Protection Structures of Glass Fiber Reinforced Plastic ...561581/FULLTEXT01.pdfAuthor: Marko...

Protection Structures of Glass Fiber Reinforced

Plastic – Static Analysis

Marko Nikolic

Degree project in Solid Mechanics

Second level, 30.0 HEC Stockholm, Sweden 2010

www.reinertsen.se

DOCUMENT: 240‐MT‐002 DATE: 2011‐06‐17

English Title

Protection Structures of Glass Fiber Reinforced Plastic Static Analysis

Svensk titel

Skyddsstrukturer i Glasfiberarmerad Plast Statisk Analys

Author: Marko Nikolic

Reinertsen Sverige AB Svärdvägen 27 182 33 STOCKHOLM SWEDEN Tel +46-8-544 767 70 Fax +46-8-768 30 60

Abstract

The oil- and gas industry has increasingly begun to switch from oil platforms and instead started to install the modules, process stations, etc. directly on the seabed. Some parts are more sensitive to external loads than others, and it is crucial to protect them to avoid damage on the structures and even gas/oil leakage. Protection covers made of glass fiber reinforced plastic (GRP) is becoming more frequently used in the offshore industry due to its low cost and good mechanical properties. Common load cases that the GRP cover could be exposed to have been identified and an investigation has been carried out to see what influence different factors like lay-up sequence and the number of plies has on the GRP cover. A fast and effective working method for future projects regarding GRP covers has been developed with the usage of Ansys and Excel.

Analysis showed that for the installation and trawl net friction load cases the number of failed layers are very much dependent on the lay-up sequence of the GRP cover. Installation should be done vertically in order to prevent ply failure. For the trawl impact and Trawl Over-Pull load cases the numbers of failed plies are almost independent of the lay-up sequence.

The conclusion is that lay-up sequences of [0/90]s and [-45/45]s are the most appropriate ones for this type of GRP cover and for the considered load cases. A total of 48 plies were recommended to ensure a completely intact protection structure for installation and trawl net friction, and only get small local failure at the trawl impact and over-pull load cases.

DOCUMENT TITLE

Protection Structure of Glass Fiber Reinforced Plastic

DOCUMENT NUMBER

240‐MT‐002 DATE

2011‐06‐17

CUSTOMER

Reinertsen Sverige AB PROJECT NUMBER

240‐MT‐002 PROJECT MANAGER

Jonas Loberg 1 2011‐06‐17 Master Thesis Report MN EH/OJ JLREV. DATE DESCRIPTION PREPARED CHECKED APPROVED

AUTHOR Marko Nikolic

CHECKED …………………………………..

APPROVED …………………………………..

PATH S:\SPA\Bilagor\Rapportmall_engelska.dot

Protection Structures of Glass Fiber Reinforced Plastic Author: Marko Nikolic 240-MT-002

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PREFACE

This master thesis has been done together with Jonas Elgered as the final part of the Master of Science in vehicle engineering programme, department of solid mechanics at the Royal Institute of Technology (KTH) in Stockholm. The thesis work was conducted at Reinertsen Sverige AB in Stockholm, Sweden, during the spring semester 2011, January-June.

I would like to express my deepest gratitude to the head of the subsea department, Jonas Loberg, and Reinertsen Sverige AB for giving me office space, access to hardware, software, literature and last but not least knowledge and experience.

I would like to thank the staff at the subsea department; Fredrik Axelsson, Gunnar Gustafsson Erik Hallberg and Ola Johansson for the help and guidance, and all my colleagues at Reinertsen Sverige AB for helping me with all the practical matters when coming to a new area.

Finally, thanks to my supervisor at the Royal Institute of Technology (KTH), department of solid mechanics, Jonas Neumeister for his support and advice during this master thesis.

Stockholm, 17th of June 2011

Marko Nikolic


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SAMMANFATTNING

Olje- och gasindustrin har börjat övergå från oljeplattformar för att i större utsträckning istället installera moduler, processtationer etc. direkt på havsbotten. Viss utrustning är mer känslig för externa laster än andra och det är därför viktigt att skydda dessa för att undvika skada på strukturen, men även olje- och gasläckage. Skyddsstrukturer tillverkade av glasfiberarmerad plast blir allt vanligare inom offshore industrin pga. de goda mekaniska egenskaperna samt de låga tillverkningskostandena. Vanligt förekommande laster som GRP strukturen kan utsättas för har identifierats och en undersökning har gjorts för att ta reda på hur stor inverkan olika faktorer som t.ex. lamellsekvens och antalet lameller har på skyddsstrukturen.

En snabb och effektiv arbetsmetod för framtida projekt beträffande GRP strukturer har tagits fram med hjälp av Ansys och Excel. De analyserade lamellsekvenserna är [0/90]s, [-45/45]s samt [0/90/45/-45]s.

Analysen visade att för de två lastfallen; installation och trawl net friction, så är resultaten starkt beroende av vilken lamellsekvens som används. Installation bör ske vertikalt för att undvika att lameller går sönder. För de två kontaktlastfallen; trawl impact och trawl over-pull så är antalet lameller som går sönder i stort sett oberoende av vilken av de tre lamellsekvensen som används.

Slutsatsen är att lamellsekvenserna [0/90]s och [-45/45]s är att föredra, medan [0/90/45/-45]s inte alls lämpar sig för denna typiska GRP struktur, enligt behandlade lastfall. Totalt 48 lameller bör användas för laminaten [0/90]s och [-45/45]s för att försäkra att inga lager går sönder vid installation och trawl net friction, samt att endast mindre lokalt brott uppstår för lastfallen trawl inpact och over-pull.


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TABLE OF CONTENTS

PREFACE ...........................................................................................................................3

SAMMANFATTNING .......................................................................................................4

1 INTRODUCTION ..........................................................................................................7 1.1 Background .......................................................................................................................................... 7 1.2 Aim of Thesis ........................................................................................................................................ 7 1.3 Working Method .................................................................................................................................. 7 1.4 Abbreviations and Definitions ............................................................................................................ 8

2 GRP COVER DESIGN ..................................................................................................9

3 LITTERATURE STUDY ..............................................................................................10 3.1 Introduction to Composites ................................................................................................................. 10 3.2 Glass Fiber Reinforced Plastic ............................................................................................................ 10 3.3 Laminate Theory .................................................................................................................................. 11 3.4 Stacking Sequence for UD-Plies .......................................................................................................... 12

4 MATERIAL PROPERTIES .........................................................................................12 4.1 Material Data Obtained from Manufacturer .................................................................................... 12 4.2 Rules of Mixtures ................................................................................................................................. 14 4.3 Material Strengths ............................................................................................................................... 16

5 FAILURE CRITERIA ...................................................................................................17 5.1 Failure Criteria Associated with Failure Modes ............................................................................... 18 5.2 Failure Criteria not Associated with Failure Modes ......................................................................... 20 5.3 Summary of Failure Criteria .............................................................................................................. 21

6 LOAD-, MATERIAL- AND DESIGN FACTORS ......................................................22

7 METHODOLOGY .........................................................................................................25 7.1 Calculation Method, Tool and Software ............................................................................................ 25 7.2 Assumptions and Model Simplifications ............................................................................................ 25 7.3 Local Coordinate System, Mesh and Element Types ........................................................................ 25 7.4 Loads………. ........................................................................................................................................ 27 7.5 Application of Loads and Boundary Conditions ............................................................................... 28 7.6 FEM of Composites in Ansys .............................................................................................................. 33

8 RESULTS ........................................................................................................................34 8.1 Installation ............................................................................................................................................ 35 8.2 Trawl Net Friction ............................................................................................................................... 37 8.3 Trawl Overpull ..................................................................................................................................... 39 8.4 Trawl Impact ........................................................................................................................................ 41

9 DISCUSSION AND CONCLUSIONS ..........................................................................44 9.1 Comparison Between Ansys and LS-Dyna ........................................................................................ 44 9.2 Discussion ............................................................................................................................................. 45 9.3 Conclusions ........................................................................................................................................... 46


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10 FUTURE WORK ...........................................................................................................47

11 REFERENCES ...............................................................................................................48 APPENDICES Appendix A – Calculation sheet for UD-ply Appendix B – The Shell181 element Appendix C – DAF Calculation Appendix D – Ansys Script Appendix E – Additional Results


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1 INTRODUCTION

1.1 Background The oil- and gas industry has increasingly begun to switch from oil platforms and instead started to install some of the equipment directly on the seabed. Due to that and since the fish trawling becomes more advanced, it becomes more important to protect the equipment installed on the seabed. Some parts are more sensitive to external loads than others, and it is crucial to protect them to avoid damage on the structures and even gas/oil leakage.

As a final step in the education at KTH solid mechanics, a master thesis is to be performed. Reinertsen Sverige AB has offered a master thesis project where protection structures of glass fiber reinforced plastic are investigated.

1.2 Aim of Thesis Reinertsen aims to establish themselves as providers of consulting services for fiberglass protection structures for the oil and gas industry. A first step in this effort is to perform a thesis dealing with the subject. This thesis is intended to give Reinertsen more knowledge about the currently valid standards and regulations for subsea operations of GRP structures. This report tries to serve as a method for future projects concerning GRP covers.

1.3 Working Method This work is divided into two parts.

The first part deals with a research study in order to get an understanding and an overall picture about the offshore industry, composites, failure criteria and relevant standards. Previously projects carried out in the field of glass fiber reinforced plastic structures have also been studied.

