Cyril Gruau and Didier Picart- Numerical Prediction of High Explosive Ignition Under Low Velocity...

8/3/2019 Cyril Gruau and Didier Picart- Numerical Prediction of High Explosive Ignition Under Low Velocity Impact

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F O U N D A T I O N S O F C I V I L A N D E N V I R O N M E N T A L E N G I N E E R I N G

No. 1 2008

Publishing House of Poznan University of Technology, Pozna 2008

ISSN 1642-9303

Cyril GRUAU, Didier PICART*

CEA Le Ripault, F-, 37260 Monts, France.

NUMERICAL PREDICTION OF HIGH EXPLOSIVE

IGNITION UNDER LOW VELOCITY IMPACT

Received: 21 July 2008

Accepted: 7 November 2008

In the framework of low velocity impact studies, dedicated to safety analyses of

plastic bonded explosives (PBX), we propose a numerical tool, designed for predicting

the ignition of a HMX (high melting point explosive) based composition. The major

results are the use of a concrete-like constitutive law for the PBX and an efficient imple-

mentation of an ignition criterion. It has been shown that the calculation tool is able to

accurately predict the results when the ignition is diluted. For localized ignition into

shear bands or macro cracks, some differences between numerical and experimental

results have been discussed..

Key words: energetic materials, ignition, finite element simulations, cracks

1. INTRODUCTION

The high explosive (HE) of interest is composed of a poly-dispersed dis-

tribution of HMX grains (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) which

are mixed with several per cent of polymeric binder. An isostatic compaction

process is used to reduce the porosity. Its mechanical response is similar to the

behavior exhibited by PBX9501 (95%wt. HMX, 5%wt. binder) or EDC37

(91%wt. HMX, 9%wt. binder)- two similar compositions [1].

Pyrotechnic devices during their lifecycle are subjected to normal load-

ings such as temperature variations or transport induced vibrations or accidental

* Corresponding author. Tel.: +33-(0)2-4734-4173; fax: -.

E-mail address:[email protected] (D. Picart)


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34 Cyril Gruau, Didier Picart

loadings and among these a specific attention is focused on low energy impacts.

The artificial difference between low and high energy impacts is due to the vio-

lence of the obtained reaction. For high energy mechanical insults, the energetic

material is subjected to a pressure above 1 GPa applied during a short character-

istic time of 1 s. A shock-to-detonation transition is exhibited leading to a vio-

lent burst. Such a mechanism was widely studied in the last century and engi-

neering models can be found to predict its occurrence.

For low velocity mechanical impacts, ignition of the energetic material

can also be observed, leading to a combustion or a deflagration. Several impact

conditions could generate this reaction. Here, we will limit our attention to one

kilogram projectiles (steel made, with a 60 mm diameter, hemispherical or flatnosed), launched at 50-100 m/s on axisymetrical targets (the HE being confined

between two metallic plates with a thickness ranging from 1 to 20 mm) [2,3].

Numerical simulations and measurements have shown that a mean pressure of

few kilobars is applied and the reaction is observed approximately 50 s after

impact.

Safety analyses of pyrotechnic structures involve many parameters such

as target configuration (shape, materials and boundary conditions) and mechani-

cal loadings (characteristics of the projectile and its movement law), which pre-

vents us from dealing only with the experimental techniques. On the other hand,

the prediction of the violence of the reaction is hardly tractable. Hence, we have

chosen to focus our attention on the ignition stage which is the very first phe-

nomenon that must be correctly predicted in the framework of safety analyses.

The aim of this paper is to describe the numerical tool designed for the

ignition prediction. This tool is based on a finite element code, a concrete-like

constitutive law whose parameters have been determined for the studied mate-

rial and an ignition threshold. Then, the needs related to numerical techniques

and constitutive laws in order to deal with localized ignition are detailed and

discussed.

