impact welding

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Journal of the Mechanics and Physics of Solids 53 (2005) 2501–2528 www.elsevier.com/locate/jmps

Numerical and experimental studies of the mechanism of the wavy interface formations in explosive/impact welding A.A. Akbari Mousavia,, S.T.S. Al-Hassanib a

Department of Metallurgy and Material Science Engineering, Faculty 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 Received 30 November 2004; accepted 6 June 2005

Abstract Explosively driven impact welding is a true example of multidisciplinary research as the phenomena associated with it fall under the various branches of engineering science. A great deal of the work in, and collaboration between various specialised fields have been expended on the subject. However, a comprehensive quantitative theory capable of giving an accurate description and prediction of the parameters and of the characteristic features of explosively welded components does not exist. Most of the investigators considered the welding process as a solid state welding process, but some believed that the process is a fusion welding process. Interfacial waves are the most discussed aspect of explosive welding. The presence of jet in the collision region, and the transient fluid-like behaviour under high pressure have led many investigators to seek an explanation and a characterisation of these waves in terms of a flow mechanics of one kind or another. In this study, part of the welding process was numerically analysed. A finite difference engineering package was used to model the oblique impact of a thin flyer plate on a relatively thick base. The results were validated by data from carefully controlled experiments using a pneumatic gun. Straight and wavy interfaces and jetting phenomena were modelled, and the magnitude of the waves and the velocity of jet predicted. The numerical analysis predicted a hump ahead of the collision point. Wave formation Corresponding author. Tel.:+98218012999; fax: +98218006076.

E-mail address: [email protected] (A.A. Akbari Mousavi). 0022-5096/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jmps.2005.06.001

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appears to be the result of variations in the velocity distribution at the collision point and periodic disturbances of the materials. Higher values of plastic strain were predicted in wavy interfaces. Bonding was found to be a solid state welding process. Phase changes which occur may be due to high temperatures (but less than the melting temperature) at the collision point. r 2005 Elsevier Ltd. All rights reserved. Keywords: Explosive welding; Wavy interface; Straight interface; Jet formation; Numerical simulation

1. Introduction Explosive welding is best known for its capability to directly join a wide variety of both similar and dissimilar combinations of metals that cannot be joined by any other welding or bonding method, because of dramatically different melting points (see Fig. 1). Furthermore, the process is capable of joining these combinations over large surface areas due to the ability to distribute the high energy density available in the explosive over the welding area in an economical fashion. In the reverse manner, the energy can also be concentrated to produce welds on small areas. Furthermore, the process can clad one or more different metal layers onto either, or both faces of a base plate. During the high velocity oblique collision of metal plates, a high velocity forward jet is formed between the metal plates if the collision angle b and collision velocity Vp are in the range required for bonding (see Fig. 2). The surface layers on the metals, containing non-metallic films such as oxide films that are detrimental to the establishment of a metallurgical bond, are swept away in the jet. The metal plates themselves cleaned of any surface films by the jet action are joined at an internal point under the influence of a very high pressure that is obtained near the collision region. The pressure has to be sufficiently high and for a sufficient length of time to achieve inter-atomic bonds. The velocity of the collision point, V c , governs the time

Fig. 1. Explosive welding process.

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Fig. 2. Explosive welding parameters.

available for bonding. This high pressure also causes considerable local plastic deformation of the metals in the bond zone. The bond is metallurgical in nature and usually as strong or stronger than the weaker material. The quality of the bond depends on careful control of the process parameters. These include material surface preparation, plate separation, the explosive load, detonation energy and detonation velocity Vd. The selection of parameters is based upon the mechanical properties, density, and shear wave velocity of each component. Considerable progress has been made to establish the optimum operational and physical parameters required to produce an acceptable bond and welding windows (of various parameters such as flyer plate velocity-impact angle and impact pressure-impact angle etc.) have been proposed by different authors.

2. Theories of welding and wave formations Various mechanisms have been introduced to describe the explosive welding process in the early stages of development. Some researchers considered it to be essentially a fusion welding process (Phillipchuk, 1961) which relies on the dissipation of the kinetic energy at the interface as a source of the heat sufficient to cause bilateral melting across the interface and diffusion within the molten layers. Such fluid diffusion leads to gradual transition from one material to another. In explosive welding the transition is very sudden, even in those cases where pockets or layers of solidified melt appear locally. Other investigators (Crossland and Williams, 1970) regarded the process as a pressure weld operation. This depends on large plastic deformations at the interface to allow clean surfaces to be formed and a solid diffusion process to take place, providing that a high-pressure level is maintained for a sufficient length of time. In explosive welding, the peak pressures are maintained for a few microseconds only and the coefficient of diffusion is small. In addition, the interfacial waves, vortices and/or melt pockets often observed cannot be accounted for by either pressure welding or pure melting mechanisms. The interfacial grain deformation and wave formation suggest that the mechanism of welding must be

