Chapter 1
Damage in Composite Structures: Notch Sensitivity

1.1 Introduction

Owing to its construction, where two basic constituents, fibres and matrix, are combined, a composite structure shows a wide variety of types of damage. Damage may be specific to one or both of the constituents or involve interaction of the two. Furthermore, depending on the scale over which phenomena are described, damage may have different forms ranging from micro-voids or inconsistencies and cracks of the fibre/matrix interphase to large-scale delaminations, holes and laminate failures.

Here, the emphasis is placed on damage that is no smaller than a few fibre diameters with the understanding that this damage most likely is the result of creation and coalescence of damage at smaller scales, which are beyond the scope of this book. Within this framework, the most common forms of damage are matrix cracks, fibre/matrix interface failures, fibre failures, through-thickness failures (holes and cracks) and inter-ply failures such as delaminations. Of course any combination of these may also occur as in cases of impact damage. Representative forms of damage and their corresponding scales are shown in Figure 1.1.

Figure 1.1 Typical damage at various scales of a composite structure

In advanced composites typical of aerospace structures, the matrix has much lower strength than the fibres. Failure then typically initiates in the matrix and the associated damage is in the form of matrix cracks. These cracks usually appear in plies with fibres not aligned with the directions along which appreciable loads are applied [1]. Matrix cracks may also be present in a composite right after curing due to curing stresses [2] or tooling problems where heat uptake or cool-down during the cure cycle is not uniform [3].

This does not mean that damage may not initiate at a location where a small flaw (resin-rich region, resin-poor region, void and contamination) is present. Ideally, a damage model should start at the lowest possible scale where damage initiated and track the latter as it evolves and grows. As can be seen from Figure 1.1, however, this process may require bridging at least three to four orders of magnitude in the length scale. This means that separate models for the individual constituents are needed at the lower scales at which even the material homogeneity is in doubt. To minimise computational complexity, models that address macroscopic structures start at larger scales, the ply level or, less frequently, at somewhat lower scales and focus on aggregate flaws such as notches.

In general, a notch can be considered any type of local discontinuity such as a crack, hole, and indentation. Here, the definition of a notch is generalised and is not confined to a surface flaw. It can also be a through-the-thickness discontinuity. Notches act as stress risers and, as such, reduce the strength of a structure. The extent of the reduction is a function of the material and its ability to redistribute load around the notch. The possible range of behaviour is bounded by two extremes: (i) notch insensitivity and (ii) complete notch sensitivity.

1.2 Notch Insensitivity

This is the limiting behaviour of metals. Consider the notched plate at the top left of Figure 1.2. The shape and type of the notch are not important for the present discussion. Now assume that a purely elastic solution is obtained in the vicinity of the notch for a given far-field loading. Typically, there is a stress concentration factor kt and, for an applied far-field stress s, the stress at the edge of the notch is kts. This is shown in the middle of Figure 1.2. If the material of the plate is metal, then, for sufficiently high values of the far-field stress s, kts exceeds the yield stress sy of the material. As a first-order approximation, one can truncate the linear stress solution in the region where the local stress exceeds the yield stress (shown by a dashed line in the middle of Figure 1.2) by setting the stress there equal to the yield stress. To maintain force equilibrium, the region where the stress equals sy must extend beyond the point of intersection of the horizontal line at sy and the linear stress solution such that the areas under the original curve corresponding to the linear solution and the modified 'truncated' curve are equal.

Figure 1.2 Stress distribution in the vicinity of a notch-insensitive material

For sufficiently high s and/or sufficiently low sy value, the material on either side of the notch yields and the stress distribution become the one shown on the right of Figure 1.2.

This means that the stress aligned with the load on either side of the notch is constant and there is no stress concentration effect any more. The stress is completely redistributed and only the reduced area due to the presence of the notch plays a role. More specifically, if Ftu is the failure strength of the material (units of stress), the force Ffail at which the plate fails is given by the material strength multiplied by the available cross-sectional area:

with w and 2a the plate and notch widths, respectively, and t the plate thickness.

At the far-field, the same force is given by

The right-hand sides of Equations 1.1 and 1.2 can be set equal and a solution for the far-field stress that causes failure can be obtained:

A plot of the far-field stress as a function of normalised notch size 2a/w is shown in Figure 1.3. The straight line connecting the failure strength Ftu on the y-axis with the point 2a = w on the x-axis gives the upper limit of material behaviour in the presence of a notch.

Figure 1.3 Notch-insensitive behaviour

It should be pointed out that, for this limiting behaviour, the shape of the notch is not important. The specimen with the hole and the dog-bone specimen shown in Figure 1.3 are completely equivalent.

1.3 'Complete' Notch Sensitivity

At the other extreme of material behaviour are brittle materials that are notch-sensitive, such as some composites and ceramics. In this case, if there is a stress riser due to the presence of a notch with a stress concentration factor kt, failure occurs as soon as the maximum stress in the structure reaches the ultimate strength of the material. For a far-field applied stress s, this leads to the condition:

The situation is shown in Figure 1.4. Here, there is no redistribution of stress in the vicinity of the notch. For the case of an infinite plate in Figure 1.4, or a very small notch, the far-field stress to cause failure is given by rearranging Equation 1.4:

For finite plates, with larger notches, finite width effects reduce further the strength of the plate. In the limit, as the notch size approaches the width of the plate, the strength goes to zero:

Equations 1.5 and 1.6 are combined in Figure 1.5, which shows the notch-sensitive behaviour.

Figure 1.4 Stress distribution in the vicinity of a notch-sensitive material

Figure 1.5 Notch-sensitive material

1.4 Notch Sensitivity of Composite Materials

The types of behaviour discussed in the previous two sections are the two extremes that bracket all materials. It is interesting to see where typical composite materials lie with respect to these two extremes. Experimental data for various composite laminates with different hole sizes under tension are shown in Figure 1.6. The test data are taken from Ref. [4].

Figure 1.6 Test results for composite laminates with holes under tension

Note that two curves, very close to each other, are shown for the 'completely notch-sensitive' behaviour. One corresponds to the [15/-15]s and the other to the [15/-15/0]s laminate.

It is seen from Figure 1.6 that the composite data fall between the two curves. More importantly, even at very small holes, there is a significant drop of the strength towards the curve of complete notch sensitivity and, at higher hole diameters (2R/w > 0.7), the data tend to follow that curve. However, the fact that the data start at the top curve and drop towards the lower curve suggests that composites have some load redistribution around a notch but the redistribution is limited. A damage zone or process zone is created at the edge of the hole with matrix cracks, broken fibres and delaminations. This process zone limits the stress to a value equal or close to the undamaged failure strength. As the load is increased, the stress inside the process zone stays constant. The size of the process zone increases and the strains in the material next to the hole increase. As the load is increased further, a point is reached where the structure can no longer store energy and fails. In general, therefore, composites are notch sensitive but they do have some limited...