2. A NUMERICAL TOOL FOR IGNITION PREDICTION

2.1. Ignition thresholdDeflagrations and detonations induced by low velocity impacts are not the

results of shock-to-detonation transitions, since the pressures generated by these

impacts are too low. We actually considered that the material ignites when a

sufficient mechanical energy is locally dissipated in the vicinity of defects

within the HE microstructure. Investigations are being made to identify and

model the involved hot spot mechanisms. Among all the local mechanisms pro-


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Numerical prediction of high explosive 35

posed by Field et al. [4], an ignition by low velocity impact is probably caused

by frictional heating of the preexisting or induced closed micro cracks [5].

When the levels and the durations of the pressure and plastic shear rate

are sufficient, frictional heating is assumed to lead to an ignition. A few ignition

criteria have been proposed, relying on the macroscopic pressure (denoted p

for its positive part) and macroscopic plastic shear strain rate pl . Here, we

adopted a criterion based on the work of Browning and Scammon [6] in the

following equation

1d)()(1

0

3

2

***

=

pl

t nn

ig

ig

p

p

t

t

c

(1)

where the time to ignition is igt , *c is the threshold value, *t is a characteristic

time, *p is a characteristic pressure.

The Browning and Scammon ignition criterion [7] is based on the dissipa-

tion generated by friction between grains. Knowing (i) the macroscopic pressure

and the macroscopic plastic shear rate determined by a numerical tool simulat-

ing the impact and (ii) assuming a simple microstructural arrangement of the

grains (for Browning and Scammon the HE microstructure is a 3D regular

sphere packing of identical HMX grains) the surface area of the contact between

two spheres, the contact pressure, and the relative velocity of the two spheres

involved in the contact can be calculated. The last two quantities determine the

dissipation at the local scale.

Then, the dissipation enters into the heat equation as a source term. Local

heating is computed adding the heat released by the HE decomposition. A nu-

merical parametric study has been made by Browning and Scammon assuming

diluted hot-spots. They have shown that a power law relates the dissipation, the

surface contact between the particles (the hot-spot) and the time to ignition [7].

This parametric study determines the value of the exponent n (equal to 0.447).

When (1) is met, ignition is assumed to occur.

2.2. Finite element codeThe ignition criterion relies on the computation of the macroscopic pres-

sure and the macroscopic plastic shear rate, inside the high explosive, seen as a

continuum. Several material models and several types of simulation software

have been used to compute the stresses and strains inside a target impacted at

low velocity. For the first test reported in the literature (called Steven tests),

Dyna2D was employed with a double Jones-Wilkins-Lee equation of state, in


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conjunction with a reaction model [8]. Dyna2D and Spronto were also used with

a statistical crack mechanics model [9]. Then, 3D computations were performed

using LS-Dyna and ALE3D whilst taking a perfect plasticity model for the ma-

terial [10-11].

Fig. 1: Isotropic hardening curve in tension and compression (unconfined). Measure-

ments were made up to a strain value of 20% (see Fig. 2). It means that the softening

branch in compression (negative hardening) is assumed

The finite element code Abaqus/Explicit was chosen to run the computa-

tions. This choice was motivated by several reasons. Firstly, we had to deal with

continuous solids exhibiting strong nonlinear behavior under finite strains.

Hence, a Lagrangian finite element method was convenient for our purpose.

Secondly, during such impacts, the strain rate could overcome 105s

-1meaning

that we are in the fast transient dynamic domain. The contact between the pro-

jectile and the target was strongly nonlinear and we focused our attention on an

explicit time integration scheme. Thirdly, preliminary tests on low velocity im-

pacts showed that Abaqus Explicit exhibited a better energy conservation, a

stronger stability and broader functionalities than hydrocodes [12].

2.3. Constitutive behaviorsThe internal microstructure of HE is close to the one observed for con-

crete materials (coarse grains embedded into a matrix formed by the fine crys-

tals and the binder). All the mechanical tests made on this material have exhib-

ited similar trends for the two class of materials. A nonlinear response is regis-

tered during uniaxial compressive tests and the maximum stress is six times the


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tensile failure stress. If a confining pressure is applied, the failure stress in-

creases and the behavior turns to a ductile one.

