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Explosive welding of metal plates
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
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Explosive welding of metal plates S.A.A. Akbari-Mousavi a,∗ , L.M. Barrett b , S.T.S. Al-Hassani b a
School of Metallurgy and Material Engineering, University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran b School of Mechanical, Aerospace and Civil Engineering, University of Manchester, P.O. Box 88, Manchester M60 1QD, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper describes a study of explosive welding of metal plates. The properties of a locally
Received 7 August 2006
prepared mix of 77/23 ammonium nitrate and fuel oil (ANFO) explosive and the dynamics of
Received in revised form
the plates are investigated and the results from welding tests presented. The strength of the
27 August 2007
clad plates is measured and ultrasonic inspection performed to identify and locate defects.
Accepted 3 September 2007
The welding process is simulated using a finite element-based computer model. A brief description of the modeling process is given along with the results from the simulations for comparison with measured parameters.
Keywords:
© 2007 Elsevier B.V. All rights reserved.
Explosive welding Pin contact method Simulations ANFO Titanium Stainless steel
1.
Introduction
Explosive welding is generally used to bond two dissimilar metal plates and is most often used when the combination of metals makes conventional fusion welding impractical. The technique enables very large sections of plate to be clad in a single operation. The quality of the joint is generally good with high mechanical strength and as it is a ‘cold method’ the bonded metals retain their pre-bond properties. The usual arrangement for explosive welding has the two plates (flyer and base) placed one above the other separated by a distance of about one or two times the thickness of the flyer plate. The explosive, usually in powder form is placed on the upper plate inside a surrounding wooden frame. Its type, thickness and composition are selected to yield a specific energy release and a specific velocity of detonation (the
∗
Corresponding author. Tel.: +98 21 82084096; fax: +98 21 88006076. E-mail address: [email protected] (S.A.A. Akbari-Mousavi). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.09.028
speed at which the detonation front travels across the explosive layer). The explosive is detonated using a small booster charge and detonator placed at one end of the frame. The expansion of the gaseous detonation products accelerates the cladding plate across the stand off gap forcing it to collide obliquely at relatively high velocity with the lower (base) plate, Fig. 1. On impact the two surfaces at the collision zone become plastic causing a jet of both metals to be ejected from between the two plates. This jet scours and cleans the surfaces of the plates leaving clean metal amenable to bonding. Whilst the explosive welding process is generally successful, expensive failures occur and often the cause(s) is unknown. To improve the understanding of the process a mathematical model to simulate the mechanics was developed. This paper describes an experimental study to obtain data to assist the development of this model. The charac-
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225
Fig. 1 – The explosive welding arrangement.
teristics of ammonium nitrate explosive are described, the dynamics of the plates examined and the results from several welding tests presented. A brief description of the modeling process is given along with results from the computer simulations.
2.
Experimental procedures
The experimental program was in two phases. The aims of the first phase were to determine the velocity of detonation
Fig. 2 – Pin contact method for measuring flyer plate velocities. (a) Experimental arrangement, (b) pin arrangement.
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of the explosive and the velocity of impact of the cladding plates for different combinations of stand off distance, plate thickness and explosive thickness. The second phase of the experimental program involved welding various thicknesses of titanium and stainless steel cladding plates to mild steel base plates.
2.1.
The explosive
As the velocity of detonation (VoD) of commercial explosives is generally too fast for successful welding of parallel plates most applications use a ‘slower’ powder mix of ammonium nitrate and diesel fuel oil (ANFO) and an inert material such as perlite or sand. In the tests reported here the explosive mix was approximately 75% ANFO 25% perlite. A booster charge made of about 250 g of the high explosive C4 was used to set off the ANFO. The thickness of the ANFO explosive layer covering the surface of the flyer plate used in the welding tests was in the range 80–235 mm. A few tests were also carried out using PETN explosive which has a relatively high VoD. As the explosive was not intentionally compacted during the explosive welding operation its average density depended on the thickness of the layer (the thicker the layer the more it settles and the greater its density). The average density of different thickness of explosive was measured by simply weighing a number of different size wooden boxes filled with the explosive. The base of the boxes was square, approximately 0.4 m × 0.4 m, and the heights were between 50 and 300 mm. In each case the explosive was levelled but not compacted. The increase in average density with thickness was generally found to be linear, increasing from 518 kg/m3 for a 50 mm thick layer to 532 kg/m3 for a 300 mm thick layer.
2.2. VoD
Measurement of flyer plate velocity and explosive
The relationship between collision angle ˇ, velocity of detonation VoD, collision point velocity Vw and plate impact velocity Vp is (see Fig. 1 and Crossland, 1982) Vp = 2Vw sin
ˇ 2
As the collision point velocity Vw is the same as the velocity of detonation of the explosive VoD, in parallel welding configurations, the VoD of the ANFO mixture can be estimated using a simple array of electrical contact pins, Fig. 2. Contact between the flyer plate and the pins completes electrical circuits which produce a series of alternating positive and negative voltage pulses which are displayed and stored on an oscilloscope, Fig. 3. Contact between the plate and pin 1 generates a negative voltage pulse, contact between the plate and pin 2 produces a positive voltage pulse, and contact between the plate and pin 3 generates another negative pulse and so on. The collision velocity is calculated from the distance between the axially spaced pins (1 and 2) and the time delay between the first two pulses on the signal trace. The downward velocity of the plate may be determined from the time delays between the following negative pulse and positive peaks and the difference in the relative heights of the pins.
Fig. 3 – A typical signal trace from the plate velocity measuring electronics.
2.3.
Plate welding
The plates listed in Table 1 were welded to 50 mm thick mild steel base plates. Each base plate, approximately 800 mm × 400 mm × 50 mm, was placed directly onto the smooth sandy floor of the firing range and the flyer plate (with slightly larger dimensions to create a small overlap) supported above it on small equal height spacers. The separation of the plates varied between 3 and 24 mm. Stages in the setting up procedure are shown in Fig. 4. After welding the plates were subjected to ultrasonic examination and measurements were made of the shear strength of the bond using the simple jig shown in Fig. 5. The samples were subjected to a shearing force by mounting the jig upright in the jaws of an Instron testing machine and applying the load vertically.
3.
Modeling the explosive welding process
A computer model of the welding process was developed using the 2D commercial general purpose finite difference software package, AUTODYN (Anon., 1997). The plates, the explosive, the sandy base and the air surrounding the plates were divided into subgrids made up of rectangular cells, their material properties being extracted from program libraries. Each subgrid could be analyzed using one of several different numeric processors (e.g. Lagrange, Euler, Shell, etc.). The Lagrange processor fixed the material inside the cells and was used for the plates: the Euler processor allowed the material to move from cell to cell and was used to process the explosive. Time steps for the analysis were automatically computed to ensure accuracy and stability of the solution. Parameters such as pressure, velocity, acceleration, stresses and strains, displacement energy, etc., were calculated for each cell and made available at the end of every time step. Contour or vector plots and graphs to show the history of a parameter were generated on demand. The mesh size of about 2 mm was chosen for mod-
Test no. 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Flyer plate material Stainless steel, 314 Stainless steel, 314 Stainless steel, 314 Quench hardened high strength steel, 4340 Mild steel, EN1 Titanium Titanium Titanium Titanium Titanium Titanium Titanium Titanium Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel
Explosive
Dynamic angle, ˇ (◦ )
Flyer plate thickness (mm)
Measured flyer plate velocity (m/s)
Stand off distance (mm)
Explosive thickness (mm)
Measured VoD of different types of explosives (m/s)
PETN PETN PETN PETN
15 Parallel Parallel 15
10 10 20 10
350 560 350 350
0 10 20 0
9 9 75 9
7450 7450 5170 7450
PETN ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture
15 Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel
10 3 3 6.35 6.35 6.35 6.35 6.35 6.35 3 3 6 6 6 6 12 12 12 12
350 460 610 300 335 450 540 620 265 280 380 210 250 300 330 245 300 340 400
0 3 6 6 3 6 9 12 6 3 6 3 6 9 12 6 12 18 24
9 107 107 80 135 135 135 135 153 107 107 135 135 135 135 235 235 235 235
7450 2050 2050 2000 2250 2250 2250 2250 2175 2050 2050 2250 2250 2250 2250 2400 2400 2400 2400
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Table 1 – Welding tests with PETN and ANFO explosives
227
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Fig. 4 – Stages in the preparation for explosive welding. (a) The polished plates (800 mm × 400 mm), (b) wooden frame resting on the flyer plate, (c) filling the frame with ANFO explosive, (d) booster charge near the top of the frame, (e) the plates after detonation of the explosive (the edges of the flyer plate have sheared off).
