Experimental Characterisation of Parameters Controlling the Compressive Failure of Pultruded Unidirectional Carbon Fibre Composites

. The classical kink-band formation models predict that the compressive strength of UD carbon fibre reinforced composite materials (UD CFRP) is governed by fibre misalignment as well as of the mechanical shear properties. A new image analysis procedure for experimental determination of the fibre misalignment, the Fourier transform misalignment analysis (FTMA), has been developed. Moreover, a modified asymmetric Iosipescu test specimen geometry has been developed and validated for accurate measurement of the composite material shear properties without parasitic effects due to axial splitting. In the test procedure the shear strain distribution is measured using Digital Image Correlation (DIC) and the results calibrated based on FEA modelling results. Using the measured properties as input, the predictions of the classic compressive strength models have been compared with measured compressive strengths. Finally, an alternative approach to the classical kink band equilibrium has been proposed and demonstrated to provide more accurate predictions than the classical models.


Introduction
Generally the failure of composites is a complex mix of competing failure mechanisms.This is because of the in-homogeneity of the composite materials where failure can occur in any of the constituents, their interfaces and by interaction between them.Depending on constituents, interfaces and loading scenarios, different failure mechanisms may be lead to failure of the material.An overview of the most common compressive failure mechanisms in unidirectional (UD) fibre composite materials is presented in Fig. 11, Hahn and Williams [1] and Fleck [2].The competition between the failure mechanisms can be visualised by failure mode maps as the one shown in Fig. 2, Fleck [2].This work has focused on the on the elastic perfectly plastic kink band model by Budiansky [3], where the critical compressive stress s c can be determined as: where τ y is the shear yield stress, γ y is the shear yield strain, and f o is the initial fibre misalignment.
Assuming linear elastic behaviour in shear (i.e.G=τ y /γ y ) Eqn. (1) can be formulated in terms of the shear modulus G.
Eqns. ( 1) and ( 2) are often written in the same equation and both referred to as the elastic perfectly plastic model.The elastic perfectly plastic kink band model has also been the subject of several suggestions for improvements, including Budiansky and Fleck [4] who extended the model to incorporate strain hardening, kink band inclination, combined external compressive and shear loading, and finally finite fibre stiffness.However, but the simple perfectly plastic formulation [3] remains a central part of recent studies by Soutis et al. [5], and Lee and Soutis [6].[7], showing excellent agreement between measured and predicted strengths.See also Kratmann [8] for an overview.Taking the classical kink band model by Budiansky [3] as the basis for this work, the principal parameters controlling the kink band formation in UD CFRP laminates, i.e. the initial fibre misalignment f o and the composite material shear properties, defined by the shear modulus G and the shear yield strain  y .were determined experimentally.For evaluation of the models, the compressive strength was also measured.

The FTMA Method -A New Method for Fibre Misalignment Measurement
Of the parameters controlling fibre kinking, the fibre misalignment is probably the most difficult to quantify, as no standardised measuring techniques exist.Fibre waviness/misalignment is considered a manufacturing defect or imperfection, and its characteristics depend on the specific manufacturing process involved.Examples hereof are the differences between the repetitive waviness introduced by braiding or weaving, local waviness of a UD prepreg being layed out in a mould, and the random waviness in pultruded UD composites as sketched in Fig. .

Applied Mechanics and Materials Vols. 24-25
The pultruded UD composites studied in this work are considered to be randomly misaligned as the micrograph in Fig. 5 shows, i.e. although a few fibres follow each other; fibres next to those have a significantly different orientation.The fibre waviness/misalignment is 3-dimensional by nature.Dedicated measuring techniques developed specifically for the quantification of fibre misalignment and waviness are limited, see [9], [10], [11], [12].In this work a novel image analysis procedure named Fourier transform misalignment analysis (FTMA) for measuring fibre misalignment in unidirectional fibre composites has been developed [13].The FTMA method, which is a 2D technique measuring the fibre directions in section planes prepared by poslishing, measures angles of individual fibre segments isolated by Fourier noise filtering.Working with relatively low magnification micrographs (10 optical magnification) thousands of fibres can be identified, their angle measured and a statistical fibre misalignment distribution generated for the analysed plane, see Fig. 6 (sample analysis results).Areas of 30mm  38mm have been analysed using the FTMA method, identifying approximately 300,000 fibres in less than 30 minutes using on an Intel E8400, 23GHz, 4 GB RAM running Windows XP 64-bit.From these analyses it is assessed that the FTMA method, is probably the most precise and computationally efficient analysis tool for measuring fibre misalignment that are currently available.