Fig. 2: Measurements vs. model response for several triaxial tests. The order of magni-

tude of the pressure ranging from 100 to 300 MPa during impact, and the strain ranging

from 50 to 100%; the conformity between the model and the data is acceptable

Table 1. Material parameters used for the HE composition (same notation as

Abaqus/Explicit documentation)

parameters value

density 1800 kg.m-3

Youngs modulus 4 GPa

Poissons ratio 0.4

Friction angle (=tg) 20

Dilation angle 1

Eccentricity e 0.1

Initial yield stress at zero pressure 5 MPa

Compressive stress softening slope - 53 MPa

Hardening in compression see Fig. 1

Hardening in tension see Fig. 1


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The model proposed by Lubliner et al. [13] and Lee and Fenves [14] is

used here (native in Abaqus/Explicit). It involves a hypoelasticity law relating

the effective stress tensor to the total and plastic strain rate tensors, a pressure

dependent yield function (linear Drucker-Prager criterion mixed with the influ-

ence of the third invariant of the stress tensor) and non-associated time inde-

pendent plasticity with isotropic hardening. Dilation, dissymmetry between the

tensile and the compression states of stress altogether with isotropic damage, are

taken into account. For the sake of simplicity, readers are invited to refer to the

Abaqus documentation for a detailed description of the constitutive law (same

notation used in this paper). Material parameters are given in Table 1 and Fig-

ure 1. A comparison between the model response and triaxial experiments isgiven in Figure 2.

Some features of the material behavior have not been accounted for such

as damage anisotropy due to the oriented microcracking, rate dependent plastic-

ity, a cap yield surface describing compaction at high pressure and a transition

between brittle and ductile behavior. Strain softening has been taken into ac-

count assuming a negative hardening evolution (not measured).

Some other materials were used in the target/projectile configurations

such as stainless steel, Plexiglas (PMMA), Teflon (PTFE) and transparent glass.

Glass and Plexiglas are supposed to stay in the elastic regime during the impact.

An elastic perfectly plastic constitutive law was applied for steel and isotropic

hardening was added for PTFE. Parameters are given in Table 2.

Table 2. Parameters for the materials used during the impact experiments

parameters steel Plexiglas glass Teflon

Density (kg.m-3) 7850 1190 2510 2200

Youngs modulus (GPa) 210 3.3 81 0.46

Poissons ratio 0.3 0.34 0.28 0.46

Initial yield stress (MPa) 400 9

Ultimate yield stress (MPa) 400 20

2.4. Diffused ignition: numerical vs. experimentsIn (1), the ignition threshold c* must be calibrated using an experimentaldatabase and numerical tests simulations. Four configurations were used to fit

the threshold (Fig. 3). Table 3 gives the velocities enclosing the experimental

velocity thresholds.

Previous impact test configurations were dedicated to a velocity threshold

determination. However, their design prevents us from determining the ignition

location and the ignition time of reactive cases. That is the reason why a new


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configuration with a transparent visualization window was designed (Fig. 4

left), allowing fast video recording.

Table 3. The highest velocities leading to non reactive tests and the lowest one leading to

reactive tests for the four configurations used to calibrate the ignition criterion

configurations highest non reactive velocities lowest reactive velocities

target 1 projectile 1 77 m/s 84 m/s




A round nosed projectile was launched at 103 m/s and impacted the struc-

ture. A punctual ignition is observed at 60 s after the impact (Fig. 5). This ex-

perimental flashing phenomenon is due to local ignition, which is roughly lo-

cated at the target center and near the HE rear face.

Numerical results have been obtained using 2D axisymetric simulations

of the configurations using reduced integration linear finite elements. The char-

acteristic size of the elements has been fixed to 250 m after a convergence

study (the diameter of the target is typically equal to 200 mm depending on the

configuration used). Frictionless contact was used except between HE and steel

where a 0.2 constant friction coefficient was adopted. The same conditions wereused irrespective of the result presented in this paper.

Numerical results obtained for the configuration reported in Figure 5

show very good accordance with the experimental observation. The ignition is

predicted 53 s after the impact located at the rear face of the HE and dot-

shaped. This comparison validates the capability of the numerical tool to predict

diffuse ignition inside a target. We are going to see that localized shear banding

and fracture could develop the predictions of which in these cases could be dif-

ficult.

