Composites-Final-Report-no.-2

THE UNIVERSITY OF MANCHESTER

Virtual Reality Testing of a Composite Tube

Finite Element Analysis of Tube Laminate

Arya Dash – 8074797

Harsh Dewra – 8576151


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Contents 1. NOMENCLATURE ....................................................................................... 1

2. SUMMARY ................................................................................................. 2

3. INTRODUCTION........................................................................................ 2

4. AIMS AND OBJECTIVES ............................................................................ 3

5. RESULTS AND DISCUSSION ...................................................................... 3

Design Evaluation ................................................................................................................................ 3

Tube Failure Evaluation ...................................................................................................................... 3

Comparison of Results ........................................................................................................................ 5

Maximum Twist................................................................................................................................... 5

Evaluation of Load-Carrying-Capacity of the Tube ............................................................................. 6

6. PROPOSED DESIGN IMPROVEMENTS ........................................................ 6

7. CONCLUSIONS .......................................................................................... 7

8. REFERENCES ............................................................................................ 8

Nomenclature Φ – Winding Angle

α – Lay-up Angle no. 1

β – Lay-up Angle no.2

ρ – Twist Angle

𝛾𝑥𝑦 – Shear strain

R – Radius

L – Length

κx- Curvature in x

κy – Curvature in y

κxy- Curvature in xy


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Summary This report is an extension of the analysis of a laminated composite tube using

finite element method based on advanced laminate theory when subjected to an

axial compression load, which was modelled using the code: ABAQUS. By

applying a 25 kN of axial compressive load and using a lay-up with winding

angle of [–39°/–75°/–39°/–75°], the failure modes were predicted for each

layer under Maximum Stress Failure (MSF) Criterion and Tsai Wu Failure (TWF)

Criterion. The results from the FE analysis were seen to be more accurate than

the theoretical results. It was found that failure occurred in layers 1 and 3 under

Tsai Wu failure criterion but no failure was observed with the MSF criterion. The

maximum twist angle was found to be - 11.1° making the analytical solution

17% inaccurate. The load-carrying capacity of the tube under the TFW criterion

was predicted to be 23kN, where failure was observed in layer 1. Due to high

stress interaction, Tsai-Wu provided more accurate results. Some qualitative

performance guidance on performance improvements has also been provided.

Introduction The formation of the composite pipe is such that it consists of four laminated

layers with the winding angles having a lay-up of [-39°/-75°/-39°/-75°]. The

optimal winding angles were found through an iteration process using the maxim

in order to achieve the maximum angle of twist before failure would be predicted

by the maximum failure stress criterion. The software utilised for assessing the

design is ABAQUS which ideal for finite element simulations, this provided the

platform for one to determine failure modes through the Maximum Failure Stress

(MSF) and Tsai-Wu Failure (TWF) Criteria.

The composite pipe is wounded by tape by means of a biaxial winding process,

covering a length of 300mm along longitudinal axis of the pipe. This also

satisfied the criteria such that there was no gap or overlapping along the pipe

surface and the prepeg utilised contained a thickness of 0.25mm. The

arrangements of the biaxial winding angles and composite layers are outlined in

Figure 1.

Figure 1: Biaxial Winding of Fibres and Composite layers and winding angles

-39


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Aims and Objectives To use ABAQUS to visualise the behaviour of the four different layers

when subjected to 25 kN axial compression load.

To predict the failure modes of the different layers under two different

failure criteria: Maximum Stress Failure and Tsai-Wu Failure.

To compare the theoretical results with the simulated ones in terms of

failure modes and angle of twist and compare and evaluate their

differences.

To assess the maximum load taken by the tube without failure based on

Tsai-Wu criterion

To suggest improvements to the design

Results and Discussion

Design Evaluation

The assessment of the design of a multi-layer tube on finite element analysis

involved the use of two different failure criteria: the Maximum Stress Failure

(MSF) and the Tsai-Wu Failure (TWF) criteria. A maximum value from each of

these criteria that exceeded 1 would indicate that failure has occurred. ABAQUS

code was used to compute winding angles of -39° and -75° along with an axial

compression load of 25kN where the behaviour of four different layers and their

failure modes were observed. The twist angle was also computed and evaluated

with the theoretical value.

Tube Failure Evaluation Figures 2 and 3 show the MSF criterion and TWF criterion plots respectively. It

can be seen that under the TWF criterion, FE results predict failure in layers 1 (innermost layer) and 3. Moreover, in contrast to the MSF criterion, failure is

more likely to occur in layer 1 and 3, rather than 2 and 4. Similar trends are observed for the tube under the TWF criterion with the weakest points of the tube proving to be the end-regions.


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Figure 2: Maximum Stress Failure (MSF) criterion contour plots for layers 1-4

Figure 3: Tsai-Wu criterion contour plots for layers 1-4

The MSF criterion predicts that a material will fail when the magnitude of stress

in any direction exceeds its corresponding allowable level in that direction (i.e. tensile, compressive and shear strengths). This theory is most widely used for

unidirectional composites. The main advantage of this criterion is that it specifies what kind of failure will occur. However, MFS does not consider interactions between the various stress components, and therefore, has the potential to be

inaccurate. This could be the reason because of which the tube did not fail under maximum stress failure criterion in this exercise.

What the MSF fails to incorporate, the TWF achieves. Here, the high stress interaction between multi-axial stress-states were accounted for. Similar to the

MSF, any value exceeding 1 will indicate failure of the material. Normally, it is computed by considering all the principle stresses, some experimental data, and

the coupling between them, and is therefore known to produce much more accurate results than the MSF criterion. The sections of the tube within this study are therefore concluded to fail as detailed in table 1 from above sections.