eling of the plates. It was found that the size of mesh was also important in visualizing the large velocity vectors which indicated jetting at the interface. In the areas close to the collision zones where the jet forms, mesh sizes of about 0.02 mm were used. A friction coefficient of 0.3 was also included in the model. The mesh tied constraints were used to express the bonding when its criteria reached. The position tolerance parameter was set to be equal to the distance within which nodes on the slave surface must lie from the master surface in order to be tied. Nodes on the slave surface that were farther away from the master surface than this distance were not constrained by the tie. The value for this tolerance distance was 5% of the typical element size in the master surface. For a node-based master surface, the tolerance distance was based on the average distance between nodes in the master surface. The adjust parameter was set to move all tied nodes
on the slave surface onto the master surface in the final configuration. The constraint ratio parameter was used for the two surfaces with rotational degrees of freedom. This parameter was set equal to the fractional distance between the master reference surface and the slave node at which the translational constraint should act. The attempt was made to choose this distance such that the translational constraint acts precisely at the interface. The AUTODYN software contained equations of state for metals and several commercial explosives (but did not include ANFO mixtures). The Johnson–Cook constitutive equation (Johnson and Cook, 1983) as suggested by Al-Hassani (2001) and Akbari Mousavi (2001) was used to describe the mechanical behavior of the plates and the Williamsburg equation of state (Byers Brown and Braithwaite, 1993a,b; Byers Brown, 1992; Byers Brown and Behain, 1991) was chosen as the EoS
229
1670 0.7 0.022 0.32 380 2200 55 Ti-6Al-4V, Aged. ∗
4450 1500
178
1800 0.5 0.02 0.3 350 2000 82 7830 310
169
1793 1.03 0.014 0.26 510 2000 81.8 7830 792
159
1811 1.00 0.022 0.36 275 2000 81.8
Hardening exponent (n) Hardening constant, B (MPa) Hardness (MPa) Shear modulus (GPa) Bulk modulus (GPa)
160 7896 350
304 stainless steel 4340 quench and hardened high strength steel EN1 mild steel Titanium*
Low detonation velocity explosives cannot be modeled with the Jones–Wilkins–Lee (JWL) equation of state (Lee et al., 1968) due to the thick reaction zone at the detonation front compared with high explosives. Williamsburg equation of state (Byers Brown and Braithwaite, 1993a,b; Byers Brown, 1992; Byers Brown and Behain, 1991) is therefore used to model the low detonation explosives. The Williamsburg equation of state is a semi-empirical equation of state which relates the specific internal energy U to the specific volume V and the specific entropy S. Pressure is also calculated by means of U, V and S. The small number of parameters required are found by fitting
Density (kg/m3 )
3.1. Williamsburg equation of state for ANFO mixtures
Yield stress, A (MPa)
for the ANFO explosive. An algorithm for the EoS was written and linked into the AUTODYN software (Anon., 1997) along with the necessary parameters for a variety of ANFO/perlite mixtures (Akbari Mousavi, 2001). Table 2 lists the mechanical properties of the materials used in this study and their Johnson–Cook parameters (Johnson and Cook, 1983). The Jones–Wilkins–Lee (JWL) (Lee et al., 1968; Cook, 1958; Horton, 1988) equation of state was used to model the PETN explosive. The input parameters and other data needed to describe the explosive are tabulated in Table 3.
Material
Fig. 5 – Arrangement for measuring the shear strength of welded plates. (a) The test jig and sample, (b) the sample under test.
Table 2 – Mechanical properties of the metals used in this study and their Johnson–Cook parameters
Strain rate constant (C)
Thermal softening exponent (m)
Melting temperature (K)
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Table 3 – Jones–Wilkins–Lee (JWL) and Chapman–Jouguet (C–J) parameters for PETN and ANFO Explosive
Detonation velocity (m/s)
PETN PETN Pure ANFO ANFO mixture
7450 5170 4930 2230
Density (kg/m3 ) 1500 880 820 500
C–J energy (MJ/m3 ) 8.56 5.025 5.322 3.822
to the principal adiabats calculated using a detonation code SIRIUS (Byers Brown, 1994). SIRIUS incorporates the Theostar (Horton, 1988) and Murnaghan (Horton, 1988) equations of states (for detonation products and silica, respectively), which are based on statistical mechanics and intermolecular potentials. The reference state in the Williamsburg equation of state is the detonation state, which is assumed to be ideal, i.e. satisfying the assumptions of the Chapman–Jouguet theory (Cook, 1958). The main assumption is that the reaction zone, in which the explosive decomposes to form stable molecular products in chemical and phase equilibrium, is extremely thin and flat. The Williamsburg equation of state for energy of order N in terms of reduced variables v is
U U(V, S) = ref −1 ∞ N
1 + ˇ ˛¯ k k k
k=1
1 + ˇk
(1)
C1 (GPa)
C2 (GPa)
r1
r2
ω
22.00 6.2 5.168 1.332
625.3 348.62 420.1 –
23.29 11.288 444 –
5.25 7.00 3.55 –
1.6 2.00 1.6 –
0.28 0.24 0.41 –
and where ˛˙ k (k) = ˛k + 2ık log()
(8)
and RG is the gas constant The adiabatic gamma coefficient s is computed as 1 k g−1 k N
s = g +
1−
k=1
1 k
(9)
with k = 1 + ˇk v ˛¯ k
(10)
The Gruneisen gamma coefficient G is
where V , Vref
=
C–J pressure (GPa)
and
= exp
S − S ref
nref R
1 ˛˙ k k f k N
(2)
G = g − 1 −
1−
k=1
The equations involve 4N + 4 basic parameters (the ˛k , ˇk , k , ık , and Uref , Vref , Sref , nref ). The reference values of Uref , Vref , Sref and nref are Chapman–Jouguet (C–J) values. The equation relating pressure to volume can be shown to be P = (g − 1)
U V
(3)
1 k
(11)
The specific isochoric heat capacity Ch = (∂U/∂T)v is found from 2 nref RG 2ϕ 1 ˛˙ k k =f + + Ch f f
k N
k=1
1−
1
k
(12)
where g(v, ) is given by
g = 0 +
N k=1
k 1 + ˇv ˛¯ k
(4)
and
∞ = 0 +
N
k ,
0 = 1 +
k=1
N
˛k k
(5)
k=1
and the functions ˛¯ k are defined as ˛¯ k (˛) = ˛k + ık log(). The temperature is expressed as T=f
U nref RG
(6)
where f(v, ) is given as
f =
N k=1
˛˙ k k 1 −
1 1 + ˇk v ˛¯ k
(7)
Fig. 6 – Log–log plot of pressure vs. volume. The circles are SIRIUS values and the solid line is the WBG fit. The dashed vertical lines are for the C–J and initial volumes.
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4.
Experimental results
4.1.
Flyer plate velocities and plate welding tests
4.1.1.
Plate contact velocity
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Velocity measurements were made using different thicknesses of steel and titanium plate and at least two thicknesses of explosive. Collision point velocities obtained for several combinations of plate and explosive thickness varied between about 1700 and 2300 m/s with most being around 2100 m/s. Two tests with commercial PETN explosive gave plate collision velocities which were very close to the published VoD value of 7300 m/s.
Fig. 7 – The WBG fit of natural log plot of principal adiabats against density for 77/23% ANFO/silica mix with initial density of 0.534 g/cm3 for pressure P, the dashed vertical lines are for the C–J and initial volumes.
where
ϕ=
N
ık k 1 −
k=1
1
k
The sound speed C = C=
(13)
(∂P/∂ )S is obtained from
PVs
(14)
3.1.1. The above equations were imported as a subroutine into the AUTODYN code The pressure against the specific volume and density along the adiabat are shown in Figs. 6 and 7, respectively. The circles are SIRIUS values and the solid line is the WBG fit. The dashed vertical lines are for the C–J and initial volumes, respectively.
Fig. 8 – ANFO/perlite mixture-velocity of detonation vs. explosive thickness (VoD meter and pin measurement).
Fig. 9 – Distance traveled vs. time for titanium flyer plates.
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titanium clad steel plates however showed no areas of poor bonding. In a test with a small (25 cm square) inclined plate arrangement and the high explosive (PETN) the plates only partially bonded and bonding did not occur until approximately half way along the plate, about 12 cm from the booster charge.
4.2.2.
Fig. 10 – Downward velocity of flyer plate.
A few measurements of the explosive VoD were made using an optical system but in general the methods were unreliable. The results are shown in Fig. 8. Although the data is scattered the VoD in general increases with explosive thickness.
4.1.2.
Flyer plate velocity in downward direction
The time delays between the pulses from the pins in the horizontal arm of the T were used to estimate the flyer plate downward velocity, Fig. 9. It should be noted that time zero on the X-axis is the time at which the flyer plate makes contact with pin 2 and not when the plate first starts to move. The bottom graph in Fig. 9 was compiled from the results of experiments with thickness of explosive layer. In general the flyer plate velocities were higher for the larger explosive thicknesses. Most measurements of downward velocity of the flyer plate showed that the flyer plate was still accelerating when it hit the ground. A typical result for a 6 mm thick stainless steel is shown in Fig. 10. The velocity profile determined from a computer simulation is shown for comparison and is discussed later.
