HYPERVELOCITY IMPACT SIMULATION ON HARD BALLISTIC … · 2019-02-11 · There are many suitable...

HYPERVELOCITY IMPACT SIMULATION ON HARD BALLISTIC COMPOSITES

Dr. M. May, T. Lässig

(Fraunhofer-Institute for High-Speed-Dynamics, EMI, Germany)

Abstract Over the last years an increasing amount of polymer-matrix composites have been used in ballistic armor systems, for example in flak jackets or vehicle protection. This class of materials is characterized by an excellent weight specific stiffness and ballistic performance. Typical armor systems include Aramid fibers (Twaron®, Kevlar®), PP-fibers (Tegris®, Curv®) or ultra-high molecular weight polyethylene (UHMWPE) fibers (Dyneema®, Spectra®). In particular, systems based on UHMWPE fibers have gained a lot of interest due to their extraordinary ballistic performance. Experimental testing at high and hypervelocity impact conditions is a very difficult and financially expensive task. The design process of multi-material armor systems therefore requires predictive numerical models for describing the response of UHMWPE composites under shock loading. In this paper a modeling approach for UHMWPE composites is presented allowing the simulation of ballistic impact onto plat panels. The stress tensor is decomposed into a hydrostatic and a deviatoric stress tensor. For low pressure, the material response is dominated by the deviatoric component of the stress tensor. The deviatoric stress tensor is described by the linear-elastic orthotropic properties as well as potential plastic flow and strain hardening. For high pressure, the stress tensor is dominated by the hydrostatic stress component. The hydrostatic stress component can be described by the shock equation of state. The model is then calibrated for a selected hard ballistic composite (DYNEEMA® HB26) using an available extensive experimental data base allowing accurate description of the linear-elastic, plastic, and shock response for this particular composite material. Hypervelocity impact experiments were performed on DYNEEMA® HB26 panels for impact velocities ranging from 2000 m/s up to 6600 m/s. Impact velocities and residual velocities were measured. The tests were modeled using the commercial FE package ANSYS AUTODYN. The numerical predictions capture the main mechanisms observed during hypervelocity impact testing. Also, the predicted residual velocities behind the target are in good agreement with the experimental evidence.

NAFEMS World Congress 2015 inc. the 2nd International SPDM Conference | San Diego, CA, 21-24 June 2015

nafems.org NAFEMS World Congress 2015 inc. the 2nd International SPDM Conference | San Diego, CA, 21-24 June 2015

1. Introduction Over the last years an increasing amount of polymer-matrix composites have been used in ballistic armor systems, for example in flak jackets or vehicle protection systems. This class of materials is characterized by an excellent weight specific stiffness and ballistic performance. Typical armor systems include Aramid fibers (Twaron®, Kevlar®), polypropylene fibers (Tegris®, Curv®) or ultra-high molecular weight polyethylene (UHMWPE) fibers (Dyneema®, Spectra®) [1]. In particular, systems based on UHMWPE fibers have gained a lot of interest due to their extraordinary ballistic performance [2, 3, 4]. Traditionally, the assessment of the ballistic performance of protective materials is done by impact testing. However, experimental testing at high and hypervelocity impact conditions is a very difficult and financially expensive task. For the design process of multi-material armor systems it is therefore desirable to possess modelling capability allowing an accurate prediction of the response of UHMWPE composites subjected to these extreme loading conditions. There are many suitable modeling approaches for composite materials subjected to low or high velocity impact [5, 6, 7] considering orthotropic material properties and failure criteria. However, for hypervelocity impact, an additional aspect has to be considered: the shock wave emanating from the point of impact. This is usually done using an equation of state describing the relationship between pressure, density and energy of the material [8]. In the first part of the paper a physically based modeling approach is presented allowing prediction of the response of UHMWPE cross-ply composites subjected high- and hypervelocity impact loading. A calibration strategy for the model is outlined in the second part of this paper. Finally, the model is validated against hypervelocity experiments conducted in an impact velocity range of 2 km/s to 7 km/s. 2. Material The material of interest for this paper is Dyneema® HB26. This UHMWPE material provides an excellent strength to weight ratio and ballistic performance making it interesting for application in armor systems such as helmets, wests or armor panels for vehicles and aircraft. The material consists of UHMWPE fibers manufactured in a gel-spinning process followed by hot drawing. Fibers are then spread flat



