Experimental Method for Tensile Testing of Unidirectional Carbon Fibre Composites Using Improved Specimen Type and Data Analysis

This paper presents an experimental method for tensile testing of unidirectional carbon fibre composites. It uses a novel combination of a new specimen geometry, protective layer, and a robust data analysis method. The experiments were designed to test and analyze unprotected (with conventional end-tabs) and protected (with continuous end-tabs) carbon fibre composite specimens with three different specimen geometries (straight-sided, butterfly, and X-butterfly). Initial stiffness and strain to failure were determined from second-order polynomial fitted stress–strain curves. A good agreement between back-calculated and measured stress–strain curves is found, on both composite and fibre level. For unprotected carbon composites, the effect of changing specimen geometry from straight-sided to X-butterfly was an increase in strain to failure from 1.31 to 1.44%. The effect of protection on X-butterfly specimens was an increase in strain to failure from 1.44 to 1.53%. For protected X-butterfly specimens, the combined effect of geometry and protection led to a significant improvement in strain to failure of 17% compared to unprotected straight-sided specimens. The observed increasing trend in the measured strain to failure, by changing specimen geometry and protection, suggests that the actual strain to failure of unidirectional carbon composites is getting closer to be realized.


Introduction
Carbon fibre composites are a unique material with exceptional mechanical properties and therefore widely utilized for structural applications in the aerospace, automotive, and wind energy sectors. The most basic mechanical properties important for the design and application of such materials are stiffness and strength. These mechanical properties are obtained from static tensile test of unidirectional (UD) fibre composites. Accurate determination of stiffness is challenging since the stress-strain curve is typically not well defined at the start of test, and it might also not be linear; especially for carbon fibre composites, the stress-strain curve is clearly non-linear [1,2]. It is also challenging to determine the actual strength since it requires that test specimens fail by tensile failure in the gauge section, away from the grips [3][4][5]. This is a challenge for all UD fibre composites, and it is even more difficult for high strength composites, such as carbon fibre composites. During tensile testing of a test specimen, tensile load in the specimen is introduced through shear load by the action of lateral gripping at the end regions of the specimen. For UD fibre composites, due to the alignment of fibres, shear strength is considerably lower than tensile strength. Thus, the test specimen is likely to fail in shear at the grip region due the introduced high shear stresses. Use of end-tabs increases thickness at the ends of the specimen, and this leads to reduction of shear stress in the composite. End-tabs also protect the specimen from being damaged by the serrated grip surfaces. However, stress by Huntsman GmbH, Switzerland. The fabric stacking sequence for the composites was [b/0] S . The resin/hardener mix of 100:28 (parts by weight) was degassed before infusion. The infusion was performed perpendicular to the fibre direction under a vacuum pressure of 10 mbar. The infused fibre/matrix assembly was cured at 75 • C for 5 h, and then at 40 • C for 19 h. The area of the manufactured composite laminates was 1200 × 600 mm 2 , and with thickness in the range 2.1-2.2 mm.

Protected Carbon Composites
UD carbon/vinyl ester composite laminates (called C) were supplied by Fiberline Composites A/S, Denmark, in the form of pultruded profiles with a cross-sectional area of 105 mm × 1.9 mm. The carbon fibre type was 50 k PAN-based fibre (Mitsubishi Chemical Corporation, Tokyo, Japan).
Protected carbon composite laminates (G/C/G) were manufactured by sandwiching a layer of UD carbon composite between two layers of UD glass composites, with total thickness in the range 6.1-6.5 mm. First, the glass composite layers were mounted temporarily with clamps in the wanted position. Holes for guide pins were drilled at the diagonal position. Fixation with pins was found important to keep the layer in position during the bonding operations. The composite surfaces to be bonded were then slightly ground and cleaned with ethanol. A structural epoxy adhesive (3M, DP460) was applied on one surface of each of the two glass composite layers, and with some extra thickness in the middle to obtain a flow and thereby to avoid trapping of air bubbles. Similarly, the adhesive was applied on both sides of the carbon composite layer in a uniform layer. The composite layers were placed carefully in position using the guide pins and were pressed between two steel press plates using clamps. The adhesive was cured at room temperature for 24 h, followed by post-curing at 40 • C for 16 h.

Geometry and Tabs
Three different test specimen geometries were used in the study: (1) Rectangular shaped specimens, denoted straight-sided, see Figure 1a, based on well-known and widely used standards like ISO 527-5:2009 [17] and ASTM D3039 [18]. (2) Standard non-straight sided specimens, denoted butterfly, see Figure 1b, specially designed based on a previous study at DTU Wind Energy [13]. (3) Elongated non-straight sided specimens, denoted X-butterfly see Figure 1c, having a longer length and reduced curvature has been developed at DTU Wind Energy, and is presented here for the first time. All test specimen geometries have 70 mm long gripping regions from the ends of the specimen.
For unprotected test specimens (C and G), biaxial glass composite was used as end-tabs (see Figure 1). Straight-edged end-tabs were used for the straight-sided specimens, and tapered end-tabs (tapered over 70 mm length) were used for the butterfly and X-butterfly specimens. For unprotected glass composites (G), only the straight-sided test specimen geometry was used. For protected test specimens (G/C/G), UD glass composite was used as protective layer (continuous end-tabs) (see Figure 2).

Preparation
The straight-sided test specimens were obtained by using a circular saw with a carbide steel-tipped blade. The butterfly and X-butterfly test specimens were obtained by using a CNC milling machine. For the test specimens of unprotected composites, biaxial glass composite laminate (Electro-Isola A/S, Vejle, Denmark) with a thickness of 2 mm

Preparation
The straight-sided test specimens were obtained by using a circular saw with a carbide steel-tipped blade. The butterfly and X-butterfly test specimens were obtained by using a CNC milling machine. For the test specimens of unprotected composites, biaxial glass composite laminate (Electro-Isola A/S, Vejle, Denmark) with a thickness of 2 mm

Preparation
The straight-sided test specimens were obtained by using a circular saw with a carbide steel-tipped blade. The butterfly and X-butterfly test specimens were obtained by using a CNC milling machine. For the test specimens of unprotected composites, biaxial glass composite laminate (Electro-Isola A/S, Vejle, Denmark) with a thickness of 2 mm was used as end-tab material, with the fibres positioned at ±45 • to the specimen long direction. The surfaces of the specimens at the end-tab areas were slightly ground using a disc sander and were cleaned with ethanol. The end-tabs were bonded to the specimens using a structural epoxy adhesive (3M, DP460) with a cure cycle of room temperature for 24 h and 40 • C for 16 h.