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associated with a flow process. Otto and Carpenter (1973) suggested that interfacial shear occurs during welding and attributed the weld to the effect of the heat generated by shearing at the interface. This could cause sufficient heating of the boundary layers to achieve a bond, and could also account for the wave formation. Since in this shearing mechanism no role is assigned to a jet in the bonding process it was found inadequate by Bahrani and Crossland (1964). An alternative theory was proposed by Hammerschmidt and Kreye (1984) that explosion bonding was a fusion welding process. During the process, the interface achieves a very high temperature, above the melting point, for a few microseconds. This is followed by cooling at about 105 K/s creating an ultra-fine grain size. They disprove the solid-state welding theory noting that the peak pressure is maintained for only a few microseconds which is not adequate to allow sufficient diffusion. A later study by Onzawa et al. (1985) arrived at a similar conclusion. They performed interface observations using scanning electron microscopy (SEM) and transition electron microscopy (TEM). The authors proposed a model of the bonded zone in which the bond region is composed of several layers between steel and titanium of which the total thickness is less than 60 mm. In the centre of the interface there is an amorphous area with a thickness between 0.05 and 0.2 mm including some very fine grains in the 0.01 mm range. The existence of this amorphous layer within the bonding zone has been observed in various combinations of metal and is interpreted as the basic mechanism of explosive welding (El-Sobky, 1983). On the basis of experimental evidence it is generally accepted that the phenomenon of jet formation at the collision point is an essential condition for welding. The jet chemically cleans the mating surfaces by removing films and other contaminants, thereby making it possible for the atoms of the two materials to approach to within inter-atomic distances when subjected to the explosively produced pressure waves. The collision pressure associated with the dissipation of kinetic energy must reach a sufficient level and be maintained for a sufficient length of time at this level to achieve the stable inter-atomic bonds. In this case, the impact velocity determines the pressure, whereas the velocity at the collision point governs the time available for bonding. There are important similarities between explosive welding and liquid impact. For example, jet formation occurs from under an impacting liquid drop or wedge depending whether or not the contact periphery moves supersonically (no jet) or subsonically (there is a jet). Additionally, there can be ripple (wave formation) when liquid drops impact metals. The analytic solutions of the pressure and jet velocities of liquid drops impact can be found in (Lesser, 1981; Lesser and Field, 1983a, b) and photographic records of the shock structure, jet velocities and the conditions for jetting using the 2-d gel technique were reported in (Field et al., 1985). In another study, Lesser and Field (1983a, b) showed how spallation of drops formed the jet. Wave formations at an interface between colliding liquids were studied by Wilson and Brunton (1970). Theories of wave formations fall within the following categories (Reid, 1974): Indentation mechanism, flow instability mechanism, vortex shedding mechanism and stress wave mechanism. The mechanisms proposed by Bahrani and Crossland

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(1966), Bahrani et al. (1966), Bergman et al. (1966) and Abrahamson (1961) can be grouped together as an indentation mechanism. These authors described how the interface would attain its characteristic shape by periodic indentation of the parent plate and hump formation ahead of the stagnation point by the flyer plate and vice versa. Another theory of wave formation was proposed by Hunt (1968) and Robinson (1975). They suggested that waves in explosive welding were an example of Helmholtz instability, which occurred when there was a difference of velocity between adjoining streams. In the flow instability mechanism described by Robinson (1975) the waves are created behind the collision zone as a result of a velocity discontinuity across the interface which involves a salient jet. This is contrary to the flow instability mechanism expressed by Hunt (1968) in which the waves are created ahead of the collision point due to a velocity discontinuity across the interface and the jet. Other researchers Cowan et al. (1971) and Kowalick and Hay (1971) were probably the first to note the similarity between the interfacial waves in explosive welding and von Karman’s vortex streets generated behind an obstacle. They proposed that the diameter of the obstacle should be taken as the thickness of the reentrant jet. A stress wave mechanism of wave formation was proposed by El-Sobky and Blazynski (1975). The authors noted that waves were observed on surfaces of metals which had been subjected to oblique collision, where neither welding nor jetting has occurred. They considered the problem of surface disturbances ahead as well as behind the collision point to be caused by successive interference from rarefaction waves in both plates as well as multi-layered welding. In this mechanism, the waves were generated in front of the collision point, while the vortices are created subsequently. The wave formation mechanism was attributed by Plaksin et al. (2003), to the regular instabilities that were induced by oscillating detonation waves and that were transmitted through the interface of the impact materials. 2.1. Modelling explosive and impact welding Few attempts have been reported in the literature to numerically simulate the explosive welding process. El-Sobky and Blazynski (1975) studied the process using a liquid analogue. Their logic was founded on the similarity between hydrodynamic fluid behaviour and material deformation in explosive welding. In the latter case, the application of a high value of pressure at the interface, results in the materials being unable to support shear stresses and for a short period of time they behave as a liquid. In metals there is a transition from inviscid flow to viscous flow, as stresses decrease solidification begins. This aspect of a liquid implies that in any liquid analogy mechanism, only the initial stages are important. The transient response of metal plates under explosive loading were analysed by Lazari and Al-Hassani (1984) employing a finite element method. Rectangular cross-section elements of uniform thickness and widths were chosen. In their work, material non-linearity due to plasticity and strain-rate was analysed numerically. Large displacements were adequately solved using non-linear ordinary differential equations using the finite element method. The principle of virtual displacements in Lagrangian deformation was used to derive the equations of motion. The problem was treated as a normal

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transient loading of plane stress elements of rectangular shape. In this analysis, kinematically equivalent concentrated loads at the nodes represented the uniformly distributed explosive load. Explosive welding process was simulated by Oberg et al. (1984) by means of Lagrangian finite difference computer code, but only produced jetting. The explosive welding process were also modelled by Akihisa (1997). He only produced waves but no jetting. In addition, the author assumed that symmetric or asymmetric shear flow distribution was generated in the flyer and parent plates and the modelling was performed based on this supposition. 2.2. Impact welding using a pneumatic gun Small metal plates (40 mm square) were impact welded to mild steel bases by firing them at an obliquely mounted target fixed to one end of a 63 mm bore gas gun. Pneumatic guns have been developed specifically for studying impact welding (McKee and Crossland, 1997; Szecket, 1979) but required extensive refurbishment and redesign (Akbari Mousavi, 2001; Al-Hassani, 2001). The oblique collision of the two plates results in solid state welding. This achieved similar impact conditions to those in the explosive welding process (See Fig. 3a). An essential difference is that in the gas gun the flyer plate velocity is constrained to be normal to the flyer plate surface, whereas in explosive welding the direction of the velocity of the flyer plate is not well defined. According to Birkhoff et al. (1948) this direction bisects the angle SBC (see Fig. 3b). It would be possible to simulate this condition by inclining the flyer plate to the normal to the axis of the gun. However, this requires accurate alignment of the inclined flyer plate (attached to the sabot) to the inclined target plate. However, as the precise direction of Vp in explosive welding is not known, there seems no real purpose in this additional complexity. If the gas gun can provide similar impact conditions to those in explosive welding process, the velocities and angles measured in the gas gun experiments can be validated by the explosives

Fig. 3. Simulation rig to guide a pneumatically driven flyer plate to impact an oblique target with velocity Vp. (b) Birkholf velocity diagram.