and subsequently coated with polyurethane (resin volume fraction 17 %). Finally, the resulting cross-ply sheets (laminate [0/90]n) are hot pressed resulting in panels of thicknesses up to 50 mm. The manufacturing process for Dyneema® HB26 is described in detail by Russell et al. [9]. The cross-ply structure of Dyneema® HB26 can be visualized by dark field microscopy as shown in Fig. 1. The structure shows layers of 0°- and 90°-direction of four fibers through the thickness each.

Figure 1: Microsection analysis of Dyneema® HB26, dark field microscopy [10].

3. Model description The modelling strategy adopted in this paper follows the suggestions by Clegg et al. [12] and Wicklein et al. [13]. The stress tensor is decomposed into the deviatoric stress tensor and the hydrostatic stress tensor. The deviatoric stress tensor describes the orthotropic material properties, plasticity and failure. The hydrostatic stress tensor describes the pressure dependent properties governed by the equation of state. The orthotropic material properties are defined as follows:



⋅

−−

−−

−−

=

12

13

23

33

22

11

12

13

23

3322

23

11

13

33

23

2211

12

33

31

22

21

11

12

13

23

33

22

11

100000

01

0000

001

000

0001

0001

0001

τττσσσ

νν

νν

νν

γγγεεε

G

G

G

EEE

EEE

EEE

(1)

Following Chen et al. [14], a quadratic yield function and an associated flow rule are used for describing the orthotropic hardening seen in shear dominated loading scenarios.

( )kaaaa

aaaaaf ij

=++++

++++=21266

23155

22344331113

33222322111223333

22222

21111

2222

22

σσσσσ

σσσσσσσσ (2)

The constants aij and hardening parameter k define the shape and size of an ellipsoid describing the plastic flow curve in stress-space.

A three-dimensional formulation of the classical Hashin criterion was used for describing failure of the composite.

1

2

,31

31

2

,12

12

2

,11

11 =

+

+

failfailfail σσ

σσ

σσ

(3)

1

2

,23

23

2

,12

12

2

,22

22 =

+

+

failfailfail σσ

σσ

σσ

(4)

1

2

,31

31

2

,23

23

2

,33

33 =

+

+

failfailfail σσ

σσ

σσ

(5)

Post-failure behavior is described by an energy based approach. A linear softening law is applied reducing the element stress to zero as shown in Fig. 2. The strain at failure is calculated from the element length and the fracture energy. As a consequence, the formulation is insensitive to mesh size effects.



Figure 2: Post-failure softening.

The shock response of Dyneema HB26 is described using a polynomial form of the equation of state [10]

( ) eBBAAAP 0103

32

21 ρµµµµ ++++= , (6)

where

10

−=ρρµ (7)

and

µµ

++

=Γ1

10 BB. (8)

Eq (6) describes a polynomial equation of state with the current density ρ, the reference density ρ0 and internal energy e. The effective bulk modulus A1 is calculated from the orthotropic stiffness. The coefficients A2 and A3 are calibrated against flyer plate experiments [12]. B0 and B1 are calculated using the definition of the Mie-Grüneisen Gamma in eq (8). 4. Calibration strategy The model described in the previous sections can be divided into four main sections: linear orthotropic elasticity, plasticity, failure with post-failure softening and equation of state. The following subsections describe the required experimental programme for calibrating the material model.



