Finite Element Design Model

FINITE ELEMENT MODELING: DESIGN MODEL
SRI International is performing research under contract to FAA to protect critical aircraft components against fragments resulting from uncontained failure of a turbine engine. As part of this program we are developing computational models to perform finite element analyses of fragment impact. The impacts are highly dynamic events, including strong nonlinear effects such as impact, penetration, and large deformation and failure of materials. We use analysis to guide and understand the impact experiments, and we use the results of the experiments to guide development of the models. To perform the analyses, we are developing a detailed material model for yarns and fabric, and a design model that is described here.

The design model that 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-DYNA3D 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

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

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.

Test 20 1 ply Zylon Gripped on 4 edges 25 g fragment

Test 29 4 plies Zylon Gripped on 4 edges 96 g fragment

Test 58 1 ply Zylon Gripped on 2 edges 25 g fragment

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.

RESULTS FOR SIMULATED GAS GUN TESTS
SUMMARY OF DESIGN MODEL
The design model as implemented in LS-DYNA3D 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.

Contact Us
Don Shockey
Director, Center for Fracture Physics
Phone: 650-859-2587
Email: donald.shockey@sri.com