Thin-Walled Structures 127 (2018) 617–628
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Full length article
Numerical modeling based on coupled Eulerian-Lagrangian approach and experimental investigation of water jet spot welding process
T
⁎
M. Alitavolia, , A. Darvizehb, M. Moghaddama, P. Parghouc, R. Rajabiehfarda a
Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran c Department of Mechanical Engineering, Ahrar Institute of Technology & Higher Education, Rasht, Iran b
A R T I C LE I N FO
A B S T R A C T
Keywords: Coupled Eulerian-Lagrangian Water jet Spot welding Johnson-Cook damage Finite element simulations
Due to the relatively high degree of complexities involved with water jet spot welding process, the experimental and conventional numerical methods are hardly capable of providing all comprehensive analysis. In present paper, water jet spot welding of copper, brass and aluminum plates has been examined experimentally using a gas-gun. Considering the details of the whole process, numerical modeling of jet formation and interaction between jet and solid surface have been performed, employing the coupled Eulerian-Lagrangian (CEL) approach. In addition, Jonson-Cook damage model has been utilized to predict the damage initiation in solid surfaces. The velocity profiles of jet along axial and radial directions; and also time history of jet are obtained to describe the variation of velocity in different points of jet with time. Results confirm that the presented method has been successful in predicting the behavior of jet during the process, and plate deformation and failure patterns.
1. Introduction Spot welding is one of the most convenient processes to create a quick and permanent joint between lightweight industrial metallic parts and is an integral part of manufacturing processes especially in automotive industry. Currently, electrical resistance welding is the most applied method in spot welding. However it has some limitations. For instance, welding of metals with far melting points and oxidization of surfaces. Alternative methods such as explosive welding [1], laser spot welding [2], and impact spot welding have been introduced to overcome the limitations of conventional methods of spot welding. The latter proposes high quality, steady and reliable connection between parts by creating solid phase bonding and interlock between surfaces. For this purpose, a high velocity projectile [3–8] or slug of water [9–11] impacts a pre-determined point and a permanent connection would be created at the neighboring zone. The high pressure produced by impact of liquid jet with solid surfaces, lasts for very short intervals of time and is followed by a rapid radial flow of the liquid at speeds which may be several times higher than the impact speed itself [10]. After the maximum peak, the pressure decreases and reaches to a steady state at stagnation point, lasting for a relatively longer time [9]. Areas welded by impact spot welding are generally characterized by wavy and plane texture [8] and the regions with the wavy structure generally being more strongly welded [12]. Observations of Turgutlu et al. [8] showed
⁎
that the wavy surface increases the area of intimate contact between the two mating surfaces, and enhances interlock and the interaction between the jets from the two surfaces, followed by an almost instantaneous release of load, serves to bond the two metal plates permanently. Salem and Al-Hassani [9,10] found that the amplitudes and lengths of waves increase monotonously with radial distance from the center of impact. They also reported the presence of a central unwelded region. When the speed of a fluid jet is high enough to produce pressures in the vicinity of impact well in excess of the yield shear stress of the target material it can be assumed that the target in this area can flow as an inviscid fluid [9]. High velocity impact of water jet, generates an extremely high pressure on the target surface, and can cause serious damages such as material removal and erosion. Therefore it is important to study the different aspects of this process such as the impact pressure and stresses generated on the solid surface. Several experimental researches have been performed to study the effects of water jet impact on solid surfaces [13–15]. In water jet spot welding, usually a small amount of water is used and the diameter of the jet is too small and the process lasts for only a few microseconds. Therefore high-tech tools are needed to observe and study the process. On the other hand, numerical methods such as FEM are powerful and cost effective tools which can be employed for comprehensive studies of engineering processes including problems related to water jet forming, cutting and welding [16–18].
Corresponding author. E-mail address:
[email protected] (M. Alitavoli).
https://doi.org/10.1016/j.tws.2018.02.005 Received 26 November 2017; Received in revised form 2 February 2018; Accepted 8 February 2018 0263-8231/ © 2018 Elsevier Ltd. All rights reserved.