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welding trials in the field provided that both resulted in similar interface geometries for similar experimental conditions. The experimental results were reported by Akbari Mousavi et al. (2005). Similar interface morphologies were obtained for both tests under similar welding conditions and therefore the velocity measurements can be justified. Although, more accuracy was usually achieved with a double diaphragm system, however, using the single diaphragm in our system, velocities can be reproduced to 10 or 15 m/s. This range of error was acceptable in the explosive welding process. The gas gun has a number of advantages over explosives for studying impact welding. It is easy and safe to use and experiments can be performed quickly with reproducible results. It allows the essential parameters to be varied independently over a wide range of values, to enable the full construction of the welding window. The main features of the gun are as follows: It consists of four main components, a pressure chamber approximately 2 m long, a 63 mm bore 2-m-long barrel, a bursting disc fitted between the pressure chamber and the barrel and a target holder (please see the Figs. 2–20 to 2–24 in reference (Akbari Mousavi, 2001)). The target holder could be bolted tightly to the end of the barrel to make an airtight seal or clamped in a stand off position to leave the barrel open. In the former case the barrel was usually evacuated which enabled a higher projectile velocity to be realised, and silent firing (because of the absence of a shock wave in the barrel). The targets were mild steel blocks, approximately 40 mm square and 30 mm thick and were supported in a holder shaped to hold the target at an angle to the axis of the barrel. Several holders with different angles of inclination (between 81 and 351), were used in the experiments. The projectile glued to the sabot fitted in the barrel just in front of the bursting disc. The flyer plates used in the tests were 40 mm square 3 mm thick and made from, copper, stainless steel, titanium or zirconium. A few tests were also done with thinner flyer plates. For most tests nylon sabots were used to support the flyer plate. Compressed helium was used to achieve maximum projectile velocity and for most experiments the barrel was evacuated and the target end of the gun closed. A number of methods for measuring projectile velocity were investigated. The most reliable used two 25 swg enamelled wire stretched across the bore of the gun and sealed into the barrel wall. The wires were separated by a distance of 50 mm and were located approximately 25 mm in front of the target. The wires were connected to a simple electrical circuit, which produced a voltage transient when the projectile made contact. The voltage transients were recorded on a high-speed digital storage oscilloscope (1 GHz sampling rate). Velocities up to 1000 m/s were measured using this arrangement. The following combinations of metals were welded: Stainless steel on to mild steel, titanium on mild steel.

2.2.1. Johnson– Cook constitutive equations In Johnson–Cook constitutive equation (Johnson and Cook, 1983), the von-Mises yield stress is given as s ¼ ðA þ B
n Þð1 þ C ln
_ p Þð1  T nm Þ,

(1)

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where
is the equivalent plastic strain,
_p is the plastic strain-rate for
_ 0 ¼ 1:0=s, T* is the homologous temperatureðT  T room Þ=ðT melt  T room Þ, and T is the absolute temperature for 0pT*p1.0. The five constants are A, B, n, C, and m. The expression in the first set of brackets gives the stress as a function of strain for
_p ¼ 1:0 and T n ¼ 0. The expressions in the second and third set of brackets represent the effects of strain rate and temperature, respectively. At the melting temperature (T  ¼ 1) the stress approaches zero for all strains and strain rates. The material constants are determined from straining tests performed in tension or torsion. Although various test techniques can be used to obtain the constants for this model, the following approach has commonly been used. First, the yield and strain hardening constants (A, B, and n) are obtained from isothermal tension and torsion tests at relatively low strain rate (_
p p1:0). Secondly, the strain rate constant C is determined from torsion tests at various strain rates and from tension tests (Quasi-static and Hopkinson bar) at two strain rates. Finally, the thermal softening constant m is determined from Hopkinson bar tests at various temperatures. The model takes into account strainhardening, strain-rate hardening, and thermal softening. The mechanical properties of the materials used in this study and their Johnson–Cook parameters equation (Eq. (1)) are summarised in Table 1. 2.2.2. Simulation of impact welding Numerical simulations of the experiments described above were carried out using AUTODYN-2d version 4.1 13 (AUTODYN Code, 2001). The simulations modelled the interaction between a mild steel base plate and flyer plates of titanium (Ti), stainless steel (SS) and zirconium (Zr). In all cases the base plate was modelled as a 30-mm-thick 40-mm-square block and the flyer plate as a 3-mm-thick 40-mm-square plate. Several combinations of impact velocity (250–1000 m/s) and impact angle (8–341) were considered. The Euler processor in which the numerical mesh is fixed in space and the physical material flows through it was used. The materials at the point of collision were considered to behave as a liquid. In addition, although in Eulerian formulation, the mesh is fixed and the material flow through the meshes, the size of the mesh plays an important role from the computational timing point of view and stability. In modelling impact and explosive welding, the size of mesh was also important in visualising the jetting particles and interface profiles. The meshes were more refined in the area where the jet forms. A mesh size of about 0.02 mm was used in this study for the areas close to the collision zones. Comprehensive descriptions can be found in (Akbari Mousavi, 2001; Al-Hassani, 2001). The data obtained from the simulations were validated by the explosive welding trials as well as impact welding tests. The explosive welding trails used to validate the AUTODYN simulations were reported in (Akbari Mousavi et al., 2005).

