Autodesk Moldflow Insight 2017 R2 Fiber orientation ...help.autodesk.com.s3.amazonaws.com/sfdcarticles/kA23A000000mU1NSAU...The implementation of the ORE closure in AMI 2017 R2 necessitate

Autodesk®

Autodesk Moldflow Insight 2017 R2

Fiber orientation Accuracy Validation Report

A new Moldflow rotational diffusion (MRD) model is developed and implemented. The closure approximation of the fourth order orientation tensor is changed from Hybrid to Orthotropic and used along with the MRD model. This document shows the results of the validation test for AMI 2017 R2 release. Results from majority of test cases with the improved model halved the discrepancies between the experimental and predicted data compared to that of previous release, which uses Folgar-Tucker model as default. In other words, the new release gives a much better overall orientation prediction compared to the older release. Therefore, the MRD model with Orthotropic closure is set as the new default for the 3D analysis in this release. This is in line with the dual domain and midplane analyses that already use orthotropic closure.

FIBER ORIENTATION (3D) SOLVER VALIDATION

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Contents

Introduction ................................................................................................................. 3

Fiber Orientation Solver Enhancement ....................................................................... 4

Moldflow Rotational Diffusion (MRD) Model. ............................................................. 4

Implementation of Orthotropic closure ...................................................................... 6

Fiber Orientation Validation ........................................................................................ 7

BASF Plate .............................................................................................................. 7

Delphi Plaque and Disks .........................................................................................16

Bradford Disk ..........................................................................................................43

DSM Plaque ...........................................................................................................49

Mechanical Plaque .................................................................................................55

Comparison of predictions by different models .........................................................57

Conclusions ...............................................................................................................58

Acknowledgements ....................................................................................................58

References .................................................................................................................59


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Introduction It is a known fact that reduction in warpage of injection molded part is of high importance in

plastic products, and that fiber orientation distribution in a reinforced thermoplastic has

effect on the warpage of an injection molded plastic. Over the years, beginning from the

seminal work of Jeffery [1], a lot of fiber orientation models have been developed. The

Jeffery’s model that accounts for the kinematics of a single rigid ellipsoid in a Newtonian

suspension was extended in terms of fiber orientation distribution function in the generalized

Fokker–Planck or the Smoluchowski equation, with the rotational diffusion term accounting

for the effect of interaction between multiple inclusions [2]. Folgar-Tucker (F-T) model [3]

gave an empirical expression for the rotational diffusion parameter as proportional to the

shear rate (�̇�), with a coefficient of interaction (𝐶𝑖) being the constant of proportionality. The

formula is as given in Eqn. (1).

𝐷𝑟 = 𝐶𝑖�̇� (1)

The Folgar-Tucker model does not lend itself to commercial implementation in the form of

orientation distribution function. Advani and Tucker [4] did recast the model in terms of a

second order orientation tensor, given in Eqn. (2). This form of the model is what has been

the default fiber orientation model in AMI until the AMI 2017 technological preview, where

the reduced strain closure (RSC) replaced it. Further improvement has been made to the

Advani-Tucker form of the Folgar-Tucker model

DA

Dt= (W ∙ A − A ∙ W) + ξ(D ∙ A + A ∙ D − 2 ∶ D) + 2CIγ̇(I − 3A) (2)

where A= ⟨pp⟩. The unit vector p directs along the fiber length, and the bracket “⟨ ⟩” is the average over a volume domain. The trace of A, tr (A), is unity because of the normalization condition. The orientation tensor A is symmetric and has only five independent components.

The Folgar-Tucker model can be decomposed into two parts. The hydrodynamic

contribution (�̇�ℎ) and the diffusive contribution (�̇�d), given as �̇� = �̇�ℎ + �̇�d

Subsequent improvement to the F-T model is either to improve the kinematic part (which is

due to flow hydrodynamic contributions to fiber orientation) or the interaction part, which

accounts for the effect of fiber-fiber interaction.

