User Manual

Wound Composite Modeler For Abaqus Abaqus Version 6.13-1 © 2013 SIMULIA, Inc.

User’s Manual

Table of Contents 1

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4 5 6 7

Background ................................................................................................................................................4 1.1 Plug-in Overview .................................................................................................................................5 1.2 Top-Level Icons ..................................................................................................................................6 COPV (Tank) Creation ...............................................................................................................................7 2.1 Model & Tank Initialization ..................................................................................................................7 2.1.1 Model Creation............................................................................................................................8 2.1.2 Tank Creation .............................................................................................................................8 2.2 Liner Geometry Assignment ...............................................................................................................9 2.2.1 Geodesic Liner Profile ................................................................................................................9 2.2.2 Elliptical, Spherical Liner Profiles ..............................................................................................10 2.2.3 From-Part Instance Liner Profile ...............................................................................................11 2.2.4 User-Defined Profile..................................................................................................................11 2.2.5 Transition Radii .........................................................................................................................11 2.2.6 Defining the Dome Set Properly ...............................................................................................12 2.2.7 Viewing Dome Geometry in Sketcher .......................................................................................14 2.2.8 Adjusting Spline Refinement .....................................................................................................15 2.3 Winding Layout .................................................................................................................................16 2.3.1 Layer Manager Dialog ..............................................................................................................16 2.3.2 Layer Shape Controls ...............................................................................................................17 2.3.2.1 End Fraction Override ...............................................................................................................18 2.3.2.2 Transition Radius Override .......................................................................................................18 2.3.2.3 Transition Radius Override (Ignoring End Cap) .......................................................................19 2.3.2.4 Transition Angle ........................................................................................................................20 2.3.2.5 Overlap Fraction .......................................................................................................................21 2.3.3 Helical Layers ...........................................................................................................................23 2.3.3.1 Controlling the Wind Angle at the Turnaround Radius .............................................................24 2.3.3.2 Varying Wing Angle over Cylinder Section ...............................................................................25 2.3.5 Helical Layer with Friction .........................................................................................................27 2.3.6 Doily & Hoop Layers .................................................................................................................27 2.3.7 Layer-Level Mesh Controls .......................................................................................................28 2.4 Mesh Partitioning ..............................................................................................................................29 2.5 Mesh Creation...................................................................................................................................30 2.6 Properties Creation ...........................................................................................................................31 2.6.1 Material Properties ....................................................................................................................32 2.6.2 Material Orientations .................................................................................................................33 2.6.3 Uvarm Subroutine .....................................................................................................................33 Geometry/Element Formulations .............................................................................................................35 3.1 Axisymmetric Continuum Geometry .............................................................................................35 3.2 3D Continuum Geometry ..............................................................................................................37 3.2.1 Cylindrical Elements .................................................................................................................38 3.3 3D Shell Geometry........................................................................................................................39 3.3.1 Shell Geometry Controls ...........................................................................................................39 3.3.2 Shell Liner Controls...................................................................................................................41 3.3.3 Composite Layups ....................................................................................................................41 3.3.4 Shell Output ..............................................................................................................................42 3.4 Axisymmetric Shell Geometry .......................................................................................................42 Running the Analysis ...............................................................................................................................42 Output Processing....................................................................................................................................43 Sample Test Cases ..................................................................................................................................44 Micromechanics Module ..........................................................................................................................45 7.1 Plug-in Overview ...............................................................................................................................46 7.2 Plug-in Usage ...................................................................................................................................47 7.2.1 Fiber Packing Arrangement ......................................................................................................47 7.2.2 Fiber Volume Fraction ..............................................................................................................48 7.2.3 Fiber Elastic Properties .............................................................................................................48 7.2.4 Matrix Elastic Properties ...........................................................................................................49 7.2.5 Thermal Expansion Properties .................................................................................................50 2

7.2.6 Density Properties.....................................................................................................................50 7.3 Plug-in Output ...................................................................................................................................50 7.4 Micromechanics Theory....................................................................................................................51 7.4.1 Micromechanics unit cell geometry...........................................................................................51 7.4.2 Unit cell boundary conditions ....................................................................................................52 7.4.3 Volume-averaged ply properties ...............................................................................................52 8 Installation of WCM Plug-in ......................................................................................................................54 9 References ...............................................................................................................................................54 WCM References .........................................................................................................................................54 Micromechanics References ........................................................................................................................54 Abaqus References ......................................................................................................................................55

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1 Background The process of filament winding has become a popular technique in a wide variety of industries for creating extremely high stiffness-to-weight structures. Aerospace industry applications include rocket propellant tanks and solid rocket motors casings. Automotive industry applications include high pressure fuel storage tanks for hydrogen powered automobiles. The difficulty in accurately analyzing the behavior of filament wound structures derives from the varying orientation of the wound filaments throughout the structure. The standard capabilities of commercial finite element codes are inadequate to model the variation of fiber orientation in a practical way. Thus, the Wound Composite plug-in for Abaqus was warranted. This Wound Composite Modeler for Abaqus plug-in was developed to analyze a wide variety of axisymmetric or three-dimensional, wound composite pressure vessels. This documentation describes the capabilities and usage of the plug-in.

Figure 1.1-1: Composite Overwrapped Pressure Vessel

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1.1

Plug-in Overview

The Wound Composite Modeler for Abaqus plug-in is a vertical application which is designed to facilitate the creation of an entire axisymmetric or three-dimensional finite element model of a composite overwrapped pressure vessel (COPV). The model created is a representation of the full tank. The plug-in automates the creation of the tank geometry and its corresponding mesh and element-by-element material property and orientation assignments. The plugin is brought up by selecting Wound Composite Modeler (Show/Hide) under the Plugins drop down menu. The WCM plugin follows the same tree structure of the model and output data base trees, therefore, the model tree must be displayed in order to work in the WCM. To toggle the model tree on and off, click CTRL-t.

Figure 1.1-1 Wound Composite Modeler Tree It may be necessary to widen the tab region to make room for the entire WCM tab by clicking and dragging the edge shown in red below.

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Figure 1.1-2 Widening Room for Dialogs

1.2

Top-Level Icons

The icons shown at the top of the Wound Composite Modeler tab provide a number of high-level functions. The first icon, , brings up a dialog of a list of example problems that may be run automatically. Various analyses testing the many different features of the plugin are available for automatic creation and submission.

Figure 1.2-1 Example Problem Dialog

The post processing icon, , brings up a dialog that is used to automatically generate path plots of output quantities such as stress and strain along the length of any given layer.

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Figure 1.2-2 Path Plotting Dialog

The workshop tool icon, , is used to bring up a utility to create a Workshops folder. Executing this dialog will create a Workshops folder with a number of subfolder underneath. In each subfolder will contain .doc and .pdf files with the workshop instructions and any other files associated with the workshop such as .cae files.

Figure 1.2-3 Workshop Creation Dialog

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COPV (Tank) Creation

2.1

Model & Tank Initialization

The process of building a COPV model inside the WCM consists of the following five steps. 1. Initialize the WCM Model and tank attributes such as 2D or 3D.

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2. The second step involves defining the geometry over which the filament wound layers will be placed. This can be done with analytic expressions such as spherical or elliptical dome shapes, or the underlying geometry can be defined by simply creating a node set on a part representing the liner. 3. The third step is generating a table of layers wrapped over the liner. The termination conditions at both end of the tank are specified along with layer thickness, wind angle, layer material properties and more. 4. The fourth step is specifying partitions which are used to help improve mesh quality. 5. The fifth step is assigning the mesh sizes and generating the mesh. 6. The sixth step is to generate the material orientations and material properties throughout the tank. 2.1.1

Model Creation

The first step in the creation of a COPV model is to first associate a model that exists in the .cae database with a WCM database object to be stored on the mdb.models[currentModelName].customData object. By doing this, the WCM initializes the WCM data object on the persistent customData object. This object is saved onto the database and can be accessed during later Abaqus/CAE sessions. To create a WCM model, select the Models item in the WCM tree, right click, and select Create. The Model Properties dialog is displayed next to the WCM tree. A list of analyses types is provided to choose the element types to be assigned to the tank. Clicking the Create button creates the WCM custom data object that will be used to store the remainder of the tank information.