Determination of the Composite Material Shear Properties
The Iosipescu shear test has been used to characterise the shear properties of pultruded unidirectional carbon fibre reinforced composites.The testing was based on the ASTM standardised Iosipescu shear test [14], which was modified with respect to the geometry, see Fig. 7.The proposed asymmetric test specimen geometry with horizontally aligned fibres in combination with GFRP tabs prevents axial splitting from occurring, and thereby provides more consistent measurements with less experimental scatter.The shear modulus and shear yield strain have been determined using the modified Iosipescu shear test combined with Digital Image Correlation (DIC), see Fig. 8 (sample DIC measurements of in-plane shear strains).The conventional and the proposed Iosipescu test specimen geometries have been tested and validated using both linear and non-linear finite element analyses.The obtained results have been compared and statistically evaluated.It has been shown that the modified test specimen geometry yields the same absolute results as the conventional Iosipescu geometry, but without change in the stress distribution during the test and with less experimental scatter.For full details see [15].represent the area from which the shear strain is determined as the average value [15].

Determination of Compressive Strength
Two variants of pultruded unidirectional carbon fibre reinforced polymer (UD CFRP) have been investigated experimentally [16].The only difference between the variants was the resin system, which for one variant was a vinylester system (Var1), and for the other an improved resin system (Var2).For both material systems the fibre misalignment, shear stress-strain relationships and compressive strength have been determined experimentally.For the measurement of the compressive strength three different test methods were used.A simple four point bending test (ISO 14125 [17]) which is used by Fiberline for quality control.To supplement this Mechanical Combined Loading (MCL) compression tests [18] have been carried out by Risø DTU, National Laboratory for Sustainable Energy, Denmark.The MCL-test is a pure compression test, compliant with ISO 14126 [19], where the end-to-shear load ratio is kept fixed throughout the test by a mechanical mechanism.Finally, a four point bending test of a sandwich beam with skins made from the pultruded CFRP lamellae was developed specifically for this investigation [16], see Fig. 9.

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It was found that the Var2 material system, which exhibits pronounced strain hardening in shear, is approximately 10% stronger than the Var1 system, which exhibits approximately elastic perfectly plastic shear behaviour.Using as input the fibre misalignment measurements based on the FTMA method (see Fig. 10 for sample visualisation of results), and the CFRP shear properties measured using the modified Iosipescu test setup, the compressive strengths were estimated.Examples of typical compressive kink band failure are shown in Fig. 11 for the Var1 material system.It was found that the classical compressive strength model by Budiansky [3] should not be used in its linearized form, and that the extended model by Budiansky and Fleck [4] also fails to predict the compressive strength, although designed to account for strain hardening.The classical compressive strength models [3], [4] are based on kink band equilibrium considerations, and an alternative approach to treat the experimental data was proposed in [16].A good correlation with the experimentally recorded compressive strength values was found, and it was further found that transverse kink band stresses and the kink band inclination angle can not be neglected for composites exhibiting pronounced strain hardening in shear.

Conclusions
The work presented has treated the compressive failure of UD CFRP composite materials manufactured using pultrusion.Special emphasis has been focused on accurately measuring the properties governing the compressive failure, according to the classical strength models by Budiansky [3] and Budiansky and Fleck [4].To achieve this, a new method for fast and accurate measurement of the fibre misalignment, the FTMA method, has been developed, validated and benchmarked against other existing methods.In addition, a modified Iosispescu asymmetric test specimen has been developed and validated for accurate measurement of UD composite material shear properties without parasitic effects due to axial splitting.In the test procedure the shear strain distribution is measured using Digital Image Correlation (DIC), and the results calibrated based on FEA modelling results.Finally, the predictions of the classic compressive strength models have been compared with measured compressive strengths, using the measured material properties as input.A good correlation with the experimentally obtained compressive strength values was found, and it was further found that transverse kink band stresses and the kink band inclination angle can not be neglected for composites exhibiting pronounced strain hardening in shear.

Fig. 2 .
Fig. 2. Failure mode map by Fleck [2], with the shear modulus G along the first axis and shear strength k normalised with respect to the fibre misalignment f o on the second axis.Fiberline's pultruded CFRP lamella have been added marked with .

Fig. 3 .
Fig. 3. Post mortem micrograph of UD CFRP tested in 3 point bending, showing kink band formations on the compressed side (left).

Fig. 6
Fig. 6 FTMA of UD CFRP (a) open bath pultrusion, (b) closed injection pultrusion (Fiberline).The histograms represent the distribution of single fibre orientations, with the mean orientation equal to 0º.The white lines in the micrographs represent the domain borders.

Fig. 7 .
Fig. 7. Sketch with dimensions and photo of the modified asymmetric Iosipescu specimen geometry.The grey areas of the sketch indicate the tabs, and the horizontal lines in the gauge area the fibre orientation [15].

Fig. 8 .
Fig. 8. (a) DIC measurement of ε xy distribution for tabbed symmetric specimen.(b) DIC measurement of ε xy distribution for proposed tabbed asymmetric specimen.The white boxes represent the area from which the shear strain is determined as the average value [15].

Fig. 10 .Fig. 11 .
Fig. 10.Visualisation of the 2D variation of the domain mean angle (fibre misalignment angle) over the gauge area of a Var1 sandwich specimen.