Most of the works on fiber orientation kinematics has been focused on improving either the

closure approximation of the fourth order tensor in terms of the second order tensor or

slowing down fiber orientation evolution so as to match the rate of alignment in experimental

observation. Among the closure approximations, the Hybrid closure has been the default

for fiber orientation prediction in AMI. One of the more recent and more accurate orthotropic

fitted closures have been developed and implemented as a new features for this release.

An objective improvement to the rate of alignment predicted by the Advani-Tucker model is

the reduced strain closure (RSC) [5-6], which was the default for AMI 2017 technological

preview. The model is:

DA

Dt= (W ∙ A − A ∙ W) + ξ{D ∙ A + A ∙ D − 2[ + (1 − κ)( − ∶ )] ∶ D}

+ 2κCIγ̇(I − 3A)

(3)

The Folgar-Tucker model is essentially an isotropic rotary diffusion model, where fiber

interaction is assumed to be isotropic. More recently, Phelps and Tucker [7-8] developed


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an anisotropic rotary diffusion model. The anisotropic rotary diffusion model accounts for

anisotropy in fiber-fiber interaction, but it is limited because of the number of coefficients

that must be fitted to get improved predictions. The reduced strain form of this model is

available in AMI but currently used for long fiber model, and it is:

DA

Dt= (W ∙ A − A ∙ W) + ξ{D ∙ A + A ∙ D − 2[ + (1 − κ)( − ∶ )] ∶ D}

+ γ̇{2[C − (1 − κ) ∶ C] − 2κ(trC)A − 5(C ∙ A + A ∙ C)

+ 10[ + (1 − κ)( − ∶ )] ∶ C}

(4)

Here, the rotary diffusion tensor C is constructed from A and D as:

C = b1I + b2A + b3A2 + b4

D

γ̇+ b5

D2

γ̇2

, (5)

where bi (i = 1, …, 5) are scalar constants and selected by matching experimental steady-

state orientation and requiring stable orientation solutions. Setting b1 = CI and bi = 0 (i = 2,

…, 5) reduces the ARD-RSC model of Eqn. (4) to the RSC model of Eqn. (3).

Fiber Orientation Solver Enhancement The development and implementation of the MRD model and the implementation and use

of the Orthotropic closure are the two main improvements for this release. There are other

additional bug fixes and internal fiber solver enhancements-such as further enhanced to

the RSC model. The default RSC parameter is changed from 0.05 to 0.1.

Moldflow Rotational Diffusion (MRD) Model.

This model is the latest contribution to the AMI fiber orientation models in 3D. It was a

modified version of the Folgar-Tucker model in the Advani-Tucker orientation tensor form.

Essentially, the model modified the diffusive contribution to the model and keeps the

kinematic part (the hydrodynamic contribution) intact. The MRD model is characterized by

four parameters Ci D1, D2 and D3. Fiber interaction coefficient Ci corresponds to the

magnitude of the rotational diffusion while coefficients of asymmetry D1, D2 and D3 show

how the rotational diffusion is biased towards the direction of the principal vectors of fiber

orientation tensor. The higher the value of the correspondent D coefficient, the more

rotational diffusion is biased towards the direction of the correspondent principal vector.

The default values for D𝑖 coefficients are D1=1.0, D2=0.8, D3=0.15, and they are used

when automatic calculations is selected under “Di Options for Moldflow 3D”.

To use the MRD model for analysis in AMI 2017 R2, go to the study task pane, right click

the material and click edit, you will get a window that allows you to edit the thermoplastic

material. Click the Filler/Fiber tab, choose Moldflow Rotational Diffusion model under

“Fiber orientation calculation (3D) by”. Click on “Edit setting”, a “Fiber Orientation Model

Parameters” window will pop-up. You can either use the Automatic calculations for “Ci

Options for Moldflow 3D model” and “D𝑖 Options for Moldflow 3D” or specify the interaction

coefficient you desire by clicking the down arrow. The interaction coefficient has only one

parameter to specify while the D𝑖 has 3 parameters that could be specified if the default


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automatic calculation is not used. (See Figure 1- Figure 3) for an example window for the

use of MRD model).