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Chizari et al. [18] investigated water jet spot welding of metallic parts numerically and experimentally. They used Equivalent plastic strain at high strain rate and shear stress at the collision point as welding criterion and their numerical results confirmed that central contact region remains un-bonded. Recently, CEL method has been implemented in FEM to avoid the undesired mesh distortion through large deformations caused by large strain rates in cutting, forming and welding problems [19–21]. In CEL method both Eulerian and Lagrangian meshes are used in same model. Therefore it's sufficient to model an assembly of fluid and solid structure interacting with each other [22,23]. Hsu et al. [23] studied high-speed water jet impact on solid surfaces numerically, using CEL method. Their CEL simulation predicted peak and stagnation pressure of impact and also geometrical parameters such as deformations of target plate with a good precision. Though numerous experimental investigations have been performed to study the effects of high velocity water jet, only handful number of researches have been carried out to understand the complex behavior of the mentioned process, numerically. The present paper describes an experimental investigation of spot welding of Aluminum, Copper and Brass plates with different thicknesses, subjected to impact by water jets with different amounts of water and kinetic energies, using a Gas-Gun apparatus. Also the CEL technique has been employed to simulate the whole process, including the formation of jet, to investigate the associated parameters accurately. In addition, Johnson-Cook damage model has been used to investigate the failure of the specimens under high speed water jet impact.
Fig. 1. Illustration of deformation in Eulerian and Lagrangian mesh; and concept of Eulerian volume fraction.
2. Numerical simulation 2.1. Coupled Eulerian-Lagrangian in FEM Eulerian analysis is a suitable technique for problems in which the material undergoes extreme deformations, especially in modeling of fluid flow. Through an eulerian analysis in FEM, the nodes are completely fixed in space and the material flows through elements which will remain undeformed during the analysis. This advantage would let the material to experience extreme deformations and strain rates, with elimination of the possibility of element distortion. On the other hand, in Lagrangian analysis nods are fixed within the material and the material boundary coincides with elements boundaries. Therefore the elements would deform, as the material deforms. The Lagrangian technique is well suited for the problems in which the material is in solid state. Nevertheless, in case of problems in which the strain rate in solid medium is too high and the material acts like a fluid medium, e.g. in granular materials [20], the eulerian analysis would be more effective. Many practical issues in engineering analysis are neither pure Lagrangian nor pure Eulerian problems [25], therefore it's needed to model an assembly consist of Eulerian and Lagrangian domains together to achieve realistic simulations. In ABAQUS [26], CEL technique has been implemented to solve the problems in which, Eulerian and Lagrangian domains interact with each other, i.e. fluid-structure problems. The Eulerian analysis in Abaqus explicit is based on Eulerian volume fraction (EVF) technique. In this technique, in each time increment as the material flows through elements, the percentage of the material filled in an each element is calculated. If the whole element is filled with material, its EVF is one and if no material present in the element, its EVF would be zero. If material volume fraction in an element is less than one, the remainder of the element is automatically filled with void material. Void material has neither mass nor strength. Fig. 1 illustrates a schematic of deformation in Eulerian and Lagrangian mesh with representation of the concept of EVF in Eulerian analysis. To perform an eulerian analysis in Abaqus, an eulerian domain must be defined for the material to flow in and also a Lagrangian part should
Fig. 2. Initial EVF of water.
be defined inside the Eulerian domain only to determine the initial EVF and position of material. Fig. 2 shows the initial position of water inside the Eulerian domain and nozzle in the present study. 2.2. Material models 2.2.1. Mie-Grüneisen equations of state To provide a hydrodynamic material model to define the behavior of fluids, an equation of state (EOS) should be determined. Modeling of incompressible viscous and inviscid laminar flow can be achieved by using the linear Us − Up form of the Mie-Grüneisen equation of state. According to Mie-Grüneisen equations of state, the pressure can be expressed as a linear function of internal energy [26]. The most common form of Mie-Grüneisen equations of state is:
p − pH = Γρ (Em − EH )
(1)
where p and Em are pressure and internal energy per unit mass respectively. pH and EH are the Hugoniot pressure and specific energy per unit mass which are functions of density ρ , only. Also Γ is the Grüneisen ratio and is defined as
Γ = Γ0
ρ0 ρ
related to the Hugoniot pressure by 618
(2)
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EH =
PH η 2ρ0
Table 2 Material parameters of OFHC copper and aluminum 6061-T6.
(3)
where η is the nominal volumetric compressive strain and is expressed by Eq. (4). Substituting Eqs. (2) and (3) in Eq. (1) yields to Eq. (5).