3. Experimental results—weld interfaces The shape of the interface fell roughly into three classes, straight, smooth wavy or wavy with some vortex shedding (Akbari Mousavi, 2001; Al-Hassani, 2001).

Yield stress (MPa)

1006 350 Armco-Iron 175 4340 792 Mild Steel 310 Titanium 1500

Density (Kg/ Bulk modulus m3) (Gpa)

Shear modulus (Gpa)

Hardness (MPa)

Hardening constant (MPa)

Hardening exponent

Strain rate constant

Thermal softening exponent

Melting temperature (1K)

7896 7890 7830 7830 4450

81.8 80 81.8 82 55

2000 2000 2000 2000 2200

275 380 510 350 380

0.36 0.32 0.26 0.3 0.32

0.022 0.06 0.014 0.02 0.22

1.00 0.55 1.03 0.5 0.7

1811 1811 1793 1800 1670

160 164 159 169 178

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Table 1 Mechanical properties of the materials used in this study and their Johnson–Cook parameters equation (Eq. (1))

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Photographs of the various interfaces seen in samples taken from impact welding of 3 mm stainless steel, titanium and zirconium flyer plates to 30 mm mild steel base plates are shown in Figs. 4–7, respectively. Figs. 4–6 show that at a constant angle wavelength increases with impact velocity. In some cases, a gradual change in wavelength along the direction of welding which was due to a change in impact angle

Fig. 4. (a) Interface after impact at 151(  70), materials: 3 mm stainless steel flyer plate (top) 30 mm base plate (bottom), velocity of impact: 470 m/s. (b) Interface after impact at 151 (  70), materials: 3 mm stainless steel flyer plate (top) 30 mm base plate.

Fig. 5. (a) Interface after impact at 111 (  70), materials: 3 mm titanium flyer plate (top) 30 mm base plate, (bottom), velocity of impact: 486 m/s. (b) Interface after impact at 111 (  140), materials: 3 mm titanium flyer plate (top) 30 mm base plate (bottom), velocity of impact: 606 m/s.

Fig. 6. Interface after impact at 111 (  140), materials: 3 mm zirconium flyer plate (top) 30 mm base plate (bottom), velocity of impact: 550 m/s.

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following plate contact, was observed (see Fig. 7). This matter was already reported by Bahrani and Black (1966). 3.1. Results of the numerical simulation The distributions of contact pressures, stresses, strains, angle of contact and contact velocities around the contact area were plotted for every impact angle, impact velocity and material combination. Material locations, velocity distribution and the pressure contours along the plates are shown for an impact angle of 151 and impact velocity 584 m/s in Figs. 8–10. A novel achievement was the simulation of the

Fig. 7. Interfaces after impact at 151—584 m/s impact velocity—3 mm stainless steel flyer plate-change of wave length along the interface (  140).

Fig. 8. AUTODYN simulation of impact welding—material location.

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Fig. 9. AUTODYN simulation of impact welding—velocity vector profile.

Fig. 10. AUTODYN simulation of impact welding—pressure distribution—wavy interface.

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Fig. 11. AUTODYN simulation of impact welding—pressure distribution—straight interface.

wavy interface commonly seen in the experiments (see Figs. 8–10). Jetting was also observed in the graphical output from the simulations (see Figs. 8–11). In the instances where the numerical analysis predicted a wavy interface, their amplitude and wavelength were similar to those found by experiment. In some cases, the simulations produced a straight bond line (see Fig. 11). 3.2. Wave formation of symmetric arrangements In order to investigate the interface wave formation and jetting resulting from two identical plates impacting each other, two 6 mm stainless steel plates inclined at 151 degree impacting each other at velocity of 650 m/s were modelled. This cannot be achieved by impact tests in practice and only by explosive welding. Fig. 12 shows the material locations, 11.2 ms after first collision. The creation of a hump and the formation of a jet are seen in Figs. 12–19. The jet material is mostly from the base plate and its velocity is about 4000 m/s. Apart from the jet, the highest velocity vectors are at the collision point. Considering the last wave near the collision point, it is seen from Fig. 13 that a very high velocity field is produced at the wavy interface zone and a very high pressure occurred at the collision point (Fig. 14). Higher values of pressure are seen in the flyer plate than in the base plate which is probably due to loss of more material from the base than the flyer plate. A very localised high temperature regime around the collision point was seen, but the highest temperature was lower than the melting temperature of the steel (see Fig. 15). A plastic strain of

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Fig. 12. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—material location (shown on a large scale).

Fig. 13. Simulation of two 6-mm-thick stainless steel impacting at a velocity of 650 m/s and an inclination of 151—velocity distribution.

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Fig. 14. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—pressure distribution.

Fig. 15. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—temperature distribution.

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Fig. 16. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—effective plastic strain distribution.

Fig. 17. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—effective plastic strain-rate distribution.

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Fig. 18. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—normal stress distribution.

Fig. 19. Simulation of two 6-mm-thick stainless steel plates impacting at a velocity of 650 m/s and an inclination of 151—shear stress distribution.