Experimental Design
A schematic diagram representing the design of the experiments is shown in Figure 3. The unprotected and protected carbon composite specimens with the three different specimen geometries (straight-sided, butterfly, and X-butterfly) were analyzed. As shown in the diagram, the effect of specimen geometry was analyzed by comparing the different specimen geometries for composites with the same specimen protection. The effect of specimen protection was analyzed by comparing unprotected and protected carbon composite specimens with the same specimen geometry. Finally, the combined effect of specimen geometry and protection was analyzed by comparing the unprotected straight-sided carbon composite specimens with protected X-butterfly carbon composite specimens. was used as end-tab material, with the fibres positioned at ±45° to the specimen long direction. The surfaces of the specimens at the end-tab areas were slightly ground using a disc sander and were cleaned with ethanol. The end-tabs were bonded to the specimens using a structural epoxy adhesive (3M, DP460) with a cure cycle of room temperature for 24 h and 40 °C for 16 h.

Experimental Design
A schematic diagram representing the design of the experiments is shown in Figure  3. The unprotected and protected carbon composite specimens with the three different specimen geometries (straight-sided, butterfly, and X-butterfly) were analyzed. As shown in the diagram, the effect of specimen geometry was analyzed by comparing the different specimen geometries for composites with the same specimen protection. The effect of specimen protection was analyzed by comparing unprotected and protected carbon composite specimens with the same specimen geometry. Finally, the combined effect of specimen geometry and protection was analyzed by comparing the unprotected straight-sided carbon composite specimens with protected X-butterfly carbon composite specimens.

Fibre Volume Fraction
The fibre volume fraction of the carbon composite was determined using the gravimetric method (ASTM D3171-15, ASTM D2584). Five samples with a rectangular area of 15 × 15 mm 2 were cut from the composite laminates. The density of the samples was measured using the buoyancy method based on Archimedes' principle. The fibre weight fraction of the samples was determined by the resin burn-off technique. The fibre volume fraction of the composite was calculated by standard Equations [19] using densities of carbon fibre, and matrix as 1.77, and 1.20 g/cm 3 , respectively. The density of carbon fibre was measured based on gas pycnometry method. The measured fibre volume fraction and porosity content were found to be 67 ± 1% and 0.7 ± 0.3%, respectively.

Composite Volume Fractions
The volume fraction of carbon composite in the protected carbon composite specimens (G/C/G) was determined as follows: The fibre volume fraction of the carbon composite was determined using the gravimetric method (ASTM D3171-15, ASTM D2584). Five samples with a rectangular area of 15 × 15 mm 2 were cut from the composite laminates. The density of the samples was measured using the buoyancy method based on Archimedes' principle. The fibre weight fraction of the samples was determined by the resin burn-off technique. The fibre volume fraction of the composite was calculated by standard Equations [19] using densities of carbon fibre, and matrix as 1.77, and 1.20 g/cm 3 , respectively. The density of carbon fibre was measured based on gas pycnometry method. The measured fibre volume fraction and porosity content were found to be 67 ± 1% and 0.7 ± 0.3%, respectively.

Composite Volume Fractions
The volume fraction of carbon composite in the protected carbon composite specimens (G/C/G) was determined as follows: where V C , t C , and t G/C/G are volume fraction of carbon composite, thickness of unprotected carbon composite layer, and thickness of protected carbon composite.
To determine the thickness of the adhesive layer, samples of the protected carbon composites with a rectangular area of 25 × 25 mm 2 were cut from the tab area of the tested specimens. The samples were cast into cylindrical blocks of epoxy resin. Edges of the blocks were ground and polished. By using an optical microscope (Leica S9i, Wetzlar, Germany), the thickness of the adhesive layer (t A ) between the carbon and glass composite layers was measured using ImageJ software (see example in Figure 4a). The measured average thickness of glue layer based on two different samples of each protected specimen type was 0.14 ± 0.06 mm. Based on 10 sets of measurements on a same sample, the uncertainty of measurement was found to be 0.002 mm. The microstructure of carbon composite was examined using scanning electron microscope (Vega3 Tescan, Brno, Czech Republic) at 400× magnification. A uniform distribution of fibres was observed, with no sign of porosities (see Figure 4b), and the latter observation is supported by the measured low porosity fraction.
The volume fraction of the adhesive layer (V A ) in the protected carbon composite was determined as follows: Finally, the volume fraction of glass composite (V G ) in the protected carbon composite was determined as follows: where VC, tC, and tG/C/G are volume fraction of carbon composite, thickness of unprotected carbon composite layer, and thickness of protected carbon composite.
To determine the thickness of the adhesive layer, samples of the protected carbon composites with a rectangular area of 25 × 25 mm 2 were cut from the tab area of the tested specimens. The samples were cast into cylindrical blocks of epoxy resin. Edges of the blocks were ground and polished. By using an optical microscope (Leica S9i, Wetzlar, Germany), the thickness of the adhesive layer (tA) between the carbon and glass composite layers was measured using ImageJ software (see example in Figure 4a). The measured average thickness of glue layer based on two different samples of each protected specimen type was 0.14 ± 0.06 mm. Based on 10 sets of measurements on a same sample, the uncertainty of measurement was found to be 0.002 mm. The microstructure of carbon composite was examined using scanning electron microscope (Vega3 Tescan, Brno, Czech Republic) at 400× magnification. A uniform distribution of fibres was observed, with no sign of porosities (see Figure 4b), and the latter observation is supported by the measured low porosity fraction.
The volume fraction of the adhesive layer (VA) in the protected carbon composite was determined as follows: Finally, the volume fraction of glass composite (VG) in the protected carbon composite was determined as follows:

Tensile Properties
Tensile testing of the composite specimens was performed on a universal testing machine (Instron 88R1331, Norwood, MA,USA) with 250 kN load cell for the unprotected and protected carbon composites, and 50 kN load cell for the unprotected glass composites. The crosshead speed was 2 mm/min for all specimens. Strain was measured with two 6 mm long single strain gauges (LY11-6/350, Darmstadt, Germany) placed on the center on each side of the test specimens. Six specimens each of all specimen types (unprotected and protected) were tested.

