Carbon Fibre Composite

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Strength of Laminated Fibrous Composites Lab

  • Summary

This report compares the results of theoretical calculations undertaken to predict the tensile strength of carbon fibre reinforced composites against experimental results. Two main methods for the calculation of tensile strength are used; the rule of mixtures and the ten percent rule. These standard theories appear to be valid for the majority of cases although inconsistencies are observed for the 90°, transversely loaded, isostress condition.

  • Aims
  • To become familiar with composite materials, their structure and quality
  • To understand how carbon fibre reinforced polymer, CFRP, materials are tensile tested
  • Objectives
  • To examine samples of composites and their precursors
  • Examine typical microstructure
  • Tensile test different samples of CFRP composites
  • Introduction

This work looks at the tensile strength of different structural make-ups of carbon fibre reinforced polymers. Carbon fibres have greatest strength when they are loaded in the isostrain (0°) condition as illustrated in Figure 4.1. In the isostrain condition, the majority of the applied load is transferred to the long fibre strands whereas in the isostress condition, the load is acting perpendicular to the fibre length and yields a far lower maximum strength. When there are multiple layers of fibres in the composite, orientated in different directions, otherwise known as a mixed ply lay-up, the maximum tensile strength varies with respect to the fibre angle.

Figure 4.1 - Composite Loading

Four different composite lay-up structures are looked at in this report. Each lay-up consists of a total of 16 layers which are symmetrical about the neutral axis. The layups of the composites are:

Where subscripts:

2, 4, 8 = multiple of layers noted in the brackets

S= refers to symmetry about the neutral axis

A - [ 0° ]8S

B - [ 90° ]8S

C - [ +45°,-45° ]4S

D - [0°/+45°/-45°/90°]2S

The test specimens consist of a section of CFRP with metal plates attached with epoxy resin at either end as shown later on in Figure 5.1. These metal plates are purely for clamping of the CFFP section into the in the tensile testing rig as shown in Figure 5.2.

  • Experimental Method

The dimensions of the test specimens are noted for each piece prior to any testing and will be used for fair comparison in the theoretical calculation methods. Dimensions for each specimen, A-D are shown below where x and y relate to the dimensions shown in Figure 5.1.

Test Specimen

x (mm)

y (mm)

CSA (mm2)

















The test samples are loaded into the grips of the tensile testing machine as illustrated in Figure 5.2. Once the materials have been clamped into the rig, they are subjected to a tensile load as indicated by the arrows in Figure 5.2. The tensile load is applied and measured until the sample fractures. The final fracture load is recorded for comparison against theory.

Figure 5.1 - CFRP Test Specimen

Figure 5.2 - Tensile Testing of Specimen

Figure 5.3 - Theoretical Test Approximation

  • Calculating values from theory

The tensile strength of the CFRP test samples are dependant on the volume fraction of fibres and reinforcements. For all of the samples tested, the fibrous volume fraction was given as 0.6; i.e. 60% fibres, 40% reinforcement. Although the reinforcement does have some strength, the majority of the strength comes from the continuous strands of fibre, therefore, it is expected that the test sample A, with all fibres located in the 0° plane, will yield the greatest tensile strength.

For the mixed ply lay-ups, the ten percent rule will be applied which states: fibres “running at angles between 45° and 90° to the applied load will contribute 10% of the 0° strength and stiffness”1

Using the Rule of Mixtures shown below, the tensile strength of the composite may be calculated.


σC = Strength of Composite

σF = Strength of Fibres

σM = Strength of Reinforcement

VF = Volume Fraction of Fibres

VM = Volume Fraction of Reinforcement

The strength of the two constituents of the CFRP composite is given as follows:

Carbon Fibres, σF = 4600 MPa

Reinforcement Resin σM = 90 MPa

  • Case A - [0°]8S

All fibres lay within the 0° plane therefore giving a total composite strength of:

  • Case B - [90°]8S

For Case B, there is not a simple method to predict the tensile strength as it is a function of unknown properties which includes the interferance bond strength and possible voids located within the sample. In the transverse tensile condition, the strength is usually lower than the strength of the matrix meaning the fibres have a negative reinforcing effect.

Knowing this, we know that the value should be below:

Mathews and Rawlings [Ref 2] suggest a reasonable approximation is to assume the fibres are cylindrical holes which would yield a maximum tensile strength of:

  • Case C - [+45° / -45°]4S

Fibres lay both within multiple planes and are classified as a mixed ply make-up. The fibres lay in the 45° and -45° planes; therefore the 10 percent rule applies to all fibres giving a total composite strength of:

  • Case D - [ 0° / +45° / -45° / +90° ] 2S

Fibres lay within in the 0°, 45°, -45° and 90° planes; therefore the 10 percent rule only applies to 3 of the fibre layers directions (75% of the total fibres).