Figure 1. Study task pane showing how to get to the MRD model.


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Figure 2. Thermoplastic material window showing how to get to and use the MRD model.

Figure 3. Fiber Orientation model parameters option window for MRD

Implementation of Orthotropic closure

In addition to the improvement made to the diffusive contribution to fiber orientation change,

the closure approximation was changed from the Hybrid Closure to the ORE closure in AMI

2017 R2. The ORE closure is arguably the best of the class of Orthotropic fitted closure

developed after the Hybrid closure, and it has been shown in literature to give improved

fiber orientation prediction compared to the Hybrid closure [9]. The Orthotropic closure is

simply a least square fit of the fourth order orientation tensor in terms of the second order

orientation tensor. The analysis generated polynomials with coefficients suitable for

predicting the fourth order orientation tensor in terms of the second order orientation tensor.


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The implementation of the ORE closure in AMI 2017 R2 necessitate a new empirical model

for determination of the interaction coefficient. Also, the default value of the RSC factor was

changed in order for the Orthotropic closure to give the same shell orientation as that of

Hybrid closure.

There is nothing to be done in the user interface to be able to use the Orthotropic closure.

It is the only closure approximation used in the AMI2017 R2 release. To see the

improvement between the Orthotropic closure and the Hybrid closure result, user will have

to run the same study file in AMI 2017 FCS and either the default in AMI 2017 Technological

preview or chose RSC model in this release (AMI 2017 R2).

Fiber Orientation Validation The fiber orientation was calculated using the MRD model within the 3D Flow solver, for a

number of injection-molded parts. The results from AMI 2017FCS and 2017R2 are

compared against the experimental measurements. In general, the result showed that for

most test cases, the MRD model showed significant improvement over the F-T model, which

has been the default model until this release. In several cases, the MRD halved the

discrepancy between the model prediction and experiment as compared to the F-T model

prediction.

In the subsequent section the nomenclature, A11 represents the orientation tensor

component in the flow direction, A22 the component in the cross-flow direction, and A33 the

component in the thickness direction. The normalized condition of the orientation tensor

implies A11 + A22 + A33 = 1, and only two of three diagonal components are independent.

Thus, only A11 and A22 components are presented. Unless they are specified otherwise, the

default fiber parameters are used, including the automatically calculated CI value based on

the fiber aspect ratio and volume fraction, the default RSC factor κ of 0.01, and the default

values of bi parameters in the ARD model. The MRD model should reproduce the F-T results

with Di coefficients of D1=1.0, D2=1.0, D3=1.0 and same interaction coefficient.

In the plots, the nomenclature FT represents the Folgar-Tucker model in this release after

using the Orthotropic closure. FT_2017FCS represents the Folgar-Tucker model in the

2017 release using the Hybrid closure. MRD is the Moldflow rotation diffusion model. RSC

represent the reduced strain closure model with Orthotropic closure. RSC_2017FCS

represents the RSC model in AMI 2017 release using the Hybrid closure. RSC_CI is the

RSC model in this release using both the Orthotropic closure and a newly fitted calculation

of interaction coefficient in terms of volume fraction and aspect ratio.

BASF Plate

A 3mm thick BASF plaque was molded from a 50wt% Glass fiber filled thermoplastic. The

plaque is as shown below. Test results are measured from the plaque from the location

labelled A0-R4 in the plate. The results are compared with the AMI 2017R2 release

prediction. Figure 5-Figure 16 are examples of prediction of MRD model for BASF plaque

compared to experimental data provided by BASF.

To automatically estimate quality of fiber orientation predictions we used measured and

predicted data to build smoother curves by the LOESS local regression method [10] as


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illustrated on Figure 6 for MRD results for the A11 component in C3 location. The area

between the smoother curves is used to estimate the average error of the component. Then

we calculate the deviations between predictions and measurements in a location by

averaging the result over the four measured components (A11, A22, A33 and A13) and

finally we calculate the average error of the model by averaging the result over the all

locations. These final results are shown on Figure 17.