Tensile Properties
Tensile testing of the composite specimens was performed on a universal testing machine (Instron 88R1331, Norwood, MA, USA) with 250 kN load cell for the unprotected and protected carbon composites, and 50 kN load cell for the unprotected glass composites. The crosshead speed was 2 mm/min for all specimens. Strain was measured with two 6 mm long single strain gauges (LY11-6/350, Darmstadt, Germany) placed on the center on each side of the test specimens. Six specimens each of all specimen types (unprotected and protected) were tested.

Second-Order Polynomial Fitting
A general observation is that the stress-strain curves of carbon composites curve upwards [1,2], and this indicates an increasing tangent stiffness with increasing strain. Markussen et al. [2] reported an almost linear relation between tangent stiffness and strain for unidirectional carbon composites, implying a second-order polynomial relation between stress (σ) and strain (ε).
A linear relation between tangent stiffness and strain can be expressed as: where E t (= dσ/dε) is the tangent stiffness at a given value of ε, E 0 is the initial stiffness (at zero strain), and α is the stress-strain curvature coefficient, respectively. The second-order polynomial relation between stress and strain is derived by integrating the above equation with respect to ε (for intercept at origin): Between any two points on the second-order polynomial stress-strain curve, the relationship between relative increment in stress σ % = σ 2 −σ 1 σ 1 ·100 and relative increment in strain ε % = ε 2 −ε 1 ε 1 ·100 can be expressed as: For a straight line (α = 0), Equation (6) reduces to σ % ε % = 1, i.e., the relative increment in stress and strain is the same. Equation (6) will be used in Section 3.2. to calculate relative increment in failure stress based on the determined relative increments in strain to failure.
In the present study, the experimental stress-strain curves were fitted with this secondorder polynomial equation, and the fitted curves were used as practical operational stressstrain curves. Initial stiffness (E 0 ) at zero strain was determined based on the fitted stress-strain curves using Equation (5). This method of stiffness determination takes into account the shape of the whole stress-strain curve. It overcomes the challenges of not welldefined stress-strain curves at the start of test, and the non-linear stress-strain behavior of carbon composites.
As exemplified in Figure 5, some of the experimental stress-strain curves show serrations at the end of the curves, observed for both unprotected and protected test specimens. The reason of such small serrations could be due to various reasons like local failures in the specimen, slight slippage, gauge separation, or delamination. Therefore, due to these cases, a practical operational definition of failure stress and strain to failure is needed. As shown in Figure 5, failure stress was obtained as the measured ultimate stress (at maximum load). Then, strain to failure was obtained by extrapolating the fitted line to the ultimate stress. Based on the results of 36 test specimens (unprotected and protected carbon composites), the average corrected strain to failure (ε failure corrected ) was lowered by 0.02% compared to measured strain to failure (ε failure measured ); ε failure measured − ε failure corrected ≤ 0.02 %. Therefore, this correction method had an extremely small influence on the determined strain to failure value.

Back-Calculation of Stresses
During tensile testing of the protected carbon composite (G/C/G), the strain in each layer can be assumed equal to the measured strain for the whole composite due to the parallel arrangement of layers. Therefore, the corresponding stresses in each layer follow the rule of mixture relationships with the measured stress of the composite.
The stress in the carbon composite layer in the protected carbon composite (G/C/G), at a given value of strain, can be back-calculated as follows: where σC, σG/C/G, σG, and σA are stresses in carbon composite layer, protected carbon composite, glass composite layer, and adhesive layer, respectively. Moreover, VG, VA, and VC are volume fractions of glass composite, adhesive, and carbon composite in the protected carbon composite, respectively.
The stress values in the glass composite layers (σG) were assumed similar to stress values in the tested unprotected glass composites (G). The experimental stress-strain curves of unprotected glass composites (G) were fitted with the second-order polynomial (Equation (5)).
The stress values in the adhesive layers (σA) were found from an established stressstrain curve of epoxy adhesive, see Figure 6. The curve was established using the secondorder polynomial (Equation (5)) based on values of failure stress, strain to failure, and stiffness found in the manufacturer's datasheet. The approach is summarized in Appendix A.

Back-Calculation of Stresses
During tensile testing of the protected carbon composite (G/C/G), the strain in each layer can be assumed equal to the measured strain for the whole composite due to the parallel arrangement of layers. Therefore, the corresponding stresses in each layer follow the rule of mixture relationships with the measured stress of the composite.
The stress in the carbon composite layer in the protected carbon composite (G/C/G), at a given value of strain, can be back-calculated as follows: where σ C , σ G/C/G , σ G , and σ A are stresses in carbon composite layer, protected carbon composite, glass composite layer, and adhesive layer, respectively. Moreover, V G , V A , and V C are volume fractions of glass composite, adhesive, and carbon composite in the protected carbon composite, respectively.
The stress values in the glass composite layers (σ G ) were assumed similar to stress values in the tested unprotected glass composites (G). The experimental stress-strain curves of unprotected glass composites (G) were fitted with the second-order polynomial (Equation (5)).
The stress values in the adhesive layers (σ A ) were found from an established stress-strain curve of epoxy adhesive, see Figure 6. The curve was established using the second-order polynomial (Equation (5)) based on values of failure stress, strain to failure, and stiffness found in the manufacturer's datasheet. The approach is summarized in Appendix A.

Back-Calculation of Stresses
During tensile testing of the protected carbon composite (G/C/G), the strain in each layer can be assumed equal to the measured strain for the whole composite due to the parallel arrangement of layers. Therefore, the corresponding stresses in each layer follow the rule of mixture relationships with the measured stress of the composite.
The stress in the carbon composite layer in the protected carbon composite (G/C/G), at a given value of strain, can be back-calculated as follows: where σC, σG/C/G, σG, and σA are stresses in carbon composite layer, protected carbon composite, glass composite layer, and adhesive layer, respectively. Moreover, VG, VA, and VC are volume fractions of glass composite, adhesive, and carbon composite in the protected carbon composite, respectively.
The stress values in the glass composite layers (σG) were assumed similar to stress values in the tested unprotected glass composites (G). The experimental stress-strain curves of unprotected glass composites (G) were fitted with the second-order polynomial (Equation (5)).
The stress values in the adhesive layers (σA) were found from an established stressstrain curve of epoxy adhesive, see Figure 6. The curve was established using the secondorder polynomial (Equation (5)) based on values of failure stress, strain to failure, and stiffness found in the manufacturer's datasheet. The approach is summarized in Appendix A.  For the carbon composite, using the assumption of equal strain, the stress of the carbon fibres, at a given value of strain, was back-calculated as follows: where σ f , σ C , and σ m are stresses in carbon fibres, carbon composite and matrix, respectively. Moreover, V m and V f are volume fractions of matrix and fibres, respectively. The stress values in the matrix (σ m ) were found with a similar approach as used above for the adhesive layer.