a. Orthotropic elasticity Elastic constants are determined using tensile tests performed on a servo-hydraulic test machine. Unlike conventional carbon/epoxy composites, UHMWPE composites cannot be tested in tension using force-fit clamped standard specimens. This is due to the fact that the connection between the layers is fairly weak resulting in sliding of the individual plies. This was compensated by devising a new test setup utilizing a set of bolts to ensure form-fit load introduction and prevent sliding of interior plies. Two different widths of the gage section were chosen. For a material orientation of [0/90]n, the width was 4 mm in order to reduce the required force to breaking the specimen. For a material orientation of [+45/-45]n, the width of the gage section was 20 mm, see Fig. 3. The width was increased for this in-plane-shear test in order to allow reorientation of the fibers during loading.

Figure 3: Specimen for tensile tests of UHMWPE composites [10].

The forces were recorded using a 50 kN load cell. Digital image correlation was used in order to measure the true strain on the specimens. The solid lines in Fig.4 show the measured true stress-true strain curves for Dyneema HB26. The dashed line shows the model representation of the stress-strain behavior.



Figure 4: True stress – true strain curve for [0/90]n layup [10].

The through-thickness stiffness is a difficult parameter to determine. In this particular case, the stiffness in through-thickness direction was calculated from acoustic bulk sound speed measurements and material density.

2033 BcE ⋅= ρ . (9)

Another important calibration test is the out-of plane shear test as shear plugging is an important failure mode occurring in high- and hypervelocity impact situations. The out-of-plane shear properties were measured using a punch test as described in [12, 10]. Here, the composite material is placed between a loading fork and a fixed support. The fixed support is almost as wide as the loading fork thus causing localized shear failure in the gap between the loading fork and the fixed support. b. Plasticity

The nine plasticity coefficients aij described in eq (2) are typically calibrated using the test with the biggest amount of plasticity [15]. For this particular case this is the tensile test on coupons with stacking sequence [+45/-45]n, see Fig. 5. One of the parameters can be set to an artificial value. For convenience a66 was assigned a value of 1. The plasticity coefficients a11 and a22 follow from coupon tests on laminates



with stacking sequence [0/90]n. a33 was taken from through-thickness tension tests. The mixed coefficients a12, a13 and a23 could not be determined experimentally. In order to avoid significant hardening effects under combined loading states, these coefficients were set to values near zero. The remaining coefficients a44 and a55 were set equal to a66.

Figure 5: In-plane shear response measured using [+45/-45]n laminates.

c. Failure and post-failure The failure strengths required for failure prediction according to eq (3) -(5) are obtained from the tension and shear tests described before. Post-failure behavior is described using an energy-based approach. In [16] numerical sensitivity studies showed that the most critical fracture toughness parameter was the resistance to mode I delamination. Double Cantilever Beam tests were therefore performed to measure the mode I delamination fracture toughness. These investigations showed that the specimen geometry described in standard ASTM D5528 [17] is not suitable for determining the mode I interlaminar fracture toughness of Dyneema HB26. Using the specimen described in the standard it was not possible to propagate a crack as the arms of the specimen would fail in through-thickness direction. This was compensated by using extremely thick DCB specimens of thickness 26 mm as shown in Fig. 6.



Figure 6: Setup for measuring the mode I interlaminar fracture toughness using extremely thick DCB specimens.

The load was recorded using a 50 kN load cell. The test was filmed using a high-speed camera system. Markers applied onto the specimen prior to testing allowed tracking of the crack propagation. The mode I fracture toughness was determined as GIc = 790 J/m². Fracture toughness values for other loading directions were taken from micro-mechanical analyses presented by Grujicic et al. [18]. d. Equation of state

The equation of state is calibrated using data obtained from inverse flyer plate experiments. In this experiment a specimen of unknown material properties, here Dyneema® HB26, is accelerated to high velocities (200 m/s – 1100 m/s) using a powder gun. This specimen then impacts a target of well-characterized material as shown in Fig. 7.

Figure 7: Setup for inverse flyer plate experiment [10].