Material properties
Symbol
OFHC Copper [29]
Aluminum 6061-T6 [30]
η = 1−ρ0 / ρ
Modulus of elasticity Poisson's ratio Density
E[GPa] ν
124 0.34 8960
71 0.33 2710
90 292 0.31
324 114 0.42
0.025 1.09
0.002 1.34
ε0̇ [ ]
1
1
θmelt [K ] d1 d2 d3 d4 d5
1356 0.54 4.89 − 3.03 0.014 1.12
925 − 0.77 1.45 − 0.47 0 1.6
pH =
(4)
ρ0 c0 2η (s − sη)2
Yield stress constant Strain hardening constant Strain hardening exponent Viscous effect Thermal softening constant Reference strain rate
(5)
where c0 and s define the linear relationship between the shock velocity Us , and the particle velocity Up , as follows
Us = C0 + sUp
(6)
in general, C0 is the bulk speed of sound and s is linear Hugoniot slope coefficient. With the above assumptions, the linear Us − Up Hugoniot form is written as
p=
ρ0 c0 2η Γη ⎛1− 0 ⎞ + Γ0 ρ0 Em (s − sη)2 ⎝ 2 ⎠
Melting temperature J-C damage constant J-C damage constant J-C damage constant J-C damage constant J-C damage constant
(7)
2
where ρ0 c0 is equivalent to the elastic bulk modulus at small nominal strains. The linear Us − Up equation of state has been implemented in Abaqus and to fully define it, the values of three variables, c0 ,s and Γ0 should be determined. To model the behavior of fluids, density and viscosity of the fluid must be determined as well. The material parameters of water, used in this study are provided in Table 1.
⎜
σm =
(9)
where T is the material temperature, Tmelt is the melting temperature of the metal and Troom is the room temperature. Moreover to investigate the failure and material removal of plates during the process, the Johnson-Cook damage model has been employed. According to J-C damage model, failure would occur wen the equivalent plastic strain exceeds a critical magnitude which is defined as pl
⎜
⎟
(10)
Table 1 Material parameters of water [18,24]. Density (kg/m3)
Viscosity (Ns/m2)
C0 (m/s)
s
Γ0
983
0.001
1435
0
0
(11)
3d finite element modeling of water jet spot welding process has been carried out using commercial finite element software, Abaqus/ Explicit. In former FEM simulations of water jet, available in literature, the water jet had been modeled as a cylindrical slug with flat or semispherical nose [18,24], impacting the target with a constant velocity. In the present study, to perform a more realistic simulation, the process leading to formation of jet has been modeled as well. For this purpose, as it is depicted in Fig. 3a, at initial state, a portion of nozzle is filled with water and the piston is placed right behind it. With initiation of the process, piston moves with a constant velocity downwards and enforces the water to emanate from the nozzle. Since the process happens at very short intervals of time, it has been assumed to be adiabatic and the heat exchanges have been neglected. The Johnson cook constitutive law along with Johnson-cook failure have been employed to describe the behavior of metals and linear Us − Up form of the Mie-Grüneisen equation of state has been used to define the properties of water. General contact method is used to model all interactions and the friction between flyer and target plates has been modeled by a classical isotropic coulomb friction model with a friction coefficient ( μ ) of 0.25 [18]. Piston and nozzle have been considered rigid to prevent from any deformation in them. All edges of flyer and target plates have been constrained in all directions in order to perform the clamped boundary conditions. To reduce the computational cost, only the center of plates (impact zone and its neighboring area) has been meshed with fine elements with approximate global size of 0.2 mm and the rest of the plates has been discretized with coarser elements. 42480 C3D8R (8noded linear brick, reduced integration and enhanced hourglass control) have been employed to discretize the 0.5 mm thick plates. Also 72200 E3CD8R eulerian elements with approximate global size of 0.4 mm have been used to mesh the eulerian domain. It should be noted that since the fracture in plates is not localized, when a specimen was judged to fail, it was re-meshed by equal size fine elements. Fig. 3b shows the discretized 0.5 mm thick plate and the eulerian domain.
(8)
σ ε̇ ε pl = ⎡d1 + d2exp ⎛d3 m ⎞ ⎤ ⎡1+d4ln ⎛ ⎞ ⎤ (1+d5 T *) ⎢ ⎥ σ ⎝ ⎠ ⎣ ⎦⎣ ⎝ ε0̇ ⎠ ⎦
σ1 + σ2 + σ3 3
2.3. Finite element model
⎟
T − Troom Tmelt − Troom
1 s
The parameters d1 to d5 are material constants and ε0̇ is the reference strain rate. The elastic and plastic properties and also failure parameters of Copper and Aluminum are provided in Table 2.