The second part consists of identifying and analyzing the common load cases that the protection structure could be exposed to. Investigations have also been made on how different parameters like ply lay-up sequence, number of plies and the installation angle affect the identified load cases.

The analysis in this work was performed with the commercial software Ansys. [14]

An effective and manageable method for analyzing the results obtained from Ansys that could be used in future projects has been developed.

This thesis has partially been done together with Jonas Elgered which primary task was to develop a material model for layered composites in the FE program LS-Dyna. For more detailed description of the procedure in LS-Dyna, see report number 240-MT-003 written by Jonas Elgered [13].


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1.4 Abbreviations and Definitions Abbreviations BC Boundary Condition

CAD Computer Aided Design

COG Center of gravity

DAF Dynamic Amplification Factor

DNV Det Norske Veritas

FE Finite Element

FEA Finite Element Analysis

GRP Glass Reinforced Plastic

GPa Giga Pascal

MPa Mega Pascal

ROV Remotely Operated Vehicle

UD Unidirectional

ULS Ultimate Limit State

VMO Veritas Marine Operations

WB Workbench

Definitions

[-45/+45]s = [-45/+45/+45/-45] s stands for symmetric laminate sequence

[0/90]2s = [0/90/0/90/90/0/90/0] 2s stands for double symmetric laminate sequence.

Isotropy = Same mechanical properties in all directions

Anisotropy = Mechanical properties vary with direction

Orthotropy = Special case of anisotropy where the composite has three principal directions

Symbols

E Young’s Modulus

G Shear Modulus

V Volume Fraction

Weight

Shear strain

Safety factor


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Strain

Poisson’s Ratio

Density

Stress

τ Shear stress

Subscripts 1 Fiber direction

2 Transverse fiber direction

3 Thickness direction

c Compression

f Fiber

m Matrix

t Tension

2 GRP COVER DESIGN The geometry used in this work is a typical GRP cover taken from a previous project. The exact analyzed geometry is not of big importance in this report. The important thing is the working procedure for further GRP projects.

All subsea protection covers have some design requirements due to the protection from the fishing equipment. The side walls that are above a rock dumping height have to be under a certain angle to assist the trawl and fishing equipment.

According to NORSOK U-001 [1] for over-trawlable structures, the following design requirements shall apply:

a) The protective structure shall deflect all fishing equipment b) Structural corners shall have maximum true angle of 58° from the horizontal to assist

trawl- and trawl wire deflection c) Corners, ramps and equivalent structures shall penetrate the seabed to avoid snagging

from trawl warp lines and ground rope. Effects from installation tolerances and expected scouring shall be accommodated

d) The overall geometry of the structure and the size of openings, shall be such that trawl doors are prevented from entering into the structure

e) If a vertical side bracings are included, these shall be spaced to prevent intrusion and rotation of trawl equipment, without restricting subsea structure access for the intervention systems

f) All protuberances shall be designed to prevent snagging of nets g) All external edges/members which are not part of a closed protection structure shall

have a minimum radius of 250


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h) Minimum trawl speed shall be 3.0 /

The analyzed protection structure in Ansys WB is illustrated in Figure 2:1. See Section 7.2 for a detailed description of the various modifications made on the original structure.

Figure 2:1. Final design of the GRP cover used in Ansys WB

The cover does not have any hatch or equivalent for inspection inside the cover. During life time only external inspections of the cover are made to see if it has been damaged. If the GRP cover needs to be replaced, the rock dump has to be removed and the cover lifted by attaching soft slings to the small lifting holes, usually done by remotely operated vehicles (ROV).

3 LITTERATURE STUDY

3.1 Introduction to Composites The word “composite” in composite material often signifies that two or more materials are combined on a microscopic scale to form a useful material. The advantage of composites is that they usually exhibit the best qualities of their constituents and often some qualities that neither constituent possesses [2]. Typically a composite material is made of reinforcing fibers in a matrix. The main function of the fibers is to carry the load while the matrix, which is surrounding the fibers, supports and protects the fibers and keeps them in the desired locations and orientation. The matrix also acts as load transfer medium that transfer the load to the fibers. High strength to weight ratio and high stiffness to weight ratio are the main advantages and that is why scientists always tries to improve and develop composite materials.

3.2 Glass Fiber Reinforced Plastic Glass fiber reinforced plastic (GRP), is made of a plastic matrix reinforced by fibers made of glass. GRP is widely used in applications such as cars, boats, wind turbine blades and water tanks. The plastic matrix is often a thermosetting polymer like vinylester, polyester or epoxy. Glass fibers are the most common of all reinforcing fibers for polymer matrix composites. The principal advantages of glass fibers are the low cost and high strength. Polymers (commonly called plastics) are the most widely used matrix material for fiber composites. According to their structure and behavior, polymers can be classified as thermoplastics or thermosettings. The polymers that soften or melt on heating, called thermoplastic polymers, can be reshaped by application of heat and pressure. Thermosetting plastics do not soften but decompose from heating and they cannot be reshaped [3].


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The main advantages of using GRP are

High strength to weight and high stiffness to weight ratios Resistance of salt water, chemicals and the environment Low maintenance Good thermal properties Corrosion resistance Good electrical insulator Low price Easy to handle offshore

3.3 Laminate Theory A ply or a lamina is a single layer of a composite material that consists of fibers embedded in a matrix. One or more plies builds up a laminate. A ply is defined as a thin orthotropic layer of a composite material. A unidirectional ply can be classified as a transversely isotropic material i.e. one plane can be considered isotropic. The ply is usually defined so that is has three orthogonal principal axes for its material characteristics, the 1-, 2- and 3-direction. The 1-direction is along the fibers, the 2-direction is transverse to the fibers and the 3-direction is through the thickness of the ply. The directions are illustrated in Figure 3:1. This is used to denote the fact that a ply may be aligned differently from the global cartesian coordinates i.e. the x-, y- and z-axis.

Figure 3:1. Local coordinate system of a unidirectional ply When dealing with composites and laminates, a couple of approximations and assumptions are used [4]

• Matrix is homogenous, linearly elastic and isotropic. • The fibers are homogenous, linearly elastic, isotropic (or transversely isotropic),

perfectly aligned and regularly spaced. • The fiber and matrix are free from voids; there is complete bonding and no transitional

region between them.


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This does not reflect the reality because it is almost impossible to have the fibers equally distributed and there are also always voids present when manufacturing composites. This leads to the conclusion that

• The ply is then treated as an effective continuum, which is homogeny, orthotropic and most often linearly elastic.

A lamina has superior properties in the fiber direction while it has poor properties in the other two directions. The transverse modulus and the through thickness modulus are dominated by the matrix and is almost independent of the reinforcement.

3.4 Stacking Sequence for UD-Plies The biggest advantage of composites is their flexibility in design. Mechanical properties of the laminate can be altered simply by changing the stacking sequence, fibre lay-up and thickness of each ply. Long fibers are more commonly used in structures than short fibers because of the resulting higher stiffness and strength properties.

By orienting the reinforcement in different direction the composite becomes more and more isotropic in that plane; this is an advantage if the load is applied in different directions.

The deflection of a composite plate is highly dependent on the fiber direction. By simply rotating the stack of a cross ply composite [0/90] by 45 degrees to a [±45] sequence the stiffness of the plate strongly increases and the maximum deflection decreases substantially [4].

For a composite structure that should resist loads from different directions it could be advantageous to aim for more isotropic composite properties. Two commonly used quasi-isotropic ply lay-ups are [-60/0/60]s and [0/90/-45/+45]s. To reduce out-of-plane strains, coupled bending and stretching of the laminate and complexity of analysis, symmetric laminates should be used [5]. Thus, the stacking sequences that will be tested in Ansys WB are

• [0/90]s • [-45/+45]s • [0/90/-45/+45]s

A comparison between those different sequences of the reinforcement lay-up for all the different load cases will be considered in this report and a discussion on which lay-up best suits this type of GRP cover will be concluded.

4 MATERIAL PROPERTIES

4.1 Material Data Obtained from Manufacturer To determine the engineering constants of each composite ply is one of the first key steps in the design process. Usually the material data from the GRP manufacturer is insufficient and several parameters and data need to be calculated or estimated. A typical sheet of material properties obtained from manufacturers for the GRP is given in Table 4:1. The material


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properties shall be considered as preliminary and will vary between different glass fiber fabrics and manufacturing techniques. Final material properties will be established together with the current contractor in detailed design. The laminate in Table 4:1 is a woven fiber mat, i.e. a ply with fibers in more than one direction. In this case the fibers are aligned in the 0° and 90° directions. The woven fiber mat differs substantially from a cross-ply [0/90] lay-up because of its mechanical properties.

Table 4:1. Typical sheet of material data obtained from the manufacturer

One of the main disadvantages of composites is the lack of reliable data. The data is influenced by e.g. the lamination technique, temperature and pressure conditions, the manufacturing time etc. This means that each design is different compared to other situations because they are manufactured in different ways and within different conditions [6].

As can be seen in Table 4:1, the two columns with material data represent two different manufacturing techniques. The two methods above are hand lamination and vacuum infused. For a hand lamination it is impossible to get as low void fraction or as high fiber volume


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fraction as for the vacuum infused. Vacuum infused are stronger and stiffer in all directions except in bending because the hand lamination is approximately 50 % thicker due to more matrix material. In most projects, contracts with manufacturers are not signed before any analysis is done with the calculation programs. Thus, typical data is used which is then verified when the manufacturer of the GRP Covers is determined.

