Finite Element Modeling of Fragment Fabric Barriers

Overview

ARA teamed with SRI International to perform research sponsored by FAA to design barriers to protect critical aircraft components against fragments resulting from uncontained failure of a turbine engine. As part of this program, ARA is developing computational models to perform finite element analyses of fragment impact experiments. The experiments are highly dynamic events, including strong nonlinear effects such as impact, penetration, and large deformation and failure of materials. We use the analysis to guide and understand the impact experiments, and we use the results of the experiments to guide development of the models. Here we describe analyses of woven Zylon fabrics. To perform the analyses, we are developing a material model for yarns that we implement into the finite element code LS-DYNA.

Modeling Yarns

Our approach to modeling woven fabrics is to model the individual yarns explicitly. This allows us to understand the mechanisms responsible for the high ballistic resistance of polymer fabrics. The finite element model configuration for a woven fabric is shown below. Yarns are modeled individually and combined to form a fabric weave. The shapes and geometry of the yarns were taken from high resolution photographs of the fabrics used in the testing. As seen in the figures, the weave is not symmetric. Typically the warp yarns have more crimp than the fill yarns.

Yarn Model

The material model and properties used for the yarns are based on results of yarn tensile tests. We modeled an initially crimped yarn and pulled it to failure at a strain rate of 0.016/s. The measured and simulated stress-strain curves are shown below. The simulation shows very good agreement with the test results.

Effect of Boundaries

We simulated tests with three different boundary conditions as shown in the animations below. In the first case, the fabric patch is firmly gripped on all four edges, in the second case the fabric is gripped firmly along two edges and in the third case no edges are gripped. The steel fragment impacts at a velocity of 120 m/s.


Gripped 4 Sides	Gripped 2 Sides	Not Gripped

The forces on the fragment applied by the fabric are shown in the figure below. If the fabric is gripped on four edges, the peak force is the greatest, but at 50 microseconds the yarns in both directions break and the fragment penetrates the fabric. If the fabric is gripped on two edges, the initial peak force is less, but as the gripped yarns break, the ungripped yarns transfer the load to adjacent gripped yarns, resulting in a resisting force of a longer duration. For the case with no edges gripped, the fabric still provides a significant amount of resistance due to inertia.

The calculated velocity of the fragment is shown below. For the case with no edges gripped the fragment slows from 120 to about 80 m/s. This result is consistent with conservation of momentum for a simple inelastic collision. For four edges gripped the velocity is reduced from 120 to 38 m/s, and for two edges gripped the velocity of the fragment is reduced to zero. The result of this simulation: that gripping on two edges is more effective than gripping on four edges agrees with the experimental results. The result for no edges gripped shows that, if the fragment is prevented from cutting through the fabric, significant energy can be absorbed by inertial effects.

The difference in the response mechanism for the different boundary conditions is explainable in terms of load transfer. With four edges gripped, yarns in both directions under the fragment fail locally. However, for two edges gripped, the gripped yarns break locally, but the ungripped yarns do not break and are able to transfer load to adjacent gripped yarns.

Effect Of Fabric Size

To investigate the effect of fabric size, we simulated three square fabric patches of different sizes: 15 yarns, 25 yarns, and 35 yarns. The fabric was gripped on 2 edges. The steel fragment had a velocity of 120 m/s.


Gripped on 4 Edges	Gripped on 2 Edges	Not Gripped

Summary Of The Detailed Model

The detailed model can be used to study methods of modifying the barrier design to improve its efficiency. We have investigated effects of density, crimp, boundary conditions and fabric size on ballistic resistance. We plan to investigate the effect of yarn stiffness and strength and interyarn friction. We may also investigate different weave geometries, including three-dimensional weaves.

Development Of a Design Model

Above is the description of the detailed fabric model used as a fabric barrier research tool. Another component of this program is the development of a design model. The design model can be used as a tool for choosing or evaluating parameters for fragment barriers. Because it uses a simplified description of the fabric, the model runs very quickly (about 2 minutes on an SGI Origin 200 for the tests shown here) and easily allows evaluation of changes in size of fabric, number of layers, or yarn pitch. The design model implemented as a user-defined material in LS-DYNA uses shell elements with an orthotropic continuum formulation to model the fabric.