Eq. (8) represents the von Mises flow stress (σ ) as a function of the equivalent plastic strain (ε pl ), equivalent plastic strain rate (ε ̇ pl ), and dimensionless temperature (T *m ). where A , B , C and m are material constants corresponding to yield stress, strain hardening constant, viscous effect and thermal softening, ε ̇ pl respectively. Also n is the strain hardening exponent; ε ̇ is the nor0 malized equivalent plastic strain rate and T* is defined as:
T* =
C m
where σm is the mean stress and is defined as the average of the three principal stresses.
2.2.2. Johnson-cook constitutive law In the present work, Copper and Aluminum plates are chosen for finite element simulations. Flyer and target plates have been considered Elastic-Plastic materials and the Johnson-Cook (J-C) model has been utilized to describe the flow stress behavior of metals. In general, the response of material under high-speed impact conditions involves consideration of effects of strain, strain rate, and temperature [26,27]. The J-C plasticity model is a phenomenological model which takes into account quasi-static yielding, strain hardening, strain-rate hardening and thermal softening of material [28]
ε ̇ pl σ = [A + B (ε pl )n] ⎡1+Cln ⎛ ⎞ ⎤ (1−T *m) ⎢ ⎥ ⎝ ε0̇ ⎠ ⎦ ⎣
ρ [kg/m3] A[GPa] B[GPa] n
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between 0.5 and 1 mm. The other quantity which affects the quality of welding, is the distance between nozzle outlet and the flyer plate which is considered 8 mm in all experiments. Copper and brass plates are selected as target plates and for flyer plates, the specimens are made of copper, brass and aluminum. The thickness of the flyer plate in all experiments is 0.2 or 0.5 mm and for the target plates, varies between 0.5 and 1 mm. However, attention was focused on the welding of copper to copper plates with 0.5 mm thickness. By performing the experiment, high pressure produced by the gasgun drives a projectile with mass (G) of 372 or 560 gr, towards the piston. When the projectile strikes the piston, it will enforce the trapped water in nozzle to emanate and impact the flyer plate. The velocity of projectile before the impact instance was measured approximately 100 m/s in all experiments. Table 3 provides the specifications of the specimens and results of the experimental tests. 4. Results and discussion 4.1. Deformed shapes and weld interface Front view of some of successfully welded specimens are depicted in Fig. 5. 0.5 mm thick copper/copper and brass/brass spot welded plates are presented in Fig. 5a & b respectively. In Fig. 5c, spot welding of plates with same material but different thicknesses (0.5 mm copper to 1 mm copper) are provided. Also deformed shape of welded plates with equal thickness, made of different materials (0.5 mm thick brass/copper plates) is shown in Fig. 5d. Numerical and experimental deformed shapes of WJSW of specimens No. 38 & 41 are presented together in Fig. 6. By comparing the deformed shapes, resulted from experiments and numerical models, it is clear that there is a close agreement between them and the numerical model has successfully predicted the deformation pattern in plates. Though the J-C damage model has been implemented to predict the failure in copper plates, no fracture or material removal has occurred in the simulated specimens which is consistent with the experiment results. According to Figs. 5 and 6, it can be observed that the deformation patterns in all specimens are almost similar. High speed impact of water jet on flyer plate, has created a saucer shaped depression in the impacted zone whose diameter is slightly larger than the jet diameter.
Fig. 3. (a) View cut of FEM model assembly; (b) Discretized 0.5 mm thick plate (target and flyer) and eulerian domain.
3. Experimental procedure The experiments of water jet spot welding (WJSW) of plates have been performed using a gas-gun apparatus. The schematics of experimental set-ups are presented in Fig. 4. To perform the WJSW experiments, first the nozzle is filled with a column of water with height of h w and diameter of 6 mm. To regulate the amount of water (h w ) the piston can be moved towards or outwards in the axial direction. The diameters of nozzle in inlet and outlet are 6 mm and 2 mm respectively and its axial length is 21 mm. The standoff distance (SD) between the target and flyer plates are adjusted by spacer plates which are placed between them near the edges. The standoff distances in experiments varies
Fig. 4. 2D schematic representation of (a) gas-gun; and (b) water jet apparatus and specimens.