4.2 Rules of Mixtures Rules of mixtures is a collection name of formulas that estimates the composite ply properties as a function of the reinforcing fiber ( ), the matrix ( ), and the volume fraction of the two different constituents. The most understood and common way to determine the properties of a lamina from the individual constituents is to use rules of mixtures. It is of great advantage to satisfactory define material properties for a UD ply compared to a woven fabric mat. This allows the engineer to analyze laminate with different lay-ups since one can change the stacking sequence arbitrarily.

E-glass is the most commonly used glass reinforcement in GRP applications [7]. This type of glass is very cheap and has quite acceptable mechanical properties. Young’s modulus for the low cost fiber material E-glass is = 69-72 GPa and a Poisson’s ratio could be set to approximately 0.3 [4]. Young’s modulus for the matrix material, , does not change much depending on which thermosetting polymer that is used and varies between 2.6−4.6 GPa [4], and a slightly higher Poisson’s ratio, , of 0.4 should be appropriate for the matrix material. For a E-glass epoxy/polyester lamina the fiber volume fraction, Vf , is in the range of 0.3-0.75 [4] and with the volume fraction of 0.52 stated in Table 4:1 it can fairly be approximated to 0.5. Following approximated material properties according to Table 4:2 for the constituents can be used for analytical calculations until final concept review and comparison with experimental data from manufacturer is obtained.

Table 4:2. Mechanical properties of the constituents

Constituents Fiber Matrix

Young’s modulus [GPa] 70.0 3.0

Poisson’s ratio [-] 0.3 0.4

Volume fraction [-] 0.5 1 V 0.5

The shear modulus of the fiber and the matrix can be calculated with Hooke’s law as the two constituents are approximated as isotropic materials according to Section 3.3.

· Eq. 1

· Eq. 2


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As soon as the properties for fiber and matrix are known it is a simple route to calculate the mechanical properties for a UD ply.

Young’s modulus in the 1-direction i.e. fiber direction is given by

· · Eq. 3

Young’s modulus in the 2-direction i.e. transverse fiber direction is given by

Eq. 4

Poisson’s ratio in the 1-2 plane is given by

· · Eq. 5

Shear modulus in the 1-2 plane is given by

Eq. 6

In the plane of symmetry (plane 2-3), the elastic properties are isotropic; hence the following relations are used

Eq. 7

Eq. 8

Eq. 9

To calculate the shear modulus , Hooke’s law is used according to

·

Eq. 10

Poisson’s ratio in the isotropic plane 2-3 is unknown and must be estimated. A first guess for an approximation would be to take the same value as for the matrix material. However it can be assumed that the fibers will have some sort of contribution. Thus, for simplicity the same value as for the major poison ratio can be used in the preliminary design. When contract with manufacturer are signed experimental data for all material properties will be obtained.

A detailed calculation sheet of how to obtain the mechanical properties of a UD ply through rules of mixtures is attached in Appendix A.

Table 4:3 lists the input data that will be used for the FEA in Ansys WB.


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Table 4:3. Input data for Ansys WB

Charatceristic Value

Youngs modulus – Fiber direction E 36.5 GPa

Youngs modulus – Transverse fiber direction E 5.75 GPa

Youngs modulus – Thickness direction E 5.75 GPa

Poissons ratio υ 0.35



Shear Modulus G 2.06 GPa



The same density as presented in Table 4:1 will be used, 1900 kg/m , and half the thickness of the woven fabric mat is used for each UD-ply, 0.725 mm. The thickness was estimated from a previous project at Reinertsen.

4.3 Material Strengths Strengths of materials can never be calculated analytically since cracks and voids contribute to the strength value. They have to be determined experimentally. However, when comparing a UD ply to the vacuum infused laminate in Table 4:1, the ultimate in-plane shear stress should be a lot lower since fibers for a UD ply are oriented in just one direction. According to direct contact with manufacturer the ultimate out-of-plane shear strength and are both approximately 30 MPa [8]. From a conservative perspective, all ultimate shear strengths are set to 30 MPa. In comparison with tensile and compressive strength values for the vacuum infused laminate in Table 4:1, a UD-ply intuitionally should have higher strengths in the fiber direction, since all fibers are aligned in the same direction.

Accurate strength values are hard to obtain even experimentally since it depends on the lengths of the test specimen. A more conservative value for the compressive strength in the fiber direction is used in comparison with a typical value presented in [4] and the value presented in Table 4:1.

The tensile strength for a typical E-glass fiber is 3.5 GPa [9]. A simple estimation of the tensile strength of a UD ply with a volume fraction of 50 % fiber could therefore be 1.75 GPa. Tensile strength for a slightly different E glass lamina was experimentally determined to 1.00 GPa [4]. With these values, a conservative longitudinal tensile strength of 800 MPa is used for the preliminary design.


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According to a previous experience at Reinertsen, the ultimate tensile and compressive strength in the transverse 2-direction was set to 20 MPa respectively 300 MPa. In comparison with tensile strength for the resin materials, 50-70MPa [6], it seems good as a first approach.

Due to the isotropy plane, the strengths in the 3-direction are similar as for in the 2-direction.

The ultimate strain are simply estimated by using the assumption that the ply can be described as a linearly elastic material according to Section 3.3 and could therefore be calculated using Hooke’s Law according to

Eq.11

where i is the considered direction of the ply.

Mechanical strengths used in Ansys WB for each lamina are presented in Table 4:4

Table 4:4. Material strength used for a UD ply

Characteristic Value

Tensile strength 1-direction 800 MPa

Compressive strength 1-direction 500 MPa


Compressive strength 2-direction 300 MPa


Compressive strength 3-direction 300 Mpa

Shear strength 12-direction 30 MPa

Shear strength 13-direction 30 Mpa

Shear strength 23-direction 30 Mpa

5 FAILURE CRITERIA A failure criterion predicts if a composite will fail due to applied load. In other words, a failure theory is applied to a composite by the use of characteristic stresses and strains and then compared to the ultimate strengths of the composite. There are a number of failure criteria and it is quite difficult to decide which failure criteria is the best to apply. The only way to find out which criterion suits the composite the best is to perform experimental tests on the material considered. Without experimental tests the failure criteria and the material strength can only be approximated. Most of the failure criteria are actually intended to describe the “benign” load state in the absence of stress concentrations and gradients.


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The difficulty with failure criteria is to find out the ultimate levels for stresses and strains in the different directions. The strengths of a material are usually given by tests obtained from general loads such as tensile and compression of a specimen. The strength of a material due to impact, damage and other sharp edges is more difficult to obtain.

All failure criteria should be checked at the ply level, not at the laminate level.

The strengths are defined according to:

Ultimate tensile strength in direction i

Ultimate compressive strength in direction i

Ultimate shear strength in plane ij

and the ultimate strain levels are defined according to:

Ultimate tensile strain strength in direction i

Ultimate compressive strain strength in direction i

Ultimate shear strain in plane ij

Failure criteria of a composite material can be divided into different groups depending on whether the criteria are associated with failure modes or not. Failure criteria associated with failure modes are those criteria which takes the non-homogenous character of a composite material into account and distinguishes between matrix and fiber failure. This group is then divided into subgroups where some criteria are partially interactive and some are not. Failure criteria not associated with failure modes are mathematically developed formulas designed to fit experimental data from strength tests. A more schematic overview is presented below to illustrate which type of failure criteria there are.

• Associated with failure modes • Partially interactive • Non-interactive

• Not associated with failure modes • Interactive

5.1 Failure Criteria Associated with Failure Modes This group considers the non-homogenous character of composites and that it will contribute to different failure modes. Basically, it distinguishes between fiber and matrix failure. This group identifies the following failure modes:

• Fiber failure • Matrix cracking • Shear matrix cracking.


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Failure criteria associated with failure modes identifies how a composite fails but neglect stress interactions. This group can further be divided into subgroups according to following:

Partially interactive These criteria separate the matrix failure criterion from the fiber failure criterion. The equation can be dependent on either one or more stress components; therefore, stress interactions vary from one criterion to another within this group.

Two examples of partially interactive failure criteria are Hashin and Hashin-Rotem failure criterion.

Non-interactive This group does not take interactions between stresses and strains acting into account. Typically non-interactive criteria are the maximum stress criterion and the maximum strain criterion. Maximum strain criterion

Failure will occur when anyone of the strain components in the principal material axes , , exceeds the corresponding strain strength in their respective direction.

Failure occurs if

or Eq. 12

or Eq. 13

| | γ Eq. 14

For the maximum strain criterion, the partial resistance-model factor , further discussed in Section 6, depends on the choice of structural analysis method use [10].

• If a linear analysis with non-degraded properties is chosen, then • In all other cases 1.0

In order to obtain conservative predictions of fiber failure from the linear non-degraded method, a partial analysis factor shall be introduced for the maximum strain criterion related to each fiber direction of the laminate. For each fiber direction of the laminate the partial analysis factor shall be given by

Eq.15

where and are laminate moduli (stiffness) related to loading in the fiber direction of consideration. is the laminate stiffness based on initial (non-degraded) ply properties, while is the reduced (secant modulus) laminate stiffness obtained from degraded ply properties according to Figure 5:1.


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Figure 5:1. Typical stress-strain relation for a laminate containing 0°, 45° and 90° layers when loaded in 0°-direction

Figure 5:1 above illustrates how a laminate built up of 0°, 45° and 90° layer fails due to apply loading in 0° direction. For a perfectly linear elastic material, and would be identical and the resistance model factor would be 1.0.