Model Parameters

To calculate parameters for the shell material model, we use measured values for thickness and areal density of the fabric. From the measured value of strength for a single yarn (1.61e7 dyne [36 lb]), we calculate linear fabric strength (e.g. in dyne/cm) by multiplying the pitch (number of yarns/cm) by the strength of a yarn. We calculate the Young's modulus (dyne/cm2) in the two orthogonal directions along the yarns by taking the measured yarn load at 1% strain, multiplying by the pitch and distributing the load over the fabric thickness. The shear modulus in all directions is assumed to be 10% of the Young's modulus, and the Poisson's ratio is assumed to be zero in all directions. The fabric density is calculated by dividing the measured areal density by the measured fabric thickness. For multiple plies, the fabric thickness is simply the number of layers times the single layer thickness; the modulus and density values remain the same. This model assumes that for a multi-ply target the fabric yarns are all aligned in the same directions (e.g., 0 and 90 degrees).

Design Model Parameters

No. of plies	Pitch yarns/inch	Thickness (mm)	Areal density g/cm2	Force at 1% dyne	Modulus dyne/cm2	Density g/cc
1	30	0.15	0.0130	2.00e8	5.25e11	0.867
1	35	0.19	0.0158	2.33e8	4.84e11	0.832
1	40	0.23	0.0185	2.67e8	4.57e11	0.804
1	45	0.27	0.0219	3.00e8	4.38e11	0.811

Failure Model

The fabric material model is assumed to be elastic-plastic with linear hardening to failure in two orthogonal directions aligned with the yarns. The yield stress is set to 12.0e9 dyne/cm2 with 20% strain hardening. The failure criterion is based on accumulated plastic strains in the two directions both exceeding a specified limit. The limit values for strain, which depend on the number of layers, are listed below.

Failure Strain Values

No. of Layers	1	2	3	4	5	6
Strain to failure	0.035	0.060	0.085	0.110	0.135	0.150

Example Simulations

We performed simulations using the simplified model for 15 of the gas-gun tests. The calculated results of these calculations are listed in the table below. The test included Zylon targets covering the range from 30 to 45 yarns per inch, from one to 6 plies, gripped on two edges and four edges, with a range of pitch and roll angles for the fragment. Three of the simulations are shown in the animations below.

For each simulation we calculated the residual velocity of the fragment and from that, the energy dissipated by the target. For calculations in which the fragment did not penetrate the target the residual velocity was set to zero. The figure below shows a comparison between the calculated and measured energy dissipated for 15 of the gas gun tests. A linear fit through the data passing through the origin gives a slope of 1.03 and an R2 value of 0.98. The average of the errors in calculated energy dissipated for the simulations is +4.4% of the total kinetic energy of the fragment with a standard deviation of 8.7%. Although the design model does a good job overall, it tends to overpredict the dissipated energy for the tests with four edges gripped.

Summary Of The Design Model

The design model as implemented in LS-DYNA is very easy to use, with a limited number of physically-based input parameters, and runs in a few minutes on an 4-processor SGI Origin 200. It has done a reasonably good job for simulating the gas gun tests, but it has some obvious limitations in terms of modeling failure mechanisms such as yarn pull out. We need to investigate its utility for other applications such as fuselage impact tests.

A description of the fragment barriers development program can be found on the Fragment Barrier Page A description of the testing of fabric materials and barrier concepts can be found on the SRI International Fragment Barrier Page

The above analyses were performed using LS-DYNA. developed by the Livermore Software Technology Corporation (LSTC).

LS-DYNA. - General Purpose Transient Dynamics Finite Element Program.

References

Simons, J.W., D.C. Erlich, and D.A. Shockey, 2001, "Finite Element Design Model for Ballistic Response of Woven Fabrics," 2001 International Ballistics Symposium.
Abstract
Shockey, D.A., D.C. Erlich, and J.W. Simons, 1999, "Lightweight Fragment Barriers for Commercial Aircraft," 18th International Symposium on Ballistics, pp. 1192-1199.
Abstract