Upon contact of the flyer plate and the target, pressure waves emanate in the contact zone and start propagating through all plates. Each time,



the wave arrives at the free edge it is reflected. At the same time, the free surface is accelerated as shown in Fig. 8. This jump in free surface velocity can be measured using a laser interferometer system.

Figure 8: Free-surface velocity during inverse flyer-plate experiments. Solid lines are experimental data, dashed lines are simulated data.

Using the data obtained from the laser interferometer, the relationship between the shock velocity and the particle velocity (Hugoniot curve) can be derived following the standard text book procedure outlined in [19] or [10]. The equation of state can then be fitted to match the inverse flyer plate experiments. Fig. 8 shows the good correlation of experiment and simulation. 5. Application Hypervelocity impact experiments were performed using a two-stage light gas gun capable of accelerating small masses up to velocities of 10 km/s. In this example, Dyneema® HB26 targets of dimension 200 mm x 200 mm and an areal density of 15 kg/m² were mounted between two steel frames. A high-speed camera capable of recording up to 1



million frames per second was used to record the response of the target. The setup within the impact chamber is shown in Fig. 9.

Figure 9: Experimental setup for hypervelocity impact experiments on UHMWPE targets.

Hypervelocity impact experiments were performed using spherical aluminum projectiles of diameter 6 mm accelerated to velocities ranging from 2.1 km/s to 6.6 km/s. The test setup was modeled in ANSYS AUTODYN. The impacting sphere was modeled using brick elements of length 1 mm. The UHMWPE target was modeled using brick elements of length 1.5 mm in the impact region. For reasons of computational efficiency a coarser mesh was used away from the impact zone. Fixed boundary conditions were imposed on the edges of the panel. The projectile was assigned an initial velocity. Gap contact was used between impactor and target. The finite element model used in the hypervelocity impact simulations is shown in Fig. 10.

1. barrel connector 2. steel frame 3. UHMWPE panel 4. viewing direction of the

high speed camera 5. debris collector 6. specimen holder

1 2

3

5 4

6



Figure 10: Finite element model used for hypervelocity impact simulations

The model is assessed on the basis of two criteria. Firstly, the correct representation of the experimentally observed phenomenology is assessed by comparing the shape of ejecta at certain discrete moments in time. Fig. 11 shows the experimentally observed debris cloud with the numerically predicted debris cloud for three discrete times after the initial impact for the example of an impact velocity of v0=6.5 km/s. It can be seen that for all three moments in time (7 = 0.033 ms, t= 0.067 ms, t= 0.1 ms) the extent of the debris cloud is captured nicely by the finite element simulation.

Figure 11: Comparison of numerically predicted debris cloud and debris cloud recorded with high-speed cameras at an impact velocity of 6.5 km/s.



Secondly, for several impact velocities, the predicted residual velocities are compared against the residual velocities measured using high-speed cameras. Fig. 12 shows the excellent correlation between predicted and measured residual velocities. Both, the ballistic limit and the shape of the Lambert-Jonas curve are captured accurately.

Figure 12: Comparison of experimentally determined residual velocities and experimentally observed residual velocities for several impact velocities.

6. Summary and conclusions A modeling strategy for hypervelocity impact on UHMWPE composites was presented. The modeling strategy includes orthotropic linear elasticity, plasticity with strain hardening, an energy-based post failure description, and a polynomial equation of state. It was shown that measuring the properties required for calibrating the model for UHMWPE is not a trivial task. Several special setups have to be used in order to address the complex material behavior. The available ANSYS AUTODYN model was applied to a test case of hypervelocity impact on a hard ballistic composite (Dyneema® HB26). Both, the phenomenology and the residual velocity are captured accurately. The dataset used here, TL 3 [10], is going to be available to the public as a material database for AUTODYN soon.



7. Acknowledgements

The authors would like to thank DSM for providing the Dyneema panels.