Single Fibre Tensile Testing
Single carbon fibres of the same type as used by Fiberline Composites A/S to manufacture the pultruded carbon composite were tensile tested. This was performed using a semi-automated single fibre testing machine (TexTechno, Favimat+, Moenchengladbach, Germany), with a built-in vibroscope system to determine the fibre cross-sectional area. For each tested fibre, based on the measured resonance frequency, the fibre linear density (T, g/1000 m) was determined. The fibre cross-sectional area (A = T/ρ) was then determined using the measured density of the carbon fibres (ρ, 1.77 g/cm 3 ). The carbon fibres were tested with three different gauge lengths (30, 40, and 50 mm), and with a sample size of 150 for each gauge length.

Analysis of Stress-strain Curves
The measured volume fractions, V C , V G , and V A , in the protected carbon composites (G/C/G) were 30-31%, 67-68%, and 1-3%, respectively, as shown in Table 1. The measured values for each of the three specimen geometries are used in the further analysis to backcalculate the stress-strain curves for the carbon composite. Table 1. Measured composite volume fractions (%) in the three specimen geometries of the protected carbon composites (G/C/G).

Specimen Geometries
Composite Volume Fractions Two different failure modes were observed for the protected composites, as shown by the stress-strain curves in The occurrence of two different failure modes indicates that the volume fraction of carbon composite in the protected carbon composites is in the vicinity of the so-called threshold volume fraction, which defines the transition between multiple fracture and single fracture in the simple model of strength of unidirectional composites [20]. In the present study, by using the measured values of stiffness and strain to failure of the unprotected carbon and glass composites, the threshold volume fraction is calculated to be 21%. This threshold value is lower than the measured volume fraction of carbon composites of about 30-31%. Thus, only single fracture should therefore be expected according to the simple strength model. However, the failure situation is not that simple, but has a more complex nature. Failure also depends on interface toughness and absolute thickness of the layers [21], not taken into consideration in the simple strength model. In the present study, for the observed two failure modes, the first drop of stress of the stress-strain curves is assumed to represent failure of the carbon composite layer. No difference in strain to failure was found between the two failure modes. In the further presentation of stress-strain curves, the curves are shown only until their first major drop of stress, representing failure of the carbon composite layer.            Figure 9 shows the experimental stress-strain curves of straight-sided specimens, together with the average of the second-order polynomial fitted curves. On the fitted curves, a cross (×) represents the average failure point, i.e., the average of failure stress, and the average of strain to failure of the tested specimens. The dotted part at the end of the fitted curves represents the standard deviation of the failure stress and the strain to failure, i.e., there is 68% probability that the failure point will lie on the dotted line. It is found that this is a good way of representing the spread of data. Figure 9 shows the experimental stress-strain curves of straight-sided specimens, together with the average of the second-order polynomial fitted curves. On the fitted curves, a cross (×) represents the average failure point, i.e., the average of failure stress, and the average of strain to failure of the tested specimens. The dotted part at the end of the fitted curves represents the standard deviation of the failure stress and the strain to failure, i.e., there is 68% probability that the failure point will lie on the dotted line. It is found that this is a good way of representing the spread of data.
As exemplified in Figure 9 for the straight-sided specimens, an excellent agreement is found between the experimental stress-strain curves and the fitted curves. Accordingly, in the further analysis, the fitted stress-strain curves will be used. Figure 10 shows the fitted curves of the seven groups of stress-strain curves.  The contribution of the carbon composite layer in the protected carbon composites was back-calculated by the use of Equation (7). The stress-strain curves of the unprotected carbon composites are shown together with the back-calculated stress-strain curves for As exemplified in Figure 9 for the straight-sided specimens, an excellent agreement is found between the experimental stress-strain curves and the fitted curves. Accordingly, in the further analysis, the fitted stress-strain curves will be used. Figure 10 shows the fitted curves of the seven groups of stress-strain curves.
Materials 2021, 14, x FOR PEER REVIEW 11 of 20 Figure 9 shows the experimental stress-strain curves of straight-sided specimens, together with the average of the second-order polynomial fitted curves. On the fitted curves, a cross (×) represents the average failure point, i.e., the average of failure stress, and the average of strain to failure of the tested specimens. The dotted part at the end of the fitted curves represents the standard deviation of the failure stress and the strain to failure, i.e., there is 68% probability that the failure point will lie on the dotted line. It is found that this is a good way of representing the spread of data.
As exemplified in Figure 9 for the straight-sided specimens, an excellent agreement is found between the experimental stress-strain curves and the fitted curves. Accordingly, in the further analysis, the fitted stress-strain curves will be used. Figure 10 shows the fitted curves of the seven groups of stress-strain curves.  The contribution of the carbon composite layer in the protected carbon composites was back-calculated by the use of Equation (7). The stress-strain curves of the unprotected carbon composites are shown together with the back-calculated stress-strain curves for The contribution of the carbon composite layer in the protected carbon composites was back-calculated by the use of Equation (7). The stress-strain curves of the unprotected carbon composites are shown together with the back-calculated stress-strain curves for the carbon composite layer in Figure 11. For all curves, the values of the second-order polynomial parameters of initial stiffness (E 0 ) and curvature coefficient (α) are similar in the ranges 153-158 GPa and 2000-2800 GPa, respectively. Thus, a good agreement between the stress-strain curves is found (only the failure points differ between them as will be analyzed next), and this validates the applied analysis of stress-strain curves, as well as the method of back-calculation. The back-calculated stress-strain curves for the carbon composite layer lay the foundation of the forthcoming analysis on the effect of specimen geometry and protection. the carbon composite layer in Figure 11. For all curves, the values of the second-order polynomial parameters of initial stiffness (E0) and curvature coefficient (α) are similar in the ranges 153-158 GPa and 2000-2800 GPa, respectively. Thus, a good agreement between the stress-strain curves is found (only the failure points differ between them as will be analyzed next), and this validates the applied analysis of stress-strain curves, as well as the method of back-calculation. The back-calculated stress-strain curves for the carbon composite layer lay the foundation of the forthcoming analysis on the effect of specimen geometry and protection. Figure 11. Back-calculated stress-strain curves of carbon composite layer from protected carbon composites, together with stress-strain curves of unprotected carbon composites.