5.2 Failure Criteria not Associated with Failure Modes This group uses mathematical expressions to describe the failure envelope as a function of the material strength. Several criteria have been developed during the years. The only difference is that the parameters and changes in order to better fit the failure surface to experimental results. All the failure theories within this group are based on the following equation which uses normal tensor notation:

· · · 1 Eq. 16

where , 1 6 and the terms and depends on which criteria that is used.

Tsai-Wu failure criterion The interactive (or polynomial) criteria predict failure based on a combined stress state. The Tsai-Wu failure criterion is widely used around the world and is appreciated due to its simplicity to implement it into computer software by the use of normal tensor transformation [4]. Failure is assumed to occur when the following condition is satisfied


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2 2 2 1 Eq. 17

where, and are given as:

· for i=1,2,3 Eq. 18

for i=1,2,3 Eq. 19

Eq. 20

Eq. 21

Eq. 22

The parameter in Eq. 18 is obtained from the following equation

· · Eq. 23

where should be determined experimentally for each material. If is experimentally determined then 1. Alternatively values for between 0 and 0.5 may be chosen as a default, in that case 1.15. is set to zero for simplicity. Similar procedure is used to determine and but is set to zero in this work aswell.

5.3 Summary of Failure Criteria There is no widespread agreement on what represents the best failure criterion to use. There are disadvantages with all of the failure criteria that have been considered in the literature study. A main limitation of maximum strain and maximum stress is that they do not take interactions into account when predicting failure. The benefit with these criteria is that they do take into account that composites could fail in their respective constituents, i.e. by either fiber or matrix.

A lamina embedded in a laminate usually tolerates higher transverse and higher shear stresses than compared to the situation with a lamina considered alone. This means that if a criterion predicts failure of a lamina it is usually an underestimation of the strength compared to the situation with a lamina considered in a laminate. Each lamina protects and strengthens the neighboring lamina. Further, it means that layers for which transverse and in-plane shear is likely to affect failure, and consequently for which differences between failure criteria are expected to be most significant, will usually be stronger than predicted.


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For a conservative design, the engineer could use several failure criteria and select the worst case according to Figure 5:2

Figure 5:2. Conservative design

The interactive failure criteria which are developed using mathematical equations are quite hard to accept from a physical point of view. If one considers a biaxial tensile test of a composite specimen, these failure criteria depend on the compressive strength of a material, which is hard to imagine and accept. On the other hand, during the literature study it was noted that those mathematical equations, especially Tsai-Wu, fit the experimental results of a composite reasonably well.

A laminate is said to be fiber dominated when loads are primarily carried by the fibers. Since the structure is only meant to protect the pipes laying on the seabed it is allowed to have local matrix cracks. This is due to the fact that the structure is not designed to enclose oil or gas. The important thing is that the structure can maintain its capacity to carry loads.

According to DNV OS-C501 Composite Structure [10], those criteria which should be used to predict fiber failure are especially the Maximum Strain and the Tsai-Wu criteria.

Tsai-Wu is chosen as the failure criterion for all the considered load cases in this work. Tsai-Wu is very conservative since it does not tell in which way failure occurs. However, when material strengths from the manufacturer are received, the maximum strain criterion is the preferable one for load cases where contact is present. This is because too much contribution of the local stresses is not preferable.

6 LOAD-, MATERIAL- AND DESIGN FACTORS The design factors are based on the so-called Load and Resistance Factor Design Format (LRFD). This procedure deals with partial safety, model and design factors, which includes load factors and resistance factors, the load effects which are the characteristic load values and the characteristic resistance variables [10]. The design factor is obtained by multiplying characteristic values (reference values) of loads and structural resistance by calibrated coefficients such as load and material coefficients. A design load is obtained by multiplying the characteristic load by the total design factor according to


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· Eq. 24

Before choosing the partial load-, material- and design factors one has to know what limit state, safety class and failure type the material and the structure is related to.

A limit state is commonly defined as a state in which the structure ends to fulfill its function, or to satisfy the conditions, for which it was designed [10]. The term limit state shall be understood to mean that state where a structure or part of a structure no longer meets the requirements laid down for its performance or operation. All the load cases that have been considered in this work are classified as Ultimate Limit State which is related to the maximum load carrying capacity.

A safety class describes the consequences of failure when the failure mode is related to the Ultimate Limit State. The GRP cover is set to a low safety class because it implies small risk of human injury and minor environmental, economical and political consequences if it fails. The safety class would be higher if the structure would enclose oil or gas [10].

A failure type is defined as degree of pre-warning to a given failure mechanism. Each failure mechanism shall be related to one of the failure types brittle, plastic or ductile. Composites are usually classified as brittle materials. [10]

Below is a brief explanation of the factors that are relevant and used in this work.

Combined Load and Resistance Factor . In some cases it is useful to work with only one overall safety factor. The uncertainties in loads and resistance are then accounted for by one common safety factor denoted . Partial load effect factor account for uncertainties associated with the variability of the local response of the structure (local stresses or strains) whiles the partial resistance factor accounts for the uncertainties associated with variability of the strength [10]. Load Model Factor accounts for inaccuracies, idealizations and biases in the engineering model used for representation of the real response of the structure. When FE methods are used within their assumptions and limitations a model factor of 1.0 may be used. Since the accuracy of FE methods is generally very good. Geometrical uncertainties and tolerances should be included in the load model factor [10].

Resistance Model Factor accounts for differences between true and predicted resistance values, e.g. differences between test and in-situ material properties. Uncertainties or biases in a failure criterion are accounted for by the resistance model factor [10].

Center of Gravity Factor accounts for inaccuracy in COG position. For operations with a linear relation between COG shifts and loads/load effects, or operations less sensitive to COG shifts, inaccuracy in estimated COG may be accounted for by an inaccuracy factor. This factor should normally not be taken less than 1.05 [11].

Skew Load Factor accounting for the extra loading on slings caused by the effect of inaccurate sling lengths and other uncertainties with respect to force distribution if the rigging arrangement. For a statically indeterminate four points lifts a skew load factor of 1.25 is normally acceptable [11].


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Weight inaccuracy factor , for characteristic weights based on estimated weight, a weight inaccuracy factor of minimum 1.1 should be applied [11].

Consequence Factor is meant to account for severe consequences of single element failure. Lift points including attachments to object (single critical elements supporting the lift points is defined within this category) [11].

All the factors that are being used in this work is presented in Table 6:1 where the total design factors for the different load cases also is calculated.

Table 6:1. Load-, material and design factors

Factor Description Value Reference

Limit State Ultimate Limit state.

Safety class low. Failure type brittle

B DNV-OS-C501, Sec. 2, C200/C500

Combined load effect

and resistance factor for general load effects.

1.60 DNV-OS-C501, Sec. 8, B300

Load model factor 1.00 DNV-OS-C501, Sec. 9, L302

Resistance model factor, fiber failure. Tsai-Wu 1.15 DNV-OS-C501, Sec. 8,

C302, Sec. 6, C304

Center of gravity shift factor 1.05 VMO, Pt.1, Ch.3,

3.5.3.1

Weight inaccuracy factor 1.10 WMO pt.1 Ch. 3,

3.5.2.1

Skew load factor, indeterminate lifts 1.25 VMO, Pt.2, Ch.5,

2.3.2.5

Consequence factor 1.30 VMO,Pt.2, Ch.5, 4.1

, Total design factor for trawling 1.84 · ·

, Total design factor for installation 3.43 · ·

· · · ·


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7 METHODOLOGY

7.1 Calculation Method, Tool and Software CAD Autodesk Inventor 2009 was used to model the GRP cover geometry, which is then transferred into Ansys WB where all the load cases are simulated and where the GRP lay-up is modeled. Elements and procedures defined in the text apply to the use of this software. Ansys handles the pre-processing, the solving and the post-processing parts of the FE-simulations.

An Excel spreadsheet has been developed in order to analyze the results obtained from Ansys in a simple way.

7.2 Assumptions and Model Simplifications The radii in the model have been removed since LS-Dyna cannot read geometries with radii. This modification has been made in order to be able to analyze and compare the two considered FE softwares. See Figure 7:1 for the final geometry.

To reduce computational time and improve meshing quality, only one half of the full model is analyzed (except for the installation load case). To simulate the trawl a 0.25 m radius solid sphere is used.

Since the flanges of the GRP cover will be rock dumped, these are assumed to be clamped to the seabed and will not be used for the load cases except for installation where the whole structure needs to be analyzed.

7.3 Local Coordinate System, Mesh and Element Types The local coordinate system for each part of the geometry can be seen in Figure 7:1. The local coordinate looks the same for the symmetry model except that there are three local coordinate systems instead of five. The layers are stacked on each other in the positive local z-direction, i.e. the first layer is at the bottom and the last layer is on the top of the structure. The fibers are always oriented in the x-direction, e.g. when the fibers are in the 90 degrees direction the local coordinate system is rotated around the z-axis 90 degrees, which means that the y-direction is always transverse to fibers.


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Figure 7:1. Local coordinate system for each part of the geometry in Ansys WB

The ply lay-up for the GRP material is modeled using quadratic dominant mesh consisting of Shell181 elements. The trawl is modeled using tetrahedron elements, see Figure 7:2 for the symmetric geometry. A further explanation of the Shell181 element can be found in Appendix B.