3. NEEDS FOR NEW TECHNIQUES FOR LOCALIZED

IGNITION

Experiments reported previously in this paper and used to determine the

ignition threshold involve high confining pressure and high shear strain rate, but

for diffused damage into the sample. Finite element codes are known to be able

to accurately and efficiently handle such a situation. It is also admitted today

that numerical difficulties appear with strain localization, shear banding and the


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development of macro cracks into the structure. Mesh dependencies have been

reported and are still studied by researchers [15].

Fig. 3. Four axi-symmetrical impact test configurations (deformed geometries at 100 s)

are used for determining an ignition threshold

Fig. 4: Two new axi-symmetrical impact test configurations (deformed geometries at

100 s) used to determine the ignition time and location


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Unfortunately, intense shear loading is known to ignite HE materials. We

are going to report some data proving the relationship between localized me-

chanical fields and the ignition. Then, some of our numerical simulations will be

discussed.

Fig. 5: Video recording of the ignition observed on HE rear face and finite elementsimulation of the test (53 s after the impact). Values of the threshold exceeding 1 (in

white) delimit the ignited zone

3.1. Experimental evidence of localized ignition

Skidmore et al. [16] reported an observation made on a plane piece of HE(25x20x2 mm), laterally confined by metallic or glass pieces. On one of the

faces of the sample, a plunger is used to impact the material (Fig. 6). Recovering

the sample allows to made microstructural observations. If a flat-nosed projec-

tile is used, a wedge structure develops ahead of the plunger (Fig. 6). Several

shear bands developing into the sample have also been observed, sometimes

with large relative displacements of the two lips of intra-granular microcracks or

macrocracks but without any manifestation of the ignition. However, observa-


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tions have also proved that the decomposition mechanism was at work at the

leading wedge of the cone.

Fig. 6: Schematic of the punch test reported by Skidmore et al. [16]. A trace of ignition

can be observed at the microstructure level, located along the cone

These observations have been confirmed by Henson et al. [17] with light

measurements using a camera (Fig. 7). If the leading wedge of the cone is iden-

tified as a zone where the decomposition starts, a vertical crack is also observed,

possibly formed by gas spreading into the sample.

The last experiment we would like to report here is the test made using

the second configuration mentioned in Figure 4 [7]. In order to force shear bandgrowth into the sample, a sharp-edge plunger was put at the surface of the HE

piece, and impacted by a flat-nosed projectile. This configuration was numeri-

cally designed to maintain a high level of pressure in the zone where shear

bands have been expected, that is, starting from the plunger edge and propagat-

ing to the rear face of the HE. The transparent back confinement was used to

detect the light emission. Records show a ring-shaped ignition area indicating

once again the localization of the ignition.


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Fig. 7: Self-illumination of the sample, 210 s after impact of a flat-nosed projectile.

Position of the plunger at rest is indicated by the gray rectangle

3.2. Discussion on the needsA question remains about the nature of the sheared structure. Do we

need to model a macro crack to allow a large relative displacement and ignition

by a surface friction mechanism? Could the material be ignited only inside a

shear band where a relative displacement between crystals or contacting lips of

micro crack is low? The previously reported experiments cannot be used to an-

swer these questions. More data are needed e.g. via temperature measurements

made during the interrupted impact tests (to avoid macro crack formation).Experiment detailed in Figure 8 has been compared to numerical simula-

tions (Fig. 9). 55 s after the impact, a ring-shaped ignited zone is observed at

the rear face of the HE sample. The diameter of this ring was identical to the

diameter of the reacted ring viewed in the first picture of Figure 8. Unfortu-

nately, the ignition is predicted earlier during the simulations, starting from the

edge of the plunger and propagating to the rear face. There are two conse-

quences of this: first, the ignition starts at the edge and propagates inside the


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shear band (light is then assumed not to cross the sample, which is a strong as-

sumption). Second, shear-compression behavior is not well described and/or

numerical difficulties take place.