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more than 2 and a plastic strain-rate of 5  103/s were predicted for the collision zone (see Figs. 16 and 17). The normal stress distribution were more uniformly distributed than the pressure distribution (see Fig. 18) and were negative due to the down ward vertical velocity of both plates at the interface, producing compressive stresses. Shear stresses of different signs were produced at the interface (see Fig. 19). The absolute value of shear stress in the flyer plate was higher than in the base plate (above the wave interface) and is the reason for that concave wave produced at this region. It was predicted that a convex shape would be created if the shear stresses were reversed. The internal energy distribution at the collision point can also be predicted. The jet energy is predicted to be about 6 MJ/kg. At the collision point the internal energy was predicted to be about 3.6 MJ/kg.

4. Discussion 4.1. Hump formation The formation of a hump in the collision zone has been identified (El-Sobky, 1983; Crossland, 1982) as an important phenomenon having a substantial influence on the mechanism of weld formation. It is therefore of interest to briefly comment on the formation of the hump and its geometrical features. The analysis shows that the velocity field is strongly diverted in the collision direction. The driving force of this effect is the steep pressure gradient from the pressure maximum behind the point of impact, to zero pressure at the free surface ahead of the impact. The simulations show that the flyer and base plates are no longer straight, but are bent near the point of impact. As the collision point moves along the plate the impact angle increases due to initial plastic hinging and then decreases due to the smaller stand-off, i.e. the impact angle is dynamic. This dynamic impact angle substantially exceeds the angle between the plates when the surfaces are straight. This changing impact angle determines the conditions for deformation near the point of impact. The formation of a hump was observed in the simulations of the welding of stainless steel, titanium, zirconium flyer plates to mild steel base plate as well as for soft-hard material combinations (copper to steel). 4.2. Jet formation One of the most important conditions for welding is the formation of a jet at the collision point. To achieve welding, jetting has to occur. This is the main condition for welding. The high-localised pressures created at the collision point spread away at the sound velocity. Since the collision is moving forward at a subsonic rate, pressures are created at the immediately approaching adjacent surfaces, which are sufficient to spall a thin layer of metal from each surface and eject it away in the form of a jet. In practice, the surface contaminant, oxides and impurities are stripped away in the jet. For bonding to take place the two surfaces must be brought together

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sufficiently close to be within the range of the inter-atomic attractive forces. The force between the two atoms consists of attractive and repulsive forces and at a certain equilibrium distance these two forces are in equilibrium, i.e. the potential energy reaches its minimum value. For two surfaces to adhere they must be brought together to within this equilibrium distance and for this to occur it is necessary for the surfaces to be free from any oxide and other contaminant films. In theory at any oblique angle if the velocity of the collision point remains subsonic, jetting will occur. 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. By using the Euler processor in the (AUTODYN Code, 2001) simulations it was possible to show the phenomenon of jetting. The formation of a jet in the simulation of a stainless steel flyer impacting a steel base plate is shown in Figs. 12–20. It can be seen that the well defined sharply pointed collision angle of the initial geometry gradually develops into a more rounded collision geometry. The simulations indicated that dynamic angle at the collision point played an important rule in the jet formation. If both plates contribute to jetting the jetting formation is symmetric, i.e. the jet bisects the angle between the flyer and base plate. If the jet consists of only the flyer or only the base plate material the jet is asymmetric, i.e. the jet moves towards the flyer plate or base plate, and the angles between the jet and the plates are not equal. Figs. 8–10 show

Fig. 20. Interfaces after impact at 151—584 m/s impact velocity—3 mm stainless steel flyer plate-change of wave length along the interface (compare with Fig. 13).

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that most of the jet material originated from the flyer material, which has the most favourable impingement angle for jet formation. The computer simulation shows that as the jet asymmetry is decreased, the base plate increases its contribution to jetting (see Fig. 11). Another consequence of the increased degree of symmetry is that the jet loses contact with the plate surfaces in front of the collision point. The jet velocity obtained from the simulation was 15–20% lower than that obtained using the standard equation (Crossland, 1982) vj ¼ vp = sin bð1 þ cos bÞ where nj is the jet velocity. The highest predicted values of jet velocity by AUTODYN and the equation were about 4000 and 4890 m/s, respectively. The difference was attributed to the fact that the particle velocity is mesh size dependent. Larger mesh size produced lower jet velocity. The size of the mesh could not be lower than the specific value (less than 0.02 mm) due to imposed limitations to the Euler solver in the (AUTODYN Code, 2001) and stable time step value. The value of this time step depended on several parameters of the numerical method and solution so that the local time step ensuring stability was calculated for each mesh. The predicted jet thickness is, however, in agreement with that obtained using the equation (Crossland, 1982) mj ¼ m=2ð1  cos bÞ. The jet thickness was comparable with the amplitude of the waves in the interface. 4.3. Velocity distribution Figs. 9 and 13 show the velocity distribution close to the collision point. It can be seen that the highest velocities were at the collision point. High velocities created high plastic deformation. This in turn produced high values of plastic strain and shear stress at the interface. The simulation results showed the formation of a narrow band of plastic strain, a severe plastically deformed zone and high values of shear strain at the collision zone, which confirmed the prediction of Bondar (1995). However, the values of shear strain obtained were different. It was found that the values were material dependent and were predicted to be more than 2 for the materials used in this study. The periodic disturbance of the velocity profile and material deformation appears to be responsible for the creation of the wavy interface. The periodic disturbances are induced in the gun experiments by the oblique collision. This study dismissed the (Plaksin et al., 2003) mechanism of wave formation, as the waves are produced in the gun experiments in which no detonation wave exists. The detonation waves transmitted to the collision point create additional instabilities to the collision point. The birth of the jet may be related to the result of high-frequency velocity oscillation with gradually increasing amplitude. Elastic precursor is unimportant in relation to the plastic pulse that succeeds it. 4.4. Pressure distribution The pressure distribution close to the collision point during jetting is illustrated in Figs. 10, 11 and 14. Figs. 10 and 14 show that there are slight asymmetries between the plates. This is probably due to the fact that a jet from the base plate (in Fig. 10)