Figure 4. BASF Plaque


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Figure 5. BASF plaque – comparison of fiber orientation results from AMI 2017R2 3D analyses.


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Figure 7.Location C3- Average error of A11 prediction by available models in AMI for 2017R2 and 2017FCS.

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Figure 6 Location C3, component A11 – processing of the measured data and predictions by MRD model. The area between the smoothed curves (dark grey) is used to calculate the average error of the predictions.

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Figure 8. Location C3- Average error of A13 prediction by available models in AMI for 2017R2 and 2017FCS.

Figure 9. BASF plaque- Location C3 Summary of the overall deviation between measured data and

predictions by available models in AMI for 2017R2 and 2017FCS. The chart shows the average error of predictions of the four measured components (A11, A22, A33 and A13).

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Figure 10. BASF plaque Location A4 –MRD prediction compared to measured data.

Figure 11. BASF plaque Location C1 –MRD prediction compared to measured data.


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Figure 12. BASF plaque Location C2–MRD prediction compared to measured data.

Figure 13. BASF plaque Location C4–MRD prediction compared to measured data.


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Figure 14. BASF plaque Location R2–MRD prediction compared to measured data.



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Figure 17. BASF Case- Summary of the overall deviation between measured data and predictions by

available models in AMI 2017R2 and AMI 2017FCS.

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Conclusion: 2017R2 with the default model option (MRD) provides significantly improved

accuracy over 2017 FCS (FT). The average error of predictions decreased from 0.16 to

0.07. Both FT and RSC model also improved accuracy in the release 2017 R2 over 2017

FCS.

Delphi Plaque and Disks

A number of end-gated plaques and center-gated disks were molded from a 30 wt. % glass

fiber-reinforced polybutylene terephthalate (SABIC Innovative Plastics Valox 420-1001) by

Delphi Automotive LLP. The ISO-standard plaques were 80 mm wide and 90 mm long, and

the disks were 90 mm in radius. The part thicknesses for each shape varied from 1.5, 2, 3,

to 6 mm. Three different injection rates (slow, medium, and fast) were applied for each

thickness [6]. Fiber orientation measurements were performed on three sections, each

about 10 mm wide, starting at 0, 30, and 60 mm away from the gate on the cut along the

centerline of each plaque and along the radius of each disk. The sections are labeled as

locations A, B, and C, respectively, as shown in Figure 18 and Figure 19. For some parts,

experimental data from location C are not available.

Automatic estimation of the average quality of model predictions was performed by the

similar method that was described for BASF in the section above.

Figure 20-Figure 23 are examples of the summary of overall average deviation of the model

predictions from the measured data at certain location in the Delphi disk and plaque. Worth

noting is the improvement of the MRD (the new default for this release) over the Folgar-

Tucker model, which is the default model until this release.

Figure 24 is a summary of the overall comparison of the model predictions for A11, A22, A33

and A13 component of the orientation tensor compared to experimental data.

Figure 25-Figure 47 are examples of A11 and A22 components through thickness of the parts

under different filling time and at different locations.

Figure 18. Standard ISO plaque used for Delphi validation analysis

C B A


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.

Figure 19. Disk used for Delphi validation analysis.

Figure 20. Delphi 1.5mm Disk - Summary of the overall deviation between the measured data and predictions by available models in AMI for 2017R2 3D at Location B.

A B C

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Figure 21. Delphi 1.5mm Disk - Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data at Location C.

Figure 22. Delphi 3 mm Disk slow fill rate- Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data at Location B.

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Figure 23: Delphi 3 mm Disk slow fill rate - Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data at Location C

Figure 24. Delphi Case- Summary of the overall deviation of available models in AMI 2017R2 3D analyses from measured data.