Fig. 8. High speed recording of the second test case mentioned in Figure 4. A ring of

light is observed on the rear face of the HE sample, 60 s after the impact

To determine the shear-compression response of the material, dedicated

mechanical tests are currently studied. The existence of a post-pic behavior on

the stress-strain curve is a question to be addressed. Moreover, our simulations

do not involve any localization limiter. A regularization technique is probably

needed with its consequences: the experimental determination of the material

internal length and the attenuation of intense gradients which could lead to igni-

tion.

An example of mesh dependency is given in Figure 10. The target #3(Fig. 3) is impacted at 61 m/s. Increasing the mesh density by a factor of 2 gives

a completely different crack network and a different strain intensity along these

cracks. These simulations have been made using the same adjustments of the

code (distortion control, Lagrangian kinematic, material parameters). If the igni-

tion were predicted along the axisymetric axis (and for approximately the same

time step), its vertical position would change with the mesh refinement. We

have observed that an increase of the distortion control setting allows a wider


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time interval without a simulation tilt. This option of Abaqus/explicit acts as a

numerical limiter of localization.

Fig. 9. Numerical simulation of the second configuration of Figure 3, 55 s after the

impact. The ignition is detected along a ring, at the rear face of the HE piece. Unfortu-

nately, a shear band develops earlier from the plunger edge, indicating wrong time to

ignition and location

On the other hand, some HE are known to be less sensitive than the mate-

rial studied here. It is the case of TATB-based explosive compositions (for ex-

ample PBX9502 made of 95%wt. triamino-trinitrobenzene). Then, the highestvelocities must be taken into account. People performing perforation simula-

tions of structures such as concrete walls usually involve an eroding technique

to treat distorted elements. Here, mechanical fields are needed in those elements

throughout the whole simulation so as to compute the ignition criterion. The

erosion method will not be useful for this case and a specific method has to be

developed. The remeshing techniques and extended finite element method (with

a surface friction law) could be of great interest in our case to treat continuous


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to discontinuous evolution of the problem with a discrete number of cracks.

Beyond this stage, a numerical method is needed.

Fig. 10. Equivalent plastic strain fields (axisymetrical section of the HE sample), 75 s

after the impact (target 3, Fig. 3). Influence of the mesh density (doubled from one map

to the other). Same scale for the strain except the extra upper bound of each map

4. CONCLUSION

In the propellant, explosive and pyrotechnic community, an improvement

of safety of pyrotechnic devices is of unceasing interest. Even if numerous ex-

periments have been performed to detect ignition and the violence of reactionswhen a HE is submitted to a low velocity impact, the occurrence of such a catas-

trophic event is not yet well understood today.

A numerical tool has been proposed in this paper in order to predict the

ignition of a HMX-based explosive composition. This tool is based on a finite

element code, a concrete-like constitutive law, an ignition criterion and several

impact experiments to determine the criterion level. An acceptable conformity is

found between the numerical and experimental responses for diffuse ignition. A


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lot of work must be done in the future to improve the prediction. The main chal-

lenges are: (1) a better characterization of the behavior of the explosive compo-

sition when submitted, at the same time to high strain rate and high confining

pressure, (2) a detailed comprehension of the microstructural mechanisms lead-

ing to local heating and ignition of a distribution of hot-spots, (3) the develop-

ment of measurements allowing a real-time observation of heating and ignition

at the microstructural scale.

Some unacceptable differences have been observed when ignition is sus-

pected in localized shear bands or macro cracks. Mesh dependencies (which

could be associated to the softening behavior of the material) have been ob-

served with a variation of the location of the ignition area as the major conse-quence. On the other hand, some numerical method settings as the kinematic

assumption or how the code controls the distortion of the mesh have an influ-

ence on the results and prevent us from making an accurate prediction of the

time to ignition and the location of the first ignition.

Future works are then devoted to a better description of the continuous to

discontinuous transition (using remeshing techniques and/or extended finite

element method) and to replace the erosion method which implies the loss of the

mechanical fields needed to detect the ignition.

ACKNOWLEDGEMENTThe authors wish to thank the personnel of Reactive Characterization Facility,

especially F. Delmaire-Sizes, for providing experimental results.

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