4.2.
Examination of the welded plates
4.2.1.
Ultrasonic inspection
Conventional ultrasonic NDT equipment was used to identify areas of non-bonding. The data collected was processed to show plan views, so-called ‘C-scans’, of the bonded and unbonded regions of the plates, Fig. 11. Parts of the plate which were either poorly or un-bonded are shown as shaded. Most of the stainless steel clad plates had defects at the detonation end, varying in extent from small areas at the corners of the plate to much larger areas covering the entire width of the plate over axial distances of up to about 200 mm. The
Shear strength measurements of the bonded plates
Two samples were cut from the centre of each plate, one parallel and one normal to the direction of detonation and tested as described earlier. The variation of shear strength with stand off distance for stainless steel and titanium cladded plates are shown in Fig. 12a and b, respectively. This shows the shear strength of the bonded plates to increase slightly with stand off distance. There was little correlation between shear strength and explosive thickness. Fig. 13 shows the result for a 6 mm thick titanium plate. Similar results were obtained for the other titanium and stainless steel plates. In most cases there was very little difference in the bond strength of the two types of samples (Sp and St ). The shear strength of the titanium to steel weld samples were in the range 380–430MPa and were in general only slightly correlated with stand off distance and explosive load. The shear strength of the stainless steel clad samples varied between 430 and 550MPa, the highest values being for the largest stand off distance.
4.2.3.
Metallography
Photographs of the magnified (70× and 140×) interface of polished and etched samples of the plates are shown in Fig. 14. The shapes of the interface obtained from all experiments performed are summarized in Table 4. In general there were three types of interfaces, straight, smooth shallow wavy or shallow wavy with the beginnings of vortex formation. In some cases more than one type of profile was present in the same sample. Vortices were most often seen for the larger stand off distances and were very occasionally accompanied by small regions of melted metal lying between the peaks of the waves. Wavelengths where measurable were between 0.25 and 0.6 mm and amplitudes were about 0.05 mm, see Table 5.
5.
Simulation results
Some of the more important parameters extracted from the computer model are reproduced in Fig. 15a–f and summarized in Table 6.
Fig. 11 – Ultrasonic examination of welded plates (shaded areas denote poorly bonded regions). (a) 24 mm stand off, 12 mm stainless steel plate, explosive thickness 235 mm, (b) 18 mm stand off, (c) 12 mm stand off, (d) 6 mm stand off, (e) 12 mm stand off, 6 mm stainless steel plate, explosive thickness 107 mm, (f) 9 mm stand off, (g) 6 mm stand off, (h) 3 mm stand off.
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Fig. 12 – (a) Variation of shear strength with stand off distances (stainless steel plate), Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation. (b) Variation of shear strength with stand off distance (titanium cladding plate) Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation.
Fig. 15a shows examples of the temporal change in detonation gas pressure for six points at 20 mm intervals just above and along the top of the flyer plate. The pressure pulses have a very short rise time and a relatively slow decay (over a period of about 100 s). The peak amplitude increases with distance from the detonation point for the first 100 mm and then remains at a relatively constant level. The downward velocity of the flyer plate follows a similar pattern. The maximum impact velocity is relatively low near the detonation point then
gradually increases until it reaches a constant value at about 100 mm from the detonator. This variation in maximum velocity causes the flyer plate to bend as it travels towards the base, as shown in Fig. 15b. Fig. 15c–f shows examples of the pressure, shear stress, and absolute velocity contours for a 6.35 mm stainless steel flyer plate and 50 mm mild steel base plate with a 6.35 mm stand off. Typical plastic strains, at various points along a steel flyer plate are shown in Fig. 16. The peak strain increases with distance from the detonation point and in the
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stress magnitudes were also higher in regions of successful bonding.
6.
Fig. 13 – Variation of shear strength with explosive thickness Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation.
example shown it almost doubles from about 0.4 at 50 mm to 0.8 at 100 mm. It is interesting to note that for this combination of metals the point where the plastic strain exceeded 0.3 corresponds approximately to the start of good bonding in the welding test that was simulated. The predicted shear
Discussion
The lack of bonding near the detonation end of the stainless steel plates was most likely due to the initial relatively low pressure of the detonation gases and hence low plate velocity. In some cases the un-bonded area decreased as the stand off distance approached plate thickness. The increased bending resistance of the small length of plate acted upon by this lower pressure also tended to reduce initial impact velocity and angle. In most cases steady detonation and collision conditions were only reached about 100 mm from the source of detonation. The lack of un-bonded areas in the titanium welds was probably due to the lower stiffness and greater ductility of titanium. The thickness of the explosive had only a small effect on bond strength, stand off distance was more influential although the effect was small. In most cases there was very little difference in the bond strength of the two types of samples. The shear strength measurements for both the titanium to mild steel and stainless steel to mild steel welds were larger
Table 4 – The shapes of the interface obtained from all experiments performed Test no. Flyer plate material 1 2 3 4
Explosive
Flyer plate Stand off (mm) thickness (mm)
Stainless steel, 314 Stainless steel, 314 Stainless steel, 314 Quench hardened high strength steel, 4340 Mild steel, EN1 Titanium Titanium Titanium Titanium
PETN PETN PETN PETN
10 10 20 10
PETN ANFO mixture ANFO mixture ANFO mixture ANFO mixture
10 11 12 13 14 15 16 17 18 19 20 21 22
Titanium Titanium Titanium Titanium Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel
23
Stainless steel
5 6 7 8 9
Explosive thickness (mm)
0 10 20 0
9 9 75 9
10 3 3 6.35 6.35
0 3 6 6 3
9 107 107 80 135
ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture
6.35 6.35 6.35 6.35 3 3 6 6 6 6 12 12 12
6 9 12 6 3 6 3 6 9 12 6 12 18
135 135 135 153 107 107 135 135 135 135 235 235 235
ANFO mixture
12
24
235
Results Weld No weld Weld No weld
Weld Also partly straight Shallow regular waves Partial bond Partly straight bond-no bond Shallow regular waves Shallow regular waves Vortices Partial bond Wavy Shallow waves Mostly un-bonded Partial bonding Shark toothed Also partly straight Partial bonding Wavy interface Front vortex only, very thin layer of melt at the interface Front and back vortex only, very little melt at the interface
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Fig. 14 – Examples of welded interfaces (mild steel plate on the bottom). (a) 3 mm stainless steel flyer 3 mm stand off 107 mm ANFO (70×), (b) 6 mm titanium flyer 3 mm stand off 107 mm ANFO (140×), (c) 3 mm stainless steel flyer 6 mm stand off 107 mm ANFO (70×), (d) 6 mm titanium flyer 13 mm stand off 108 mm ANFO (140×).