Figure 2.1-1 WCM Model Creation Dialog 2.1.2

Tank Creation

Once the WCM model has been created, a tank is initialized by selecting the Tanks repository, right clicking, and selecting Create. The dialog brought up is shown below. The first item to be chosen is whether to model a full tank or only a partial tank by defining a symmetry plane. A number of options are provided to assign default element controls that are assigned to all of the tank‟s layers to be created. These controls can be overridden on a layer-by-layer basis as the layers are created.

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Figure 2.1-2 WCM Tank Creation Dialog

In the case of a 3D COPV model, an axis must be defined which represents the vessel centerline. A datum axis may be selected or one of the axes of a datum coordinate system. During the tank creation of the 3D COPV, the axis must be selected.

2.2

Liner Geometry Assignment

The next step in the COPV model generation process is to define the region of the liner and polar bosses over which filament wound layers will be laid. There are three ways to define the underlying liner geometry: analytically, from an existing part instance, or from x-y data. All three ways essentially require the user to define a sequence of lines, which when swept about an axis, represent the geometry over which the filament wound layers will be placed. In the case of a 3D model, the axis that the set will be revolved around must also be selected. This axis must be defined as a datum axis.

2.2.1

Geodesic Liner Profile

The geodesic-shaped dome is a specially shaped dome which results in a nearly constant strain state along much of the fiber as it wraps around the dome. The shape of the dome is directly related to the vessel radius and the wind angle of the layer at the tangent line. Geodesic liner geometry is created by selecting the Analytic category, then choosing the dome type as Geodesic. Each end of the tank may be assigned different dome types.

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Figure 2.2-1 Geodesic Dome Input

For example, Figure 2.2-2 shows a dome in blue which is constructed from a wind angle of five degrees and a dome in grey which is constructed from a wind angle of ten degrees.

Figure 2.2-2 Geodesic Dome with/without Base Wind Angle For the given geodesic wind angle, the helical turns around at a radius equal to the vessel radius at the tangent line times the sine of the wind angle. The underlying geometry follows the geodesic shape up until this turnaround radius, then is assumed to extend vertically as though the first layer abutted to an imaginary polar boss. For a radius less than this so called turnaround radius, the layer would simply intersect the extended assumed polar boss geometry. 2.2.2

Elliptical, Spherical Liner Profiles

Creation of elliptically and spherically-shaped domes is available by specifying the vessel radius at the tangent line, and in the case of the elliptical dome, the radius of the ellipse in the y-direction (minor axis).

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Figure 2.2-3 Elliptical and Spherical Domes

2.2.3

From-Part Instance Liner Profile

Wound composite layers can be made to wrap over an existing part instance that has been created within Abaqus/CAE or imported into Abaqus/CAE from other CAD programs. The liner part instance may be geometry-based or orphan mesh-based. In the case of an orphan mesh-based liner, a node set is required to be created along the entire length in a cross-section. The nodal coordinates extracted from the node set are used to create splines, which in turn, are used to generate the composite layer geometry. In the case of a geometry-based liner, again an edge-based set is created along the length of the tank. Equally spaced points are created from the geometry to serve as the basis for the splines, which, in turn, are used to generate the composite layer geometry. In the case of a three-dimensional model, the node set is not required to lie in the x-y plane as is the case for axisymmetric geometry.

Figure 2.2-4 Helical Layers on Part Instance

2.2.4

User-Defined Profile

Wound composite layers can be made to wrap over an existing part instance that has been created within Abaqus/CAE or imported into Abaqus/CAE from other CAD programs. The liner part instance may be geometry-based or 2.2.5

Transition Radii

Regardless of the type of underlying geometry used to define tank geometry, a transition radius is required for each end of the tank. As the layers wrap up to this transition radius, the layer thickness is continually building up and the slope of the outer edge of the layer is continually changing. Once this transition radius is reached, the slope of the outer edge of the layer is forced to remain constant (zero transition angle) until an intersection with the polar boss is found. Alternatively, a non-zero transition angle can be entered to change the slope of the layer until an intersection with the liner is found. This allows the thickness buildup at the polar boss regions to be controlled. Any layer with a turnaround radius less than the fillet start radius is assumed to abut to the polar boss. The transition radius entered for the liner may be overwritten on a layerby-layer basis allowing for very fine control of the polar boss thickness buildup. 11

Figure 2.2-5 From-Part Dome Input

Figure 2.2-6 Transition Radius Definition

2.2.6 Defining the Dome Set Properly The proper creation of the underlying dome set is critical to being able to generate the wound layout geometry onto an existing part instance. Improper set creation will result in the failure of the geometry creation and may result in any number of obscure Abaqus or Python errors. The set may be based on geometry edges or in the case of an orphaned mesh liner a set of nodes. Use the following guidelines for choosing the dome set shown in red for various cases: 12

Case 1: Large Fillet Polar Boss & Continuum Model: Set transition radius at the beginning of the fillet. Assign all layers abutting polar boss a radius less than the transition radius. Any layers with turnaround radii less than transition radius will abut to the polar boss, regardless of the end controls.

Case 2: Arbitrarily-shaped Polar Boss & Continuum Model: Use transition radius less than the radius of any point along the vertical face of the polar boss. Assign all layers abutting polar boss a radius less than the transition radius. Use the vertical segments of the polar boss.

Case 3: Invalid Dome Set/Transition Radius

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2.2.7 Viewing Dome Geometry in Sketcher The proper creation of the underlying dome geometry set is critical to building the tank properly. To ensure this set is being read properly by the WCM, it can be plotted by clicking on the sketch icon . As shown below, the solid yellow line represents the shape of the underlying geometry based on the set provided. The dashed vertical lines attached to either end of the solid yellow line represent the extended polar boss geometry. The dashed yellow lines slightly offset from the extended polar boss geometry represent the transition radii.

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Figure 2.2-7 Liner Geometry Sketch 2.2.8

Adjusting Spline Refinement

The underlying geometry of the tank is drawn by extracting points from the dome set provided. If the dome set is geometry-based, then the WCM will extract equally spaced points along the length of the set. The number of points to be used is based on the refinement selected. The following numbers of points are used based on the refinement:

Refinement

Number of Points

Extra Coarse

100

Coarse

150

Medium

300

Fine

450

Extra Fine

600

The first composite layer of the tank is drawn by projecting the points along the base geometry in the normal direction through a distance equal to the layer thickness at the points being generated. These projected 15

points are then combined to draw splines representing the exterior of the first layer. The second layer is then drawn in the same manner by projecting the exterior points of the first layer. Thus, by continuing this pattern, the points along the liner geometry are propagated up through all of the layers of the entire tank. The amount of time required to generate the tank part is directly related to the number of points used to draw the splines. Therefore, controlling the number of points used to draw the liner is critical in controlling the amount of time required to draw the entire tank. The refinement option allows the user to control the number of points along the liner, and thus the number of points used to draw the tank. Using coarse refinement will build the tank quickly, but in areas where one layer wraps over another, the geometry created may show inaccuracies. If the liner part is an orphan-mesh part, then the points used to define the liner geometry are the actual node points contained in the node set. In this case, the refinement option is ignored.

2.3 2.3.1

Winding Layout Layer Manager Dialog

Once the liner has been defined, the layout can be defined to overwrap the liner. Right clicking on the Layers repository and selecting Manager will bring up the Layer Manager dialog. Double clicking on the Layers repository will also bring up the Layer Manager dialog.

Figure 2.3-1 Activating Layer Manager

The entire layup can be defined and verified from with the Layer Manager dialog. Each layer is assigned a layer type, material, thickness, and wind angle. The inner and outer radius, hoop height and band width are applicable to specific layer types. A row of buttons is listed below to assist in table manipulation. The first four buttons are for adding, removing, and moving layers. The Add Rows button adds a row at the end of the table by copying all of the layer information, including controls, of the layer in which the cursor is placed. The Move Up and Move Down buttons simply move the entire layer, along with its control information, up or down. Multiple layers can be moved up and down simultaneously.

