Modeling Composites withModeling Composites with Femap … · Modeling Composites withModeling...

Predictive Engineering Femap 10.1.1 Composites Tutorial

Modeling Composites withModeling Composites with Femap 10.1.1

An Introduction to The How’s and Why’s

George Laird, Ph.D., P.E.

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Table of ContentsTable of ContentsDefining a Laminate Material in Femap ………...……………………………………..Femap Layup Editor ………….……………………………….……………………….Orthotropic Materials Overview …………………………………………..……………

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Defining an Orthotropic Material in Femap ……………………………..…………….Example 1: Creating a Submarine Laminate Model in Femap …...…………….......….

Creating the Laminate Material ………………………………………..Defining the Laminate Layup …………………………………………D fi i th L i t P t

681011 12Defining the Laminate Property ……………………………………….

Specifying Material Angles ……………………………………………Post Processing the Results ……………………………………………

Using Plate Elements to Model Honeycomb Core Composites ……………………….Classical Plate Theory Applied to Honeycomb Composites .………….

1213151718y pp y p

The Nastran PShell Property Card ……………………………………..Using the PShell Property Card for Honeycomb Composites …………Using Femap to Setup a Honeycomb Panel ……………………………

Example 2: Comparing Different Laminate Modeling Methods ……….……………...i l i d i h l

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d Material Properties used in the Example ………………………………Honeycomb Model using Solid Elements with Laminate Face Skins …Honeycomb Model using Classical Plate Theory ……………………...Honeycomb Model using Laminate Elements …………………………Results Summary ……………………………………………………….

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Conclusion ……………………………………………………………………………..3435


Defining a Laminate Material in FemapDefining a Laminate Material in Femap

To define a Laminate Material in Femap, 3 specifications must be made:• The Composite Layup that is to be used must be specified Theseused must be specified. These Layups are defined using the Layup Editor.• A Bond Shear Allowance must also be specified. The value represents the bond strength between the bonded laminate sheets. This value is used to calculate a factor of safety against shear failure between laminate panels.

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pa e s.• A Failure Theory must also be specified. If Tsai-Wu is specified, then the Tsai-Wu interaction coefficient must also be specified in th t i l d fi iti

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Femap Layup EditorFemap Layup Editor

Th l dit i FThe new layup editor in Femapallows for the easy specification of laminate configurations. This new editor allows plys to be be edited individually or collectively. It also y yallows each ply to be moved around in the layup, as well as easy editing of ply thickness and angle.

A compute button has also beenA compute button has also been added that allows the user to calculate and display the A, B and D matrices which represent the laminate behavior. These matrices are

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Orthotropic MaterialsOrthotropic Materials

Often times Composites can be modeled as Orthotropic materials. The Nastran Mat8 material pcard can be used to simulate orthotropic behavior.

h b i l f h i i l

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d The above is an example of an orthotropic material. The 1 direction could corresponds to the x direction and the 2 to the y or vise-versa. When deciding which direction is the x and which is the y, what is important is that the chosen convention is adhered to.

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Defining an Orthotropic Material in Femap

FEMAP requires the entry of 5 values:

Defining an Orthotropic Material in Femap

values:• 2 Young’s Moduli for the material’s primary directions.• A 1-2 Shear Modulus• 2 Transverse Shear Moduli, 1z & 2z• The 1-2 Poisson Ratio, the 2-1 Poisson Ratio is not required. The symmetry of the material stress tensor allows FEMAP to calculate it based upon E1 E2 and v1-2based upon E1, E2 and v1-2.

There are a number of other values that can be entered depending upon what type of analysis is going to be

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1) HMS B1-002 TY I-TSOne of the more difficult aspects of working with composites is

i li i bl i l d i k ki hgetting realistic, usable material data. Matt Piatkowski at Heath Tecna inc. provided an example of a material model they have developed.

These values were derived through correlating experimental data with FEA models. Built into this material model are a number of

2) Graphite Tapeassumptions: it is only valid for certain shapes and loading schemes. The model works well in pure flex, but does not work well when a lot of shear or twist is imposed on the structure.

Such limitations and assumptions are very important to quantify. An

3) HMS B3-001 TY4 CL1 GR9

FEA model is only as good as the assumptions that go into it.