than those reported in standard shear tests (Anon., 1999) where shear strength values were given as 350 and 400 MPa for titanium to mild steel and stainless steel to mild steel combinations. The interface shear strength of the titanium/mild steel samples was less than that for the stainless steel/mild steel bonds. This may be due to the creation of a very brittle inter-metallic compound of TiC at the interface. Stainless steel and mild steel are also metallurgically more compatible than titanium and mild steel. There was no clear evidence of any correlation between bond strength and the level of ultrasonic signals reflected from the bond interface, as reported elsewhere (Wronka, 1999). The predicted time histories of a range of physical parameters were examined. The close agreement between the predicted and measured velocities of the flyer plate, Figs. 9 and 10 were particularly encouraging as they provided support for the modeling process. Following an initial steep rise the plate velocity increases more slowly with distance reaching values of about 400 m/s after about 20 mm travel. One of the most interesting parameters analyzed was plastic strain that is proposed that a minimum level of strain in the two plates is necessary for welding. The ultrasonic data taken along with Fig. 16 indicates that in the case of the stainless steel to steel welds an effective plastic strain higher than about 0.3 is probably required for bonding. The minimum value for titanium could not be verified as all of the clad plates were well bonded. The maximum value of shear stress along both titanium and steel welded plates tended to follow the same pattern
as that for plastic strains that is increasing fairly quickly and then remaining fairly constant along the length of the plate. The magnitude of the shear stresses predicted for the bonded regions were higher than those for non-bonded regions and at face to face points were opposite in sign, see Figs. 17 and 18. To achieve welding it is believed that jetting has to occur. In theory if the velocity of the collision point remains subsonic, jetting will occur at any oblique angle. In practice, however, a minimum angle is required to satisfy the pressure requirements, i.e. the pressure must be of sufficient magnitude to exceed the dynamic elastic limit of the material to ensure deformation of the metal surfaces into a jet. If the collision point velocity is maintained at a supersonic velocity, jetting will occur above some critical angle, which is dependent on the pressure distribution at the collision point as discussed earlier. In AUTODYN analyses using the Euler formulation, because material can escape the mesh boundaries, it was possible to simulate jetting. In addition, the analysis showed particle velocities to be very high near the collision point. Where particle velocities were low jetting was assumed not to occur. Fig. 19 shows the velocity vectors for an inclined plate arrangement (case 1) and for a parallel plate arrangement (case 2). The highest velocities were produced in the inclined plate setup (Fig. 19a). The wave-like structure in the interface of sectioned samples of welded plate samples was not seen in the simulations, although there were some indications of wave formation in velocity vector plots. This was most likely due to the relatively
Table 5 – Six millimetre titanium plate to 50 mm mild steel welds using a 6 mm stand off and different thicknesses of ANFO explosive Explosive thickness (mm) 80 107 153
Wavelength (mm) 0.6 0.5 0.25
Amplitude (mm) 0.08 0.05 0.05
Velocity of detonation (m/s) 2000 2050 2175
Comments Front and back vortices, melt between the wave peaks Front vortex only, very thin layer of melt at the interface Front vortex only, very little melt at the interface
236
Test no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Measured flyer plate velocity (m/s) 350 560 350 350 350 460 610 300 335 450 540 620 265 280 380 210 250 300 330 245 300 340 400
Predicted flyer plate velocity (m/s) 340 550 340 340 340 488 630 313 348 460 532 600 275 280 365 195 255 294 324 237 310 358 394
Explosive ratio, R 0.19 0.19 0.418 0.185 0.192 3.928 3.928 1.3874 1.855 1.855 1.855 1.855 2.654 2.277 2.277 1.138 1.138 1.138 1.138 1.25 1.25 1.25 1.25
Predicted maximum impact angle (◦ ) 17.5 2.3 5.25 12 12.2 12.45 17.9 8.9 8.89 11.8 13.67 15.46 7.2 7.264 10.26 4.9 6.4 7.5 8.2 6.48 8.5 9.81 10.81
Predicted collision velocity (m/s) 1693.9 8100 5028 1683.4 1656.2 2050 2050 2000 2250 2250 2250 2250 2175 2050 2050 2250 2250 2250 2250 2400 2400 2400 2400
Predicted maximum pressure (GPa) 1.5 9.0 10.0 1.5 1.5 5.24078 6.65713 3.40021 3.78152 4.95335 5.68738 6.36417 3.00082 5.03848 6.53217 3.52304 4.59472 5.28617 5.81482 4.26927 5.55757 6.39333 7.01322
Predicted maximum shear stress (GPa) 0.1 0.06 0.03 0.1 0.1 0.262 0.332 0.170 0.189 0.247 0.284 0.318 0.150 0.251 0.326 0.176 0.229 0.264 0.290 0.213 0.277 0.319 0.350
Predicted maximum plastic strain 0.8 0.15 0.4 0.78 0.82 0.314 0.399 0.204 0.226 0.297 0.341 0.381 0.180 0.302 0.391 0.211 0.275 0.317 0.348 0.256 0.333 0.383 0.420
Terminal velocity (Gurney) (m/s) 347 554 347 347 347 920.5 920.5 780.7 919.5 919.5 919.5 919.5 1231.4 739.35 739.35 707.4 707.4 707.4 707.4 673.6 673.6 673.6 673.6
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
Table 6 – Parameters derived from the simulations
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
237
Fig. 15 – (a) Pressure/time profiles for seven points at 20 mm intervals just above and along the top of the flyer plate. Lowest curve is at the detonation end of the plate. The first point is 50 mm away from the detonation point. (b) Explosive welding simulation, distortion of the flyer plate by the detonation of the explosive. (c) Pressure contours in an explosive welding simulation (the explosive is not displayed in this image, but note the jetting and straight interface) (3 mm thick stainless steel flyer plate, 107 mm ANFO, 3 mm stand off). (d) Explosive welding simulation. Shear stress contours (6.35 mm thick stainless steel flyer plate, 6.35 mm stand off). (e) Explosive welding simulation. Velocity vector distributions (6.35 mm thick stainless steel flyer plate, 6.35 mm stand off). (f) Plate and jet velocities. (3 mm thick stainless steel flyer plate, 107 mm ANFO, 3 mm stand off).
course geometry of the elements (a compromise between resolution and computing time). The calculations for a 5 mm square mesh of cells took several days to complete mainly due to the time taken to solve the explosive equation of state. In contrast simulations of non-explosive oblique high veloc-
ity impacts which did show waves and used much smaller elements (1 mm or less) could be completed in less than 24 h. The simulations showed that the magnitude of the velocity vectors decreased as the distance from the collision point
238
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
Fig. 16 – Temporal variation of effective plastic strain for seven points along flyer contact surface, at 50, 100, 150, 200, 250, 300 and 400 mm from detonation end of plate.
Fig. 17 – AUTODYN simulations of the shear stress profiles in flyer and base plates—inclined geometry (case 1).
increased. The driving force of this was the steep pressure gradient from the pressure maximum behind the point of impact, to zero pressure at free surface ahead of the impact.
Fig. 19 – (a) AUTODYN simulations of the velocity vectors for case 1. (b) AUTODYN simulations of the velocity vectors for case 2.
Fig. 18 – AUTODYN simulations of the shear stress profiles of flyer and base plates—parallel geometry (case 2).
Pressures (of the order of GPa), and plate velocities were highest at the collision point. The high pressures and velocities created high plastic deformation which in turn produced large values of plastic strain (>2), and shear stress at the interface. The strain values were material-dependent.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
The flyer and base plates bent near the point of impact and the impact angle changed as the collision point moved along the plate. The shear stresses were highest in the simulations of plates which exhibited good bonding. This implies that a threshold value of shear stresses must be exceeded for bonding to take place in different combinations of metals. For stainless steel to mild steel combinations the threshold stress was found to be 0.5 GPa and for titanium to mild steel the threshold shear stress was 0.4 GPa. Effective strains higher than 0.35 were seen in stainless steel/mild steel welding simulations in the areas where welding took place. For titanium to mild steel effective strains were above about 0.4. The value of effective strain depended on dynamic angle, with the highest values occurring with the inclined plate arrangement.
7.
Concluding remarks
The pin contact method for measuring velocity of detonation and plate velocity worked well in the field. The velocity of detonation of the ANFO mixture was approximately 2100 m/s and plate impact velocities were between about 300 and 450 m/s. The ultrasonic examination of the welded plate showed an initial impact defect in the stainless/mild steel welded plates but no defects in the titanium/mild steel composite plates. The defect in the stainless steel plates started at the detonation end and in some cases extended about 200 mm along the plate. It correlated with the pressure distribution predicted by the computer simulations. This ‘end effect’ should be considered when welding large expensive sections of this combination of plates. Microscopic examination of sections of the welded plates showed that in general interface waves were smaller in titanium plates than in the stainless steel plates. In both cases thicker plates displayed higher amplitude waves than thinner plates. The thicker plates in general were also more strongly bonded. New data was obtained for the ANFO explosive and the good agreement between simulation and experimental results for plate velocities provides support for the newly developed equation of state for ANFO mixtures. The study shows that effective plastic strain and shear stress in the flyer and base plate are important parameters in determining whether or not bonding will occur.
Acknowledgement This work was part funded by the EPSRC.
239
references
Akbari Mousavi, A.A., 2001. The mechanics of explosive welding. Ph.D. Thesis. University of Manchester Institute of Science and Technology (UMIST), September. Al-Hassani, S.T.S., 2001. Numerical and experimental investigation of explosive bonding process variables and their influence on bond strength. EPSRC Grant GR/M10106/01, Final Report. University of Manchester Institute of Science and Technology (UMIST), Manchester, UK. Century Dynamics, Interactive Non-Linear Dynamic Analysis Software, Dynamics House, Hurst Road, Horsham, West Sussex, RH12 2DT, England. Byers Brown, W., 1992. Analytical representation of the adiabatic equation for detonation products based on statistical mechanics and intermolecular forces. Phil. Trans. Roy. Soc. A 339, 345–353. Byers Brown, W., 1994. SIRIUS Code, Williamsburg equation of state for fluids at very high density. Contract Report for ICI plc Explosive Group Technical Centre, Ardeer, February. Byers Brown, W., Behain, A., 1991. Review of Equations of State of Fluids Valid to High Density. HSE Contract Research Report, April 30. Byers Brown, W., Braithwaite, M., 1993. Wiliamsburg equation of state for detonation product fluid. Shock Compression of Condensed Matter, Colorado, Spring, June. Byers Brown, W., Braithwaite, M., 1993b. The development of the Williamsburg equation of state to model non-ideal detonation. In: Proceedings of the 10th Symposium on Detonation, Boston, MA, July. Cook, M.A., 1958. The Science of High Explosives. Reinhold Publishing Corporation, New York. Crossland, B., 1982. Explosive Welding of Metals and Its Application, second ed. Oxford Science Publications, Clarendon Press, Oxford. Horton, T.V., 1988. Analytical representation of high density fluid equations of state based on statistical mechanics. In: Schmidt, S.C., Holmes, N.C. (Eds.), Shock Waves in Condensed Matter 1987. Elsevier, pp. 77–80. Johnson, R.G., Cook, W.H., 1983. A constitutive model and data for metals subjected to large strains, high strain-rates and high temperature. In: Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands, April, pp. 541–547. Lee, E.H., Hornig, H.C., Kury, J.W., 1968. Adiabatic expansion of high explosive detonation products. Report UCRL-50422. Lawrence Livermore National Laboratory, Livermore, CA, USA. Specifications for stainless chromium–nickel steel-clad plate, sheet and strip, Ferrous Material Specifications. SA264, ASTM A264-94a, American Society of Mechanical Engineers, pp. 422–432. Wronka, B., 1999. The influence of base plate thickness and anvil on the characteristics of explosive welded joints. Insight 41 (6).