Figure 7:2. Mesh of the symmetric GRP cover and the trawl


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7.4 Loads Structural design of subsea structures in the Norwegian sector is currently governed by NORSOK U-001 [1] based on a trawl board mass up to 1900 kg. However, trawl equipment has developed and larger and heavier gear is in use. This has a direct bearing on structural design of seabed equipment and therefore new guidelines are sought. The GRP covers are smoother than the steel protection structures and hence associated with lower trawl loads than tabulated in NORSOK U-001 [1]. The analyzed load values are taken from tests done by Marintek for GRP covers and it is likely that the values in NORSOK U-001 will be revised in the nearest future.

The fishing nets, most often two, are attached to a clump weight in order to keep the nets on the seabed, see Figure 7:3. The trawl usually varies in size and shape but most of them are of rolling types and made of steel. In this work, a set of common load cases that the cover could be exposed to is considered.

Figure 7:3. Two Wire Twin Trawl

The GRP cover will be subjected to, basically, four different loads:

1. Installation 2. Trawl net friction 3. Trawl over-pull 4. Trawl impact


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The GRP cover will be subjected to load cases according to Table 7:1. An explanation of the load cases is described below:

1. Installation

Static and hydrodynamic forces acting in the GRP cover when lowering through seawater.

2. Trawl net friction

The force acting on the cover due to friction that is caused by the fishing net.

3. Trawl over-pull

The force needed to pull over the trawl of the cover due to its inclined shape.

4. Trawl impact

Due to trawling the trawl will slam into the cover with certain energy.

Table 7:1. Loads

No: Load case Load state

Value Description Failure criterion

1 Installation ULS · = 9.82 Tsai-Wu

2 Trawl net friction

ULS 2 · 50 0° Horizontal Tsai-Wu

3 Trawl board over pull

ULS 50 0° Horizontal Tsai-Wu

4 Trawl board impact

ULS 20 Trawl speed 3.0 Tsai-Wu

The DAF is a factor accounting for the global dynamic effects normally experienced during lifting but also during lowering through the water.

Since the protection cover is only approximately 8 meters long only one net will be considered to affect the structure at one time. This is because the nets are most often a very long distance from each other, approximately 100-300 meters.

7.5 Application of Loads and Boundary Conditions With the load values taken from Table 7:1 and the corresponding design factors from Table 6:1, the following design load values according to Table 7:2 are used in the FEA in Ansys WB

Table 7:2. Design loads

No: Load case Load Value GRP Design Factor Design Load 1 Installation · , 3.43 See Section 7.5.1

2 Trawl net friction 50 , 1.84 92

3 Trawl over pull 50 , 1.84 92

4 Trawl impact 20 , 1.84 36.8


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Installation During installation the cover will be subjected to both static and dynamic forces when lowering through the seawater. A Dynamic Amplification Factor (DAF) is calculated to account for the global dynamic effects normally experienced during lifting [11]. The DAF is defined as

Eq. 25

Where:

: Static submerged weight of object

: Characteristic hydrodynamic force

The procedure for calculating the DAF is shown in Appendix C.

The aim is to investigate how the lifting angle affects the structure so that the installer knows at which angle the GRP cover should be installed in order to prevent layer failure. To give an illustrative picture on how the installation case looks like, see Figure 7:4. The GRP cover is attached to slings that are used to lower the cover down on the seabed. When the installation boat is exposed to waves the boat starts to wiggle and the cover will experience high acceleration upwards due to the attached slings. The acceleration is applied in the local y-direction according to Figure 7:4. Since the cover has a very large area it will contribute to a very high DAF if the cover would be lowered horizontally; which would contribute to that almost every layer would fail. Therefore a comparison of installation angle is here considered to give a recommendation at which angle the cover should be immerged.

The DAF depends on a variety of parameters such as the number of layers due to a larger and heavier structure and the installation angle. By changing the installation angle it implies to a different projected area on the horizontal plane that is a parameter that affects the DAF and hence the total values of the acceleration that is applied to the GRP cover in Ansys WB. See Appendix C for the different values of the installation angle, the projected area the DAF and the design load used in Ansys WB.


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Figure 7:4. Direction of acceleration and soft sling attachments

By attaching ballast steel weights to the GRP cover, the cover gets heavier. This contributes to a lower DAF value. This cover will have a larger ballast steel weight on the outside of the 58° inclined surface of the cover and a smaller inside the cover to keep the larger one in the right position. This ballast steel weight can be considered as a “dead weight” which will corrode after a while in the seawater environment. Typical ballast steel weights are accounted for when calculating the DAF, which can be seen in Appendix C.

The GRP cover is locked in the local y-coordinate, i.e. in the direction of the acceleration which is applied in the local y-coordinate direction as well.

Trawl Net Friction The force that is caused by the friction of the fishing net shall be applied horizontally on all surfaces of the structure which have a slope of 0° 20° from the horizontal plane. The force is in this case applied to the cover as a surface load of 46 kN, which is half the design load according to symmetry conditions, acting in the positive global x-direction, see Figure 7:5.

Acceleration

Installation angle


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Figure 7:5. Force applied as a surface load in the global x-direction.

The cover is locked in the global x-, y- and z-direction (line C) due to rock dump. Due to usage of symmetry, the symmetry line is also locked in the z-direction (line A), see Figure 7:5.

Trawl Impact A more detailed description of the trawl impact load case can be read in report 240-MT-003 written by Jonas Elgered [12]. The maximum displacement of the trawl into the cover from the LS-Dyna simulation is transferred to Ansys WB where it will act as a boundary condition in a quasi-static simulation, see Figure 7.6. The same boundary condition as for the friction load case is used here; line A and the trawl are locked in z-direction due to usage of symmetry conditions while line C is locked due to rock dump.


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gfgfgf

Figure 7:6. Displacement of trawl from LS-Dyna simulation

Trawl Over-pull Pull-over analysis deals with the global response of the structure as the trawl gear is pulled/ forced to cross over the structure. During this phase, the structure may be subjected to relatively large horizontal (lateral) and vertical forces [14].

There are no regulations in the standards regarding the position of the trawl in a static analysis. Therefore, the trawl is placed on the very same position as for the trawl impact load case, see Figure 7:7. This position however gives some convergence problems in Ansys WB when analyzing the load case for a lay-up sequence of [-45/45]8s. The GRP cover becomes to weak, which means that the trawl crosses the GRP cover and goes into infinity and hence, no solution is obtained for the [-45/45]8s lay-up. The trawl must be placed almost at the bottom of the cover in order to obtain convergence in Ansys WB, but this would not reflect what happens in reality when the trawl is pulled/forced over the structure.

The GRP cover is again locked in the global x-,y- and z-direction (line B) and locked in z-direction due to symmetry (line A). A force of 46 kN is applied to the trawl in the global x-direction while the trawl is locked in z-direction as well (line C), see Figure 7:7.

Disp. from LS-Dyna, y-direction

Disp. From LS-Dyna, x-direction


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Figure 7:7. Boundary condition and force on the trawl

7.6 FEM of Composites in Ansys Composites are somewhat more difficult to model than isotropic material such as iron or steel because each layer may have different orthotropic material properties. The engineer must pay special attention when defining properties and orientations of the various layers. A script for building the desired composite laminate in Ansys is presented in Appendix E.

Many FE programs have different failure criteria already specified in the software but could be constructed in different ways from program to program and not coincide with the desired equation of the engineer. Due to this, a post-processing script has been developed to facilitate to analyze any failure criteria in the preferable way. The post-processing script is presented in Appendix E where an example of how to obtain the element results in the fiber direction (stresses in the x-direction) is written. A similar script is used to obtain the element results in other directions as well.

The element results are then written from Ansys to .txt files, which are then imported to an Excel spreadsheet where the desired failure criterion is analyzed and plotted. This means that any failure criterion, even those who are not even developed yet, could be analyzed by this procedure and the engineer does not need to wait for an upgrade of the FE program.

The Excel figures are very effective when the engineer wants to see if a ply could be considered non-damaged or not.

When working with FEA, the engineer should keep in mind the following:


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• Smaller elements in regions with high gradients • Higher order (quadratic or cubic) elements allow for more accurate stress predictions. • A converged solution with high quality of the results and with the fewest number of

elements is sought. • Use symmetry if possible

There are two different ways to obtain the element solutions for each layer from the simulations in Ansys WB. One is referred to Ansys WB and the other is through Ansys Classic.

Ansys WB: Under the solution tree, insert a command and paste the following /post1 inres,all FILE,'file','rst','.' set,last /input,”name of your text file”,txt

Ansys Classic: The other way to obtain the results is to transfer the setup in Ansys WB project tree to mechanical APDL and paste the following commands in the command prompt /post1 FILE,'file','rst','.' set,last /input ,”name of your ansys script”,txt Regardless of the method used, the engineer must place the script in the working directory.

Other useful commands when working with composites to see if the script is written correctly and if the GRP lay-up is properly obtained could be for example:

/psymb,layr,n followed by eplot: Displays the layer number n for all selected layered elements. Use this method to display and verify each individual layer across the entire model. /psymb,esys,1 followed by eplot: Displays the element coordinate system triad for those elements whose default coordinate system has been changed.

8 RESULTS In this section, a number of excel plots will be shown to illustrate how the different load cases affects the structure and the corresponding plies. Also, when appropriate, corresponding Tsai-Wu failure criteria plots taken from Ansys are presented to illustrate where the critical area of the structure arises and then, in an engineering manner, decide if the layer will fail or not due to applied loadings.