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Example 1: Creating a Submarine LaminateExample 1: Creating a Submarine Laminate Model in Femap

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The model to the right is a section of the submarine model shown on the previous page. The original model was built using plate elements, but in this example we will modify it so that the submarine ‘skin’ is a laminate.

The port is composed of solid elements, with an assumed material of steel. The ring of blue elements around the port are plate elements, whose purpose it is to simulate a weld. These plate elements are also

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Creating the Laminate MaterialCreating the Laminate MaterialThis model will use a single material for the laminate plies. The properties are those of a Graphite/epoxy compositeψ.

The Limit Stress/Strain section i d f l l i f ilis used for calculating failure indexes. There are a number of indexes Nastran will calculate: Hill, Hoffman, Tsai-Wu, and

i S i iMaximum Strain. Tsai-Wu requires a material dependant experimentally derived value, it is in the material definition that hi l i ifi d

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d this value is specified.We will use Hoffman’s criteria, so this value isn’t necessary for our analysis.

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ψJones, Robert M. Mechanics of Composite Materials. New York: Hemisphere, 1975. 70.


Defining the Laminate LayupDefining the Laminate Layup

After the orthotropic material is created the Layup Editoris created, the Layup Editor can be used to define how the laminate plies are situated.

The laminate that has beenThe laminate that has been defined on the right consists of 7 plys, each 0.2 inches thick. The primary direction of the plies varies by 90ºplies varies by 90 .

This is a fairly simple configuration. Often the individual plies are different

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d individual plies are differentmaterials, the top and bottom plies being composed of a somewhat tough material while the inner plies are more light-weight. Configurations such as these impart a large area moment of inertia while remaining light weight.

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Defining the Laminate PropertyDefining the Laminate PropertyWe are now just a short jump away from having a laminate property defined. The laminate definition requires the user to specify which Layup will define the the laminate.

The BondShr Allow also needs to be specified if a bond factor of safety is desired. The valuei i d b di idi h i l h b h dSh Allis arrived at by dividing the inter-ply shear stress by the BondShr Allow.

It is here that the Failure theory is also specified. This example will use Hoffman’s theory. These failure theories produce failure indexes. An index greater than 1 denotes failure. Each

l i h l i ill h i d f il i d Th i d l l h

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d ply in the laminate will have an associated failure index. The equation used to calculate the Hoffman index is shown below.

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After the elements are Specifying Material Angles

assigned the laminate property, they need to be given a specified angle that corresponds to the primary direction of the layup. The above picture specifies the directions we are interested in specifying. The ring of two elements around the port are to have an orientation tangent to the edge of the port, while all other elements need to point in the vertical direction.

Going to Modify-Update

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d Elements-Material Angleallows the user to specify the laminate direction. In the case above, a cylindrical coordinate system was created, called Cylindrical 1. Using this coordinate system, the inner ring of elements were specified as pointing in the theta direction.

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p p g


It is important to ensure that all laminate elements have an angle specified. Nastran will not run the analysis if elements are missing an angle specification. Element normals are also important if your laminate model is not symmetric. These must be specified to ensure that element orientation is consistent.

On the right is an example where a certain portion of laminate elements have unspecified angles. Often finding where these elements are is a chore. To solve the problem, I created an API script that searches for these elements, then highlights and groups them. The bottom graphic shows this. This API is called Composites Material Angle Checker, and can be

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After loads and boundary conditions are specified, the

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Post Processing the Results

For each element, there are 7 plies and each of these plies has associated data, e.g. stresses,

i f il i d h lstrains, failure indexes. The plot on the right is that of the maximum failure index for each element.

It can be seen that under this loading condition, the Hoffman failure criterion predicts a maximum index of 0.243. This value is well below 1, and therefore

e can infer that this portion of thewe can infer that this portion of the vessel is quite safe.

It should be noted that this is a failure index, NOT a factor of

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d safety. Hoffman’s equation is not linear, and should not be Construded to imply that the structure has a factor of safety of 1/0 243 or ~ 4 1

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In order to generate a factor of safety, Hoffman’s equation needs to be solved in it’s quadratic form. See Daniel, Isaac M., and Ori Ishai. Engineering Mechanics of Composite Materials. New York: Oxford, 1994. 120-124.