journal homepage: www.elsevier.com/locate/jmatprotec
Explosive welding of metal plates S.A.A. Akbari-Mousavi a,∗ , L.M. Barrett b , S.T.S. Al-Hassani b a
School of Metallurgy and Material Engineering, University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran b School of Mechanical, Aerospace and Civil Engineering, University of Manchester, P.O. Box 88, Manchester M60 1QD, UK
a r t i c l e
i n f o
a b s t r a c t
Article history:
This paper describes a study of explosive welding of metal plates. The properties of a locally
Received 7 August 2006
prepared mix of 77/23 ammonium nitrate and fuel oil (ANFO) explosive and the dynamics of
Received in revised form
the plates are investigated and the results from welding tests presented. The strength of the
27 August 2007
clad plates is measured and ultrasonic inspection performed to identify and locate defects.
Accepted 3 September 2007
The welding process is simulated using a finite element-based computer model. A brief description of the modeling process is given along with the results from the simulations for comparison with measured parameters.
Keywords:
© 2007 Elsevier B.V. All rights reserved.
Explosive welding Pin contact method Simulations ANFO Titanium Stainless steel
1.
Introduction
Explosive welding is generally used to bond two dissimilar metal plates and is most often used when the combination of metals makes conventional fusion welding impractical. The technique enables very large sections of plate to be clad in a single operation. The quality of the joint is generally good with high mechanical strength and as it is a ‘cold method’ the bonded metals retain their pre-bond properties. The usual arrangement for explosive welding has the two plates (flyer and base) placed one above the other separated by a distance of about one or two times the thickness of the flyer plate. The explosive, usually in powder form is placed on the upper plate inside a surrounding wooden frame. Its type, thickness and composition are selected to yield a specific energy release and a specific velocity of detonation (the
∗
Corresponding author. Tel.: +98 21 82084096; fax: +98 21 88006076. E-mail address: [email protected] (S.A.A. Akbari-Mousavi). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.09.028
speed at which the detonation front travels across the explosive layer). The explosive is detonated using a small booster charge and detonator placed at one end of the frame. The expansion of the gaseous detonation products accelerates the cladding plate across the stand off gap forcing it to collide obliquely at relatively high velocity with the lower (base) plate, Fig. 1. On impact the two surfaces at the collision zone become plastic causing a jet of both metals to be ejected from between the two plates. This jet scours and cleans the surfaces of the plates leaving clean metal amenable to bonding. Whilst the explosive welding process is generally successful, expensive failures occur and often the cause(s) is unknown. To improve the understanding of the process a mathematical model to simulate the mechanics was developed. This paper describes an experimental study to obtain data to assist the development of this model. The charac-
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 2 ( 2 0 0 8 ) 224–239
225
Fig. 1 – The explosive welding arrangement.
teristics of ammonium nitrate explosive are described, the dynamics of the plates examined and the results from several welding tests presented. A brief description of the modeling process is given along with results from the computer simulations.
2.
Experimental procedures
The experimental program was in two phases. The aims of the first phase were to determine the velocity of detonation
Fig. 2 – Pin contact method for measuring flyer plate velocities. (a) Experimental arrangement, (b) pin arrangement.
226
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of the explosive and the velocity of impact of the cladding plates for different combinations of stand off distance, plate thickness and explosive thickness. The second phase of the experimental program involved welding various thicknesses of titanium and stainless steel cladding plates to mild steel base plates.
2.1.
The explosive
As the velocity of detonation (VoD) of commercial explosives is generally too fast for successful welding of parallel plates most applications use a ‘slower’ powder mix of ammonium nitrate and diesel fuel oil (ANFO) and an inert material such as perlite or sand. In the tests reported here the explosive mix was approximately 75% ANFO 25% perlite. A booster charge made of about 250 g of the high explosive C4 was used to set off the ANFO. The thickness of the ANFO explosive layer covering the surface of the flyer plate used in the welding tests was in the range 80–235 mm. A few tests were also carried out using PETN explosive which has a relatively high VoD. As the explosive was not intentionally compacted during the explosive welding operation its average density depended on the thickness of the layer (the thicker the layer the more it settles and the greater its density). The average density of different thickness of explosive was measured by simply weighing a number of different size wooden boxes filled with the explosive. The base of the boxes was square, approximately 0.4 m × 0.4 m, and the heights were between 50 and 300 mm. In each case the explosive was levelled but not compacted. The increase in average density with thickness was generally found to be linear, increasing from 518 kg/m3 for a 50 mm thick layer to 532 kg/m3 for a 300 mm thick layer.
2.2. VoD
Measurement of flyer plate velocity and explosive
The relationship between collision angle ˇ, velocity of detonation VoD, collision point velocity Vw and plate impact velocity Vp is (see Fig. 1 and Crossland, 1982) Vp = 2Vw sin
ˇ 2
As the collision point velocity Vw is the same as the velocity of detonation of the explosive VoD, in parallel welding configurations, the VoD of the ANFO mixture can be estimated using a simple array of electrical contact pins, Fig. 2. Contact between the flyer plate and the pins completes electrical circuits which produce a series of alternating positive and negative voltage pulses which are displayed and stored on an oscilloscope, Fig. 3. Contact between the plate and pin 1 generates a negative voltage pulse, contact between the plate and pin 2 produces a positive voltage pulse, and contact between the plate and pin 3 generates another negative pulse and so on. The collision velocity is calculated from the distance between the axially spaced pins (1 and 2) and the time delay between the first two pulses on the signal trace. The downward velocity of the plate may be determined from the time delays between the following negative pulse and positive peaks and the difference in the relative heights of the pins.
Fig. 3 – A typical signal trace from the plate velocity measuring electronics.
2.3.
Plate welding
The plates listed in Table 1 were welded to 50 mm thick mild steel base plates. Each base plate, approximately 800 mm × 400 mm × 50 mm, was placed directly onto the smooth sandy floor of the firing range and the flyer plate (with slightly larger dimensions to create a small overlap) supported above it on small equal height spacers. The separation of the plates varied between 3 and 24 mm. Stages in the setting up procedure are shown in Fig. 4. After welding the plates were subjected to ultrasonic examination and measurements were made of the shear strength of the bond using the simple jig shown in Fig. 5. The samples were subjected to a shearing force by mounting the jig upright in the jaws of an Instron testing machine and applying the load vertically.
3.
Modeling the explosive welding process
A computer model of the welding process was developed using the 2D commercial general purpose finite difference software package, AUTODYN (Anon., 1997). The plates, the explosive, the sandy base and the air surrounding the plates were divided into subgrids made up of rectangular cells, their material properties being extracted from program libraries. Each subgrid could be analyzed using one of several different numeric processors (e.g. Lagrange, Euler, Shell, etc.). The Lagrange processor fixed the material inside the cells and was used for the plates: the Euler processor allowed the material to move from cell to cell and was used to process the explosive. Time steps for the analysis were automatically computed to ensure accuracy and stability of the solution. Parameters such as pressure, velocity, acceleration, stresses and strains, displacement energy, etc., were calculated for each cell and made available at the end of every time step. Contour or vector plots and graphs to show the history of a parameter were generated on demand. The mesh size of about 2 mm was chosen for mod-
Test no. 1 2 3 4
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Flyer plate material Stainless steel, 314 Stainless steel, 314 Stainless steel, 314 Quench hardened high strength steel, 4340 Mild steel, EN1 Titanium Titanium Titanium Titanium Titanium Titanium Titanium Titanium Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel
Explosive
Dynamic angle, ˇ (◦ )
Flyer plate thickness (mm)
Measured flyer plate velocity (m/s)
Stand off distance (mm)
Explosive thickness (mm)
Measured VoD of different types of explosives (m/s)
PETN PETN PETN PETN
15 Parallel Parallel 15
10 10 20 10
350 560 350 350
0 10 20 0
9 9 75 9
7450 7450 5170 7450
PETN ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture
15 Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel Parallel
10 3 3 6.35 6.35 6.35 6.35 6.35 6.35 3 3 6 6 6 6 12 12 12 12
350 460 610 300 335 450 540 620 265 280 380 210 250 300 330 245 300 340 400
0 3 6 6 3 6 9 12 6 3 6 3 6 9 12 6 12 18 24
9 107 107 80 135 135 135 135 153 107 107 135 135 135 135 235 235 235 235
7450 2050 2050 2000 2250 2250 2250 2250 2175 2050 2050 2250 2250 2250 2250 2400 2400 2400 2400
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Table 1 – Welding tests with PETN and ANFO explosives
227
228
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Fig. 4 – Stages in the preparation for explosive welding. (a) The polished plates (800 mm × 400 mm), (b) wooden frame resting on the flyer plate, (c) filling the frame with ANFO explosive, (d) booster charge near the top of the frame, (e) the plates after detonation of the explosive (the edges of the flyer plate have sheared off).