Total number of elements for installation load case: 7210

Total number of elements for friction load case: 2819

Total number of elements for trawl impact and trawl over-pull load case: 3280

ProtectioAuthor: M240-MT-

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Page 35(49) Sign MN

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Figure 8:2. Lay-up sequence of [-45/45] for 32 layers

Figure 8:3. Lay-up sequence of [0/90/45/-45] for 32 layers

Regardless of the number of layers in the GRP structure, the appearance looks similar as Figure 8:1-8:3 above except that less number of elements fails due to a stiffer and stronger cover.

The first conclusion to be drawn is that a vertical installation of the cover is necessary in order to prevent ply failure. The structure is however designed with a maximum installation angle of 15°. It is quite difficult to install the GRP cover exactly horizontal. A few elements around the small lifting holes fail when lowering the cover with 15°. This means that the cover needs to be manufactured with more plies to obtain zero failed elements.

0

2

4

6

8

10

12

Failed elem

ents [%]

Failed elements /layer: 32 plies

5 degrees10 degrees15 degrees20 degrees30 degrees

0

5

10

15

20

25

30

Failed elem

ents [%]

Failed elements /layer: 32 plies

5 degrees

10 degrees

15 degrees

20 degrees

30 degrees


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The second conclusion is that a fiber lay-up of the sequences [0/90]s and [-45/45]s show almost identical behavior when lowering the GRP cover with an installation angle of maximum 15°. A lay-up sequence of [0/90/45/-45] is not appropriate for the installation load case.

See Appendix F for more result figures regarding lay-up sequence, installation angle and the number of plies.

The critical elements are, irrespective of the lay-up, located around the lifting holes and propagate between the holes. An example for a lay-up of [0/90/45/-45]4s for an installation angle of 15° is shown in Figure 8:4a. A Tsai-Wu plot for [-45/45]8s for an installation angle of 15° is also shown in Figure 8:4b to show that the critical elements are around the lifting holes which is singularities in the FE program and hard to avoid, i.e. this appearance according to Figure 8:4b is not critical for the ply. The red area illustrates failed elements.

Figure 8:4a. Tsai-Wu for [0/90/45/-45]4s Figure 8:4b. Tsai-Wu for [-45/45]8s

8.2 Trawl Net Friction The friction caused by the fishing nets is not usually a critical load case since it is acting over a large area. A comparison between the different lay-ups and the number of layers of the GRP cover is made. Figure 8:5 illustrates how many percent of the total number of element that fails during the friction load case for 32 layers for the three different lay-up sequences. The conclusion is that the most critical lay-up is [0/90/45/-45]s and should not be used for the friction load case. Lay-up sequences of [-45/45]s and [0/90]s shows almost identical behavior with negligible number of failed elements with a slightly higher number of failed elements for the [-45/45]s lay-up. However, a minimum number of layers of 40 indicates that no element fails during the friction load case for [-45/45]s and [0/90]s while [0/90/45/-45] still is a critical lay-up.


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Figure 8:5. Lay-up sequence for 32 layers

A Tsai-Wu plot of layer 1 of a lay-up [-45/45]s with 32 layers can be seen in Figure 8:6. The red area illustrate the failed elements. Compare Figure 8:6 to Figure 8:5.

Figure 8:6. Critical elements for layer 1 for [-45/45]8s

An investigation has also been carried out to see what happens if the friction load is applied in other directions than in the global x-direction according to Figure 7:5. The considered directions are 45° and 90° with respect to the global x-direction. However, this cannot be

0

5

10

15

20

25

30

Failed elem

ents [%]

Failed elements/layer: 32 plies

[0/90]8s[‐45/45]8s[0/90/45/‐45]4s


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analyzed on the symmetric geometry since the loads are no longer symmetrical with respect to the structure. Regardless if the friction load is applied in the 45° direction or in the 90° degree direction, no element will fail. This means that the friction load caused by the fishing nets is dimensioned for the worst load direction which is in 0° direction.

See Appendix F for figures when the net friction load is applied in 0° direction.

8.3 Trawl Overpull Figure 8:7-8:9 shows the failed area as a function of layer number for the over-pull load case for all the different lay-ups.

Figure 8:7. Failed element for different lay-ups of 32 plies

0

100

200

300

400

500

600

Failed area

[dm^2]


[0/90]8s

[‐45/45]8s

[0/90/45/‐45]4s


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From Figure 8:7 it can be seen that no solution is obtained for the [-45/45]8s lay-up due to convergence problems. It can also be seen from Figure 8:7-8:9 that the number of failed plies is almost independent of the lay-up sequence but changes due to the amount of layers.

Figure 8:10 shows a Tsai-Wu plot for [-45/45]10s where the red area illustrates failed elements.

0

20

40

60

80

100

120

140

160

Failed area

[dm^2]


[0/90]10s

[‐45/45]10s

[0/90/45/‐45]5s

0

5

10

15

20

25

30

Layer 1

Layer 3

Layer 5

Layer 7

Layer 9

Layer 1

1

Layer 1

3

Layer 1

5

Layer 1

7

Layer 1

9

Layer 2

1

Layer 2

3

Layer 2

5

Layer 2

7

Layer 2

9

Layer 3

1

Layer 3

3

Layer 3

5

Layer 3

7

Layer 3

9

Layer 4

1

Layer 4

3

Layer 4

5

Layer 4

7

Failed area

[dm^2]


[0/90]12s

[‐45/45]12s

[0/90/45/‐45]6s


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Figure 8:10. Tsai-Wu plot for [-45/45]10s

8.4 Trawl Impact The maximum trawl displacement from LS-Dyna simulation can be seen in Table 8:1.

Table 8:1. Maximum trawl displacement from LS-Dyna

Laminate Total Thickness

[mm]

Time

[s]

X-displacement

[mm]

Y-displacement

[mm]

[0/90]8s 23.2 0.055 157 4

[0/90]10s 29.0 0.045 128 3

[0/90]12s 34.8 0.045 124 5

[-45/+45]8s 23.2 0.080 217 11

[-45/+45]10s 29.0 0.075 195 15

[-45/+45]12s 34.8 0.060 156 11

[0/90/45/-45]4s 23.2 0.060 169 5

[0/90/45/-45]5s 29.0 0.045 128 3

[0/90/45/-45]6s 34.8 0.045 123 5


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Figure 8:11. Failed area per layer for 32 plies


0

2

4

6

8

10

12

Failed area

[dm^2]

Failed area/layer: 32 plies

[0/90]8s

[‐45/45]8s

[0/90/45/‐45]4s

0

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4

6

8

10

12

14

Failed area

[dm^2]


[0/90]10s

[‐45/45]10s

[0/90/45/‐45]5s


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It is allowed that some layer fail due to the impact load case since it is very unlikely that the GRP cover will be exposed to an impact at the very same spot twice.

Figure 8:14 shows a Tsai-Wu plot for [0/90]8s lay-up where the critical elements that fails is located when analyzing the trawl impact load case. It can be seen that those elements are in the contact area between the trawl and the GRP cover.

Figure 8:14. Tsai-Wu plot for layer 2 for [0/90]8s

0

5

10

15

20

25

Layer 1

Layer 3

Layer 5

Layer 7

Layer 9

Layer 1

1

Layer 1

3

Layer 1

5

Layer 1

7

Layer 1

9

Layer 2

1

Layer 2

3

Layer 2

5

Layer 2

7

Layer 2

9

Layer 3

1

Layer 3

3

Layer 3

5

Layer 3

7

Layer 3

9

Layer 4

1

Layer 4

3

Layer 4

5

Layer 4

7

Failed area

[dm^2]


[0/90]12s

[‐45/45]12s

[0/90/45/‐45]6s


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9 DISCUSSION AND CONCLUSIONS

9.1 Comparison Between Ansys and LS-Dyna Previous projects at Reinertsen Sverige AB in the field of GRP protection structures have been studied in Ansys due to the lack of existing material models for layered composites in LS-Dyna. For one loadcase, the displacement of the trawl was extracted and implemented in Ansys as a prescribed displacement for the trawl to simulate a quasi-static analysis. As a script for a functioning material model for layered composite materials in LS-Dyna was developed in this project, that procedure is now unnecessary. However, the trawl impact load case was analyzed both in Ansys an LS-Dyna to compare the results and hence, to come to a conclusion on which FE program should be used in future projects.

The results obtained differ substantially since Ansys is a static simulation program while LS-Dyna analyzes the whole dynamic cycle. This leads to completely different answers mainly due to the more locally deflected structure in a dynamic load case. The advantage of using Ansys is that contour plots of the Tsai-Wu failure criterion can be obtained. In LS-Dyna the closest criterion available is only a combination of Chang-Chang and Tsai-Wu failure criterion. Ansys gives a remarkable underestimation of the amount of failed layers, compare Figure 8:12 and Figure 8:15. Because of this, trawl impact load case should be analyzed in LS-Dyna.

One can compare the result in Figure 8:12 to the results obtained in LS-Dyna according to Figure 8:15 below.

Figure 8:15. Impact load case in LS-Dyna

Ansys is much more user friendly, and the engineers at Reinertsen are well familiar with Ansys. However, it is recommended to analyze all the dynamic load cases in LS-Dyna as far as possible.

The over-pull load case is most likely to reflect the reality and hence, give more correct results if analyzed in LS-Dyna by applying a pull-over load on the trawl. Static analysis, as in Ansys,

0123456789

Failu

re area [dm^2]


[0/90]10s[‐45/45]10s[0/90/45/‐45]5s


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is likely to be non-conservative. Additionally, LS-Dyna does not have to deal with convergence problems as in Ansys.