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Figure 25. Delphi ISO-standard plaque, 1.5 mm thick, slow fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 26. Delphi ISO-standard plaque, 1.5 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 27. Delphi ISO-standard plaque, 1.5 mm thick, fast fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Fib

er

ori

enta

tion tensor

com

ponents

Normalized thickness

A11 (Data)

A11 (2016, RSC)

A11(2017,RSC)

A22 (Data)

A22 (2016, RSC)

A22(2017,RSC)

Location A


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Figure 28. Delphi ISO-standard plaque, 2 mm thick, slow fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 29. Delphi ISO-standard plaque, 2 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 30. Delphi ISO-standard plaque, 2 mm thick, fast fill rate comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 32. Delphi ISO-standard plaque, 3 mm thick, medium fill rate– comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 33. Delphi ISO-standard plaque, 3 mm thick, fast fill rate- comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 35. Delphi ISO-standard plaque, 6 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data

.


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Figure 36. Delphi ISO-standard plaque, 6 mm thick, fast fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 37. Delphi disk, 1.5 mm thick, slow fill rate –– comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 38. Delphi disk, 1.5 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 39. Delphi disk, 1.5 mm thick, fast fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 40. Delphi disk, 2 mm thick, slow fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 41. Delphi disk, 2 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data


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Figure 42. Delphi disk, 2 mm thick, fast fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data.


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Figure 43. Delphi disk, 3 mm thick, slow fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data.


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Figure 44. Delphi disk, 3 mm thick, medium fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data.


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Figure 46. Delphi disk, 6 mm thick, slow fill rate – comparison of fiber orientation results from AMI 2017R2 3D analyses with measured data.


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FCS.

Bradford Disk

Center-gated disks were molded from a 40 wt. % short fiber-reinforced polyamide (Technyl

C 216 V40 Natural (REP tested)) by Rhodia Engineering Plastics for the short fiber and 30

wt. % long glass fiber-reinforced polypropylenes (STAMAX 30YM240 (medium fiber

condition upgraded)) by SABIC Europe B.V. The disk geometry and dimension is given in

Figure 48 and Figure 49.



Figure 50 and Figure 51 are examples of the summary of overall average deviation of the

model predictions from the measured data at certain location in the Bradford disk. Also,

note the improvement of the MRD (the new default for this release) over the Folgar-Tucker

model, which is the default model until this release.


and A13 component of the orientation tensor compared to experimental data.

Figure 53 and Figure 54 are examples of predicted A11 and A22 component through

thickness of the parts.

Figure 48. Bradford disk used for validation analysis.


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Figure 49. Bradford disk used for validation analysis


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Figure 50. Bradford disk Location A- Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data.

Figure 51. Bradford disk Location B- Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data.

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Figure 52. Bradford Case- Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data.

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Figure 53. Bradford 1mm thick disk – comparison of short fiber orientation results from AMI 2017R2 3D analyses with measured

data.


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Figure 54. .Bradford 1mm thick disk – comparison of long fiber orientation results from AMI 2017R2 3D analyses with measured

data.


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FCS.

DSM Plaque

A Plaque molded from a 40 wt. % short glass fiber-reinforced polyamide (Akulon K224-

PG8) by DSM was simulated. The plaque geometry and dimension is given in Figure 55

and Figure 56.



Figure 57-Figure 59 are examples of the summary of overall average deviation of the model

predictions from the measured data at certain location in the DSM plate. Also, note the

improvement of the MRD (the new default for this release) over the Folgar-Tucker model,

which is the default model until this release.


and A13 components of the orientation tensor compared to experimental data.

Figure 61-Figure 66 are examples of A11 and A22 component through thickness of the parts.

Figure 55. DSM Plaque used for validation analysis.


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Figure 56. Description of measurement locations on DSM Plaque used for validation analysis.

Figure 57. DSM Plaque Location 1- Summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data.

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Figure 60. DSM Plaque - summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data

Figure 61. Fiber orientation results for DSM plaque at location S1 for AMI 2017R2 3D.

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54




55





FCS.

Mechanical Plaque

A 3mm-thick plaque shown on Figure 68 was molded from material Extron 3019HS by

Polypacific (30% glass fiber filled polypropylene). Fiber orientation in the center of the plaque

was measured by computer tomography and compared with prediction by different models.