eling of the plates. It was found that the size of mesh was also important in visualizing the large velocity vectors which indicated jetting at the interface. In the areas close to the collision zones where the jet forms, mesh sizes of about 0.02 mm were used. A friction coefficient of 0.3 was also included in the model. The mesh tied constraints were used to express the bonding when its criteria reached. The position tolerance parameter was set to be equal to the distance within which nodes on the slave surface must lie from the master surface in order to be tied. Nodes on the slave surface that were farther away from the master surface than this distance were not constrained by the tie. The value for this tolerance distance was 5% of the typical element size in the master surface. For a node-based master surface, the tolerance distance was based on the average distance between nodes in the master surface. The adjust parameter was set to move all tied nodes
on the slave surface onto the master surface in the final configuration. The constraint ratio parameter was used for the two surfaces with rotational degrees of freedom. This parameter was set equal to the fractional distance between the master reference surface and the slave node at which the translational constraint should act. The attempt was made to choose this distance such that the translational constraint acts precisely at the interface. The AUTODYN software contained equations of state for metals and several commercial explosives (but did not include ANFO mixtures). The Johnson–Cook constitutive equation (Johnson and Cook, 1983) as suggested by Al-Hassani (2001) and Akbari Mousavi (2001) was used to describe the mechanical behavior of the plates and the Williamsburg equation of state (Byers Brown and Braithwaite, 1993a,b; Byers Brown, 1992; Byers Brown and Behain, 1991) was chosen as the EoS
229
1670 0.7 0.022 0.32 380 2200 55 Ti-6Al-4V, Aged. ∗
4450 1500
178
1800 0.5 0.02 0.3 350 2000 82 7830 310
169
1793 1.03 0.014 0.26 510 2000 81.8 7830 792
159
1811 1.00 0.022 0.36 275 2000 81.8
Hardening exponent (n) Hardening constant, B (MPa) Hardness (MPa) Shear modulus (GPa) Bulk modulus (GPa)
160 7896 350
304 stainless steel 4340 quench and hardened high strength steel EN1 mild steel Titanium*
Low detonation velocity explosives cannot be modeled with the Jones–Wilkins–Lee (JWL) equation of state (Lee et al., 1968) due to the thick reaction zone at the detonation front compared with high explosives. Williamsburg equation of state (Byers Brown and Braithwaite, 1993a,b; Byers Brown, 1992; Byers Brown and Behain, 1991) is therefore used to model the low detonation explosives. The Williamsburg equation of state is a semi-empirical equation of state which relates the specific internal energy U to the specific volume V and the specific entropy S. Pressure is also calculated by means of U, V and S. The small number of parameters required are found by fitting
Density (kg/m3 )
3.1. Williamsburg equation of state for ANFO mixtures
Yield stress, A (MPa)
for the ANFO explosive. An algorithm for the EoS was written and linked into the AUTODYN software (Anon., 1997) along with the necessary parameters for a variety of ANFO/perlite mixtures (Akbari Mousavi, 2001). Table 2 lists the mechanical properties of the materials used in this study and their Johnson–Cook parameters (Johnson and Cook, 1983). The Jones–Wilkins–Lee (JWL) (Lee et al., 1968; Cook, 1958; Horton, 1988) equation of state was used to model the PETN explosive. The input parameters and other data needed to describe the explosive are tabulated in Table 3.
Material
Fig. 5 – Arrangement for measuring the shear strength of welded plates. (a) The test jig and sample, (b) the sample under test.
Table 2 – Mechanical properties of the metals used in this study and their Johnson–Cook parameters
Strain rate constant (C)
Thermal softening exponent (m)
Melting temperature (K)
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230
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Table 3 – Jones–Wilkins–Lee (JWL) and Chapman–Jouguet (C–J) parameters for PETN and ANFO Explosive
Detonation velocity (m/s)
PETN PETN Pure ANFO ANFO mixture
7450 5170 4930 2230
Density (kg/m3 ) 1500 880 820 500
C–J energy (MJ/m3 ) 8.56 5.025 5.322 3.822
to the principal adiabats calculated using a detonation code SIRIUS (Byers Brown, 1994). SIRIUS incorporates the Theostar (Horton, 1988) and Murnaghan (Horton, 1988) equations of states (for detonation products and silica, respectively), which are based on statistical mechanics and intermolecular potentials. The reference state in the Williamsburg equation of state is the detonation state, which is assumed to be ideal, i.e. satisfying the assumptions of the Chapman–Jouguet theory (Cook, 1958). The main assumption is that the reaction zone, in which the explosive decomposes to form stable molecular products in chemical and phase equilibrium, is extremely thin and flat. The Williamsburg equation of state for energy of order N in terms of reduced variables v is
U U(V, S) = ref −1 ∞ N
1 + ˇ ˛¯ k k k
k=1
1 + ˇk
(1)
C1 (GPa)
C2 (GPa)
r1
r2
ω
22.00 6.2 5.168 1.332
625.3 348.62 420.1 –
23.29 11.288 444 –
5.25 7.00 3.55 –
1.6 2.00 1.6 –
0.28 0.24 0.41 –
and where ˛˙ k (k) = ˛k + 2ık log()
(8)
and RG is the gas constant The adiabatic gamma coefficient s is computed as 1 k g−1 k N
s = g +
1−
k=1
1 k
(9)
with k = 1 + ˇk v ˛¯ k
(10)
The Gruneisen gamma coefficient G is
where V , Vref
=
C–J pressure (GPa)
and
= exp
S − S ref
nref R
1 ˛˙ k k f k N
(2)
G = g − 1 −
1−
k=1
The equations involve 4N + 4 basic parameters (the ˛k , ˇk , k , ık , and Uref , Vref , Sref , nref ). The reference values of Uref , Vref , Sref and nref are Chapman–Jouguet (C–J) values. The equation relating pressure to volume can be shown to be P = (g − 1)
U V
(3)
1 k
(11)
The specific isochoric heat capacity Ch = (∂U/∂T)v is found from 2 nref RG 2ϕ 1 ˛˙ k k =f + + Ch f f
k N
k=1
1−
1
k
(12)
where g(v, ) is given by
g = 0 +
N k=1
k 1 + ˇv ˛¯ k
(4)
and
∞ = 0 +
N
k ,
0 = 1 +
k=1
N
˛k k
(5)
k=1
and the functions ˛¯ k are defined as ˛¯ k (˛) = ˛k + ık log(). The temperature is expressed as T=f
U nref RG
(6)
where f(v, ) is given as
f =
N k=1
˛˙ k k 1 −
1 1 + ˇk v ˛¯ k
(7)
Fig. 6 – Log–log plot of pressure vs. volume. The circles are SIRIUS values and the solid line is the WBG fit. The dashed vertical lines are for the C–J and initial volumes.
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4.
Experimental results
4.1.
Flyer plate velocities and plate welding tests
4.1.1.
Plate contact velocity
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Velocity measurements were made using different thicknesses of steel and titanium plate and at least two thicknesses of explosive. Collision point velocities obtained for several combinations of plate and explosive thickness varied between about 1700 and 2300 m/s with most being around 2100 m/s. Two tests with commercial PETN explosive gave plate collision velocities which were very close to the published VoD value of 7300 m/s.
Fig. 7 – The WBG fit of natural log plot of principal adiabats against density for 77/23% ANFO/silica mix with initial density of 0.534 g/cm3 for pressure P, the dashed vertical lines are for the C–J and initial volumes.
where
ϕ=
N
ık k 1 −
k=1
1
k
The sound speed C = C=
(13)
(∂P/∂ )S is obtained from
PVs
(14)
3.1.1. The above equations were imported as a subroutine into the AUTODYN code The pressure against the specific volume and density along the adiabat are shown in Figs. 6 and 7, respectively. The circles are SIRIUS values and the solid line is the WBG fit. The dashed vertical lines are for the C–J and initial volumes, respectively.
