laboratory fibre composites

Royal Institute of Technology (KTH)

Laboratory assignment

SD2414 Fiber composites – Materials and Manufacturing

Teacher: Magnus Burman Students: Benjamin Krank, Simon Börjeson, Vivian van der Burgt Group number: 6 Date: 11 March 2011

This report describes the predictions of different laminate properties of a manufactured glass fiber – polyester composite. First the results are presented in the tables below and the manufacturing procedure is shown. This summarizes all the data of the laminate. In the second part the calculations of mechanical properties are given and explained. These predictions will be taken into consideration in the discussion part.

Part 1 Manufacturing of Laminates

1.1 Results Layer 1 2 3 4 Total

Reinforcement notation

C (Combi)

Dimensions [cm] 38x40 38x40 38x40 38x40

Weight [g] 103,5 108,5 105,5 105,9 +/‐ 420

Fiber type

Approximate areal weight [g/m2]

0°

45°

‐45°

90°

Mat

Total

E‐glass

350

‐‐‐

‐‐‐

200

100

650

Stacking sequence # Stacking sequence 2 C/C/C/C

Resin type Unsaturated Polyester

Predicted resin weight 450,8 g

459,3 g.

Weight of resin

Weight of initiator 6,1 g.

Weight of unused polyester 65 g.

Weight of used polyester 394,3 g.

Room temperature Predicted gel time Resin mixed (at what time)

19°C 45 min 13:09

Resin gels (at what time) Actual gel time

13:54 46 min

Orientation [0/0/0/0]

1.2 Calculations

First we calculated the total volume of the fibres and the matrix. ρ E‐glass = 2600 kg/ m³ ρ Polyester = 1200 kg/ m³

The fibres have a fiber volume of approximately 0.3. This means that 161 ml is 30% and the matrix volume is 70%. This will bring us to the next calculation:

The total weight needed for the Polyester is:

, .

1.3 weight percent initiator has to be add to the unsaturated polyester.

0,013 450,8 5,9 .

Part 2 Prediction of Laminate Properties

2.1. Calculations

1. Consider the reinforcement only and calculate weight fraction of fibers. You need to calculate separate weight fractions for each reinforcement type and fiber type.

0.515 0.485 The composite is separated into the different oriented layers, which have the weight fractions

0.538, 0.308 and 0.154 These weight fractions account for the weight of the whole composite including fibers and matrix in each fiber orientation respectively.

Furthermore, the weight fractions only of the fibers in each direction is calculated in the following: · 0.277 · 0.158 · 0.0792 2. Then calculate the volume fractions of the different reinforcement layers and the matrix e.g. using Equation 3­2 in Åström. · 0.329 · · 1 0.671

0.177, 0.101, 0 and 0.051 are calculated in the same way as .

3. Estimate the moduli in the 0°, 90°, and 45° directions using “rule of mixtures”. Include reinforcement efficiency factors (beta­factors) where necessary.

The efficiency factors were taken from the tables as follows: 1, ° 0, ° 0.1 and 0.375 ° The Young’s modulus is calculated as ·

·

·

Thus, the values for the different layers are . , . and 70 and 3.85 . . considering the material properties

4. Estimate the moduli in the 0°, 90°, and 45° directions using “the 10% rule”. · · 25.59

·

The ‐factors in the different directions are ° 1, ° 0.1, ° 0.1, ° 0.1as well as 0.375. Thus, the ‐factors are 0.627, 0.420 and 0.142. With these values, the Young’s moduli are calculated with · and get . , . and . .

5. Estimate strengths in the 0°, 90°, and 45° directions using “rule of mixtures”. Include reinforcement efficiency factors where necessary. Use an approximate failure strain of 2%.

The strengths are calculated with ̂· , and assuming a maximum and amount to strain of ̂ 0.02.

6. Estimate strengths in the 0°, 90°, and 45° directions using “the 10% rule”. · ̂ 511.6

· .

.

.

2.2. Discussion

Rule of Mixtures Orientation

E

0° 16.31 325 90° 10.99 219 45° 5.86 116

Table 1: results E­modulus and Strength.

10% ‐ rule E

16.03 320.5 10.73 214.6 3.64 72.8

The 10%‐rule bases its results on the properties of a unidirectional lamina. Depending on the fibre direction the actual stiffness is calculated by adding a factor, λ. For a 0‐degree fibre direction this factor is set to 1 and for 45° and 90° fibre angles the factor is set to 0.1 (this explains the name of the rule). Experience has shown that this factor gives results that agree relatively well to reality. However the method is not designed to be applied on CSM‐mats.

Despite this, the 10%‐ rule is still applied on stiffness calculations of CSM‐fibre. This could well be a source of error.

The Rule of Mixtures method could be regarded as more accurate than the 10% rule since it analyses the fibre and matrix separately. To calculate the fibre stiffness for a particular angle a reinforcement efficiency factor is introduced β. The factor takes into account the amount of fibres that are effective in the direction of interest.

By comparing the results of the two different methods, Table 1, one can realize that they give very similar stiffness values for 0‐ and 90 degree fibre directions. The 10% rule seems to generate slightly lower values, i.e. more conservative results. However, for a fibre angle at 45 degrees the methods generate completely different numbers.