Ply Draping Modelling for Structural Analysis and Manufacturing - P174

 

Ply Draping Modelling for Structural Analysis and Manufacturing
Practice document
Document Type	Practice
Document Identifier	174
Themes	Materials deposition and consolidation management
Tags	Deposition Forming Development to production Reinforcement architecture Process modelling Quality
Objective functions	Cost Maintain Rate Maintain Quality Increase
MSTE workflow	Development

Overview

This article will provide an introduction to ply draping modelling that is used to aid structural analysis and manufacturing. It will provide information on the difference between developable and undevelopable surfaces and how the type of surface affects fibre orientation. It will also discuss the importance of a material’s lock angle when using kinematic draping modelling to predict potential wrinkling. This will be followed by a discussion on the parameters that affect the draping results and how the results of the analysis can be used to produce a flat pattern. Finally, an example of how the choice of draping strategy affects the structural performance of a part will be presented.

Introduction

Ply draping modelling can support structural analysis and manufacturing of composite components. This article includes information on how to perform the modelling, as well as information on how it can improve the accuracy of finite element analysis results and be used to aid in manufacturing.

Significance

It is important for practitioners who are planning on performing FEA of composite structures to understand how ply draping affects fibre orientation and subsequently, how fibre orientation affects the accuracy of the results. The reader will also learn how ply draping modelling can be used to create flat patterns that can be used manually or with automated ply cutters to improve the quality and consistency of ply layups.

Practice

The following items should be considered when simulating ply draping:

Developable and Undevelopable Surfaces

Part geometry is a critical parameter when performing ply draping modelling and can dramatically affect fibre orientation. The fibre orientation of flat or singly curved surfaces remains practically constant across the surface as shown in Figure 1. This type of geometry is referred to as a developable surface as the surface can be flattened onto a plane without distortion.

Figure 1 – Developable surface where fibre orientation remains constant

For a doubly curved surface, like that shown in Figure 2, the ply must deform to follow the surface. This is called an undevelopable surface. This deformation occurs by in-plane shearing of the fabric and results in changes in the fibre orientation across the surface.

Figure 2 – Undevelopable surface where deformation occurs due to in-plane shearing and results in changes in fibre orientation

Lock Angle

During draping of a woven fabric over an undevelopable surface the fibres undergo in-plane shearing. With enough deformation the fibres begin to rub against each other preventing further in-plane deformation. At this point the shear force increases dramatically and results in out-of-plane deformation of the fibres. This results in wrinkling of the layup. For a woven fabric the angle between the warp fibres (primary direction) and weft fibres (secondary direction) is typically 90°. As the part deforms the fibres do not change length so the angle between the warp and weft fibres changes. The shear angle is the difference between the original angle (90°) and the distorted angle. The lock angle, as shown in Figure 3, defines the maximum measured in-plane shear angle before the fabric begins to deform out-of-plane. When a fabric reaches its lock angle the ply begins to wrinkle or bridge.

Figure 3 – In-plane shear deformation of a woven fabric

Kinematic Draping Model

Most commercial software uses some form of kinematic draping theory when performing ply draping modelling. In this theory the ply is idealized using the pin-jointed net model. The model assumes the fibres are inextensible and each crossover point acts like a pin joint with no slippage. The deformation takes place by pure rotation of the fibres around the pins. It also assumes uniform surface contact. These assumptions allow the model to calculate the location of each crossover point on the surface of the part.

There are two primary methods that different types of software use to apply kinematic draping theory to a particular geometry. The first method is the geodesic line method. In this method two intersecting fibres are constrained to the surface. They are defined by geodesic paths that intersect at the point of initial contact between the ply and the geometry. The geodesics end at the edges of the part. Many geodesics may be created until the whole geometry is draped.

