Area method

Another, straight forward way to measure the ERR of a material is to determine the strain energy directly from the load-displacement curve [111]. For this, the sample is unloaded and reloaded at several crack lengths. Or, for a truly linear elastic material equivalently, straight lines are drawn from several points on the load-displacement curve to zero as it is shown in Figure 3.14 for a load displace- ment curve of a DCB test. The area ∆Ai, delimited by two unloading-loading lines and the load displacement curve, corresponds to the energy that was re- quired to propagate the crack from crack length a(i−1) to ai. This energy is then divided by the created crack surface to obtain G according to:

G(a1) = ∆A1

B(a1− a0)

, G(a2) = ∆A2

B(a2− a1)

, . . . (3.20)

This method is clearly the closest to the definition of energy release rate (see Equation (3.13)). However, there are some limitations in its use. Namely, when the crack is propagating with jumps, there is also kinetic energy that needs to be

3. MATERIALS AND METHODS Displacement Load a₁ a₀ a₂ a₃ a₄ a₅ DA₁ DA₂ DA₃ DA₄ DA₅

Figure 3.14: Illustration of the area method on a mode I delamination load-

displacement curve.

taken into account. Also, it is necessary to allow for a certain crack propagation and thus the measured ERR is an average over this crack propagation which is not desirable - especially at the beginning of the R-curve when G(a) changes rapidly with crack length.

3.5

Summary

In this chapter the fabrication of the composite material and the test specimens was described. The way of placing the sensor fibre and guiding it out of the composite has worked properly for this simple geometry. However, there is no standard or best practice of including an FBG as strain sensor in composite parts. This is clearly a field for future improvements.

Further, two methods for distributed strain sensing with FBGs were described. Even though the OLCR-based method has produced very good results, the com- plexity of the instrumentation and the low measurement speed limit its applica- tion. The multiplex method is a good alternative. Even if the direct measure- ments of the strain are only point-wise, it is possible to deduce a quasi-continuous strain distribution. Additionally, this method is much faster, can be used in fa- tigue, and commercial interrogators are available.

3.5 Summary

Finally, a description of the inverse identification method using the measured strain distributions and different experimental approaches to measure the energy release rate of a delamination crack based on fracture mechanics was given.

Chapter 4

Crack - Sensor interaction

Throughout this work, embedded optical fibres were used to measure strain in the vicinity of a crack tip. Despite the small diameter of only 125µm, the fibre sensors were an order of magnitude larger than the carbon fibres of the surrounding composite material and thus formed a considerable inclusion. Two questions needed to be addressed: i) is the behaviour of the crack influenced by the presence of such a sensor and ii) does the sensor measure the strains due to the crack tip. The latter was necessary since the sensor fibre could potentially influence the strain field it was intended to measure by its own presence.

There is no analytical solution available to calculate the stress field around a crack with a long inclusion in its vicinity for an anisotropic material. Therefore, an FE-simulation of a DCB test was performed to examine the stress-strain field in and around the glass fibre. Further, the energy release rate along the crack front was determined to reveal an eventual influence of the glass fibre on the crack propagation. Since all three performed tests (mode I, mode II, and mixed mode bending) involved bending of the composite, the presence of a fibre sensor can be expected to have a similar influence for each of these tests. Therefore only mode I was investigated.

4.1

Sub-model

The glass fibre being very small, a numerical model with two scales was created to study its interaction with the crack. First, a three dimensional model of a DCB

4. CRACK - SENSOR INTERACTION y z x D RP Glass fibre

Figure 4.1: 3D model and the sub-model that was cut out to simulate the influence

of the fibre.

specimen (see section 5.1) with a crack length of 105mm was created. Hereby, the symmetry of the sample allowed to simulate only the upper half. Even though the DCB specimen has also a symmetry in the width direction, the full width of the sample was simulated, otherwise, the glass fibre (being in the middle of the sample) would have been on the boundary. The crack was simulated without bridging tractions and symmetry boundary conditions were applied to the part of the beam which was ahead of the crack tip as shown in Figure 4.1. From this global model, a small part of (20x4.5x0.5)mm in the centre around the crack tip was isolated and meshed with a much finer mesh. In this so called sub-model the glass fibre was modelled at a distance of 270µm from the crack plane. The global model and the sub-model are shown in Figure 4.1 and a zoom on the crack tip zone of the sub-model including the glass fibre is shown in Figure 4.2.

First, a displacement of ∆ = 10mm was applied at the reference point (RP) to deform the global model and the displacement field at the boundary to the sub-model was extracted from the results. This displacement field served then as