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Table 3 Specifications of the specimens and results of the tests (W, F and U correspond to successfully welded, fractured and unwelded tests respectively). Test No.
Specimen No.
Flyer material
Flyer thickness (mm)
Target material
Target thickness (mm)
G (g)
hw (mm)
SD (mm)
Results
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
38 14 13 12 31 35 42 41 40 34 22 36 45 23 28 26 46 47 32 37 33 43 44 34 27
Copper
0.5
Copper
0.5
372
6.5 6.5 6.8 7.2 6.9 7 6.6 6.7 6.6 6.8 7 7 6.8 6.5 7 7.5 6.8 6.9 7 7.2 6.7 6.7 6.8 6.8 7
0.7 1 0.7 0.7 0.7 1 0.7 0.7 0.7 1 0.5 0.7 0.7 0.5 1 0.7 1 0.7 0.7 1 0.7 0.8 0.5 1 0.7
W W W W W W W U F F F F F F F F W W W W W F W F F
560 1
372
0.2
Copper
0.5
372
Aluminum
0.2
Copper
0.5
560 372
Brass
0.5
Copper
0.5
560
0.2
Brass Copper
0.5 0.5
560 560
Fig. 6. Meshless finite element (left) and Experimental (right) deformed specimens No 38 &41.
To evaluate the quality of welding, specimens were cut in half and photographs of weld interfaces were taken by scanning electron microscope (SEM) with different magnifications which are presented in Fig. 8, for copper/copper specimens. In Fig. 8b, as it can be observed, the weld interface looks homogenous and the boundary between the two plates is hardly recognizable. With increasing the magnification, in Fig. 8c the interlock between the flyer and plate can be observed. With further magnification, a closer view of the weld interface is available in Fig. 8d. As it can be observed, wavy and plane interface has formed in the welding boundary which was also reported by Salem [9]. Turgutlu et al. [10] showed that the wavy surface created in the bonding zone of plates subjected to impact projectile, increases the area of intimate contact between flyer and target contact surfaces and enhances material interlock, resulting in permanent bond of the two metal plates. Thus, the results of SEM confirm that a high quality permanent weld has been formed between plates.
Fig. 5. Deformation of welded plates: (a) specimen no. 38; (b) specimen no. 33; (c) specimen no. 42 and (c) specimen no. 32.
Depth of the deformed area varies with radial distance from center of the plate and it is surrounded by a ring shaped sunk down area. The thickness of flyer plates decreases from inner edge of the ring towards the center of the plate which have the maximum depth and minimum thickness. This deformation pattern is more understandable in cross sectional view of target and flyer plates, and the thickness profile of flyer plate, which are presented in Fig. 7. The red marked areas denote to the ring deformation and the blue marked region is the central pit of the flyer plate, which the most thinning has occurred at this point. As it can be seen in Fig. 7, the central impacted zone the flyer plate has stretched and thinned and collision has occurred between the flyer and target plates. With impact of the jet, plastic flow has happened in flyer plate and the metal has yielded under the high pressure of the jet. 621
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Fig. 7. (a) Cross sectional view of deformation in target and flyer plates; (b) thickness profile of flyer plate; for specimen no. 38.
Fig. 8. (a) Overall view of weld interface; (b), (c) and (d): SEM photographs of weld interface, with different magnifications.