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Figure 2.3-2 Layer Manager Dialog

As changes are made to the table, they can immediately be viewed by clicking on the Sketch icon . This will sketch the layers of the table, as well as the liner. The Sketch All icon , the Sketch Top icon , and the Sketch Bottom icon, allow the user to control which portions of the tank are being sketched. This allows the user to focus on viewing parameter changes that are specific to the top, for example, while ignoring parameters specific to the bottom. This can also speed up sketching in large layups. If changes are made to the table and in the sketch mode, the Refresh icon must be clicked for the sketch to reflect the changes. Each layer has a multitude of controls that affect the thickness buildup, the shape at the end of the layer, how the layer abuts to the polar boss, and more. By clicking the Visible Columns icon , each of the controls can be displayed and modified in the table. Because there are so many, they are not displayed by default. The Default Columns icon displays the default columns. The Top Columns icon displays controls specific to the top of the tank. Likewise, the Bottom Columns icon displays controls that are specific to the bottom portion of the tank. The All Columns icon displays all controls for all of the layers. The Mesh Columns icon displays controls related to the mesh. The Symmetric Tank icon allows the bottom controls to be set identical the top controls in which case only the top controls can be modified. Regardless of which columns are shown, the information stored in each column is saved upon submission of the Layer Manager dialog. 2.3.2

Layer Shape Controls

The thickness buildup described in the sections below for helicals is very accurate throughout the tank, with the exception of the regions very near the polar bosses. Because of the many ways in which individual winding machines affect the polar boss region buildup, some tools in the WCM have been added to allow the user to control how each of the layers are shaped close to the polar boss. In order to demonstrate how these controls affect the polar boss region, a single layer will be considered which terminates near the polar boss which has a boss radius of 2.0. Each of the parameters which affect the shape will be modified to demonstrate the affect. In order to display the controls, the Top Columns icon can be clicked and the table is updated to show all of the layer controls of the top of the tank.

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Figure 2.3-3 Layer Manager Dialog

2.3.2.1 End Fraction Override The End Fraction parameter controls how the end of the layer is terminated. The thickness buildup equation described in subsequent sections approaches infinity as the radius at which the thickness is calculated approaches the turnaround radius of the layer. In reality the end of the layer tapers off. The shape of the taper can be controlled by the winding software used to wind the COPV. As a default, the WCM calculates the point, referred to as the transition point, at which the thickness buildup equations are no longer used and a rounded or straight line describes the remainder of the end cap of the layer. The distance from the turnaround point to a point at the base of the layer corresponding to the transition point is determined as a fraction of the bandwidth for helical layers and a fraction of the constant layer thickness for hoop layers. This fraction, referred to as the End Fraction, is determined automatically by the WCM but can be overridden. Below is displayed plots corresponding to End Fractions of 0.25, 0.5, 1.0, and 2.0.

Figure 2.3-4 Effect of End Fraction

2.3.2.2 Transition Radius Override The transition radius is the radius at which the slope of the outer line is abruptly overridden and continued on a straight line until an intersection with the polar boss or underlying layers is found. The sketches below were generated with the values shown. The polar boss is set to a radius of 2.0, the layer turnaround radius is set to 2.1, and the end fraction is set to 1.0 with a band width of 0.5. Therefore, the end cap of the layer begins at a radius of 3.1 - just outside of the values of each of the transition radii shown. The dashed vertical line represents the transition radius for the layer. By modifying the value of the transition radius, the thickness buildup can be controlled precisely.

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Figure 2.3-5 Effect of Transition Radius

2.3.2.3 Transition Radius Override (Ignoring End Cap) In the plots above you will notice that the WCM attempted to draw the end cap of the layer until the transition radius was reached, at which point the slope remained constant until an intersection with the polar boss was found. Alternatively, if the layer terminates inside of the transition radius, the sketching of the end cap can be ignored. The thickness buildup is based on the theoretical thickness buildup until the transition radius is reached. Then the slope remains constant until an intersection with the polar boss is found.

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Figure 2.3-6 Effect of Transition Radius while Ignoring End Cap 2.3.2.4 Transition Angle The default behavior of the layer thickness buildup is to continue the outer layer slope from at the transition point until an intersection with the polar boss is found. As an alternative, that slope can be modified by setting the transition angle to a non-zero number. A positive transition angle causes the layer to increase in thickness, while a negative transition angle causes the layer to decrease in thickness.

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Figure 2.3-7: Effect of Transition Angle 2.3.2.5 Overlap Fraction As one layer overlaps the end of another, a void is formed which contains resin, but no composite fibers. The size of the void region depends on a number of factors such as wind angle, tape tension, and whether a post-layup treatment is applied to squeeze out excess resin material. The WCM provides an overlap fraction parameter which controls length of the void region. The curved line drawn begins at a point above the transition point of the underlying layer (i.e. the point at which the end cap begins). The slope used is that of the liner if this point were projected onto the liner. The curved line then terminates at a distance equal to the overlap fraction times the thickness of the underlying layer at its end cap transition point. If the end type Tapered is specified on a hoop or a doily, the overlapping calculations are ignored.

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Figure 2.3-8 Effect of Overlap Fraction If it is determined that the overlap region intersects the transition radius of the layer, then the overlap region determined by projecting the end cap transition point in a direction parallel to the liner until an intersection with the underlying geometry is found. This approach is used because of the generality of the geometry that is possible inside the transition radius. This may cause geometry that is not reflective of the actual part. In this case, other controls can be used to modify the geometry to better match reality.

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Figure 2.3-9: Overlapping a Layer near the Transition Radius

2.3.3

Helical Layers

The helical layer types (with and without friction) of a wound composite are typically wound in such a manner as to produce an axisymmetric layup. In other words, for every helical band at + theta, there is a corresponding band at – theta to cause the overall laminate to be a balanced angle-ply (+/- theta) laminate. This assumption is implicit in both axisymmetric models and 3D models. Therefore, the wound composite plug-in requires only a single orientation angle to be given for each layer at the tangent line and the plug-in will calculate the angle-ply laminate material properties for each element within each helical layer. Helical layers may be wrapped over a liner with or without a cylindrical section. The wind angle along the cylindrical section remains constants, while the helical winding angle over the dome is described by the following equation:

 R0   R  R0   ( R)  sin        R  Rtl  R0 

n

1

Equation 2-1 Helical Wind Angle

Here, R is the radial distance from the center line to a point in the layer, R o is the radial distance from the

centerline to the turnaround point, and Rtl is the radius at the dome-cylinder tangent line, and  is the difference in degrees between the frictionless wind angle (input for the layer) and the wind angle calculated by the first term of Equation 2-1 Helical Wind Angle. A frictionless winding pattern is obtained by choosing . If friction is accounted for,  ≠ 0, then the wind angle distribution will vary as described in more detail in later sections. The wind angle distribution of helicals with our without friction are described by the equation above.

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2.3.3.1 Controlling the Wind Angle at the Turnaround Radius As a band turns around the dome, the wind angle of the entire width of the band is 90˚. As a default, the WCM modifies the turnaround radius, , by the width of the band so that the wind angle begins to drop below 90˚ immediately after the width of the band. This would be accurate if the band wrapped completely around dome. However, as a band wraps around the dome, it is orientated at 90˚ for only a short distance. Instead, many bands are required to cover the dome in the hoop direction. Therefore, the fibers are not orientated at 90˚ over the full band width around the full 360˚ circumference. In order to approximate the portion of the band that is at 90˚, the ninety degree band width factor, , may be used to reduce this distance.