Effect of Specimen Geometry
As shown in Table 2, the determined initial stiffness of unprotected carbon composites with different specimen geometries (straight-sided, butterfly, and X-butterfly) were found to be a coinciding value at 153 GPa. This validates the experimental methods since a change in specimen geometry should have no effect on the determined stiffness. For the protected carbon composites, a small difference in stiffness in the range 75-79 GPa was found between the specimen geometries, which, however, can be expected due to the small difference in their composition (see Table 1). This will be utilized in the later analysis of the contribution of the carbon composite layer. Table 2. Initial stiffness (GPa) of unprotected (C) and protected (G/C/G) carbon composites with three specimen geometries.

Carbon Composite Specimen Geometry Straight-Sided
Butterfly X-Butterfly Unprotected, C 153 ± 3 153 ± 3 153 ± 4 Protected, G/C/G 77 ± 2 75 ± 1 79 ± 1 The effect of specimen geometry on the failure point is evaluated by comparing the strain to failure of the composites. As shown in Table 3, for unprotected carbon composites, the strain to failure for straight-sided, butterfly, and X-butterfly specimens are 1.31, 1.42, and 1.44%, respectively. Comparing butterfly specimens to straight-sided ones, the effect of changing specimen geometry leads to a relative increment in strain to failure of Figure 11. Back-calculated stress-strain curves of carbon composite layer from protected carbon composites, together with stress-strain curves of unprotected carbon composites.

Effect of Specimen Geometry
As shown in Table 2, the determined initial stiffness of unprotected carbon composites with different specimen geometries (straight-sided, butterfly, and X-butterfly) were found to be a coinciding value at 153 GPa. This validates the experimental methods since a change in specimen geometry should have no effect on the determined stiffness. For the protected carbon composites, a small difference in stiffness in the range 75-79 GPa was found between the specimen geometries, which, however, can be expected due to the small difference in their composition (see Table 1). This will be utilized in the later analysis of the contribution of the carbon composite layer. Table 2. Initial stiffness (GPa) of unprotected (C) and protected (G/C/G) carbon composites with three specimen geometries.

Straight-Sided Butterfly X-Butterfly
Unprotected, C 153 ± 3 153 ± 3 153 ± 4 Protected, G/C/G 77 ± 2 75 ± 1 79 ± 1 The effect of specimen geometry on the failure point is evaluated by comparing the strain to failure of the composites. As shown in Table 3, for unprotected carbon composites, the strain to failure for straight-sided, butterfly, and X-butterfly specimens are 1.31, 1.42, and 1.44%, respectively. Comparing butterfly specimens to straight-sided ones, the effect of changing specimen geometry leads to a relative increment in strain to failure of 8.4% (= (1.42 − 1.31)/1.31). For X-butterfly specimens, the strain to failure is furthermore increased with a relative increment of 9.9% (= (1.44 − 1.31)/1.31). Thus, the use of the butterfly specimens leads to a significant increase in strain to failure, compared to the straight-sided specimens. The use of elongated X-butterfly specimens, instead of standard butterfly specimens, leads to a slight increase in the average strain to failure, but with overlapping stdvs. A similar effect of specimen geometry can be seen for the protected carbon composites, as also shown in Table 3. The results of strain to failure for the different specimen geometries are also presented in a bar graph (see Figure 12) for better visualization of the differences. Table 3. Strain to failure (%) of unprotected (C) and protected (G/C/G) carbon composites with three specimen geometries.