liquid impact. They concluded that the circumferential cracks on a brittle target after a high speed liquid jet impact are caused by the interaction of the Rayleigh surface wave and the pre-existed flaws. Fig. 11a and b provide the Mises equivalent stress and equivalent plastic strain contours in central section of flyer plate, respectively. As it can be observed, the maximum stress has exerted at the ring shaped area and the center of the plate. For the remaining portions of the plate the magnitudes of stress are relatively lesser. According to Fig. 11b, only the central saucer shaped depression is involved with plastic deformation and the maximum plastic strain has happened in the central pit, therefore the plastic deformation in flyer plate is completely localized, which is exactly expected from spot welding processes. Fig. 12 shows the Variation of jet velocity and pressure along its height, at 50 µs. The curves presented in Fig. 12 can be divided into three segments. In the first part of the graphs, the jet velocity increases dramatically and also the pressure decreases at the same time. In second part the velocity and pressure vary with a slow rate and in the third part, the velocity decreases rapidly and the pressure starts to increase. The first part is related to where the water emanates from nozzle and the last part is where the jet impacts the flyer plate. The behavior of the
4.2. Characteristics of jet and impacted surface Different stages of impact of water jet on flyer plate surface are presented in Fig. 9. As it can be seen, at initial stage, the jet emanates from nozzle with a conical front and after impacting the plate, the radial flow of water happens and head of the jet mushrooms. As it was mentioned in Section 4.1, the diameter of the sunk down area in target plate is slightly larger than the jet diameter. According to Fig. 9, the radial flow of the jet is responsible for formation of the saucer shaped depression in the flyer plate. However the central pit in the plate which the maximum thinning happens at this point, is a result of the direct impact of the center of the jet on flyer plate surface. The radial propagation of stress wave over flyer plate surface at initial instants of impact is shown in Fig. 10 for specimen no. 38. The radial compressive stress wave travels from center towards the edges of the plate till 30 μs. It is known that when a solid surface is subjected to a dynamic loading, longitudinal and transverse waves are generated in the solid. At the surface, a third wave namely the Rayleigh surface wave exists [13], which carries more than 60% of the total impact energy [31]. Bowden and Field [14] studied the brittle fracture of solids by 622
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Fig. 9. Different stages of impact of water jet on flyer plate surface, for specimen no. 38.
first part can be justified by Bernoulli's equation and conservation of mass [32]. Using the conservation of mass in inlet and outlet of the nozzle gives:
ρi Vi Ai = ρo Vo Ao
the nozzle respectively. According to Eq. (11), with decreasing the cross sectional area, water velocity would increase. The Bernoulli's equation for steady state, frictionless and incompressible flows for two points in inlet and outlet of nozzle is expressed as
(12)
1 1 Pi P + Vi 2 + gz i = o + Vo2 + gz o = const 2 2 ρ ρ
where ρ and V are density and velocity of water respectively and A is the cross sectional area. Subscripts i and o denote to inlet and outlet of
Fig. 10. Radial propagation of stress wave on flyer plate at initial instants of impact for specimen no. 38.
623
(13)
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Fig. 11. Deformed contours of; (a) Mises equivalent stress and (b) equivalent plastic strain; in central section of flyer plate for specimen no. 38.
Fig. 12. Variation of jet velocity and pressure along axial direction, at 50 µs, for specimen no. 38. Fig. 13. Pressure contour of water in eulerian domain. Table 4 Variations of water pressure and velocity through emanation from nozzle, calculated by theoretical relations and numerical model. Parameter
Vo/ Vi (Po − Pi ) [MPa]
Theoretical
Numerical result
Eq.
Result
(12) (13)
9 400
8.86 361
where P is water pressure and g and z are acceleration due to gravity and elevation of the point respectively. Since the jet flow is horizontal, z i = z o, thus increasing of jet velocity by emanating from nozzle results in decrease of its pressure. Using Eq. (12), the proportion of velocity of water in nozzle outlet and inlet can be calculated. Also employing the Eq. (13) would give the difference between the pressure of water in inlet and outlet of nozzle. The compression between mentioned parameters calculated from theoretical relations and numerical results are presented in Table 4. As it can bee seen, there is a good agreement between them. Pressure contour of water in eulerian domain is presented in Fig. 13. As it can be seen, the maximum pressure is at nozzle inlet and also near the impact zone, which confirms the above explanations. The Variation of impact velocity with time is provided in Fig. 14. As it can be seen in Fig. 10, the jet impinges on the plate at 15 µs and the delay in impact velocity graph is due to this reason. At initial stage, the jet velocity reaches to a maximum peak with magnitude of 1100 m/s for a short instant and then starts to decrease. After the initial peak, till 100 µs, the
Fig. 14. Variation of impact velocity with time.
velocity reaches to 600 m/s from 750 m/s and after that, it starts to fall with a rapid rate. This reduction in velocity is due to the decrease of the water volume behind the nozzle, which contains a lesser magnitude of kinetic energy. Fig. 15 provides the velocity profile of the jet along the radial direction. As is clear, the velocity profile is a polynomial in 2D plane and as the radial distance from center of jet increases, the velocity increases as well. Therefore, according to Fig. 15, the minimum velocity is at jet axis and its variations are considerable. It can be concluded that none uniform distribution of thickness in flyer plate is due to the variations of jet velocity in radial direction and also the shear flow of water. Results of the numerical model show that after emanating from nozzle, different elements of the jet have dissimilar velocities and also the difference between the velocities of different points, varies with 624
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Fig. 15. Velocity profile of the jet along radial direction.