The second method is the energy method. Elements are laid one by one on the surface of the model from the defined starting location and in the defined draping direction. The elements are laid on the part surface until the part edge is reached. The elements are then laid in the direction perpendicular to the primary direction. Draping elements continue to be created until the surface is completely covered. For each element the search algorithm calculates the node locations based on minimizing the shear strain energy. During draping of a woven

Parameters that Affect Draping Results

When the draping simulation is completed, the results will provide information on the fibre orientation of each element and the shear distortion between the warp and weft fibres. If elements exceed the lock angle of the fabric the analyst can make adjustments to improve the results. This includes varying the draping starting point, changing the initial ply orientation, or adding darts to the fabric.

Starting Location

Changing the starting location of the ply draping process can alter the maximum observed shear angle and change the fibre orientations across the part. The part shown below was draped using a woven solver with two different starting points as indicated in Figure 4. The fibres were initially oriented in the longitudinal and transverse directions of the part.

Figure 4 – Draping starting locations

Figure 5 shows that for the first starting location the shear angle remains close to 0° in the wider cross-section of the part. The maximum shear angles occur along the sides of the part in the transition from the wider to thinner cross-section. The shear angle continues to vary away from 0° along the sides of the part in the thinner cross-section. The maximum shear angle was 46.4°.

Figure 5 – Shear angles for starting location 1

For the second starting location the shear angles along the sides of the part in the transition area are close to 0° although the fibres are oriented approximately 45° from the longitudinal and transverse directions of the part. This is shown in Figure 6. The maximum shear angle is now observed on the side of the wide cross-section and has a value of 45.7° as shown in Figure 7.

Figure 6 – Shear angles at 0° for starting location 2

Figure 7 – Maximum shear angle for starting location 2

When comparing the maximum shear angles for the two draping starting locations for this particular geometry, it is noted that the values are quite close to each other, but they occur at different locations. Additionally, the fibre orientations across the part are different between the two starting locations.

Initial Ply Orientation

Adjusting the initial ply orientation will also change the draping results. When the ply is initially oriented at +/-45° the maximum shear angle is observed along the top and the sides of the narrow region for both starting locations 1 and 2 as shown in Figure 8. For starting location 1 the maximum shear angle is 43.7°. For starting location 2 the maximum shear angle drops significantly to 35.1°. This shows that changing the initial ply orientation can potentially reduce the maximum shear angle. However, the ply orientation is often selected based on other factors such as structural performance, so it is not always feasible to adjust this parameter.

Figure 8 – Maximum shear angle for +/-45° ply

Ply Darts

Ply draping modelling also provides the ability to predict the effects of adding ply darts (cuts) to the fabric. To demonstrate this concept the height of the part used in the previous examples was increased. The modelling software was used to predict the shear angles when the ply was draped starting at location 1 and with a ply orientation of 0°/90°. Figure 9 shows that the increase in height of the part caused the maximum shear angle to increase and exceed the lock angle in the transition region between the wide and narrow sections of the part.

Figure 9 – Shear angles for initial layup with no ply darts

Ply darts were then added on both sides of the part at the start of the transition region from the wide to narrow sections of the part as shown in Figure 10. This resolved the issue because the shear angle no longer exceeded the lock angle as shown in Figure 11. However, it did result in an abrupt change in fibre orientation at the location of the ply dart.

Figure 10 – Ply dart location

Figure 11 – Shear angles for layup that includes ply darts

Flat Patterns

Draping modelling can be used to create flat patterns based on the geometry of the part, starting location, ply orientation, and ply darts. Flat patterns can then be used to create templates for material trimming or can be imported to ply cutting equipment to automate the process. This improves the accuracy and the consistency of each layup during production and helps to ensure that fibre orientations match the inputs used for structural analysis.

Figure 12 shows the flat pattern for starting location 1 and Figure 13 shows the flat pattern for starting location 2. Since the second starting location is in the middle, and not the end of the part, the corners in the widest section of the part are no longer perfectly square. Figure 14 shows the flat pattern for starting location 1 but includes ply darts. Flat patterns can be especially useful in these situations because the pattern ensures the darts are at the same location and are the same length for every part.

