integral does not account for the contact and load transfer across the band of the kinked fibers.
• On the other hand, the DIC-based method uses the actual displacement and strain fields on the surface of the specimen, provided that the contours selected do not include delaminated regions, thus resulting in an improved R-curve.
• Delamination associated with the propagation of the kink-band from the initial notch was also observed in the CC tests.
• In addition, the presence of delamination invalidates the assumption of a two-dimensional crack, and of constant strain through the thickness of the laminate (assumption used in Eq. (6)).

5. Conclusions

• This paper presents a new method to measure the crack resistance curves in CT and CC test specimens manufactured using cross-ply CFRP composite laminates.
• The method was implemented in a ”Matlab” code that obviates the need of any complex pre- and post-processing of the test data, either based on FEM or standard data reduction methods, and enables the real-time generation of R-curves during a test.
• The mean value of the associated cohesive zone is 3.4 mm.
• The DIC-based method is an improvement over FE-based data reduction methods because it is based on the actual displacement field on a pre-defined contour that does not include delaminated regions.
• The values computed for the fracture toughness using the CC specimen do not account for the energy dissipated by the delamination that accompanied the propagation of the kink-band.

Figures

Fig. 11. Load–displacement in a CT test specimen.

Fig. 14. Load–displacement in a CC test specimen.

Fig. 12. R-curves extracted from a CT specimen using FEM and DIC.

Fig. 13. R-curves extracted from all CT specimens using DIC, and corresponding mean R-curve. Each symbol corresponds to one CT test.

Fig. 1. Points M and N before and after crack propagation.

Fig. 2. Different position of the discontin

Fig. 15. R-curves extracted from a CC specimen using FEM and DIC.

Fig. 3. Relation between the crack length and time for different values of a.

Table 1 IM7-8552 ply elastic properties.

Fig. 5. Conservation integral. Fig. 6. Contour used for the calculation of the J-integral.

Fig. 8. Geometry of compact compression test specimen (after [14], dimensions in mm).

Fig. 10. Strain field obtained by ARAMIS: eyy(x), with 0–y perpendicular to the crack.

Fig. 7. Geometry of compact tension test specimen (after [14], dimensions in mm).

Fig. 9. Compact tension test specimen and DIC system.

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This paper presents a new methodology to measure the crack resistance curves associated with fiberdominated failure modes in polymer–matrix composites.