Carbon Composite Specimen Geometry
Straight-Sided Butterfly X-Butterfly . For X-butterfly specimens, the strain to failure is furthermore increased with a relative increment of 9.9% (= (1.44 − 1.31)/1.31). Thus, the use of the butterfly specimens leads to a significant increase in strain to failure, compared to the straight-sided specimens. The use of elongated X-butterfly specimens, instead of standard butterfly specimens, leads to a slight increase in the average strain to failure, but with overlapping stdvs. A similar effect of specimen geometry can be seen for the protected carbon composites, as also shown in Table 3. The results of strain to failure for the different specimen geometries are also presented in a bar graph (see Figure 12) for better visualization of the differences.  As clearly shown by the results in Table 3, the straight-sided specimens are not able to fully realize the maximum strain to failure of unidirectional composites. It is well documented that a stress concentration region exists at the start of the end-tabs, which is increasing the susceptibility of the material to fail in that region. De Baere et al. [6] reported a stress concentration factor of 1.27 for straight-sided carbon/PPS composite specimens with straight-edged end-tabs of glass/epoxy composite. Korkiakoski et al. [13] performed a finite element analysis of straight-sided (ISO 527-5:2009) UD glass/epoxy specimens and found a stress concentration factor of 1.32 at the start of the end-tabs.
The use of butterfly-shaped specimens with low curvature together with long tapered end-tabs is known to reduce the risk of failure at the end-tabs. Korkiakoski et al. [13] also performed finite element analysis of butterfly-shaped UD glass/epoxy specimens, and reported a stress concentration factor of only 1.02 at the start of the tapered end-tabs. Similarly, De Baere et al. [9] used dumbbell shaped carbon/PPS specimens, and reported significantly higher strength values than for straight-sided specimens. However, such nonstraight-sided specimens are known to split in the longitudinal direction from the edges As clearly shown by the results in Table 3, the straight-sided specimens are not able to fully realize the maximum strain to failure of unidirectional composites. It is well documented that a stress concentration region exists at the start of the end-tabs, which is increasing the susceptibility of the material to fail in that region. De Baere et al. [6] reported a stress concentration factor of 1.27 for straight-sided carbon/PPS composite specimens with straight-edged end-tabs of glass/epoxy composite. Korkiakoski et al. [13] performed a finite element analysis of straight-sided (ISO 527-5:2009) UD glass/epoxy specimens and found a stress concentration factor of 1.32 at the start of the end-tabs.
The use of butterfly-shaped specimens with low curvature together with long tapered end-tabs is known to reduce the risk of failure at the end-tabs. Korkiakoski et al. [13] also performed finite element analysis of butterfly-shaped UD glass/epoxy specimens, and reported a stress concentration factor of only 1.02 at the start of the tapered end-tabs. Similarly, De Baere et al. [9] used dumbbell shaped carbon/PPS specimens, and reported significantly higher strength values than for straight-sided specimens. However, such non-straight-sided specimens are known to split in the longitudinal direction from the edges of the curved area [9]; this damage mode is known as longitudinal splitting. It occurs due to low shear resistance of the UD composites and can cause premature failure. In the present study, such longitudinal splitting cracks were indeed observed on the surface of the outer glass composite layer of protected butterfly and X-butterfly specimens. Likewise, such longitudinal splitting cracks are also expected to occur in the unprotected butterfly and X-butterfly specimens, although difficult to detect visually due to the extensive broomlike failure between the end-tabs (see Figure 13). Longitudinal splitting did not seem to influence the final failure, since failure always occurred in the region of the gauge section (see later discussion in Section 3.3). So, based on the observations in the present study, longitudinal splitting was not found to be the cause of final failure of the specimens.
of the curved area [9]; this damage mode is known as longitudinal splitting. It occurs due to low shear resistance of the UD composites and can cause premature failure. In the present study, such longitudinal splitting cracks were indeed observed on the surface of the outer glass composite layer of protected butterfly and X-butterfly specimens. Likewise, such longitudinal splitting cracks are also expected to occur in the unprotected butterfly and X-butterfly specimens, although difficult to detect visually due to the extensive broom-like failure between the end-tabs (see Figure 13). Longitudinal splitting did not seem to influence the final failure, since failure always occurred in the region of the gauge section (see later discussion in Section 3.3). So, based on the observations in the present study, longitudinal splitting was not found to be the cause of final failure of the specimens.
The X-butterfly specimens are designed with a lower curvature, compared to the butterfly ones, to minimize shear stresses at the edges of the specimen, and to have a smoother stress field [13]. Thus, as expected, a slight improvement was observed in the strain to failure of the specimens with X-butterfly geometry. It can be speculated that the non-identical tested materials volume of the three different specimen geometries in itself may result in variation of strain to failure due to a size effect; as the probability of finding a defect increases with materials volume as typically analyzed with the weakest link Weibull model [23]. Wisnom et al. [24] analyzed the size effect on strength of unidirectional carbon/epoxy composites, and a 14% reduction in failure stress was measured for an increase in materials volume by a factor of 500. In the present study, considering only the gauge section of the specimens, the materials volume of the straight-sided, butterfly, and X-butterfly specimens are 4580, 1720, and 920 mm 3 , respectively. Considering the whole section of the specimens between the grips, the tested materials volume of the straight-sided, butterfly and X-butterfly specimens are 4580, 9380, and 8080 mm 3 , respectively.
In straight-sided specimens, a constant stress state exists due to the constant material volume throughout the whole section between the grips. However, in butterfly and Xbutterfly specimens, the stress state varies along the length, with highest stress state occurring in the central rectangular section. A size effect model was established based on Weibull's [23] derivation of probability of failure for non-uniform stress state. The established model calculates the ratio of stresses in the gauge section of the two specimen geometries (butterfly and straight-sided) for the same probability of failure. For the butterfly specimens, dimensions and stresses are integrated over the tested material's volume. Details of the model will be presented elsewhere [25]. For a Weibull modulus of 41, which previously has been found by Wisnom et al. for UD carbon composites [24], the established model predicts 1.3 and 2.5% relative increment in failure stress for the butterfly and X-butterfly specimens compared to the straight-sided ones. These values are relatively small compared to the determined relative increment in failure stress of 9.3 and 10.9% for Figure 13. Examples of failed unprotected and protected carbon composite specimens: (a1,a2) straight-sided, (b1,b2) butterfly, and (c1,c2) X-butterfly.
The X-butterfly specimens are designed with a lower curvature, compared to the butterfly ones, to minimize shear stresses at the edges of the specimen, and to have a smoother stress field [13]. Thus, as expected, a slight improvement was observed in the strain to failure of the specimens with X-butterfly geometry.
It can be speculated that the non-identical tested materials volume of the three different specimen geometries in itself may result in variation of strain to failure due to a size effect; as the probability of finding a defect increases with materials volume as typically analyzed with the weakest link Weibull model [23]. Wisnom et al. [24] analyzed the size effect on strength of unidirectional carbon/epoxy composites, and a 14% reduction in failure stress was measured for an increase in materials volume by a factor of 500. In the present study, considering only the gauge section of the specimens, the materials volume of the straightsided, butterfly, and X-butterfly specimens are 4580, 1720, and 920 mm 3 , respectively. Considering the whole section of the specimens between the grips, the tested materials volume of the straight-sided, butterfly and X-butterfly specimens are 4580, 9380, and 8080 mm 3 , respectively.
In straight-sided specimens, a constant stress state exists due to the constant material volume throughout the whole section between the grips. However, in butterfly and X-butterfly specimens, the stress state varies along the length, with highest stress state occurring in the central rectangular section. A size effect model was established based on Weibull's [23] derivation of probability of failure for non-uniform stress state. The established model calculates the ratio of stresses in the gauge section of the two specimen geometries (butterfly and straight-sided) for the same probability of failure. For the butterfly specimens, dimensions and stresses are integrated over the tested material's volume. Details of the model will be presented elsewhere [25]. For a Weibull modulus of 41, which previously has been found by Wisnom et al. for UD carbon composites [24], the established model predicts 1.3 and 2.5% relative increment in failure stress for the butterfly and X-butterfly specimens compared to the straight-sided ones. These values are relatively small compared to the determined relative increment in failure stress of 9.3 and 10.9% for unprotected butterfly and X-butterfly specimens, respectively. These values of relative increment in failure stress were calculated using Equation (6) based on the determined relative increments in strain to failure of 8.4 and 9.9%, as presented above. Altogether, it is found that the potential size effect phenomenon is relatively small compared to the effect of specimen geometry.