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and from the flyer plate (in Fig. 14) has not yet been formed. Fig. 10 shows that the pressure maximum in the base plate is closer to the plate surface than in the flyer. This is probably due to the loss of the flyer plate material into the jet which reduces the pressure on the surfaces in the flyer, but not in the base. The opposite situation can be seen in Fig. 14. The simulations show that increasing the impact angle for a similar impact velocity reduces the impact pressure (see Table 2). Pressures in the range 1–15 GPa were obtained at the collision points. 4.5. Straight to wavy interface The transition from a straight to a wavy interface appears to be related to an increase in the plastic strain and shear stress. Higher plastic strain and shear stress were seen in the cases where wavy interfaces were formed. For steel, the transition from a straight to a wavy interface occurred when the plastic strain exceeded 0.5 and the shear stress exceeded 0.5 GPa. For titanium, the transition occurred when the plastic strain was greater than 0.9 and the shear stress was greater than 0.5 GPa. 4.6. Wavelengths and amplitudes The predicted and measured wavelengths and amplitude for titanium flyer plates impacting a mild steel base plate are shown in Tables 2. For higher impact angles there was some correlation between interface wave size and the velocity and impact angle. The largest wavelength and amplitudes were predicted to be in the stainless steel to mild steel rather than the titanium to mild steel. The experiments showed that the wavelength was not uniform along the interface (see Fig. 7). Shallow waves appeared at the initial sections of the bond, with deeper waves in the end. The results suggest that the change of the wavelength was due to changes in the impact angle along the interface. Similar results were predicted by numerical modelling (see Fig. 20). In practice, weld interfaces often contain vortices following the wave peaks. These were not predicted by the simulations, probably due to the fact that solid mechanics constitutive equations rather than fluid mechanics equations were used to describe material behaviour. The simulations, however, predicted deeper waves for the cases that created vortices. Waves were also observed in symmetrical arrangements. The velocity discontinuities were noticed across the surfaces of the plates behind the collision zone. Therefore, this study supports the Robinson theory of wave formation (Robinson, 1975). The wave shape is perfectly symmetric for metals with similar density (stainless steel to mild steel) and becomes increasingly asymmetric as density differences increase (titanium to mild steel or zirconium to mild steel). The simulations predicted surface waves ahead of the collision point (Figs. 8–20) in agreement with El-Sobky and Blazynski (1975) and Chadwick et al. (1968). However, the correlation between the size of waves created after impact and those resulting from the disturbance of stress waves was not clear.

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Impact Collision Predicted velocity (m/s) velocity (m/s) maximum pressure (GPa)

Predicted wavelength (mm)

Measured wavelength (mm)

Impact Predicted velocity (m/s) amplitude (mm)

Measured amplitude (mm)

Comments

8 8 8 11

300 350 400 376

2155 2514 2874 1970

5.19 6.05 6.92 6.5

— — — 0.16

— — — 0.15

300 350 400 376

— — — 0.05

— — — 0.06

11

428

2243

7.40

0.18

0.15

428

0.05

0.05

11

486

2547

8.40

0.25

0.2

486

0.05

0.05

11

606

3175

10.48

0.25

0.25

606

0.05

0.05

11 15 15

675 632 467

3537 2441 1804

11.68 10.94 8.08

0.5 0.1 —

0.45 0.12 —

675 632 467

0.05 0.05 —

0.045 0.05 —

15 15

612 641

2364 2476

10.59 11.09

— 0.6, 1.25

— 0.6, 1.2

612 641

— 0.2, 0.42

— 0.2, 0.4

15 23

735 711

2839 1819

12.72 12.30

0.8 0.7

0.8 0.65

735 711

1 0.1

0.8 0.15

23

761

1947

13.17

0.65

0.7

761

0.16

0.18

No weld No weld No weld Also partly straight Also partly straight Shallow regular waves Also partly straight Wavy Wavy Mostly unbonded Straight Some tails to peaks Shark toothed Also partly straight Wavy

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Table 2 Predicted and measured welding parameters, wavelengths and amplitude of interface profile for a 3 mm titanium flyer impacting a 30 mm mild steel base plates

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4.7. Bond and no-bond cases Bonding did not occur at impact angles above 231 for both flyer plates, and not for titanium flyer plates below 111, (plastic strain less than 0.3 and shear stress less than 0.4 GPa for titanium). Kowalewskij et al. (1979) and Simonov (1991) reported that bonding occurs when the collision velocity is higher than a threshold value dependent on shear wave velocity. The experimental evidence from this study show that this is only partially true and that successful welding also depends on impact angle. (No weld occurred for titanium at 81 impact angle although their collision velocities were in the ranges where bonding might be expected to take place, see Table 2). 4.8. Effect of flyer plate thickness on the wavelength Correlation was sought between the thickness of flyer and base plates with wavelength. Experiments by Al-Hassani et al. (1984) showed that increasing the thickness of flyer or base plates increases the wavelength of the deformation in the interface. Simulations of 1.5, 3 and 6-mm-thick copper flyer plates impacting at a velocity of 650 m/s at an angle of 151 on a 15-mm-thick copper base carried out. The results predicted the increase of wavelengths with flyer plate thickness (see Table 3). 4.9. Temperature Johnson–Cook equation (Johnson and Cook, 1983) includes the effect of temperature on flow stress and on the plastic strain. The computer simulations show that the pressure at the collision zone caused an increase in the temperature close to the surface )see Fig. 15). As there is no time for heat transfer in metals, the result is an ideal metal–metal bond without melting or diffusion. The temperature at the interface just after impact was predicted to be lower than the melting temperature of both materials, but high enough for phase changes to occur, i.e. similar to what happens in tempering or martensetic formation in steels. This temperature increase is of very short duration and drops after the impact.