Figure 2.3-10: Specifying 90 degree Factor

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Figure 2.3-1:1 Contour Plot of Wind Angle (90° in red)

2.3.3.2 Varying Wing Angle over Cylinder Section In many circumstances the wind angle of a helical may vary over the length of the cylindrical section of a tank. Setting the bottom wind angle, as shown in red below, will linearly vary the wind angle over the length of the cylinder from the bottom wind angle to the top wind angle. The beginning and end points of the variation are determined by calculating the points above and below the cylinder section with radii equal to .995 the radius of the cylinder. In order for this approach to be valid, the cylinder section must remain perfectly flat (not tapered, nor contain any imperfections). The thickness calculation based on Equation 2.3.4 uses the wind angle at the tangent line as part of the calculation to determine the thickness. The smallest of the top and bottom wind angles is used as the wind angle at the tangent line in Equation 2.3.4. As a result, the thickness of the layer varies over the cylinder region.

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Figure 2.3-92 Varying Wind Angle over Cylinder

2.3.4

Helical Layer Thickness Buildup

The thickness specified in the winding layout table is the thickness at the cylinder tangent line. As the layer traverses the dome to the polar boss, the thickness of the helical layer gradually builds up as described by the equation below.

Equation 2-2: Helical Thickness Buildup

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2.3.5

Helical Layer with Friction

A helical layer with-friction requires the wind angle and turnaround radius both be specified. The wind angle distribution is determined from of Equation 2-2 Equation 2-2: Helical Thickness Buildupwith the value of n set to 1.0. This equation essentially bounds the with-friction curve between two frictionless curves. The first curve is frictionless curve based on the wind angle given. The second curve is the frictionless curve based on a wind angle that would reproduce the turnaround given. The difference in wind angles (δ) between the two curves is simply ramped down linearly (for n=1.0) over the length of the layer with the turnaround specified by the user. The resulting with-friction wind angle curve is shown in red in the figure below.

90 80

Wind Angle

70 60 50 40 30 20 Theta2 10 Theta1 0

R1

R2

Dome Radius

Rtl

Figure 2.3-103 Wind Angle with Friction in Red

2.3.6

Doily & Hoop Layers

The TOP DOILY, BOTTOM DOILY, and HOOP type layers consist of a constant thickness and constant wind angle layer. Doilies can be specified to either be placed over the top of the tank (TOP DOILY) or over the bottom of the tank (BOTTOM DOILY) in the case of a full tank model. Doilies cannot extend over the full length of the cylinder (see section below describing hoops). Modeling a doily requires the inner-most termination point to be entered as a radius. The outer-most termination point may be entered as either a radius or Y-Position measured from the center of the tank. The WCM determines the washer-shaped ply which is wrapped over other layers as shown in Figure 2.3-11. A doily is constructed with a uniform thickness and usually of an orthotropic material. The primary material direction is rotated from the meridional axis of the tank by the value of the wind angle. Just as helicals, a layer consists of fibers at + and - angles at the same position through the thickness of the layup, thus resulting in an axisymmetric behavior. For example, a wind angle of 90.0 degrees results in the primary material direction of the doily being in the tank‟s hoop direction.

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Figure 2.3-114 Doily Layer in Blue (Only half of the tank is shown)

Modeling a hoop entails specifying the y-coordinates of the termination. The y-coordinates are measured from the center of the tank, which is determined half way between the two extreme y-coordinates of the liner. A uniform-thickness layer which begins in the cylinder region and terminates at a position along the tank axis is shown in Figure 2.3-125. A hoop layer is usually orthotropic like a doily with the primary material direction rotated from the meridional axis of the tank by the value of the wind angle – typically 90 degrees.

Figure 2.3-125 Hoop Layer in Blue (Only half of the tank is shown) The end cap of doilies and hoops have an optional end type specification, Tapered, not available with helicals. This end type simply linearly varies the thickness of the end cap from zero at the end of the layer to the full thickness at a distance equal to the band width from the end point. A unique characteristic of this end cap is that when a layer overlaps this end type, no bridging calculations are used. In other words, the base of the overlapping layer exactly matches the geometry of the end cap. 2.3.7

Layer-Level Mesh Controls

Clicking on the Mesh Columns icon displays mesh specific controls of the layer as shown in the figure below. These controls allow individual layers to be assigned mesh controls that give the user significant controls over the characteristics and quality of the final mesh. The layer-level controls override the tank-level mesh controls described in Section 2.1.2 . The number of elements through the thickness of a particular layer may be specified in this dialog. Resulting mesh seeds are applied through the thickness of the layer at the base of the dome, or in the case of an attached cylinder, at the interface between the dome and cylinder. The mesh seeds are also applied on the segment of the partitions (described in the next section) passing through the layer of interest. The element formulation may be assigned to the layer by selecting any combination of the HYBRID, REDUCED, or INCOMPATIBLE MODES formulations. Layer-level controls are not available for shell elements.

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Figure 2.3-136 Layer-Level Mesh Controls Tab Input 2.4

Mesh Partitioning

The mesh partitioning options allow for the creation of partitions through the thickness of a layer all along the length of the layer. The spacing of the partitions can be biased toward the top of the layer, the bottom of the layer, or evenly spaced throughout the layer.

Figure 2.4-1: Geometry/Mesh with and without Partitioning

The partitions control the mesh in a couple of ways: 

They prevent the mesher from creating skewed elements as shown to the left in Figure 2.4-2. A mesh modified with partitions is shown to the right in Figure 2.4-2.



They allow for the application of mesh seeds and constraints through the thickness all along the length of the layer as opposed to having only a single mesh seed constraint at the bottom of the dome. This helps to ensure the number of elements through the thickness remains uniform throughout the layer.

29

Figure 2.4-2: Geometry/Mesh with and without Partitioning If a partition passes too close to an existing vertex, the mesh creation may fail as shown in the figure below. In order to insure that the partitions do not terminate too close to an existing vertex, the sketcher mode may be entered by clicking on the sketch icon while the partition properties are being edited. For example, in a particular layup, one partition terminates very near the vertex. This may result not only in a poorly formed mesh in this region, but may also prevent the mesher from generating a mesh altogether. To eliminate this particular partition line, click the Remove Individual Partitions icon , thren pick on the line to be removed and hit the Done button. This process will ensure a nicely formed mesh will be created throughout the tank.

Figure 2.4-3: Removing Individual Lines from Partitions

2.5

Mesh Creation

The next step in the COPV model creation is generating a mesh on tank. Double clicking the mesh icon displays the Mesh Properties dialog. Since the number of elements and element types are assigned at the tank and layer levels, only the number of elements along the length of the tank needs to be specified. The number of elements specified is assigned as the total number assigned to the top and bottom domes.

30

Figure 2.5-1: Mesh Generation Inputs Upon submission of the Mesh Properties dialog, the WCM applies the mesh seeds to the part and attempts to mesh it. In some circumstances an inadequate mesh, or not mesh at all, is obtained. The following are some troubleshooting tips regarding meshing:  Very poorly shaped elements: This is usually caused by an inadequate number of elements along the length of the tank. Increase the number of elements along the length of the tank so that the aspect ratios of the elements in the cylindrical section of the tank do not exceed 2 to 1.  No mesh on a face: This often occurs because a partition passes too closely to an existing vertex for the mesher to honor the mesh seeds. Edit the partitions and remove any lines passing very near a vertex.  No mesh at all on a 3D tank: This can occur if too few elements were chosen in the hoop direction.  Very slow creation for 3D models. Reduce the number of segments in the hoop direction and the number of lines used for mesh partitioning. In the cylinder region of the tank, only use mesh partitions near the transitions from cylinder to dome. Mesh seeding, setting the sweep direction, and meshing all are slowed down by the number of cells in the tank. If after trouble shooting a mesh you are still not able to generate a mesh on a tank, attempt to generate the mesh directly within the Abaqus/CAE mesh module. For example, on some 3D models the mesher may fail to generate a mesh, but if sections are meshed individually in sequence the mesher is able to generate a mesh. If you are able to use the tools in the mesh module to generate an adequate mesh, you can then right click on the mesh icon in the WCM tree and select Set as Completed. This will indicate to the WCM that an adequate mesh has been created and will allow the final step of the property generation to be completed.