Therefore giving a total composite strength of:

  • Results

Listed in Table 7.1 is the results collected from the experimental procedure along with a conversion into stress by the formula Stress=Force/Area. This has then been converted into Mega-Pascal's for comparison to theoretical results.

Table 7.1 - Results from CFRP Tensile Load Testing

CFRP Section

Force (kN)

CSA (mm2)

σ (kN/mm2) 6SF

σ (MPa) 4SF

A - [0°]8S





B - [90°]8S





C - [+45°/-45°]4S





D - [0°/+45°/-45°/90°]2S





Table 7.2 - Comparison of Theoretical and Experimental Results



% Error of

CFRP Section

σ (MPa) 4SF

σ (MPa)

Experimental Results

A - [0°]8S




B - [90°]8S




C - [+45°/-45°]2S




D - [0°/+45°/-45°/90°]2S




Figure 7.1 - Image of Tensile Tested CFRP Samples

  • Discussion

Comparing the results obtained in both the experimental to theoretical calculations it can be seen that there is close match. As expected, the composite sample loaded in the isostrain direction yielded the greatest maximum tensile strength and similarly the composite sample loaded in the isostress direction yielded the lowest maximum tensile strength. In case C and D, where the lay up structure is [+45°/-45°]4S and [0°/+45°/-45°/90°]2S respectively, the maximum tensile strength values lie between the isostrain and isostress values. This shows that in the isostrain condition the applied load is efficiently transferred to the fibres and where the fibres lie between 45 and 90 a proportion of the load is transferred.

The minor discrepancies in the results could be down to a number of factors which include the imperfections in the direction of the fibre layers. It is almost impossible to obtain parallel fibres in the manufacturing process and one reason why there is a design safety factor built into to many engineering projects. The volume fraction given of for each constituent of the matrix may also be slightly wrong leading to minor errors in the results. Any flaws located in the samples tested will create errors. Flaws can often occur where the fibres are densely packed as the resin cannot wet the surface of the fibre. As the volume fraction of the fibre in this test is near the maximum value, this is fairly possible.

As briefly discussed in section 6.2, the maximum strength of a transversely loaded composite is complex to calculate. According to Mathews and Rawlings, 2006, loading the fibres in a transverse direction has a negative effect on the matrix strength, acting more like impurities than a load bearing constituent. This was observed as the tensile strength of the experimental section yielded a lower value than the strength of the resin. However, taking the assumption that the fibres are hollow proved inconsistent with experimental procedure. The value obtained in the experiment was much closer to the matrix strength thus leading to the assumption that there was a strong bond between the fibres and reinforcement.

The ten percent rule for predicting the strength of a CFRP composite appears to be a reliable method from the 2 mixed ply experiments undertaken in this report. Although it is a good method for predicting the strength of standard mixed ply, there may be doubt over its application to mixed ply where the make up fraction of each fibre in each direction is not equal. For example, if a similar 16 layer, balanced composite of [90°6/45°/-45°]2S is tensile tested, the results would be expected to be closer to the standard [90°]8S than the answer obtained using the 10% rule as the majority of layers are in this direction 90°.

From the image in Figure 7.1 it can be seen that the samples fractured in the direction of the fibres. This would be expected as the tensile strength perpendicular to the fibre is much smaller than that along the length of the fibre. The only exception to this the 0° loaded fibres as all the tensile stress is located in this direction. In this particular case, the facture is at several points along the length of the fibres. The observed fracture coincides with the theory of crack propagation in composites. Consumption of energy in fracturing composites follows the process listed below. It is the ‘pull out of fibre's and ‘debonding between fibres' processes that are visible in all cases. The ‘fracture of the matrix' and ‘fracture of the fibres' can also be easily seen in the [90°]8S and [0°]8S cases respectively.

Process of fracture:

  • Plastic deformation of the matrix
  • Fracture of the matrix
  • Plastic deformation of the fibres
  • Fracture of the fibres
  • Pull out of fibres
  • Debonding between fibres and matrix
  • Conclusion

The rule of mixtures and ten percent rule used in this report appear to be reasonably accurate and therefore valid for the tensile tests conducted. The only major discrepancy is with the transversely loaded sample in which the theoretical value is difficult to obtain without further information on the CRFP bonding properties.

Further work could be conducted to see if the rule of mixtures applies to other mixed ply layups as briefly discussed in section 8. To reduce the errors in the results, further testing of identical samples could be tested and the results averaged.