9.2 Discussion This work has been analyzed assuming linear relationships. The analysis does not take into account that plies fail progressively, which means that the whole analysis is performed linearly regardless if there is local failure or not in the GRP structure. If a non-linear analysis is considered it has to include a failure criterion in the analysis so that the material properties updates for every time step.

The Tsai-Wu 3D failure criterion is not considered appropriate for laminated structures. It was developed as a 2D failure criterion of a single UD-ply, which very often turns out to give poor results for a laminate. Theoretically, a 3D failure criterion would be appropriate for contact problems, if there was a 3D failure criterion. To extend a 2D failure criterion to a 3D model is actually not recommended. However, the Tsai-Wu failure criterion is a very conservative failure criterion which does not tell in what way the element fails. It is well known that a different failure criterion gives different answers. The question arises how should the analyst react to that? The problem lies in the material and the failure criterion used and has almost nothing to do with the FE-code. There is no failure criterion that could be used on all composite materials.

As an already existing working material model has been developed in previous projects at Reinertsen Sverige AB, the focus has not been to produce a better script for the material model. However, the question that arises is if the Shell181 element is appropriate for analyzing simulations where contact is present as for trawl impact and trawl over-pull. The Shell181 element use shell theory and cannot calculate the out of plane stress. The out of plane stress should not be excluded from the results as this have a large influence in contact problems. However, it is still possible to evaluate lay-up sequence dependency of the results obtained.

Important, when analyzing this type of GRP cover, is to decide how to respond to the failed elements. The GRP cover could be exposed to trawl net friction load twice during its lifetime but as trawl impact and trawl over-pull are loads with very small contact area the GRP was assumed to not be subjected to those load cases twice at the very same spot.

As the GRP cover only is a protection structure, the important thing is that the load carrying capacity remains. Thus partially failed layers were accepted for the two trawl load cases, impact and over-pull, as local failure of some elements was very hard to avoid with high stress concentrations due to contact. In the two other load cases, installation and trawls net friction, the loads are applied over a large area and failure was either in singular points close to holes or edges, or in a quite large region. Failure in large regions was not accepted as the structures load carrying capacity would be degraded for additional load cases.

A low safety class was used in this work which relates to the consequences of failure for the GRP cover. This is however a matter of interpretation in Offshore Standard DNV-OS-C501 [10]. Either the safety class should be chosen regarding if the GRP cover itself fails or if the underlying pipe that is being protected fails. If the GRP cover fails it will not have major consequences while if the pipe, containing oil or gas, fails it will have catastrophic


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consequences. For clarity, contact with the authors of Offshore Standard DNV-OS-C501 is recommended.

When analyzing the two contact problems, which are assumed to occur at the same spot of the GRP cover, locally failed elements have not been excluded. At first, the trawl impact load case should occur before the trawl is forced to cross over the GRP cover and since element fails during this load case they are considered to be intact when analyzing the trawl over-pull load case. This is a more conservative procedure and should be used in future projects.

The design factors are calculated based on standards which are mainly for pipes which mean that all the design factors are very conservative. Hopefully, factors for protection structures of GRP are developed in the nearest future.

9.3 Conclusions Installation Installation should be done vertically in order to prevent layer failure. The quasi-isotropic lay-up [0/90/45/-45]s was clearly the worst lay-up sequence for this load case. The other two lay-ups [0/90]s and [-45/45]s showed almost identical behavior and the GRP stayed completely intact for 40 layers when the installation angle was 15°, see Figure 8:1-8:3 in Section 8.1 and Figure E1-E6 in Appendix E.

Trawl Net Friction The quasi-isotropic lay-up [0/90/45/-45]s was poor for the trawl net friction load case while the other two lay-ups [0/90]s and [-45/45]s did not have any failed element for a GRP cover of 40 layers, see Figure 8:5 in Section 8.2 and Figure E7-E8 in Appendix E.

Trawl Over-Pull None of the lay-up sequences gave significantly better results than the others. The amount of failed plies is almost identical while the failed areas are significantly larger for a lay-up of [0/90]s and [-45/45]s for 32 and 40 layers. For 48 layers no noticeable difference can be observed. Approximately 25 layers stay intact regardless of the number of layers studied here in the GRP structure.

Trawl Impact Since a well-developed material model for composites has been formulated it is now recommended to analyze the trawl impact load case in LS-Dyna.

It is quite hard to tell which lay-up sequence is better than the other for this load case when analyzing in Ansys. Clearly one can see, from Figure 8:12-8:14, that a lay-up sequence of [0/90/45/-45]s shows least amount of layers that fails while the other two lay-ups [0/90]s and [-45/45]s have almost identical number of failed plies. At least 20 layers stayed intact for all number of layers used in the GRP cover, see Figure 8:11-8:13.

The same result can be observed in report 240-MT-003 [12]that different stacking sequences of UD-plies does not have a large influence on the number of failed layers. At least 10 layers stayed intact independent of how many plies the GRP cover had.


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Summary of Conclusion For this specific GRP cover the lay-up sequence [0/90]s are slightly preferable before the [45/-45]s while the quasi-isotropic lay-up [0/90/45/-45]s clearly was the least suitable one, at least when all load cases were evaluated with the 3D Tsai-Wu failure criterion. The reason why trawl impact and trawl over-pull are almost independent of the lay-up sequence is because when applying loads in the thickness direction of a laminate the strength are almost independent of the reinforcing fibers and the matrix must take the entire load.

10 FUTURE WORK Contact with the authors of Offshore Standard DNV-OS-C501 should be made in order to get the correct statement regarding the safety class which has an influence of the total design factor for the different load cases.

Importing the displacements from LS-Dyna to Ansys feels unnecessary since a well-structured method has been developed which now can be used to evaluate the results directly from LS-Dyna.

Tests on the specific composite material have to be made in order to decide which failure criterion that suits this type of GRP cover the best.

An investigation on the different element types that could be used for a composite in Ansys could be done. The results of the output are very dependent on which element that is used.


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11 REFERENCES [1] NORSOK Standard U-001 Subsea Production Systems, Rev 3, October 2002

[2] Mechanics of composite materials, Robert M. Jones, Hemisphere Publishing Corporation

[3] Analysis and performance of fiber composites, 2nd edition, Bhagwan D. Agarwal and Lawrence J, Broutman]

[4] Foundations of fibre composites by Dan Zenkert and Mark Battley, Paper 96-10, KTH

[5] Handbook of Composites, 2nd edition, by George Lubin, Edited by S.T. Peters]

[6] Manufacturing of Polymer Composites, B.T Åström

[7] NORSOK M-001 Materials selection

[8] Direct contact with Fredrik Axelsson, former employee at Reinertsen Sverige AB

[9] An introduction to Composite Materials, Derek Hall

[10] Offshore Standard DNV-OS-C501 Composite Components, October 2010

[11] VMO “Rules for Planning and Execution of Marine Operations”, May 2004

[12] Protection structures of glass fiber reinforced plastic, report nr. 240-MT-003, Jonas Elgered.

[13] Ansys 12.1

[14] DNV-RP-F111, Interference between trawl gear and pipelines, Oct. 2010


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Appendices


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Appendix A

Calculation sheet for UD-ply


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Appendix A – Calculation sheet for UD-Ply

Rule of Mixture UD-ply

Youngs modulus for fiber

Youngs modulus for matrix

Poissons ratio for matrix

Volume fraction fiber

Volume fraction matrix

poissons ratio for fiber

Shear modulus for fiber

Shear modulus for matrix

Youngs modulus 1-direction

Youngs modulus 2-direction

Due to isotropy plane

Shear modulus 12-direction

Due to isotropy plane

Poissons ratio 12-direction

Poissons ratio 21 direction

Due to isotropy

Estimated poisson 2-3 for the laminate:

Shear modulus for the isotropic plane

Ef 70 109⋅:=

Em 3 109⋅:=

vf 0.3:=

vm 0.4:=

Vf 0.5:=

Vm 0.5:=

GfEf

2 1 vf+( )⋅:= Gf 2.692 1010

×=

GmEm

2 1 vm+( )⋅:= Gm 1.071 109

×=

E1 Ef Vf⋅ Em Vm⋅+:= E1 3.65 1010×=

E2Ef Em⋅

Vf Em⋅ VmEf⋅+:= E2 5.753 109

×=

E3 E2:=

G12Gf Gm⋅

Vf Gm⋅ VmGf⋅+:= G12 2.061 109

×=

G13 G12:=

ν12 Vf vf⋅ Vmvm⋅+:= ν12 0.35=

ν21 E2ν12E1

⋅:= ν21 0.055=

ν13 ν12:= ν31 ν21:=

ν23 0.35:=

G23E2

2 1 ν23+( )⋅:= G23 2.131 109

×=


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Appendix B

The Shell181 Element


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Appendix B – Calculation sheet for UD-Ply

The shell181-element is a 4-noded finite strain element. It is suitable for analyzing thin to moderately thick shell structures. It has six degrees of freedom at each node: translation in the x, y and z directions, and rotations about the x, y and z axes. This element may have several layers of orthotropic material, each layer having different orientation and material properties.

The shell181 element has fully nonlinear capabilities including large strain and allows 255 layers to be defined. The layer information is input using the section commands rather than real constants. The shell181 element can be seen in figure B1. For notation, see Ansys 12.1 help manual.