Figure 678: Mechanical Plaque


56



The average deviations between predictions and experiments are shown on Figure 69


57




FCS.

Comparison of predictions by different models

Comparison of average deviations between experiments and predictions for different

constitutive models is shown on Error! Reference source not found.. In average with the

default settings the deviations from the experiment by the 2017 R2 are approximately half

of the deviations from the 2017 FCS. The improvement is achieved due to the more

accurate constitutive model (MRD), more accurate closure (orthotropic) and a revised fit of

the model parameters. Both F-T and RSC models also show improved accuracy across all

validation cases.

Figure 68: Mechanical Plaque - summary of the overall deviation of available models in AMI for 2017R2 3D analyses from measured data

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Conclusions Results of the prediction of the new MRD model along with the Orthotropic closure

approximation result has been reported for the BASF, Delphi, and Bradford and DSM test

cases. In the addition to the MRD, the RSC, ARD-RSC and F-T models are also available

in the solver. The new MRD model improved the core orientation prediction for the BASF

test cases and gives an overall improved prediction over the existing default and other AMI

fiber solver models. In general, for most cases the overall average discrepancy between

the MRD and the data is almost half of the existing default results and better than other

existing fiber models. The MRD is, therefore, set as the default fiber model in this release.

There is also a considerable improvement to the RSC and F-T models predictions due to

the use of more accurate closure approximation and better automatic calculations of model

parameters.

Acknowledgements Autodesk, Inc. wishes to thank BASF SE, Delphi Automotive LLP, DSM Engineering

plastics, Bradford and the Oak Ridge National Laboratory for providing experimental

measurements and models of their molded parts, which were used in this report.


59

References [1] G. Jeffery," The motion of ellipsoidal particles immersed in a viscous

fluid" Proc Roy Soc London A 1923;102:161–79.

[2] R. B Bird, C. Curtiss , R. C. Armstrong, O. Hassager. Dynamics of

polymeric liquids.Kinetic theory, 2nd ed., vol. 2. New York, NY: John

Wiley & Sons, Inc. 1987.

[3] F. Folgar and C. L. Tucker III, “Orientation Behavior of Fibers in Concentrated Suspensions,” J. Reinf. Plast. Compos., vol. 3, no. 2, pp. 98–119, Apr. 1984.

[4] S. G. Advani and C. L. Tucker III, “The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites,” J. Rheol., vol. 31,

no. 8, pp. 751–784, 1987.

[5] J. Wang, J. F. O’Gara, and C. L. Tucker III, “An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence,” J. Rheol., vol. 52, no. 5, pp. 1179–1200, 2008.

[6] C. L. Tucker III, J. Wang, and J. F. O’Gara, “Method and Article of Manufacture for Determining a Rate of Change of Orientation of a Plurality of Fibers Disposed in a Fluid,” 7,266,469, 2007.

[7] J. H. Phelps and C. L. Tucker III, “An anisotropic rotary diffusion model for fiber orientation in short- and long-fiber thermoplastics,” J. Nonnewton. Fluid Mech., vol. 156, no. 3, pp. 165–176, Feb. 2009.

[8] J. H. Phelps, “Processing-Microstructure Models For Short- And Long-Fiber Thermoplastic Composites,” Ph.D. Thesis, University of Illinois at Urbana-Champaign, 2009.

[9] B. O. Agboola, D. A. Jack, S. Montgomery-Smith, "Effectiveness of recent fiber-interaction diffusion models for orientation and the part stiffness predictions in injection molded short-fiber reinforced composites" Compos. A: Appl. Sci. Manuf., 43, 1959 (2012).

[10] J. Fox and H.S. Weisberg, "An R Companion to Applied Regression", Sage, 2011


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Autodesk Moldflow Insight 2017 R2 Fiber orientation ...help.autodesk.com.s3.amazonaws.com/sfdcarticles/kA23A000000mU1NSAU...The implementation of the ORE closure in AMI 2017 R2 necessitate