Th i t l i t b diThe inter-laminate bonding factor of safety is shown on the right. The bonding index see a maximum at the center of the elements This is what we wouldelements. This is what we would expect to see as predicted by classical plate / beam theory. There should be zero shear force on the surfaces and a maximum at the centerline.

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Using Plate Elements toUsing Plate Elements to Model Honeycomb Composites

Nastran and Femap both allow for the use of the PShell property card for honeycomb composites. This section ofhoneycomb composites. This section of the tutorial deals with how Classical Plate Theory can be used to define a plate element which reasonably replicates the behavior of a Honeycomb Core be av o o a o eyco b Co eComposite.

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Classical Plate Theory Applied toClassical Plate Theory Applied toHoneycomb Composites

T/2It i i t t t b th t th i j T/2

D

It is important to remember that there is one major assumption made in classical plate theory with respect to honeycomb composites; it is assumed that all of the in-plane stresses are carried by the facesheets. The following y grelationships can be derived:

Et 3 12 td ⎞⎛

Membrane Stiffness I’ is the bending moment of Inertia per unit width

21 ν−=

EtK 3

121

2232' dtdI −⎟

⎠⎞

⎜⎝⎛ +=

Bending Stiffness If d >>t, then the following can be assumed:

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d

21'ν−

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4'

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The NastranThe Nastran PSHELL Property CardProperty Card

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Using the PSHELL Card for Honeycomb PanelsUsing the PSHELL Card for Honeycomb Panels

PID P t ID T/2PID - Property IDMID1 - This entry specifies the material number of

the facesheets.T - The total thickness of the facesheets.MID2 Thi t l ifi th t i l

T/2

D

MID2 - This entry also specifies the material number for the facesheets.

12I/T3 – The inertia of the facesheets is entered here. If the facesheets are thin, and the core is thick, then it can be assumed that:thick, then it can be assumed that:

• I = TD2/4If the facesheets are relatively thick, then• I = 2/3 [D/2 + T/2]3 – D3/12

MID3 This entry specifies the material number of

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d MID3 – This entry specifies the material number of the honeycomb core.

Ts – This value is the shear thickness and in the case of a honeycomb core, is D.

NSM – Non Structural Mass must be added to the

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card. For a honeycomb core, NSM = D • rhocore


Using FEMAP to Setup a Honeycomb PanelUsing FEMAP to Setup a Honeycomb Panel

Th FEMAP l t tThe FEMAP plate property definition interface is fairly easy to use.

The Thickness of the f h t i t d

The facesheet material facesheets is entered as usual.

The bending stiffness can also be entered, with values obtained from classical

is specified here.

The core material is specified

obtained from classical plate theory equations.

Shear thickness, or in the case of honeycomb panels, D/T l b t d

here.

The mass of the core must also be added. This is done

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d D/T, can also be entered. through the addition of Nonstructural mass.

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Example 2: Comparing Different LaminateExample 2: Comparing Different Laminate Modeling Methods

In this example we will build a honeycomb composite model in three different ways.

1. Using solid elements for the core,1. Using solid elements for the core, and laminate elements for the face sheets.

2. Using plate elements, which utilize classical plate theory to represent theclassical plate theory to represent the core and face sheets all in one property.

3. Using a laminate element which will encompass the face sheets as well as

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d encompass the face sheets as well as the core all in one property.

We will then compare the pros and cons of each methods, and evaluate the results.The models are simply supported, with a body load of 10 G’s. Each configuration is modeled as

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half symmetric.

Predictive Engineering Femap 10.1.1 Composites Tutorial–

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The material properties for the face sheets and the core are shown above.The face sheets are graphite composite, while the core is modeled as an isotropic material

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Honeycomb Panel Using Solid Elements for theHoneycomb Panel Using Solid Elements for the Core and Laminate Elements for the Face Sheets

Thi fi d l b il i H lThis first model was built using Hex elements for the core, and Laminate elements for the face sheets.

The Laminate elements are given an offset of 0.05 to compensate for their thickness.

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The Layup for the face sheets is shown on the right. The face sheets are 0.1 inches thick being composed of 8 plys, each 0.0125 inches thick. These plys are oriented so as to perform in an isotropic manner.