However, drawbacks do exist and in this case, the criterion finds it difficult to identify the mode of failure under loading.


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Comparison of Results

Table 1 above shows the results obtained from the simulation for both criteria

and compared with the results obtained from the MSF using Classical Laminate

Theory. As expected, the results are consistent and agreeable. The higher failure

values for layers 2 and 4 compared to layers 1 and 3 are observed at the end

regions of the tube, with the majority of the mid-section of the tube showcasing

stress-state uniformity. This indicates that the end regions of the tube are also

the weakest areas, and can be visualised in figures 1 and 2.

It can also be concluded that the results from the FE modelling are more

accurate than the Classical Laminate Theory. This is because the classical

Laminate Theory assumed [𝐾] to be equal to zero in order to simplify the

analysis. However, the FE model solves the governing equations in its full form

i.e

Maximum Twist The maximum (anticlockwise) shear strain occurs in Layer 1 and 3. Figure 4

below shows that the maximum shear strain 𝛾𝑥𝑦 is equal to 16.1E-03 in Layer 1.

Figure 4: Shear strain γxy contour plot of the composite tube.

Lay-up Angle Layer

CL Theory (CW 1)

Finite-Element (FE)

MSF MSF TWF

α = –39° 1

0.866 0.8322 1.081

3 0.8409 1.059

β = –75° 2

0.935 0.8942 0.8963

4 0.9172 0.9138

Table 1: Classical Laminate Theory Vs FE Simulation failure results for all layers


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Angle of twist (𝜌) is thus given below as:

𝜌 =𝛾𝑥𝑦𝐿

𝑅×

180

𝜋=

0.0161 × 0.3

0.025×

180

𝜋= − 11.1°

The Analytical result of the twist angle from CW-1 was found to be -12.985°.

This gives a percentage error of approximately 17% between for the Classical Laminate Theory, implying a reasonable prediction.

Evaluation of Load-Carrying-Capacity of the Tube Layer Maximum values

1 9.941e-01

2 8.246e-01

3 9.743e-01

4 8.407e-01

Table 2: Tsai-Wu failure criteria for a load of 2300 N

The initial results obtained using the TWF criterion for the tube using a 25kN load are outlined in table 1 in the above section. It was seen that the tube had

failed in certain layers and therefore required the compression to be decreased in order to avoid failure. Here, the load was decreased until the TWF criterion yielded a maximum value of 0.994 across the tube, resulting in a maximum

load-carrying capacity of approximately 23kN. The maximum value for Tsai Wu failure criterion was obtained on layer 1 as shown in figure 5 whereas the peak

values across all other layers has been tabulated in Table 2 above.

Figure 5: Tsai-Wu Contours for a load of 23kN on Layer 1

Proposed Design Improvements The more accurate FE Analysis indicated that the curvatures are not exactly

ignorable. In any Laminate Analysis, there are typically three important

parameters that may be varied:

Thickness of each lamina

Winding angles


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Arrangement of the laminae

Analysis 1 revealed that [-30.5/-30.5/-30.5/-30.5] also gave a maximum twist

of -12.98 degrees. Due to its symmetry [B]=0, thereby resulting in no coupling

between extension and shear. This could potentially be a promising option to

consider. Finally, these combinations can be tested against the desired criteria.

A wide range of coating options is available to improve the strength, durability or

the physical properties of the laminates, depending on the environments they are designed for. A list of possible scenarios is given below:

In wet environment: The outer layer may be coated with Rip-stop Nylon that provides ultra-waterproof properties.

PVOH and PPH coatings to improve structural strength. However, these may not be the best options under heavy fatigue loading.

Varying temperature and pressure environments: Specular Coatings

Use of Advanced Composites: For extreme conditions of operation, the choice of advanced composites may also be a viable option. These include

Carbon Reinforced Phenolic Composites and Self-Healing Composites.

Conclusions FE gives more accurate results than the Simplified Analytical results that

assumed the no curvature.

Maximum failure mode values were very similar using both the Classical

Laminate Theory and FE analysis in conjunction with the MSF criterion.

FE analysis showed no failure under the MSF criterion; however, under the

TWF criterion, layers 1 and 3 expected failure.

The maximum angle of twist was found to be in good agreement with the

theoretical value.

Tsai-Wu criterion allows a maximum load of 23kN without failure.

The MSF is the simplest criterion, but not as accurate or as reliable as

others

The TWF criterion is more accurate than the MSF as it considers the

interaction between different stress-states, and is therefore a favoured

choice among many.

The properties of the laminate can be varied by varying the thickness of

each lamina, winding angles and the arrangement of the laminae.

Different coatings such as nylon, PVOH and PPH can be used to improve

the performance of the laminate. Advanced laminates may be used for

highly demanding environments, but this comes at a huge price.


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References [1] Advanced Composites. NASA (2016). [online] Available at:

http://technology.nasa.gov/materials_and_coatings/mat-advancedcomposites.html (Accessed 01 May 2016)

[2] Willams J.H. and Kousiounelos P.N. (1978). Thermoplastic fibre coatings enhance composite strength and toughness. Fibre Science and Technology.

[online] Available from www.sciencedirect.com

[3] Zhou, Z (2016). Classic Laminate Theory. Composite Lecture Notes, The

University of Manchester. Available from www.my.student.manchester.ac.uk (Accessed 01 May 2016)

http://technology.nasa.gov/materials_and_coatings/mat-advancedcomposites.html

http://technology.nasa.gov/materials_and_coatings/mat-advancedcomposites.html

http://www.sciencedirect.com/

http://www.my.student.manchester.ac.uk/

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Composites-Final-Report-no.-2