2.6

Properties Creation

Then final step in the creation for a COPV model is to generate the properties. This process involves generating material properties, section definitions and material orientations. Clicking on the properties icon opens up the Material Properties dialog.

31

Figure 2.6: Material Properties dialog 2.6.1

Material Properties

The assignment of material properties to the tank begins by assigning section definitions based on the materials provided for each layer in the winding layout table. The plug-in then determines which layers have orthotropic materials assigned to them (*ELASTIC, *CONDUCTIVITY, or *EXPANSION). The elements in the orthotropic layers are assigned transformed material definitions and section assignments. Field variable dependent elastic and expansion properties are not supported. The calculation of orthotropic materials properties is performed by first creating wind angle bins for each orthotropic material. That is to say, all the elements assigned a given orthotropic material are grouped together based on wind angle and put into bins. The local wind angle of each element is calculated from Equation 2.3.3 based on the coordinates of a point at the bottom of the layer which is projected normal from the layer to the centroidal coordinates of the element. The range of wind angles assigned to a bin is chosen by the user as the wind angle increment in the Tank Manager Dialog as shown in Figure 2.6.1. Wind angle bins are then generated from 0 to 90 degrees based on the wind angle increment. For example, 90 bins would be created for a wind angle increment of 1 degree. All elements with wind angles falling within the range of a given wind angle bin is assigned a single material property based on the wind angle of the bin. No materials are created for bins which have no elements associated with them. The orthotropic materials for each wind angle bin are calculated as angle-ply laminate (±θ) materials, where the angle θ is the bin wind angle. The orthotropic material properties input by the user are for the composite lamina (single-ply) with 1=fiber direction, 2=transverse and 3=normal. The plug-in transforms these material properties to the following global directions for axisymmetric-continuum and axisymmetric-shell geometry: 1meridional, 2=radial, and 3=hoop, and the following global directions for three-dimensional geometry: 1=meridional, 2=hoop, and 3=radial. These transformed material properties, along with a section definition, are assigned to each wind angle bin and a unique material definition is created. Material properties other than orthotropic *ELASTIC, *CONDUCTIVITY, and *EXPANSION are assigned directly to the wind angle bin material without being altered and are also written to the include file. Anisotropic *ELASTIC and *EXPANSION are not supported.

32

Figure 2.6.1: Wind Angle Bins of 0.5 Degrees

2.6.2

Material Orientations

The material orientation assignments are generated along with the material properties. Each layer is assigned its own material orientation definition which references the part feature coordinate system "TankCenter", as well as a discrete field definition, WCM_tankName_AddRot, which is used to assign an additional rotation for each element with regard to the coordinate system "TankCenter".

2.6.3

Uvarm Subroutine

Since the material properties of the fiber have been smeared and transformed into axisymmetric coordinate system, output quantities such as stress and strain are not readily available along the fiber direction. For this reason, a toggle has been added to allow the creation of a UVARM subroutine which facilitates the calculation of material properties along and transverse to the fiber direction. An output request is automatically generated requesting Field Output for the corresponding UVARM variables. The strain measured used are logarithmic, so the NLGEOM flag must be activated; otherwise the logarithmic strains will show up as zero. By default, the plug-in creates five UVARM output variables for axisymmetric shell and continuum geometries are as follows: 

UVARM1: wind angle in degrees



UVARM2: logarithmic strain along the fiber direction



UVARM3: logarithmic strain transverse to the fiber direction



UVARM4: logarithmic in-plane shear strain



UVARM5: stress in the fiber direction



UVARM6: stress transverse to the fiber direction



UVARM7: in-plane shear stress

33

Because we have the logarithmic strain in the pressure vessel coordinate reference frame and we know the wind angle at each point along the dome, we are able to rotate these strains into a fiber direction coordinate reference frame. For three-dimensional analyses, additional terms are added for fibers at the negative of the wind angles. Specifically, the output variables are as follows: 

UVARM1: wind angle in degrees



UVARM2: logarithmic strain along the fiber direction (positive angle)



UVARM3: logarithmic strain along the fiber direction (negative angle)



UVARM4: logarithmic strain transverse to the fiber direction (positive angle)



UVARM5: logarithmic strain transverse to the fiber direction (negative angle)



UVARM6: logarithmic in-plane shear strain (positive angle)



UVARM7: logarithmic in-plane shear strain (negative angle)



UVARM8: stress along the fiber direction (positive angle)



UVARM9: stress along the fiber direction (negative angle)



UVARM10: stress transverse to the fiber direction (positive angle)



UVARM11: stress transverse to the fiber direction (negative angle)



UVARM12: in-plane shear stress (positive angle)



UVARM13: in-plane shear stress (negative angle)

For Heat Transfer analyses, UVARM2 and UVARM3 are filled with the heat flux along and fibers and transverse to the fibers. For Coupled Temp-Displacement analyses two additional variables are added as the heat flux along the fiber direction and transverse to the fiber direction. For the axisymmetric case these are: 

UVARM8: heat flux along the fiber direction



UVARM9: heat flux transverse to fiber direction

For the three-dimensional case, the additional variables are: 

UVARM14: heat flux along the fiber direction



UVARM15: heat flux transverse to fiber direction

An option is provided for allocating more memory for user-output variables. This is useful if the UVARM subroutine is to be expanded to include more user-defined output variables. The plug-in then sets the *USER OUTPUT VARIABLES keyword option in every material definition automatically. A source file, wcUvarmUtils.py, is provided to allow automatic merging of user-defined UVARM coding with that created by the plug-in. Two functions are provided: writeDeclarations and addExtra. The first inserts declarations statements immediately following the generic declaration statements of the UVARM subroutine described in the Abaqus User‟s Manual. The second inserts coding immediately following the plug-in‟s coding for filling its default UVARM variables. The uvarm argument passed into both routines is the file object to be written to. The nextUvarm argument is the first available UVARM (an integer) for user-definition. For example, referring to the lists above, for an axisymmetric stress analysis the nextUvarm variable would be set to 8. The UVARM subroutine is not available in Abaqus/Explicit so the UVARM toggle is stippled for the procedures related to Abaqus/Explicit. def writeDeclarations(uvarm): uvarm.write(" C

User-Defined Declaration Statements \n")

uvarm.write("

REAL pi\n")

....

34

def writeExtra(uvarm, nextUvarm): uvarm.write("C

User-Defined Uvarm Coding \n")

uvarm.write(“

CALL GETVRM('PE',ARRAY,JARRAY,FLGRAY,JRCD,JMAC, ,\n")

uvarm.write("

& JMATYP,MATLAYO ,LACCFLA)

\n")

.... Figure 2.6.3: User-Defined Modifications to UVARM Subroutine

3

Geometry/Element Formulations

The WCM provides the options of generating solid geometry or shell geometry in both 2D and 3D. For solid geometry, the default mesh controls are assigned when the tank is being generated. The element assignments chosen will be assigned to all of the layers of the tank by default. However, when editing the layup the element type may be overridden on a layer-by-layer basis, with the exception of shell geometry.

Figure 3.1: Tank-level Mesh Controls 3.1 Axisymmetric Continuum Geometry Choosing the element family as Continuum will result in the creation of axisymmetric continuum elements. For axisymmetric geometry, Abaqus/CAE requires that the one and two local directions of the elements be in the X-Y plane. A material orientation is applied to each layer which references a single Cartesian coordinate system that is aligned with the global coordinate system. The coordinate system is then rotated on an element-by-element basis to account for the continually changing orientation of the fibers. A discrete field, as shown below, is created to rotate the local Cartesian coordinate system about the Z-axis such that the 1-axis is parallel to the base of the layer.

35

Figure 3.1-1: Discrete Field of Material Rotations The rotation of the fibers out of the plane is accounted for by rotating the material properties to the local coordinate system. The resulting orientations which vary on an element-by-element basis are shown below. The 1-axis is shown in red and the 2-axis is shown in green.