Figure B1. Shell181 element used in Ansys


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Appendix C

DAF Calculation


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Appendix C – DAF Calculation Obvious-, straight forward-, and standard equations are excluded from Table C1 and can be found in the calculation sheet for the DAF.

Table C:1

Factor Description and typical value Reference

Significant wave height of design sea state. Higher value gives more conservative safety factor. Typical value is between 1‐4 meter.

VMO, Pt.2, Ch.6, 2.3.3.2

Characteristic single amplitude vertical velocity of crane tip. VMO, Pt.2, Ch.6, 2.2.3.1

Characteristic single amplitude vertical acceleration of crane tip.

VMO, Pt.2, Ch.6, 2.2.4.1

Hook lowering velocity. Typical value is 0.5 m/s but that is very conservative and usually the speed is lower for covers.

VMO, Pt.2, Ch.6, 2.3.3.2

Slamming impact velocity is the minimum of two alt. equations.

VMO, Pt.2, Ch.6, 2.3.3.2

VMO, Pt.1, Ch.1, p6

Slamming coefficient. For smooth circular cylinders it should not be taken less than 3.0 but for other geometries should not be less than 5.0.

VMO, Pt.2, Ch.6, 2.3.3.1

The characteristic slamming impact force on the bottom of the object when penetrating the water surface.

VMO, Pt.2, Ch.6, 2.3.3.1

The lift force component due to carrying buoyancy forces caused by waves. Buoyancy force is the minimum of two alt. equations.

VMO, Pt.2, Ch.6, 2.3.4.1

The characteristic vertical relative velocity between object and water particles, (max. when depth=0).

VMO, Pt.2, Ch.6, 2.3.4.2

Drag coefficient as a function of depth, which may be determined by theoretical and/or experimental methods. Typical conservative value is 2.0.

VMO, Pt.2, Ch.6, 2.4.2.5

Added mass coefficient. Typical conservative value is 2.0 for very light structures compared to volume. For very heavy structures could go down to 0.6.

VMO, Pt.2, Ch.6, 2.4.2.3


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The following calculation sheet is illustrating the procedure to calculate the DAF. For this specific case the cover has 40 plies and is lowered with an installation angle of 15 degrees.

Calculation methodology for DAF

Number of layers

Thickness of each ply

Total thickness of the structure laminate

Projected area on the horizontal plane

Significant wave height Wave period

Characteristic crane tip acceleration

Hook lowering velocity

Density of sea water

Total area of the structure

Characteristic crane tip velocity

Volume of object

Density of ply

Ballast steel weigth

Mass of object in air Distance from water plane to centre of gravity of submerged part of object.

Volume of displayed water

kN 10 3 N≡

lager 40:=

t 0.000725m:=

ttot lager t⋅:= t tot 0.029 m=

Aproj sin 15π

180⋅⎛⎜

⎝⎞⎟⎠

59.5⋅ m2:= A proj 15.39973 m2

=

Hs 2.5m:= Tp 5s:=

vctHs 1.8⋅

22 π⋅

Tp:= vct 2.82743

ms

=

actHs 1.8⋅

22 π⋅

Tp

⎛⎜⎝

⎞⎟⎠

2⋅:= act 3.55306

m

s2=

vc 0.5ms

:=

ρ 1025kg

m3:=

Atot 66.968m2:=

Vtot Atot ttot⋅:= Vtot 1.94207 103× L=

rho 1900kg

m3:=

ballast 2 4343.2⋅ kg 2 246.4⋅ kg+:= ballast 9.1792 103× kg=

mair rho Vtot⋅ ballast+:= mair 1.28691 104× kg=

depth 0m:=

Vdisp 1.0 Vtot⋅:= Vdisp 1.94207m3⋅=


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Slamming force

Slamming impact velocity

Minimum slamming impact velocity

Slamming coefficient

Projected area

Characteristic slamming impact force

Buoyancy force

Crane wire stiffness

Characteristic buoyancy force

The need not to be taken greater than 0.5

times the total buoyancy of the handled object

Drag force

The characteristic veritcal relative velocity between object and water particles may be taken as:

vs1

vct2 3.1 Hs⋅

m

s2⋅+

40.528

4 vc⋅

vct2 3.1 Hs⋅

m

s2⋅+

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

0.44−

⋅ 1.645+⎡⎢⎢⎢⎣

⎤⎥⎥⎥⎦

⋅ vc+:=

vs1 2.83984ms

=

vs_min vct2 3.1 Hs⋅

m

s2⋅+:= vs_min 3.96792

ms

=

vs min vs1 vs_min, ( ):= vs 2.83984ms

=

Cs 5.0:=

Ap Aproj:= Ap 15.39973m2=

Fslam 0.5 ρ⋅ Cs⋅ Ap⋅ vs2

⋅:= Fslam 318.24641kN⋅=

Kc 150 106⋅

Nm

:=

Fρ1Hs Ap⋅ ρ⋅ g⋅

12 π⋅ g⋅ mair⋅

20 Kc⋅ Hs⋅−

⎛⎜⎝

⎞⎟⎠

2:= Fρ1 387.07006kN⋅=

Fρ Fρ2 0.5 Vtot⋅ ρ⋅ g⋅:= Fρ2 9.76068kN⋅=

Fρ min Fρ1 Fρ2, ( ):= Fρ 9.76068 103× N=

vr vct2 3.1 Hs⋅

m

s2⋅ e

0.32− depth⋅

Hs

⎛⎜⎜⎝

⎞⎟⎟⎠

2

⋅+:= v r 3.96792ms

=


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design_factor 3.43:=

Drag coefficient

The characteristic drag force

Inertia force

Added mass koefficient

Added mass of the object

The characteristic water particle acceleration

The characteristic interia force due to combined acceleration of object and water particles

Total force

The characteristic hydrodynamic force on object when lowered through water surface

The static submerged weight of object

Dynamic amplifikation factor

Total design factor for installation

Total load value applied in FE program

Cd 2:=

Fdrag 0.5 ρ⋅ Cd⋅ Ap⋅ vr2

⋅:= Fdrag 248.52073 kN⋅=

Cm 2:=

madd ρ Vdisp⋅ Cm⋅:=

aw 3.1m

s2e

0.32− depth⋅

Hs⋅:= aw 3.1m

s 2=

Fm mair madd+( ) act⋅ ρ Vdisp⋅ aw⋅+ madd aw⋅+:= Fm 78.38319 kN⋅=

Fhyd Fslam2 Fρ

2+ Fdrag

2+ Fm

2+:=

Fhyd 411.43957kN⋅=

Fstatic mair g⋅ ρ Vdisp⋅ g⋅−:= Fstatic 106.68177kN⋅=

DAFFhyd Fstatic+

Fstatic:= DAF 4.8567=

design_load DAF g⋅ design_factor⋅:=

design_load 163.36389m

s2=


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Table C2a-C2c shows how the installation angle affects the DAF, the projected area and the acceleration load in Ansys WB for different number of layers

Table C2a. 32 Layers

Angle Aproj DAF Ansys

5 5.19 2.48 83

10 10.33 3.71 124

15 15.40 4.96 166

20 20.35 6.21 208

30 29.75 8.56 288

Table C2b. 40 Layers


5 5.19 2.47 83

10 10.33 3.64 122

15 15.40 4.86 163

20 20.35 6.01 203

30 29.75 8.35 280

Table C2c. 48 Layers


5 5.19 2.47 83

10 10.33 3.59 120

15 15.40 4.76 160

20 20.35 5.92 199

30 29.75 8.14 273

Protection Structures of Glass Fiber-Reinforced Plastic Description etc Project no 0000000

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Appendix D

Ansys Script (Only for Reinertsen Sverige AB)

Protection Structures of Glass Fiber-Reinforced Plastic Author: Marko Nikolic 240-MT-002

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Appendix E

Additional Results

In the following appendix, results of the installation and Trawl Net Friction are shown. All figures show percent of failed elements as a function of layer

number.


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Appendix E – Results Installation

Figure E1. [0/90] 40 layers Figure E2. [0/90] 48 layers

Figure E3. [-45/45] 40 layers Figure E4. [-45/45] 48 layers

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

1 4 7 10 13 16 19 22 25 28 31 34 37 40

5 Degrees

10 Degrees

15 Degrees

20 Degrees

30 Degrees

% of failed elements(7210 elements)

Layer number

0

0,5

1

1,5

2

2,5

3

3,5

1 4 7 10131619222528313437404346

5 Degrees

10 Degrees

15 Degrees

20 Degrees

30 Degrees


Layer number

0

1

2

3

4

5

6

7

8

1 3 5 7 9 111315171921232527293133353739

5 Degrees10 Degrees15 Degrees20 Degrees30 Degrees


Layer number

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

1 4 7 10131619222528313437404346



Layer


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Figure E5. [0/90/45/-45] 40 layers Figure E6. [0/90/45/-45] 48 layers

Trawl Net Friction

Figure E7. 40 layers, 0-degree friction Figure E8. 48 layers, 0-degree friction

0

5

10

15

20

25

1 4 7 10 13 16 19 22 25 28 31 34 37 40



Layer number

0

2

4

6

8

10

12

14

16

18

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46



Layer number

0

2

4

6

8

10

12

14

16

18

1 3 5 7 9 111315171921232527293133353739

[0/90]10s

[‐45/45]10s

[0/90/‐45/45]10s

% of failed elements (2819 elements)

Layer number

0

1

2

3

4

5

6

7

1 4 7 10131619222528313437404346

[0/90]12s

[‐45/45]12s

[0/90/‐45/45]12s


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