Fig. 17. Fracture in flyer plates (a) aluminum (b) brass (c) copper.
wave is responsible of forming this cracks. Field [15] studied the static indentation of glass by a solid sphere and cylinder. Their results showed a main ring fracture and undamaged central area and it was observed that the ring fracture was composed of many small fractures rather than one continuous crack. Though aluminum, copper and brass are considered as ductile metals, however, in high strain rates, metals most likely show a transition from ductile plastic yielding to brittle fracturing. For a 0.2 mm thick plate, subjected to impact with velocity up to 1000 m/s, the strain rate would be significantly high. As it was shown in Section 4.2, with increase of the radial distance from center of the jet, the impact velocity increases as well. Also, the high speed radial flow of jet can cause shear flow around the central impacted area of flyer plate. It can be deduced that formation of ring fracture and undamaged central area may be related to these phenomenon. A comparison between the experimental and numerical fractured target plates of aluminum (specimen No. 23) is presented in Fig. 18 and as it is clear, there is a close agreement between them. In numerical results, formation of the relatively large polyhedral hole with scabbed edges can be observed as well and the patterns of fracture in both front and rear views of the plates in numerical and experimental results are similar. Except that in experiments, the bulge is relatively steeper. This could be due to the difference in applying the boundary conditions in experiment and numerical model. In experiment, the spacer plates are placed between the flyer and target plates, thus by applying the loads, this spacers would act as supports and keep the regions near the edges remain undeformed. But in numerical models, only the nodes on the edges of the plates are clamped. Thus the bulging continue to the edges, with a smoother slope. Fig. 19 shows the stress contour on the undeformed and deformed shapes of fractured flyer target. In Fig. 19b, the black areas denote to the failed elements. By comparing Fig. 19a and b, it can be seen that the amount of removed material in numerical model (region marked with red circle), is almost equal to the detached section of flyer plate which has been welded to target plate. According to Figs. 18 and 19, it can be concluded that implementation of Johnson-Cook damage model in FEM can yield to a good prediction of material failure through impact of liquid jet on solid surfaces.
Fig. 16. Time history of impact pressure on the surface of flyer plate.
time. Thus giving all elements of the jet a constant and uniform velocity would not be appropriate and may yield to considerable errors. It should be noted that since the process takes place at very short intervals of time, experimental measurement of velocity profile of the jet is seldom possible. Fig. 16 shows the time history of impact pressure at the central impacted region of flyer plate surface. At initial stage of impact, pressure has reached to a maximum peak with magnitude of 600 MPa. This pressure pulse is known as water hammer phase and its magnitude depends on impact velocity and mechanical properties of water and flyer material. By comparing Figs. 10, 14 and 16, it can be deduced that the peak pressure of plate and peak velocity of jet occur almost at the same the time which last for a very short period of time and are comparable with the time when the stress wave propagates over the flyer plate surface (15–30 µs). After the water hammer phase, pressure falls down and reaches to stagnation point with fluctuating behavior which lasts for a relatively longer time. 4.3. Fracture and material detachment As it can be seen in Table 3, in almost all of specimen with 0.2 mm thick flayer plates, failure has happened (except for test no. 23). Fig. 17 shows the failure in flyer plates of aluminum, Brass and copper plates with 0.2 mm thickness, caused by impact of high velocity water jet on their surface. As it can be observed, a circular undamaged central region of flyer plate has been detached and welded to the target plate. A relatively large polyhedral hole with scabbed edges has been created in surrounding region of the fracture zone. Also a major bulge has formed from fractured edges up to exterior edges of flyer plate. Such fracture pattern was also observed in high velocity liquid impact on brittle solids in previous researches. Shi et al. [13] investigated the damage pattern on a PMMA (poly methyl methacrylate) block surface after impacts of 329 m/s water jets and observed a central undamaged area, surrounded by circumferential cracks in the block, and concluded that the Rayleigh 625
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plates for specimens no. 38 and 41. As it can be seen, for specimen no. 38, in flyer and target plates, the magnitudes of PEEQ in ring shaped zone are above 0.6 and 0.7 respectively. Further more in central region of target plate, the magnitude of PEEQ falls down below the threshold. Hence, numerical results show a central unwelded zone, surrounded by a welded region in specimen no. 38. According to Fig. 20b, for specimen no. 41, the values of PEEQ in flyer plate are above 0.7 in both center and ring shaped zones. But in target plate, magnitude of PEEQ is below the threshold in all regions. Therefore no bonding has been created in specimen no. 41, which is in agreement with experimental results. Time history of shear stress for points in the central pit of plates and near the ring shaped zones for specimen no. 38 are provided in Fig. 21. In ring shaped region, magnitude of the shear stress in both flyer and target plates are about 140 MPa at collision time (34 µs). Also, as it can be seen, the shear stresses in colliding elements of the two plates are in opposite directions, which is a proof of a good bonding. In central pit, at collision time (15 µs), the shear stress in plates are in same direction and their magnitudes are relatively lower than what is was observed in results of ring shaped region. It can be concluded that no bonding has happened in the central region, which was also shown in PEEQ diagrams. According to numerical results, the shear stress threshold for a good bonding in copper plates are less than what it was reported by Chizari et al. [7,18], which can be due to the difference in mechanical properties of copper and aluminum. However, the PEEQ thresholds and pattern of shear stress for flyer and target plates were in agreement with the results reported by Chizari et al.