Figure 3.1-2: Local Coordinate Systems of Axisymmetric Continuum Elements

36

3.2 3D Continuum Geometry If three-dimensional continuum geometry is chosen, the default element formulation, the sweep angle, and information regarding the axis of rotation must be entered. The sweep angle must be chosen as 90, 180, 360, or a user-specified angle which must be less than 90 degrees. The WCM draws the exterior of the layup and revolves it around the axis selected by the user through the chosen angle. Partitions of the layers are then generated to differentiate between the layers. The swept geometry can be further partitioned into segments in the hoop direction by assigning a number greater than one to the Number of Segments entry. Each segment may be assigned a different number of elements. This may be useful if, for example, one section of the tank comes into contact with another object. In order to capture the more severe strain gradients, the section coming into contact is meshed with a finer density.

Figure 3.2-1: 3D Continuum Tank Properties

Assigning more than one segment is also useful for post-processing. Nodes sets of each layer are generated for each segment and are made available for post-processing using the WCM path plotting tool.

37

Figure 3.2-2: Path Plotting at Segments The material orientation convention of three-dimensional geometry differs from that of two-dimensional geometry. The local 1-direction, like in the axisymmetric case, is along the meridional direction of a given layer. However, the 2 and 3 directions are reversed. For three-dimensional geometry, the 2-direction is in the hoop direction and the 3-direction is normal to the surface of the tank. This is consistent with the requirements of three-dimensional shells in that the third direction must always be normal to the shell. A Cylindrical coordinate is used to define the local material directions. An additional rotation discrete field is created in the same manner as the axisymmetric case except that it is applied to the 2-direction of the Cylindrical coordinate system as opposed to the 3-direction of the Cartesian system defined in the axisymmetric case. 3.2.1 Cylindrical Elements Cylindrical elements are used to model axisymmetric three-dimensional geometry which experiences asymmetric deformation. They use trigonometric interpolation functions to determine displacements in the hoop direction. Although each element requires more memory than a corresponding brick element, fewer elements are required in the hoop direction to accurately capture non-axisymmetric behavior such as tank bending. Below is an example analyzing bending of a COPV. It is modeled with a constant number of elements along the length, but a varying number of elements in the hoop direction. Comparison quantities are the rotations at the support, maximum displacement at the center of the tank and the maximum stress at the center of the tank. Convergence studies show mesh convergence with 30 brick elements and 6-8 cylindrical elements.

Model

Memory (GB)

Runtime (Min.)

Φ (radians)

Max u (m)

Max σ (Mpa)

Hex – 20

15

20

.0467

.00604

15.38

Hex – 30

25

37

.0473

.006067

15.31

38

Hex – 40

38

88

.0474

.006071

15.29

Cyl - 4

4

6

.0434

.00589

17.42

Cyl - 6

7

10

.04287

.005802

15.51

Cyl - 8

10

15

.04266

.005787

15.36

Figure 3.2-3: Convergence Study of Cylindrical vs. Brick Elements

3.3 3D Shell Geometry The building of COPV tank models using shell elements versus continuum elements differs only slightly. The element type is chosen when the tanks is created. The termination of the shell model near the polar boss is specified when defining the liner. The layup definition doesn‟t change at all except that no layer-by-layer mesh controls are necessary. The output processing is also very similar. 3.3.1 Shell Geometry Controls Selecting the 3D Shell geometry button will cause the additional options to be activated as shown in Figure 3.1.3-1. Three-dimensional shell geometry, like the three-dimensional continuum geometry, can be swept between 0 and 360 degrees. Each segment may be assigned a different number of elements as shown in Figure 3.3-2. The axis of revolution of the shell model is chosen in the exact same manner as that of the three-dimensional continuum model.

39

Figure 3.3-1: 3D Shell Tank Creation Options

Figure 3.3-2: Differing 3D Shell Segment Meshes

40

3.3.2 Shell Liner Controls The full liner geometry is chosen in the same manner as continuum geometry. The only additional item required for defining the shell geometry is the point at which the shell terminates. Because of the myriad of polar boss shapes, this may not always be a trivial thing to do. The point should be at the base of layers because the stack is determined by the normal

Figure 3.3-3 Shell Termination Radius Specification 3.3.3 Composite Layups The composite layup definitions of the elements along the liner are determined by examining the element stack at the centroid of each shell element. The shell element geometry, shown in red in Figure 3.1.3-3, is determined from the surface of the liner. The composite layup properties for a given element are filled by determining the stack layup beginning at the centroid of element and extending in the direction normal to the liner through all of the layers of the present. The layup is scaled over the length of the element by determining the stack thickness at the nodes of elements. The thicknesses at the nodes are assigned via the *NODAL THICKNESS specified in a discrete field. Because of the axisymmetric geometry and wind angle orientation assumptions, the composite layup definitions are grouped together in the hoop direction to minimize the number of sections, thus improving performance in the solvers.

41

Figure 3.3-4: Laminated Composite Layup 3.3.4 Shell Output The path plotting utility is available for shell models, as well as, continuum models. However, all available shell section points are required to be output in order to fully use the path plotting utility. Since the WCM does not generate new or modify existing output requests, the user will need to modify existing field output request in order extend them to the entire shell cross section. When the WCM generates the composite layups, it specifies that the default number of integration points through the thickness of a layer is to be used which is 3. Therefore the maximum number of section points through the thickness of any point in the tank is three times the number of layers. Any field output request which is to be read by the path plotting utility will need to be modified as shown below.

Figure 3.3-5: Field Output Request for all Section Points

3.4 Axisymmetric Shell Geometry Choosing axisymmetric shell geometry results in line geometry created at the inner surface of the axisymmetric domes. The procedure for determining the shell section definitions for axisymmetric shells follows the same procedure as that of the three-dimensional shells. The nodal thicknesses are also calculated in the same manner as the three-dimensional shell elements.

4

Running the Analysis

Upon generation of the model mesh, sections and material properties, a job definition with the same name as the tank is also created. With all of these, a run-ready job is created and ready to be submitted. However, a number of potential problems may arise. Firstly, the Uvarm routine may need to be renamed from .f to .for, or vice versa. Other problems which can occur are related to running on a queuing system, or a cluster. These potential problems are related to the files that are referenced by the input file and by the UVARM subroutine if present. A queuing system on a cluster usually runs a job on any number of nodes (servers) and the particular nodes may vary from one job to another. In order to ensure that the proper files are available during a run, the cluster queuing software is configured to copy certain types of files to whichever node the job ends up being run on. Typically user subroutines and include files are properly copied to the node by the queuing software. However, the UVARM subroutine written by the Wound Composite Modeler references a file with the extension .ang. This file contains wind angle information read by the UVARM routine. By default, the Wound Composite Modeler hardwires the path of this file assuming it to be that of the current working directory detected during the UVARM generation. When running on a queuing system, this path needs to be modified to a path which will remain valid regardless of the node on which the job is run. In order to do this, the function is made available in wcUvarmUtils.py. This function is called in order to set the path of the .ang file. The fullPathName name variable is set in the first line of the function using the current working directory.

def getWindAngleFilePath(tankName): fullPathName = '%s%s%s.ang' % (os.getcwd(), os.sep, tankName) #fullPathName = "/your_directory/%s.ang" % tankName return fullPathName

42

Uncomment the line in blue (remove the # sign) and insert a directory which will contain the .ang file and will be accessible from any node on the cluster. This will allow the Uvarm subroutine to properly read the wind angle information.

5

Output Processing

When the plug-in generates the COPV model, it automatically generates node sets named Layern along the bottom of each layer where n is the layer number. The dialog accessed from by clicking on the post processing icon, , automates the process of creating path plots along the interface between layers using these node sets. The dialog is shown in the figure below. For each layer selected from the table, the script first details the elements only in that particular layer, then sorts the nodes in the Layern node set from one end to another, and creates an x-y curve of the chosen field variable along the list of nodes. Finally, all of the x-y curves are combined into a single path plot as shown in Figure 4-2. The field output variable, step number, and frame number must be selected prior to opening up the dialog. An option to smooth out the curves is provided. The path plots can often contains significant spikes in regions where on layer overlaps another. The Smoothing Factor option simply smooths out these spikes.