Fig. 8 – ANFO/perlite mixture-velocity of detonation vs. explosive thickness (VoD meter and pin measurement).
Fig. 9 – Distance traveled vs. time for titanium flyer plates.
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titanium clad steel plates however showed no areas of poor bonding. In a test with a small (25 cm square) inclined plate arrangement and the high explosive (PETN) the plates only partially bonded and bonding did not occur until approximately half way along the plate, about 12 cm from the booster charge.
4.2.2.
Fig. 10 – Downward velocity of flyer plate.
A few measurements of the explosive VoD were made using an optical system but in general the methods were unreliable. The results are shown in Fig. 8. Although the data is scattered the VoD in general increases with explosive thickness.
4.1.2.
Flyer plate velocity in downward direction
The time delays between the pulses from the pins in the horizontal arm of the T were used to estimate the flyer plate downward velocity, Fig. 9. It should be noted that time zero on the X-axis is the time at which the flyer plate makes contact with pin 2 and not when the plate first starts to move. The bottom graph in Fig. 9 was compiled from the results of experiments with thickness of explosive layer. In general the flyer plate velocities were higher for the larger explosive thicknesses. Most measurements of downward velocity of the flyer plate showed that the flyer plate was still accelerating when it hit the ground. A typical result for a 6 mm thick stainless steel is shown in Fig. 10. The velocity profile determined from a computer simulation is shown for comparison and is discussed later.
4.2.
Examination of the welded plates
4.2.1.
Ultrasonic inspection
Conventional ultrasonic NDT equipment was used to identify areas of non-bonding. The data collected was processed to show plan views, so-called ‘C-scans’, of the bonded and unbonded regions of the plates, Fig. 11. Parts of the plate which were either poorly or un-bonded are shown as shaded. Most of the stainless steel clad plates had defects at the detonation end, varying in extent from small areas at the corners of the plate to much larger areas covering the entire width of the plate over axial distances of up to about 200 mm. The
Shear strength measurements of the bonded plates
Two samples were cut from the centre of each plate, one parallel and one normal to the direction of detonation and tested as described earlier. The variation of shear strength with stand off distance for stainless steel and titanium cladded plates are shown in Fig. 12a and b, respectively. This shows the shear strength of the bonded plates to increase slightly with stand off distance. There was little correlation between shear strength and explosive thickness. Fig. 13 shows the result for a 6 mm thick titanium plate. Similar results were obtained for the other titanium and stainless steel plates. In most cases there was very little difference in the bond strength of the two types of samples (Sp and St ). The shear strength of the titanium to steel weld samples were in the range 380–430MPa and were in general only slightly correlated with stand off distance and explosive load. The shear strength of the stainless steel clad samples varied between 430 and 550MPa, the highest values being for the largest stand off distance.
4.2.3.
Metallography
Photographs of the magnified (70× and 140×) interface of polished and etched samples of the plates are shown in Fig. 14. The shapes of the interface obtained from all experiments performed are summarized in Table 4. In general there were three types of interfaces, straight, smooth shallow wavy or shallow wavy with the beginnings of vortex formation. In some cases more than one type of profile was present in the same sample. Vortices were most often seen for the larger stand off distances and were very occasionally accompanied by small regions of melted metal lying between the peaks of the waves. Wavelengths where measurable were between 0.25 and 0.6 mm and amplitudes were about 0.05 mm, see Table 5.
5.
Simulation results
Some of the more important parameters extracted from the computer model are reproduced in Fig. 15a–f and summarized in Table 6.
Fig. 11 – Ultrasonic examination of welded plates (shaded areas denote poorly bonded regions). (a) 24 mm stand off, 12 mm stainless steel plate, explosive thickness 235 mm, (b) 18 mm stand off, (c) 12 mm stand off, (d) 6 mm stand off, (e) 12 mm stand off, 6 mm stainless steel plate, explosive thickness 107 mm, (f) 9 mm stand off, (g) 6 mm stand off, (h) 3 mm stand off.
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233
Fig. 12 – (a) Variation of shear strength with stand off distances (stainless steel plate), Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation. (b) Variation of shear strength with stand off distance (titanium cladding plate) Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation.
Fig. 15a shows examples of the temporal change in detonation gas pressure for six points at 20 mm intervals just above and along the top of the flyer plate. The pressure pulses have a very short rise time and a relatively slow decay (over a period of about 100 s). The peak amplitude increases with distance from the detonation point for the first 100 mm and then remains at a relatively constant level. The downward velocity of the flyer plate follows a similar pattern. The maximum impact velocity is relatively low near the detonation point then
gradually increases until it reaches a constant value at about 100 mm from the detonator. This variation in maximum velocity causes the flyer plate to bend as it travels towards the base, as shown in Fig. 15b. Fig. 15c–f shows examples of the pressure, shear stress, and absolute velocity contours for a 6.35 mm stainless steel flyer plate and 50 mm mild steel base plate with a 6.35 mm stand off. Typical plastic strains, at various points along a steel flyer plate are shown in Fig. 16. The peak strain increases with distance from the detonation point and in the
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stress magnitudes were also higher in regions of successful bonding.
6.
Fig. 13 – Variation of shear strength with explosive thickness Sp parallel to the direction of the detonation, St perpendicular to the direction of the detonation.
example shown it almost doubles from about 0.4 at 50 mm to 0.8 at 100 mm. It is interesting to note that for this combination of metals the point where the plastic strain exceeded 0.3 corresponds approximately to the start of good bonding in the welding test that was simulated. The predicted shear
Discussion
The lack of bonding near the detonation end of the stainless steel plates was most likely due to the initial relatively low pressure of the detonation gases and hence low plate velocity. In some cases the un-bonded area decreased as the stand off distance approached plate thickness. The increased bending resistance of the small length of plate acted upon by this lower pressure also tended to reduce initial impact velocity and angle. In most cases steady detonation and collision conditions were only reached about 100 mm from the source of detonation. The lack of un-bonded areas in the titanium welds was probably due to the lower stiffness and greater ductility of titanium. The thickness of the explosive had only a small effect on bond strength, stand off distance was more influential although the effect was small. In most cases there was very little difference in the bond strength of the two types of samples. The shear strength measurements for both the titanium to mild steel and stainless steel to mild steel welds were larger
Table 4 – The shapes of the interface obtained from all experiments performed Test no. Flyer plate material 1 2 3 4
Explosive
Flyer plate Stand off (mm) thickness (mm)
Stainless steel, 314 Stainless steel, 314 Stainless steel, 314 Quench hardened high strength steel, 4340 Mild steel, EN1 Titanium Titanium Titanium Titanium
PETN PETN PETN PETN
10 10 20 10
PETN ANFO mixture ANFO mixture ANFO mixture ANFO mixture
10 11 12 13 14 15 16 17 18 19 20 21 22
Titanium Titanium Titanium Titanium Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel Stainless steel
23
Stainless steel
5 6 7 8 9
Explosive thickness (mm)
0 10 20 0
9 9 75 9
10 3 3 6.35 6.35
0 3 6 6 3
9 107 107 80 135
ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture ANFO mixture
6.35 6.35 6.35 6.35 3 3 6 6 6 6 12 12 12
6 9 12 6 3 6 3 6 9 12 6 12 18
135 135 135 153 107 107 135 135 135 135 235 235 235
ANFO mixture
12
24
235
Results Weld No weld Weld No weld
Weld Also partly straight Shallow regular waves Partial bond Partly straight bond-no bond Shallow regular waves Shallow regular waves Vortices Partial bond Wavy Shallow waves Mostly un-bonded Partial bonding Shark toothed Also partly straight Partial bonding Wavy interface Front vortex only, very thin layer of melt at the interface Front and back vortex only, very little melt at the interface
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Fig. 14 – Examples of welded interfaces (mild steel plate on the bottom). (a) 3 mm stainless steel flyer 3 mm stand off 107 mm ANFO (70×), (b) 6 mm titanium flyer 3 mm stand off 107 mm ANFO (140×), (c) 3 mm stainless steel flyer 6 mm stand off 107 mm ANFO (70×), (d) 6 mm titanium flyer 13 mm stand off 108 mm ANFO (140×).