Table 3 Flyer plate thicknesses and their corresponding wavelength Flyer plate thickness (mm)

Wavelength (mm)

1.5 3 6

0.55 0.6 0.65

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5. Solid state processor fusion process Two theories have been proposed to explain the bonding process. The first theory developed was based on the concept of a solid-state welding process (Bahrani and Crossland, 1964; Crossland, 1982). It was hypothesised that the significant plastic shearing in the wave formation resulted in the creation of clean surfaces on both metals. The combination of the adjoining clean surfaces and the very high pressures was assumed to result in solid state bonding, with no melting occurring. This supports the hypothesis that wave formation is a result of extreme metal deformation and that the bonding occurs with no melting and very little diffusion (Bahrani and Crossland, 1964; Crossland, 1982). Hammerschmidt and Kreye (1984) and Onzawa et al. (1985) proposed an alternative theory that explosion bonding is a fusion welding process. Several layers of molten metals were created and followed by cooling at about 105 K/s creating an ultra-fine grain size. The numerical modelling in this study has not confirmed the fusion theories of Hammerschmidt and Kreye (1984) and Onzawa et al. (1985) because the temperature at the collision point is not high enough to melt the metals or to achieve the very high cooling rate needed to reach normal temperature. The results of the numerical simulations in this study provide some evidence for solid state bonding as the calculated temperatures are less than the melting temperature, no diffusion occurs and the peak pressure is maintained for a very short time. However, the phase changes shown by TEM and SEM analyses are not predicted by the solid state theory but may be due to the temperature exceeding that needed for phase transformation to occur. Solid state theory does not account for phase changes. 5.1. Evaluation of the past proposed criteria for bonding The theories that included more operational parameters in their proposed equation at the collision region generally supply the best predictions of bonding. The equations that only relate flyer plate velocity and the yield stress or Vickers hardness (Cowan et al., 1971) give poor results since the collision velocity or the impact angle is not defined in their equations. Like wise, the collision velocity by itself can not give an overall picture of what happens at the collision point. The theories based on the collision velocity (Kowalewskij et al., 1979; Deribas et al., 1975) as an only criterion for bonding successfully predicted bonding for constant impact angles. The Deribas et al. (1975), Wittman (1973) and Stivers and Wittman (1975) empirical equations, with a careful choice for the so-called k parameter gives a better prediction of bonding. The plastic strain criterion proposed in this study considers the combination of both impact angle and impact velocity at the collision point.

6. Evaluation of the theories of wave formation in explosive welding The appearance of periodic wave is not confined to interfaces in explosive/impact welding. Similar effects can be found on solid surfaces subjected to erosion action

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of high speed liquid film, jet drags, steam turbine blades and the interface of air and sea. In fact the wave formations in explosive/impact welding are regarded as special case of the general phenomenon of interfacial wave formation under certain flow circumstances. The presence of a hump was seen in simulations of welded samples. In this study, the vortices were not modelled. However, the indentation mechanism of Bahrani and Crossland (1966), Bahrani et al. (1966), Bergman et al. (1966) and Abrahamson (1961) that described the wave formation by periodic indentation of the base plate and hump formation ahead of the stagnation point by the flyer plate was not supported by the simulation results since the hump was also seen when straight interfaces were produced. In the von-Karman vortex street mechanism of wave formation (Cowan et al., 1971; Kowalick and Hay, 1971; Reid and Sharif, 1976), the main assumption is that the wave formation depends on collision velocity. As collision velocity increases a transition from straight to wavy interface occurs and waves form without vortices. Increasing the collision velocities result in the creation of only front or front and back vortices. The experimental results (welding window) of this study (Akbari Mousavi, 2001; Al-Hassani, 2001) suggested that this might be true for a constant impact angle, but various wave morphologies were seen for the same collision point velocity. As example was, welding stainless steel to mild steel plate, at a collision velocity of 2200 m/s, a straight interface was produced at smaller angle. If the impact angle was further increased, sinusoidal waves without vortices were produced. A subsequent increase of impact angle led to the formation of waves with front and back vortices. Changes in the collision velocity alone could not account for the formation of the various wave shapes across the whole welding window. The surface waves were seen ahead of collision point, however, the size of waves created from the simulation did not correlate with the size of surface waves formed ahead of the collision point. Therefore, stress wave mechanism proposed by El-Sobky (1983), El-Sobky and Blazynski (1975) and Chadwick et al. (1968) were also not supported in this study. This study shows that the velocity discontinuities between the surfaces of the plates may possibly account for creation of a wavy interface rather than the velocity discontinuities between the jet and the base plate as proposed by Hunt (1968) (the waves were also seen in modelling symmetrical welding). The various interface morphologies observed in the interface depended on the degree of severity of the velocity distribution across the surfaces of the plates, i.e. the amount of shear deformation and plastic strain. The greater the shear deformation, the more the changes in the morphology of the interface. That is, at low shear deformation interfaces are straight, as shear deformation increases transition takes place to a wavy interface. A further increase in shear produces regular waves with vortices. It is shown in the work of Robinson (1975) that the velocity profile has one or two inflection points across the interface, therefore the simulation results supported Robinson’s theory.