Figure 5-1: Path Plot Dialog

43

Figure 5-2: Plot of Wind Angles

Figure 5-3: Wind Angle Contour Plot

6

Sample Test Cases

A number of QA problems have been included with the plug-in. Since these tests are fairly small but test all of the plug-in functionality, it is recommended that these be run and experimented with in order to familiarize oneself with the workings of the plug-in. Multiple tests may be selected to be run at one time. Three test modes are provided: 

Generate Model: Generates geometry, mesh, and material properties.



Run Full Analysis: Generates and runs model. The displacements in the y-direction at the ends of tank are extracted and compared to archived results.

44

An Abaqus/CAE model named “WcmTestModel_1-1” is created, for example, when test 1.1 is run. Thus if a particular feature is of interest, you can scan through the test descriptions and run the test that best describes the feature of interest. The resulting model will be created and readily available for editing and testing.

Figure 6-1 QA Test Manager Dialog

7

Micromechanics Module

Analysis of laminated composite structures using the Finite Element Method in Abaqus includes a composite laminate as a homogeneous material with anisotropic properties. This typically requires the input of throughthe-thickness composite lay-up, defined by the individual ply angles, thickness of the plies, and the material properties of the plies. The individual plies are assumed homogeneous and exhibit transverse isotropy which require the use of directionally dependent ply properties. However, a ply typically constitutes of two constituents; the reinforcing fibers arranged in a continuous supporting matrix. Therefore, the properties of the composite ply are governed by the properties of the fiber, the properties of the matrix, and the fiber volume fraction. Figure 2.6-1 is a schematic illustration of the influence of the fiber and matrix properties on the global response of a finite element structural model. Traditionally, the composite ply properties are estimated based on Rule-of-mixtures formulae [1]. Although these closed-form solutions provide reasonable estimates of the composite ply properties, they do not account for the micro-structural arrangement of the fibers in the matrix. A micromechanics model that incorporates the lamina microstructure in calculating the anisotropic ply properties has been developed. This

45

documentation discusses its usage and provides some insight into the underlying theory for obtaining the volume-averaged ply properties.

Figure 2.6-1 Schematic of the relationship between a composite structure and the constituents

7.1

Plug-in Overview

Obtaining the composite ply properties using the Micromechanics plug-in primarily requires input of the fiber properties, matrix properties, and fiber volume fraction, along with a selection of the microstructure for the composite lamina. Invoking the plug-in begins by selecting the Plug-Ins->Micromechanics main menu item which brings the Composite Micromechanics dialog box, depicted in Figure 7.1-1. All the required input for this plug-in is provided through this dialog box. The plug-in calculates the lamina properties by simulating uniaxial states of stresses in the composite. These volume-averaged uniaxial states of stresses are further discussed in of this manual.

46

Figure 7.1-1 Micromechanics Dialog Box

7.2

Plug-in Usage

The micromechanics model depicted in Figure 7.1.1 requires input of the fiber properties, the matrix properties, the fiber volume fraction, and the microstructural arrangement of the fibers in the matrix. The details of the input are described in this section.

7.2.1

Fiber Packing Arrangement

The plug-in calculates the properties of the lamina taking into account the microstructural arrangement of the fibers in the matrix. Two options are provided: Hexagonal Packing and Square Packing. Based on the option selected (Microstructural Arrangement), the plug-in displays a schematic of the generated finite element model, as depicted by Figure 7.2.1.

47

Figure 7.2.1: Schematic of the model for the two fiber packing options.

7.2.2

Fiber Volume Fraction

Volume fractions of the constituents is one of the influencing factors of the resulting composite lamina properties. This is provided by the input box next to Fiber Volume Fraction, as depicted by Figure 7.2.2.

Figure 7.2.2: Fiber volume fraction input box

7.2.3

Fiber Elastic Properties

Properties of the fibers are provided through the fiber properties section of this plug-in as depicted in the following Figure 7.2.3. It is assumed that the fibers are circular and exhibit transverse isotropy with the plane of isotropy coinciding with that of the ply. Here, it is assumed that the “1” direction is the fiber direction and the plane 2-3 is the plane of isotropy. Similar assumption applies to the ply properties calculated through this plug-in where “1” direction stands for the fiber direction or longitudinal direction, “2” direction stands for the transverse or the matrix direction, and “3” direction indicates the thickness direction. A material name can be provided for the fiber in the box next to Fiber Material Name. Based on the assumption of transverse isotropy, the required elastic properties to fully describe the mechanical behavior of the fibers are E11 (Extensional Modulus – E11), E 22 (Extensional Modulus – E22), 12 (Poissons Ratio – Nu12),  23 (Poissons Ratio – Nu23),

and

G12 (Shear Modulus – G12) which are supplied by the user in the appropriate data boxes as shown

in Figure Figure7.2.3-1.

Owing to the difficulty in obtaining experimentally measured shear modulus of the 48

fibers an Estimate option is provided. Upon clicking this button, a dialog box as depicted in Figure 7.2.3-2 is displayed with an estimate of G12 , based on E 22 and 12 , and the formula used. Note that upon the execution of the plug-in a fiber material with the provided name and material properties will be created in a model named HexPackModel or SqPackModel depending on the selection of the microstructural arrangement option.

Figure7.2.3-1: The fiber elastic properties.

Figure 7.2.3-2: Estimate for fiber shear modulus. 7.2.4

Matrix Elastic Properties

Matrix elastic properties are supplied to the plug-in in the matrix properties section as depicted in the following Figure 7.2.4. It is assumed that the matrix is isotropic and therefore requires only the Extensional modulus and the Poissons ratio. A material name can be provided for the matrix in the box next to Matrix Material Name. Based on the assumption of isotropy, the required elastic properties to fully describe the mechanical behavior of the matrix are E (Extensional Modulus – E) and  (Poissons Ratio – Nu) which are supplied by the user in the appropriate data boxes as shown in Figure 7.2.4. Note that upon the execution of the plug-in a matrix material with the provided name and material properties will be created in a model named HexPackModel (for hexagonal packing microstructural arrangement option) or SqPackModel (for square packing).

49

Figure 7.2.4: The matrix elastic properties. 7.2.5

Thermal Expansion Properties

In addition to calculating the elastic properties of the ply, the thermal expansion coefficients of the ply can be requested to be calculated by selecting Include Thermal Expansion Properties option (see Figure 7.2.5 below) and then providing the coefficients of thermal expansion for the fiber and the matrix materials. Note that the fibers are assumed transversely isotropic and therefore only require two coefficients of thermal expansion  11 (provided through Alpha 11 - Fiber) and  22 (provided through Alpha 22 - Fiber) whereas the matrix is isotropic and only require  (provided through Alpha - Matrix). The coefficients of thermal expansion for the composite are calculated by simulating a load case where the finite element model is subjected to a uniform temperature change.

Figure 7.2.5: Thermal expansion properties 7.2.6

Density Properties

In addition to calculating the thermo-elastic properties of the ply, the composite ply density can also be calculated based on rule-of-mixtures formula. Although this property does not require the use of a finite element model for calculation, it is included here as density is one of most frequently used composite properties. This calculation can be requested by selecting the Include Densities option as depicted in Figure 7.2.6 and providing the Fiber Density and Matrix Density for the fiber and the matrix materials respectively. The calculated ply density is listed next to Composite Density: label. Note that this sub-option uses the volume fraction supplied through input box depicted in Figure 7.2.2.

Figure 7.2.6: Density properties 7.3

Plug-in Output

The primary function of the plug-in is to calculate the composite ply properties based upon the supplied fiber and matrix properties. The resulting composite ply properties are displayed through a message box an example of which is depicted in the following Figure 7.3. As illustrated in Figure 7.3, the properties of the fiber, the matrix and the composite are presented in the message box. The same information is also written to a text file titled “Composite_Properties.txt” which is created and placed in the current working directory. In addition to the above mentioned text file, the plug-in creates a material with the resulting ply properties. The name of the ply material is the same as that supplied in the input dialog box and depending on the

50

microstructural arrangement the ply material is either located in the model named „HexPackModel‟ (hexagonal packing arrangement) or „SqPackModel‟ (for square packing assumption).