8. References

[1] E. S. Greenhalgh, V. M. Bloodworth, L. Iannucci and D. Pope, "Fractorgraphic observations on Dyneema® composites under ballistic impact," Composites: Part A, vol. 44, pp. 51-62, 2013.

[2] B. Lee and J. W. J. Song, "Failure of spectra polyethylene fiber-reinforced composites under ballistic impact loading," J Compos Mater, pp. 1202-1226, 1994.

[3] L. Vargas-Gonzalez, S. Walsh and B. Scott, "Balancing the back-face deformation in helmets: the role of alternative resins, fibers, and fiber architecture in mass efficient head protection," in 26th International Symposium on Ballistic, Miami, FL, 2011.

[4] U. Heisserer and H. Van der Werff, "The relation between Dyneema fiber properties and ballistic protection performance of its fiber composites," in 15th International Conference on Deformation, Yield and Fracture of Polymers, Kerkrade, NL, 2012.

[5] J. Hou, N. Petrinic and C. Ruiz, "Prediction of impact damage in composite plates.," J Compos Sci Technol, pp. 273-281, 2000.

[6] A. Johnson, A. Pickett and P. Rozycki, "Computational methods for predicting impact damage in composite structures," Composites Science and Technology, vol. 61, no. 15, pp. 2183-2192, 2001.

[7] M. May, M. Nossek, N. Petrinic, S. Hiermaier and K. Thoma, "Adaptive multi-scale modeling of high-velocity impact on composite materials," Compos Part A - Appl S, pp. 56-64, 2014.

[8] M. Meyers, Dynamic behavior of materials, New York, NY: John Wiley & Sons, 1994.

[9] B. P. Russell, K. Karthikeyan, V. S. Deshpande and N. A. Fleck, "The high strain rate response of ultra high molecular-weight polyethylene: From fiber to laminate," International Journal of



Impact Engineering, vol. 60, pp. 1-9, 2013.

[10] T. Lässig, L. Nguyen, M. May, W. Riedel, U. Heisserer, H. van der Werff and S. Hiermaier, "A non-linear orthotropic hydrocode model for ultra-high molecular weight polyethylene in impact simulations," Int J Impact Eng, pp. 110-122, 2015.

[11] R. Clegg, D. White, W. Riedel and W. Harwick, "Hypervelocity impact damage prediction in composites: part I - material model and characterization," Int J Impact Eng, pp. 190-200, 2006.

[12] M. Wicklein, S. Ryan, D. White and R. Clegg, "Hypervelocity impact on CFRP: testing, material modelling and simulation," Int J Impact Eng, pp. 1861-1869, 2008.

[13] J. Chen, A. Allahdadi and C. Sun, "A quadratic yield function for fiber-reinforced composites," J Compos Mater, pp. 788-811, 1997.

[14] ANSYS, "AUTODYN composite modelling revision 1.3," Canonsburg PA USA, 2010.

[15] T. Lässig, W. Riedel, U. Heisserer, H. van der Werff, M. May and S. Hiermaier, "Numerical Sensitivity Studies of a UHMWPE Composite for Ballistic Protection," in 13th International Conference of Structures Under Shock and Impact (SUSI), New Forest, UK, 2014.

[16] ASTM, "ASTM D5528-13: Standard Test Method for Mode I Interlaminar Fracture Toughness of unidirectional Fiber-Reinforced Polymer Matrix Composites," ASTM International, 2013.

[17] M. Grujicic, P. Glomski, G. Arakere, W. Bell and B. Cheeseman, "Material modeling and ballistic resistance analysis of armor-grade composites reinforced with high performance fibers," J Mater Eng Perfom, pp. 1169-1182, 2009.

[18] I. Rohr, H. Nahme and K. Thoma, "Material characterization and constitutive modelling of ductile high strength steel for a wide range of strain rates," Int J Impact Eng, pp. 401-433, 2005.



HYPERVELOCITY IMPACT SIMULATION ON HARD BALLISTIC … · 2019-02-11 · There are many suitable...

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