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7. Conclusions The impact conditions at the collision zone in explosive welding were successfully simulated using a pneumatic gas gun. The straight, wavy interfaces and jetting phenomena were modelled. The formation of interface waves and the phenomenon of jetting were reproduced. The numerical analyses predicted a hump in the interface at impact, the jet and wave formation. The present simulations predicted the magnitude and velocity of jet and waves. Wave formation appeared to be the result of periodic disturbances of the material and variations in the velocity distribution. The values of plastic strain were higher in the interfaces when waves were present. An increase in the impact angle at the same impact velocity decreased the impact pressure, which agrees with the high and low explosive modelling results. The transition from straight to a wavy interface appears to be due to an increase in the plastic strain and shear stress. Higher plastic strain and shear stress were seen for wavy interfaces (wave formation regime). For steel, the transition to wavy interface occurred with the plastic strain greater than 0.5 and shear stress greater than 0.5 GPa, for titanium the plastic strain greater than 0.9 and shear stress greater than 0.5 GPa. For higher impact angle there was a slight dependence of velocity and impact angle on the size of waves. Simulations predicted higher wavelengths and amplitudes for steel plate than titanium plate. Theories that described the bonding occurred when the collision velocity is higher than a threshold value were not supported by this study due to the fact that no weld occurred for titanium at an 81 impact angle while their collision velocities were in the range of cases where bonding takes place. Simulation shows the creation of surface waves ahead of the collision point which are in agreement with the (El-Sobky, 1983; El-Sobky and Blazynski, 1975) and (Chadwick et al., 1968). However, the correlation between the size of waves created after impact with those resulted from the disturbance was not clear. The amplitude and wavelength of the interface profile was shown to be dependent on flyer plate thickness. Jet velocity and thickness predicted from the simulation were in reasonable agreement with the proposed past theories. The jet thickness was comparable with the amplitude of the interface wave profile. Temperatures near the interface during the impact were predicted to be lower than the melting temperatures of both materials and therefore cast some doubt to (Hammerschmidt and Kreye, 1984) and (Onzawa et al., 1985) theories. Bonding theory was found to be a solid state welding process. Phases changes which occur may well be due to the high temperature (but less than the melting temperature) at the collision point. The AUTODYN simulations of the impact welding process help to understanding the conditions required for the wave formation. There are, however, limitations to the Euler solver in the AUTODYN code. In particular, the convergence issues related to the resolution of the model, the non-inclusion of friction effect which means that it is not possible to simulate the material surface roughness effect.

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Acknowledgements The authors would like to express their gratitude to Dr. M. Barrett for his assistance in experiments carried out with the gas gun. Special thanks to Engineering Physical Science Research Council (EPSRC) for financial support of the research work reported in this paper. Thanks are also due to Century Dynamics for the use of AUTODYN-2D software.

References Abrahamson, G.R., 1961. Permanent periodic surface deformations due to a travelling jet. J. Appl. Mech. 83, 519–528. Akbari Mousavi, A.A., 2001. The mechanics of explosive welding. Ph.D. Thesis, University of Manchester Institute of Science and Technology (UMIST), Manchester, UK. Akbari Mousavi, A.A., Burley, S.B., Al-Hassani, S.T.S., 2005. Simulation of explosive welding using the williamsburg equation of state to model low detonation velocity explosives. Int. J. Impact Eng. 31, 719–734. Akihisa, A.B.E., 1997. Numerical study of the mechanism of a wavy interface generation in explosive welding. JSME Int. J. Ser. B 40 (3), 395–401. 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. Al-Hassani, S.T.S., Salem, S.A., Lazari, G.L., 1984. Explosive welding of flat plates in free flight. Int. J. Impact Eng. 1 (2), 85–101. AUTODYN Manuals, 2001. Century Dynamics. Bahrani, A.S., Crossland, B., 1964. Explosive welding and cladding. An introductory survey and preliminary results. In: Proceedings of Instrumental Mechanical Engineering, pp. 264. Bahrani, A.S., Crossland, B., 1966. Some observations on explosive cladding welding. In: Annual Conference AD. ASTME, pp. 66–112. Bahrani, A.S., Black, T.J., Crossland, B., 1966. The mechanics of wave formation in explosive welding. Proc. Royal Soc. Ser. A 296, 123. Bergman, O.R., Cowan, G.R., Holtzman, A.H., 1966. Experimental evidence of jet formation during explosion cladding. Trans. Metal Soc. AIME, 646–653. Birkhoff, G., Macdougall, D.P., Paugh, E.M., Taylor, G., 1948. Explosives with lined cavities. J. Appl. Phys. 19, 563–582. Bondar, M.P., 1995. Localisation of plastic deformation on contacts determining the formation of a strong joint. Combust., Explos Shock Waves 31 (5), 612–616. Chadwick, M.D., Howd, D., Wildsmith, G., Cairns, J.H., 1968. Explosive welding of tubes and tube plates. Br. Weld. J. 15, 480–492. Cowan, G.R., Bergman, O.R., Holtzman, A.H., 1971. Mechanics of bond wave formation in explosive cladding of metals. Metall. Trans. 2, 3145. Crossland, B., 1982. Explosive Welding of Metals and its Application. Oxford University Press, New York. Crossland, B., Williams, J.D., 1970. Explosive welding. Metall. Rev. 15, 79–100. Deribas, A.A., Simonov, V.A., Zakcharenko, I.D., 1975. Investigation of explosive welding parameters for arbitrary combinations of metals and alloys. In: Proceedings of the Fifth International Conference on High Energy Rate Fabrication, vol. 4(1), pp. 1–24. El-Sobky, H., 1983. Mechanics of explosive welding. In: Blazynski, T.Z. (Ed.), Explosive Welding, Forming and Compaction. Applied Science Publishers, Barking, pp. 189–217. El-Sobky, H., Blazynski, T. Z., 1975. Experimental investigation of the mechanics of explosive welding by means of a liquid analogue. In: Proceedings of the Fifth International Conference on High Energy Rate Fabrication. Denver, Colorado, vol. 4(5), pp. 1–21.

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