Figure 12 – Flat pattern for starting location 1

Figure 13 – Flat pattern for starting location 2

Figure 14 – Flat pattern for starting location 1 with ply darts

Fibre Orientation

Changes in the ply draping strategy will affect the fibre orientations of the part. This includes changes to the starting location, initial ply orientation, and the location and length of ply darts. Variations in the fibre orientations can affect the analysis results as well as real world performance. The analysis of the conic shell shown in Figure 15 provides a good example.

Figure 15 – Conic shell

The conic shell was modelled using unidirectional fabric. The first strategy shown in Figure 16 started the draping process on the edge of the part with the initial ply orientation along the hoop direction. A single dart was included that began at the ply draping starting location and ended at the apex of the part. A flat pattern of this draping strategy is shown in Figure 17. This strategy resulted in fibre orientations that varied around the circumference of the part and also resulted in an abrupt fibre orientation change at the ply dart location as shown in Figure 18.

Figure 16 – Draping strategy 1 starting location

Figure 17 – Draping strategy 1 flat pattern

Figure 18 – Draping strategy 1 fibre orientation results

The second strategy that is shown in Figure 19 split the ply into quarters that were draped individually. Each quarter ply started the layup on the edge of the part with the initial ply orientation along the hoop direction. The flat pattern for draping strategy 2 is shown in Figure 20. This draping strategy resulted in fibre orientations that remained oriented in the hoop direction and didn’t vary around the circumference of the part as shown in Figure 21.

Figure 19 – Draping strategy 2 starting location

Figure 20 – Draping strategy 2 flat pattern

Figure 21 – Draping strategy 2 fibre orientation results

A structural analysis was performed once the ply draping modelling was completed. Figure 22 shows the analysis setup with the top edge fully fixed and a pressure applied to the conical faces.

Figure 22 – Structural analysis setup

When comparing the results shown in Figure 23, the maximum deflection was almost 2.5 times larger for strategy 1 compared to strategy 2. This was because the fibre orientation varied across the surface for strategy 1 while it remained consistently in the optimal hoop direction for strategy 2. For this reason, the deflection pattern also varied for strategy 1 while remaining consistent for strategy 2.

Figure 23 – Deflection results for conic shell structural analysis

The optimal configuration to carry the load in this scenario is for the fibres to be oriented in the hoop direction. The longitudinal stress increases significantly in areas where the fibres are oriented at a different angle. This is observed in Figure 24 which shows the longitudinal stress was significantly higher for strategy 1 compared to strategy 2. The stress pattern also dramatically varied across the surface for strategy 1 while remaining consistent for strategy 2.

Figure 24 – Longitudinal stress results for conic shell structural analysis

Figure 25 shows that strategy 1 also introduced a large shear stress component along the edge of the part, while the shear stress for strategy 2 was almost zero. This was due to the unsymmetric deflection pattern that was created by the variation in fibre orientation across the surface.

Figure 25 – Shear stress results for conic shell structural analysis

Closing Remarks

This example demonstrates that it is critical for the analyst to understand the draping process that will be implemented during manufacturing. The choice of draping strategy employed during manufacturing affects the fibre orientations and ultimately affects the structural results. If the draping strategy is not understood by the analyst, the results of the structural analysis may be misleading.

Related pages

• See Webinar on Fiber Architecture
• See Webinar on Fabric Forming
• See Page on Overview of Finite Element Analysis of Composite Structures
• See Case Study on Improving Quality of a Truck Fender Using Ply Draping Modelling

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About	Help

The use of multiphysics models to predict the outcome of real-world scenarios. May be analytical (closed form, "hand calculations") or computational (implementation on computers is required due to the large number of calculations involved. e.g. finite element method, finite difference method)

Most often in composite materials engineering, modelling refers to either:

• Process modelling (predicting manufacturing outcomes, or the inverse problem of predicting manufacturing parameters to achieve a desired outcome), or
• Performance modelling (predicting the stiffness/strength/suitability of a structure, or the inverse problem of the material properties and dimensional requirements to achieve a desired stiffness/strength/suitability of a structure)

(same as "Simulation")

Engineered materials (designed to have specific properties) made from two or more constituent materials with different physical or chemical properties. The constituents remain separate and distinct on a macroscopic level within the finished structure.