Fig. 18. comparison between the experimental (left) and numerical (right) fractured flyer plates of aluminum; (a) back view and (b) front view.
5. Conclusion Spot welding of thin copper, aluminum and brass plates was successfully carried out by high speed impact of water jet, using a gas-gun. Also numerical simulations with implementation of CEL formulation were performed to investigate the effects of governing parameters of the process of jet-solid surface interaction. In order to achieve more realistic simulations, a comprehensive modeling of the jet formation was performed. Experimental results show a saucer shaped depression in impacted zone, surrounded by a ring shaped sunk down area which the maximum thinning was accrued at central pit and ring shaped area. SEM photographs show that the weld interface is comprised of wavy and plane zones which the wavy interface seems to be dominant. In some specimens, a circular central region of flyer plate has been detached and welded to the target plate. The fracture pattern in flyer plate is similar to those observed in brittle materials which may be due to high strain rate effects. Moreover the numerical models have successfully predicted the deformation and fracture patterns. The utilized criteria confirm that the presented model has been successful in prediction of creation of bonding. The CEL technique with implementation of J-C damage model is sufficiently accurate to analyze the effects of high speed water jet impinging on solid surfaces. It was shown that the peak pressure exerted on the surface of the plate and the peak velocity of jet occur almost at the same time and last for a very short period of time which is comparable with the time required for the stress wave to propagates radially over the flyer plate surface. Numerical results show that jet velocity profile along radial direction is a parabolic in 2D plane and as the radial distance from center of jet increases, the velocity increases as well, hence velocity in jet axis is minimum and its variations are significant. Also it was indicated that the jet velocity varies along the jet height as well. Thus neglecting the velocity variations in different elements of the jet and assuming a constant and uniform distribution of velocity may not be an appropriate simplification. It was concluded that formation of ring shaped sunk down area in welded specimens and ring fracture in failed ones can be related to increase of jet velocity with radial distance from its axis. The velocity profiles of jet along the radial and axial directions after emanating from the nozzle can be used as inputs in further numerical simulations of water jet.
Fig. 19. Comparision between failed area of numerical model and detached material in experiment.
4.4. Welding criteria for numerical models In previous numerical studies in field of high speed impact welding, Chizari et al. [7,18] concluded that two parameters of equivalent plastic strain (PEEQ) at high strain rate and shear stress at collision time can be used as welding criteria. Their results indicated that for HS30 aluminum, where the magnitudes of PEEQ in flyer and target plates were above the thresholds of 0.6 and 0.7 respectively, a good bonding was created. They also reported a threshold of about 400 MPa for shear stress, for reliable bonding in aluminum and showed that where the shear stresses in the two colliding plates at the contact point were in opposite directions, the bonding was good but where they were in the same direction, bonding was poor. Fig. 20 shows the values of PEEQ along the width of flyer and target 626
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Fig. 20. Variation of PEEQ along width of flyer and target plates (a) specimen no. 38 (b) specimen no. 41.
Fig. 21. Time history of shear stress in element of contact zones (a) central pit; and (b) ring shaped region for specimen No. 38.
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