Figure 7.3: Composite properties message box.

7.4

Micromechanics Theory

The composite ply properties are calculated by simulating different states of stresses in the composite finite element model. 7.4.1

Micromechanics unit cell geometry

The finite element micromechanics model is intended to represent a continuum point in a lamina. The micromechanics model should therefore adhere to the concept of a Representative Volume Element (RVE) that statistically represents the composite lamina. In an actual lamina, the fibers are randomly arranged in the matrix and capturing the randomness requires the modeling of numerous fibers. To reduce the volume of the RVE, periodicity is assumed whereby the randomness of the fiber locations is removed and the fibers

51

are assumed to be distributed in a uniform array and the RVE volume/geometry can be minimized to contain one or two fibers. Typically, it is assumed that the packing arrangement of the fibers in the matrix is either hexagonal packing or square packing. The highlighted regions in the following figures schematically depict the unit cell geometries representing the two packing arrangements.

Figure 7.4.1-1: Hexagonal packing unit cell and the corresponding finite element model.

Figure 7.4.1-2: Square packing unit cell and the corresponding finite element model.

7.4.2

Unit cell boundary conditions

The unit cell geometry is based on periodicity implying that the unit cell can be translated in the three directions to generate the entire lamina. This is incorporated into the finite element model through periodic boundary conditions. The boundary conditions are derived using the mathematical representation of periodicity as outlined by Whitcomb et al. [2] and are further discussed by Akula [3].

7.4.3

Volume-averaged ply properties

Based on the definition of a continuum point, the stress and strain tensor components can be described by the following relations where domain D represents the domain of the continuum point (composite), V is the volume, and X is the position vector representing a point in the domain.

 

1 1  ( X ) dV ,     ( X ) dV  VD VD

Equation 7.4.3.1: Volume-averaged stress and strain tensor components. Extending the above definition to the constituents and expanding over the volume of the domain, the following relationships are obtained where  ,  f , and  m are the volume-averaged stress tensor 52

components in the composite, fiber, and the matrix whereas

 ,  f , and  m are the volume-averaged strain

tensor components and V f is the fiber volume fraction. Further discussion on volume-averaging can be found in Nemat-Nasser and Hori [4].

  V f  f  (1  V f ) m ,   V f  f  (1  V f ) m Equation 7.4.3.2: Relationship between different volume-averaged tensor components.

Using these volume-averaged stress and strain tensor components, the volume-averaged composite ply properties are calculated. However, several different load cases are needed for estimating the different ply properties and the discussion of the same follows.

Load Case 1: In the first load case,

 11  0 and  22   33   12   13   23  0 for the composite.

Note that although a

uniaxial state of stress exists in the composite, the constituents can still be subjected to multi-axial states of stresses. Using this stress state, the lamina properties E11 , 12 , and 13 are calculated. Load Case 2: In the second load case,

 22  0 and  11   33   12   13   23  0 for the composite. state, the lamina properties E 22 ,  21 , and  23 are calculated. Load Case 3: In the third load case,

state, the lamina properties Load Case 4: In this load case,

 12  0

the lamina property Load Case 5: In this load case,

Load Case 6: In this load case,

and

and

the composite. Using this stress

 11   22   32   13   23  0 for the composite.

Using this stress state,

G12 is calculated.

 13  0

the lamina property

 11   22   12   13   23  0 for E33 ,  31 , and  32 are calculated.

 33  0

Using this stress

and

 11   22   32   12   23  0 for the composite.

Using this stress state,

G13 is calculated.

 23  0

and

 11   22   32   12   13  0 for the composite.

Using this stress state,

the lamina property G23 is calculated. Uniform temperature change: In this load case, the composite is subjected to a uniform temperature change, the magnitude of which is equal to “-1e-6/Alphamatrix”. Using the obtained volume-averaged strains, the coefficients of thermal expansion of the composite are calculated. As part of the output a file titled “HEXPACKPARTVolumeAveragedResults-VF-a.txt” (for hexagonal packing) or “SQPACKPARTVolumeAveragedResults-VF-a.txt” (for square packing) where „a‟ stands for the fiber volume fraction, is created in the current working directory. This text file summarizes the volume-averaged stresses and strains of the composite and the constituents.

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Installation of WCM Plug-in

The Wound Composites Modeler for Abaqus installation disc contains a single folder named WCM which contains all the files necessary to run the plug-in. This entire folder and all its subfolders should be installed under an abaqus_plugins folder as described below and should only be run in Version 6.13 of Abaqus. When you start Abaqus/CAE, it searches for plug-in files in the following directories and all their subdirectories:   

abaqus_dir\code\python\lib\abaqus_plugins where abaqus_dir is the Abaqus parent directory. home_dir\abaqus_plugins where home_dir is your home directory. current_dir\abaqus_plugins where current_dir is the current directory.

Abaqus/CAE will import any files in these directories that match the naming convention *_plugin.py. The abaqus_dir directory for Windows is usually C:\SIMULIA\Abaqus\6.13-1 for Abaqus Version 6.13-1. Thus, if it is preferred that any user in question who has access to the Abaqus installation be allowed access to the plug-in, then the WCM folder should be copied to the abaqus_dir\code\python\lib\abaqus_plugins folder. If the plug-in should be made available only on a user-by-user basis, then the WCM folder should be copied to a folder named home_dir\abaqus_plugins in the user‟s home directory.

The plugin does not require a license. However it does check for a valid Site ID. If one is not found, an error message is raised. Additionally, any version of the plugin that is downloaded will only run in that calendar year. At the end of January of the following year, the plugin will raise an error message that a new version must be installed.

9

References

WCM References 1 Akula, M.K. Venkata, “Analysis of Filament Wound Composite Pressure Vessel using Cylindrical Elements”, SAMPE, Spring 2013. 2 Akula, M.K. Venkata, Shubert, M., “Nonlinear FEA of Composite Overwrapped Pressure Vessels”, SAMPE, Fall, 2013. 3 Akula, M.K. Venkata, Shubert, M., “Analysis of Debonding of Filament Wound Composite Pressure Vessels”, Americal Society of Composites 2013. 4 Willardson, R., Gray, D., DeLay, T., "Improvements in FEA of Composite Overwrapped Pressure Vessels", CPV Symposium 2011, Belgium. nd 5 Peters, S.T., Humphrey, W.D, and Foral, R.F., Filament Winding Composite Structure Fabrication, 2 Edition. 6 Gray, D.L., and Moser, D.J., “Finite Element Analysis of a Composite Overwrapped Pressure Vessel”, American Institute of Aeronautics and Astronautics. 7 Skinner, Michael, “Trends, advances and innovations in filament winding”, Reinforced Plastics, February 2006. 8 T. Güll, R. Immel, T. Schütz, V. Schultheis, M. Shubert, “CAE Process Chain for Strength and CrashWorthiness Prediction of Wet Wound High Pressure Composite Vessels“. NAFEMS Proceedings, November 6-7, 2007 Bad Kissingen, Germany. Micromechanics References 1 Jones RM. Mechanics of Composite Materials. Second Edition, Taylor and Francis, 1999. 2 Whitcomb JD, Chapman CD, Tang X. Derivation of boundary Conditions for Micromechanics Analyses of Plain and Satin Weave Composites, J Compos Mater, 2000;34(9):724-747. 3 Venkata Akula. Constitutive Modeling of Damaged Unidirectional Composite Laminae. PhD Dissertation, University of Wyoming, 2008. 4 Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam (1993). 54

Abaqus References For additional information on the Abaqus capabilities referred to in this brief please see the following Abaqus Version 6.12 documentation references:  Analysis User‟s Manual  Abaqus GUI Toolkit User's Manual  Abaqus User's Manual

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