Effect of Specimen Protection
The strain to failure for unprotected and protected carbon composites for each of the three different specimen geometries are shown in Table 3, and in the bar graph in Figure 12 for better visualization of the differences. The results are consistently showing higher strain to failure in the protected carbon composites compared to the unprotected carbon composites. The relative increment of strain to failure due to specimen protection is similar in the range of 4-6% for the three specimen geometries. The largest difference is seen for the X-butterfly specimens where the strain to failure is increased from 1.44 to 1.53%, giving a relative increment of 6.2% (= (1.53 − 1.44)/1.44).
In the protected carbon composites, the outer glass composite layers protect the sandwiched carbon composite from damage of the grips, and thereby acting similar to the end-tabs of the unprotected specimens. In addition, the continuous outer layers ensures that there is no sudden (or gradient) change in the thickness direction, as it is the case for straight edged end-tabs (or tapered end-tabs). Avoiding such changes in the thickness direction ensures that there are no stress concentrations due to stress singularity, which previously have been reported for UD composite specimens at the start of the end-tabs [13]. For interlayer glass/carbon/glass composite specimens, Cźel et al. [14] performed linear elastic finite element modelling to analyze stress concentrations around straight edged end-tabs. So, those specimens had both continuous protective layers (glass composite) and end-tabs. It was demonstrated that the stress concentrations at the start of the end-tabs do not affect the strain in the central carbon layer. Regions of stress concentrations occurred only in the protective glass composite layers. In the protected carbon composite specimens of the present study, with no end-tabs, regions of stress concentrations will occur at the edges of the grips. Here, as it was demonstrated in the study by Cźel et al., the outer glass composite layers will serve to restrict stress concentrations through applying a sufficient thickness of the protective layers. In addition to restricting stress concentrations at the grips, the outer glass composite layers may also help restricting growth of longitudinal splitting cracks in the curved regions of the butterfly specimens, and thereby reducing the contribution of longitudinal splitting to the final failure of the specimens. This benefit of protective layers needs to be addressed in future studies designed specifically to accurately detect and analyze the initiation and growth of longitudinal splitting cracks. Figure 13 shows representative images of failed unprotected and protected carbon composite specimens. For all specimens, a broom-like failure can be observed. Such failure mode is usually observed for UD composites due to the relative low fibre/matrix interface strength causing a high degree of fibre debonding before fibre failure [26]. As a result, extensive fibre splitting is observed upon final failure of the composite [26]. In the unprotected specimens, some broken end of fibres near the start of the end-tabs can be observed. This can be attributed to the stress concentration regions located at the start of end-tabs, as discussed above. For the unprotected specimens, the widespread failure region makes it difficult to know if the failure is valid, i.e., the specimens should fail centrally in the gauge section rather than near the end-tabs and the grips. In the protected specimens, however, for all three geometries, failure can be observed to be more restricted in the gauge section, as shown in the zoomed images in Figure 13. This observation indicates that the protective glass composite layers help promote failure of the carbon composite in the gauge section. The protective layer makes it easier to judge the validity of failure.

Combined Effect of Specimen Geometry and Protection
By using the unprotected straight-sided specimens as basis, the effect of changing to X-butterfly-shaped specimens is a relative increment in strain to failure of 9.9%, as already presented earlier. If protective layers are used, the strain to failure is furthermore increased with a relative increment of 6.9%, as also presented earlier. Thus, the combined effect of changing geometry and protecting the specimen is a relative increment of 16.8%. This represents a significant improvement in failure properties of the carbon composites, and will have direct implications for the design of structural applications, e.g., by reducing the amount of materials needed for certain load cases.
In the present study, stress-strain curves of single carbon fibres were measured and compared to back-calculated stress-strain curves from the carbon composites. Figure 14 shows the experimental stress-strain curves of single carbon fibres for 30, 40, and 50 mm gauge lengths, together with the second-order polynomial fitted curves. The experimental stress-strain curves show the scattered trend typically observed for single fibres [27,28]. An excellent agreement, however, can be observed between the fitted curves for the threegauge length; the curves are precisely falling on top of each other. The determined strain to failure of the carbon fibres for the three different gauge lengths are summarized in Table 4. It can be seen that the average strain to failure is highly dependent on the gauge length. At short gauge lengths, strain to failure values are higher, and they decrease with an increase of the gauge length. By using the unprotected straight-sided specimens as basis, the effect of changing to X-butterfly-shaped specimens is a relative increment in strain to failure of 9.9%, as already presented earlier. If protective layers are used, the strain to failure is furthermore increased with a relative increment of 6.9%, as also presented earlier. Thus, the combined effect of changing geometry and protecting the specimen is a relative increment of 16.8%. This represents a significant improvement in failure properties of the carbon composites, and will have direct implications for the design of structural applications, e.g., by reducing the amount of materials needed for certain load cases.
In the present study, stress-strain curves of single carbon fibres were measured and compared to back-calculated stress-strain curves from the carbon composites. Figure 14 shows the experimental stress-strain curves of single carbon fibres for 30, 40, and 50 mm gauge lengths, together with the second-order polynomial fitted curves. The experimental stress-strain curves show the scattered trend typically observed for single fibres [27,28]. An excellent agreement, however, can be observed between the fitted curves for the threegauge length; the curves are precisely falling on top of each other. The determined strain to failure of the carbon fibres for the three different gauge lengths are summarized in Table 4. It can be seen that the average strain to failure is highly dependent on the gauge length. At short gauge lengths, strain to failure values are higher, and they decrease with an increase of the gauge length.   Figure 15 shows the fitted stress-strain curves of single carbon fibres, together with back-calculated stress-strain curves of carbon fibres (from fitted stress-strain curves of composites, using a measured fibre volume fraction of 67%). For all curves, the values of the second-order polynomial parameters of initial stiffness (E0) and curvature coefficient (α) are similar in the ranges 224-234 GPa and 3000-4300 GPa, respectively. Thus, a good agreement between the stress-strain curves are found. It demonstrates the efficacy of the second-order polynomial fitting method for back-calculation of fibre properties, for comparison in terms of stiffness and curvature coefficient values.   Figure 15 shows the fitted stress-strain curves of single carbon fibres, together with back-calculated stress-strain curves of carbon fibres (from fitted stress-strain curves of composites, using a measured fibre volume fraction of 67%). For all curves, the values of the second-order polynomial parameters of initial stiffness (E 0 ) and curvature coefficient (α) are similar in the ranges 224-234 GPa and 3000-4300 GPa, respectively. Thus, a good agreement between the stress-strain curves are found. It demonstrates the efficacy of the second-order polynomial fitting method for back-calculation of fibre properties, for comparison in terms of stiffness and curvature coefficient values. The observed increasing trend in the measured strain to failure of the carbon composites (by changing geometry and protection) suggests that the actual strain to failure of the carbon composites is getting closer to be realized.