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Deflection results for the solid / laminate model are shown above. The peak deflection is -0.0139 inches.


Honeycomb Panel Using Classical Plate Theory toHoneycomb Panel Using Classical Plate Theory to Represent the Core and Skins in One Property

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In this model, plate elements will be used to simulate the behavior of the honeycomb panel. The equations from classical plate theory given on pages 18-21 are used to modify the behavior of the

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plate element.


The Layup for the face sheets is shown on the right. For this model, we would like to generate a material with equivalent isotropic properties.with equivalent isotropic properties.

Luckily, Femap provides a great new option to do this. There is a new option in the Layup Editornew option in the Layup Editor called Compute. If this is selected, Femap will compute all the composite properties for the layup, computing in-plane o e ayup, co pu g p a eproperties, as well as the A, B and D matrices.

8 Plies - Total Thickness = 0.1

The In-Plane properties for the layup are shown on the left. An isotropic material was used based upon these calculations.

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d In-Plane Properties

Ex = 10556320. Ey = 10556320. Gxy = 3990317.

NUxy = 0.322742 NUyx = 0.322742

Alphax = 0. Alphay = 0. Alphaxy = 0.

E = 10.55 X 106 psiv = 0.322742

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T/2 = 0.1 inches

D = 0.3 inches

D .3

T .2

I 2 D T 3 D3I

3 2 2.

12

I 8.167 10 3=

BendingStiffness 12 I

T3.

T

BendingStiffness 12.25=

ρ .0000045

NSM D ρ.ρ

NSM 1.35 10 6=

ts D

tsT

1.5=

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For the previously given material properties, the equations on pg. 20 yield the values that have been entered into the plate property definition. Actual Calculations are given above.

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Deflection results for the classical plate theory model are shown above. The peak deflection is -0.0142 inches.


Honeycomb Panel Using Laminate Elements forHoneycomb Panel Using Laminate Elements for the Core and Face Sheets

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The above model uses only laminate elements to simulate the honeycomb composite. The face sheets as well as the core material are all contained in one material property.

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The layup for the Honeycomb Composite is shown on the right.

This section of the Layup is theThis section of the Layup is the top face sheet.

This one ply represents the Core.

This section of the Layup is the bottom face sheet.

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What is so nice about the laminate element is its simplicity; in one property, everything can be specified.

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Deflection results for the laminate model are shown above. The peak deflection is -0.0137 inches.


Results Summary

Node Solution Deflection % Variance from Count Time Laminate Model

Hex Model 3381 10 s -0.0139 in 1.43 %

Classical Model 677 5 s 0 0142 in 3 5 %Classical Model 677 5 s -0.0142 in 3.5 %

Laminate Model 677 5 s -0.0137 in 0 %

Th b bl h l f h h d l Th H d L i d l lThe above table compares the results from the three models. The Hex and Laminate models correlate most closely, while the classical model deviates by about 3.5 %. All of the results are fairly consistent, but there are other considerations which contribute to deciding which is the ‘best’ method.

The Hex model is accurate, but has a significantly higher node count and therefore solution time. The

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, g y gclassical model has a small node count, but extraneous calculations are required to set up the model. The laminate model has both a low node count and is easy to set up. In addition, the laminate element formulation provides features not available with the other two methods. The laminate element can provide stress on a ply by ply bases as well as ply specific failure indices. Ply bond failure indices are also available with the laminate The laminate element seems the clear winner not only for ease of use and low

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node count, but because of the many options exclusively available to it.


Conclusion

Th th d f l i it h b l d i thi t t i l E h th dThree methods for analyzing composites have been explored in this tutorial. Each method has its good points, and some are more generally effective than others. Each has its own set of assumptions and limitations.

U i l i l l t th t d l h b l b ff ti b t it t i l hUsing classical plate theory to model honeycomb panels can be effective, but it certainly has limitations and it should not be construed to be capable of handling all of the general cases that the more expansive laminate theory can.

A i t ith ll f Fi it El t A l i thi t f l k fAs is true with all areas of Finite Element Analysis, nothing can compensate for a lack of theoretical understanding and good judgment. The forgoing explanations represent a very small piece of the world of composite analysis and is meant only as a brief introduction.

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d George Lairdwww.PredictiveEngineering.com

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