than those reported in standard shear tests (Anon., 1999) where shear strength values were given as 350 and 400 MPa for titanium to mild steel and stainless steel to mild steel combinations. The interface shear strength of the titanium/mild steel samples was less than that for the stainless steel/mild steel bonds. This may be due to the creation of a very brittle inter-metallic compound of TiC at the interface. Stainless steel and mild steel are also metallurgically more compatible than titanium and mild steel. There was no clear evidence of any correlation between bond strength and the level of ultrasonic signals reflected from the bond interface, as reported elsewhere (Wronka, 1999). The predicted time histories of a range of physical parameters were examined. The close agreement between the predicted and measured velocities of the flyer plate, Figs. 9 and 10 were particularly encouraging as they provided support for the modeling process. Following an initial steep rise the plate velocity increases more slowly with distance reaching values of about 400 m/s after about 20 mm travel. One of the most interesting parameters analyzed was plastic strain that is proposed that a minimum level of strain in the two plates is necessary for welding. The ultrasonic data taken along with Fig. 16 indicates that in the case of the stainless steel to steel welds an effective plastic strain higher than about 0.3 is probably required for bonding. The minimum value for titanium could not be verified as all of the clad plates were well bonded. The maximum value of shear stress along both titanium and steel welded plates tended to follow the same pattern
as that for plastic strains that is increasing fairly quickly and then remaining fairly constant along the length of the plate. The magnitude of the shear stresses predicted for the bonded regions were higher than those for non-bonded regions and at face to face points were opposite in sign, see Figs. 17 and 18. To achieve welding it is believed that jetting has to occur. In theory if the velocity of the collision point remains subsonic, jetting will occur at any oblique angle. In practice, however, a minimum angle is required to satisfy the pressure requirements, i.e. the pressure must be of sufficient magnitude to exceed the dynamic elastic limit of the material to ensure deformation of the metal surfaces into a jet. If the collision point velocity is maintained at a supersonic velocity, jetting will occur above some critical angle, which is dependent on the pressure distribution at the collision point as discussed earlier. In AUTODYN analyses using the Euler formulation, because material can escape the mesh boundaries, it was possible to simulate jetting. In addition, the analysis showed particle velocities to be very high near the collision point. Where particle velocities were low jetting was assumed not to occur. Fig. 19 shows the velocity vectors for an inclined plate arrangement (case 1) and for a parallel plate arrangement (case 2). The highest velocities were produced in the inclined plate setup (Fig. 19a). The wave-like structure in the interface of sectioned samples of welded plate samples was not seen in the simulations, although there were some indications of wave formation in velocity vector plots. This was most likely due to the relatively
Table 5 – Six millimetre titanium plate to 50 mm mild steel welds using a 6 mm stand off and different thicknesses of ANFO explosive Explosive thickness (mm) 80 107 153
Wavelength (mm) 0.6 0.5 0.25
Amplitude (mm) 0.08 0.05 0.05
Velocity of detonation (m/s) 2000 2050 2175
Comments Front and back vortices, melt between the wave peaks Front vortex only, very thin layer of melt at the interface Front vortex only, very little melt at the interface
236
Test no.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Measured flyer plate velocity (m/s) 350 560 350 350 350 460 610 300 335 450 540 620 265 280 380 210 250 300 330 245 300 340 400
Predicted flyer plate velocity (m/s) 340 550 340 340 340 488 630 313 348 460 532 600 275 280 365 195 255 294 324 237 310 358 394
Explosive ratio, R 0.19 0.19 0.418 0.185 0.192 3.928 3.928 1.3874 1.855 1.855 1.855 1.855 2.654 2.277 2.277 1.138 1.138 1.138 1.138 1.25 1.25 1.25 1.25
Predicted maximum impact angle (◦ ) 17.5 2.3 5.25 12 12.2 12.45 17.9 8.9 8.89 11.8 13.67 15.46 7.2 7.264 10.26 4.9 6.4 7.5 8.2 6.48 8.5 9.81 10.81
Predicted collision velocity (m/s) 1693.9 8100 5028 1683.4 1656.2 2050 2050 2000 2250 2250 2250 2250 2175 2050 2050 2250 2250 2250 2250 2400 2400 2400 2400
Predicted maximum pressure (GPa) 1.5 9.0 10.0 1.5 1.5 5.24078 6.65713 3.40021 3.78152 4.95335 5.68738 6.36417 3.00082 5.03848 6.53217 3.52304 4.59472 5.28617 5.81482 4.26927 5.55757 6.39333 7.01322
Predicted maximum shear stress (GPa) 0.1 0.06 0.03 0.1 0.1 0.262 0.332 0.170 0.189 0.247 0.284 0.318 0.150 0.251 0.326 0.176 0.229 0.264 0.290 0.213 0.277 0.319 0.350
Predicted maximum plastic strain 0.8 0.15 0.4 0.78 0.82 0.314 0.399 0.204 0.226 0.297 0.341 0.381 0.180 0.302 0.391 0.211 0.275 0.317 0.348 0.256 0.333 0.383 0.420
Terminal velocity (Gurney) (m/s) 347 554 347 347 347 920.5 920.5 780.7 919.5 919.5 919.5 919.5 1231.4 739.35 739.35 707.4 707.4 707.4 707.4 673.6 673.6 673.6 673.6
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Table 6 – Parameters derived from the simulations
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237
Fig. 15 – (a) Pressure/time profiles for seven points at 20 mm intervals just above and along the top of the flyer plate. Lowest curve is at the detonation end of the plate. The first point is 50 mm away from the detonation point. (b) Explosive welding simulation, distortion of the flyer plate by the detonation of the explosive. (c) Pressure contours in an explosive welding simulation (the explosive is not displayed in this image, but note the jetting and straight interface) (3 mm thick stainless steel flyer plate, 107 mm ANFO, 3 mm stand off). (d) Explosive welding simulation. Shear stress contours (6.35 mm thick stainless steel flyer plate, 6.35 mm stand off). (e) Explosive welding simulation. Velocity vector distributions (6.35 mm thick stainless steel flyer plate, 6.35 mm stand off). (f) Plate and jet velocities. (3 mm thick stainless steel flyer plate, 107 mm ANFO, 3 mm stand off).
course geometry of the elements (a compromise between resolution and computing time). The calculations for a 5 mm square mesh of cells took several days to complete mainly due to the time taken to solve the explosive equation of state. In contrast simulations of non-explosive oblique high veloc-
ity impacts which did show waves and used much smaller elements (1 mm or less) could be completed in less than 24 h. The simulations showed that the magnitude of the velocity vectors decreased as the distance from the collision point
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Fig. 16 – Temporal variation of effective plastic strain for seven points along flyer contact surface, at 50, 100, 150, 200, 250, 300 and 400 mm from detonation end of plate.
Fig. 17 – AUTODYN simulations of the shear stress profiles in flyer and base plates—inclined geometry (case 1).
increased. The driving force of this was the steep pressure gradient from the pressure maximum behind the point of impact, to zero pressure at free surface ahead of the impact.
Fig. 19 – (a) AUTODYN simulations of the velocity vectors for case 1. (b) AUTODYN simulations of the velocity vectors for case 2.
Fig. 18 – AUTODYN simulations of the shear stress profiles of flyer and base plates—parallel geometry (case 2).
Pressures (of the order of GPa), and plate velocities were highest at the collision point. The high pressures and velocities created high plastic deformation which in turn produced large values of plastic strain (>2), and shear stress at the interface. The strain values were material-dependent.
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The flyer and base plates bent near the point of impact and the impact angle changed as the collision point moved along the plate. The shear stresses were highest in the simulations of plates which exhibited good bonding. This implies that a threshold value of shear stresses must be exceeded for bonding to take place in different combinations of metals. For stainless steel to mild steel combinations the threshold stress was found to be 0.5 GPa and for titanium to mild steel the threshold shear stress was 0.4 GPa. Effective strains higher than 0.35 were seen in stainless steel/mild steel welding simulations in the areas where welding took place. For titanium to mild steel effective strains were above about 0.4. The value of effective strain depended on dynamic angle, with the highest values occurring with the inclined plate arrangement.
7.
Concluding remarks
The pin contact method for measuring velocity of detonation and plate velocity worked well in the field. The velocity of detonation of the ANFO mixture was approximately 2100 m/s and plate impact velocities were between about 300 and 450 m/s. The ultrasonic examination of the welded plate showed an initial impact defect in the stainless/mild steel welded plates but no defects in the titanium/mild steel composite plates. The defect in the stainless steel plates started at the detonation end and in some cases extended about 200 mm along the plate. It correlated with the pressure distribution predicted by the computer simulations. This ‘end effect’ should be considered when welding large expensive sections of this combination of plates. Microscopic examination of sections of the welded plates showed that in general interface waves were smaller in titanium plates than in the stainless steel plates. In both cases thicker plates displayed higher amplitude waves than thinner plates. The thicker plates in general were also more strongly bonded. New data was obtained for the ANFO explosive and the good agreement between simulation and experimental results for plate velocities provides support for the newly developed equation of state for ANFO mixtures. The study shows that effective plastic strain and shear stress in the flyer and base plate are important parameters in determining whether or not bonding will occur.
Acknowledgement This work was part funded by the EPSRC.
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references
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