Conclusions
This paper presents advances in tensile testing of unidirectional carbon fibre composites by using an improved specimen type by combining specimen geometry and specimen protection, together with a robust data analysis method of second-order polynomial fitting. Results of tensile testing of unprotected and protected carbon fibre composite specimens with three different specimen geometries (straight-sided, butterfly, and X-butterfly) have been presented and analyzed.
The central finding of the study is that the protected X-butterfly specimens led to an improvement of 17% on the measured strain to failure compared to rectangular-shaped specimens based on widely used standards like ISO 527-5:2009 and ASTM D3039. This represents a significant improvement in measured failure properties, and will have direct implications for the design of structural applications with carbon composites.
Additional findings of the study are hereby presented: • An excellent agreement is found between the experimental stress-strain curves and the second-order polynomial fitted curves. Accordingly, it is demonstrated that the fitted stress-strain curves can be used as practical operational curves for further analysis.

•
A good agreement between back-calculated stress-strain curves of protected carbon composites and measured stress-strain curves of unprotected carbon composites is found. Similarly, a good agreement is found between back-calculated stress-strain curves of carbon fibres and measured stress-strain curves of single carbon fibres.
Only the failure points differ between the curves. Altogether, this validates the efficacy of the applied analysis of stress-strain curves and method of back-calculation. • Initial stiffness (E0) that takes into account the shape of the whole stress-strain curve was determined based on the practical operational stress-strain curves. Initial Stiffness of unprotected carbon composites with the three different specimen geometries were found to be identical at 153 GPa. This is expected since a change in specimen geometry should have no effect on the determined stiffness.

•
Comparing butterfly specimens to straight-sided ones, the effect of changing specimen geometry was an increase in strain to failure from 1.31 to 1.42%. For the elongated X-butterfly specimens, strain to failure was furthermore increased to 1.44%. The observed increasing trend in the measured strain to failure of the carbon composites (by changing geometry and protection) suggests that the actual strain to failure of the carbon composites is getting closer to be realized.

Conclusions
This paper presents advances in tensile testing of unidirectional carbon fibre composites by using an improved specimen type by combining specimen geometry and specimen protection, together with a robust data analysis method of second-order polynomial fitting. Results of tensile testing of unprotected and protected carbon fibre composite specimens with three different specimen geometries (straight-sided, butterfly, and X-butterfly) have been presented and analyzed.
The central finding of the study is that the protected X-butterfly specimens led to an improvement of 17% on the measured strain to failure compared to rectangular-shaped specimens based on widely used standards like ISO 527-5:2009 and ASTM D3039. This represents a significant improvement in measured failure properties, and will have direct implications for the design of structural applications with carbon composites.
Additional findings of the study are hereby presented: • An excellent agreement is found between the experimental stress-strain curves and the second-order polynomial fitted curves. Accordingly, it is demonstrated that the fitted stress-strain curves can be used as practical operational curves for further analysis. • A good agreement between back-calculated stress-strain curves of protected carbon composites and measured stress-strain curves of unprotected carbon composites is found. Similarly, a good agreement is found between back-calculated stress-strain curves of carbon fibres and measured stress-strain curves of single carbon fibres. Only the failure points differ between the curves. Altogether, this validates the efficacy of the applied analysis of stress-strain curves and method of back-calculation. • Initial stiffness (E 0 ) that takes into account the shape of the whole stress-strain curve was determined based on the practical operational stress-strain curves. Initial Stiffness of unprotected carbon composites with the three different specimen geometries were found to be identical at 153 GPa. This is expected since a change in specimen geometry should have no effect on the determined stiffness.

•
Comparing butterfly specimens to straight-sided ones, the effect of changing specimen geometry was an increase in strain to failure from 1.31 to 1.42%. For the elongated X-butterfly specimens, strain to failure was furthermore increased to 1.44%.

•
It can be speculated that the non-identical tested materials volume of the three different specimen geometries in itself may result in variation of strain to failure due to a mate-rials size effect. Based on Weibull model calculations, it is found that the potential size effect phenomenon is relatively small compared to the effect of specimen geometry.

•
The protected carbon composites showed higher strain to failure compared to the unprotected carbon composites. The relative increment of strain to failure was in the range of 4-6% for the three specimen geometries. The largest difference was seen for the X-butterfly specimens where the strain to failure was increased from 1.44 to 1.53%. • An extensive broom-like failure mode was observed for all specimens. In the protected specimens, however, failure was observed to be more restricted in the gauge section. This observation indicates that the protective layers help promote failure of the carbon composite in the gauge section.
The observed increasing trend in the measured strain to failure of the carbon composites (by changing geometry and protection) suggests that the actual strain to failure of the carbon composites is getting closer to be realized. The obtained largest value of 1.53% for the protected X-butterfly specimens is likely still to be an underestimation of the actual value. Thus, there is a scope of future research to evaluate the actual strain to failure of unidirectional composites. Data Availability Statement: The datasets are available in reference [22] and [29].

Acknowledgments:
The authors would like to thank Fiberline Composites A/S, Denmark for supplying UD carbon/vinyl ester composite laminates and carbon fibres used in this study.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
Estimated stress-strain curves for adhesive and matrix. If the stress-strain curve is approximated by a second order polynomial relation, the coefficients α (stress-strain curvature coefficient) and E 0 (initial stiffness at zero strain) can be calculated based on knowledge of conventional stiffness (E 1 ) and failure properties (σ f and ε f ).
A linear relation between E 1 (conventional stiffness between strain 0.05-0.25%, with the mid value ε 1 = 0.15%) and E 0 is: The value of E 0 can therefore be written as: The second-order polynomial relation between stress and strain is: Using Equation (A2) where σ u and ε u are failure stress and strain to failure, respectively. The value of α can therefore be written as: Based on values of E 1 , σ f , and ε f for the adhesive and the matrix from the manufacturer's datasheet, values of α and E 0 can be determined (using Equations (A5) and (A2)), see Table A1. Stress-strain curves can then be estimated (using Equation (A3)), see Figure A1. where σu and εu are failure stress and strain to failure, respectively. The value of α can therefore be written as: Based on values of E1, σf, and εf for the adhesive and the matrix from the manufacturer's datasheet, values of α and E0 can be determined (using Equations (A5) and (A2)), see Table A1. Stress-strain curves can then be estimated (using Equation (A3)), see Figure  A1.  Figure A1. Estimated stress-strain curves of epoxy adhesive and vinyl ester matrix.