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SPH simulation of High-Velocity Impact Welding, the interface between copper and titanium (Nassiri et al. Applied Physics Letter (110), 23, 1601)


In the automotive, aerospace, appliance, medical device, and various other industries, there is a primary need for lightweight structures. Specifically, in the automotive industry, in order to meet the increasingly ambitious CAFE (Corporate Average Fuel Economy) standards and to reduce CO2 emissions, there is a growing interest in creating lightweight vehicles. The body-in-white of a car has conventionally been made with stamped and spot welded steel. A typical route to mass reduction is by increasing steel strength and reducing thickness. Another approach relies on the use of lower-density materials such as magnesium, aluminum and advanced composites. These materials can have increased strength/density ratios and much improved section moduli. The emerging design philosophy is to use each material where it provides the greatest value (e.g., magnesium alloys with the lowest density in locations where energy absorption is not required due to poor properties in this regard) by engineering multi-material structures. Creation of such structures requires joining of dissimilar metals. However, due to differences in melting points and the tendency to form brittle intermetallic compounds, many dissimilar metal pairs cannot be joined with traditional fusion-based techniques such as resistance spot welding, metal inert gas (MIG) welding, etc. Alternate joining techniques, such as fasteners, self-piercing rivets and adhesives offer ways to circumvent the issues with welding.

One of the most remarkable ways to accomplish dissimilar metal welding is by High-Velocity Impact Welding (HVIW). HVIW is a true example of multi-disciplinary engineering research as it incorporates solid mechanics, fluid mechanics, heat transfer, material science, and manufacturing processes. HVIW includes techniques such as EXplosive Welding (EXW), Magnetic Pulsed Welding (MPW), Vaporizing Foil Actuator Welding (VFAW), and Laser Impact Welding (LIW).

HVIW is a solid-state process involves a high-speed, oblique collision between two metals arranged in relatively simple geometries such as parallel plates or coaxial tubes (or tube-shaft). Typically, one of the joining members, the flier, is launched toward the other stationary joining member, the target. This collision, when carried out at the proper impact angle (5°-20°) and velocity (300-1000 m/s), causes the surface oxides and other contaminants to be ejected in the form of a jet, exposing virgin materials beneath. The uncontaminated surfaces are immediately brought into intimate contact by the momentum of the flier, and the induced pressure holds them together until bond formation is complete. In this technique, for a short period of time (<50µs), metals behave as non-Newtonian fluids.

The quality of this bond is dependent on process parameters, mainly impact velocity and angle. A wavy morphology is often observed during impact welding processes, provided that the impact velocity and angle are sufficient and correct, respectively (see Fig. 1).


Fig.1. Wavy morphology observed during a) EXW, b) MPW, c) LIW, and d) VFAW (Nassiri et al. 2016, Journal of the Mechanics and Physics of Solids)

In the past few years, I have been involved in several projects in this area from concept-to-commercialization and prototyping. Some of them are listed below:

Project: Characterization, Modeling, and Optimization of Magnetic Pulsed Welding (Funded by NSF)

The goals of this proposed research were to fundamentally understand the physical mechanism of Magnetic Pulsed Welding (MPW) and to assist designers in determining the expected mechanical properties of the MPW joints and optimizing the process parameters. While MPW had been used as a process for decades, the process was typically implemented based on experience and trial and error experimentation. The interdisciplinary collaboration in this research project addressed fundamental questions related to the welding mechanism during MPW.

Due to the complexity of the metal behavior during HVIW, studies in different branches of science were needed for full characterization of the process. Hence, the following aspects were investigated during my studies:

Mathematical Modeling 

Mathematical Modeling was performed using a linear stability analysis of a simplified weld model to determine if the interfacial wave could be the signature of a shear driven high strain-rate instability of a perfectly/visco-plastic material using temporal, spatial, and non-modal stability analyses. As in linear stability investigations of other continuum mechanical systems, a partial differential eigenvalue problem was formulated and solved numerically, in this case using a spectral collocation method. The solution of the eigenvalue problem yields the wavelength and growth rate of the dominant wave-like disturbances along the interface. My idea for the mathematical modeling was originated from a natural phenomenon, i.e., cloud formation (see Fig. 2).

Fig.2. Cloud formations a) Saint Martin Island, b) Taken from Capitol Hill, Seattle, WA (photo credits to

  • Temporal Stability Analysis: In temporal (eigenvalue) stability analysis, the long-time evolution of a modal disturbance (parameterized by a given, fixed real x-wavenumber k) is predicted. Temporal analysis assumes that the disturbance amplifies in time, but not in space.

Fig.3. Growth Rate in temporal analysis (Nassiri et al. 2016, Journal of the Mechanics and Physics of Solids)

  • Spatial Stability Analysis: In this technique, the disturbance is applied in time and the spatial evolution (namely, growth or decay) of linear disturbances with fixed real frequency ω is analyzed.

Fig.4. Growth Rate in spatial analysis (Nassiri et al. 2014, CIRP Annals-Manufacturing Technology)

  • Non-Modal Stability Analysis: Since the impact is a short-time highly-dynamic event, non-modal stability analysis presumably is more relevant than conventional eigenvalue analysis. A non-modal shear flow stability analysis of a perfectly plastic material was performed to investigate the transient growth of disturbances and to assess if a connection exists with the corresponding predictions obtained from the modal analysis.

Fig.5. Non-Modal Stability Analysis, top) Direct integration of Governing Equations, bottom) Backward integration of Adjoint Equations (Nassiri et al. 2014,


Numerical Simulations 

Accurately predicting such a phenomenon is difficult with a classical Lagrangian numerical algorithm. Due to the severe plastic deformation during HVIW, for years, there were lack of robust and accurate numerical tools. During my Ph.D. studies, I developed explicit finite element codes with different algorithms including Arbitrary Lagrangian-Eulerian (ALE) and Smoothed Particle Hydrodynamics (SPH). With the help of these algorithms, the key process parameters such as impact angle and velocity; general shape of the interface between welded materials; thickness of the shear zone; temperature at the interface; and even the jetting phenomena and composition of the jetted materials were simulated.

  • Arbitrary Lagrangian-Eulerian (ALE): The ALE technique combines the features of classical Lagrangian and Eulerian methods within the same mesh to maintain a high mesh quality during simulations.

Fig.6. ALE simulations (Nassiri et al. 2015, Materials & Design)

  • Smoothed Particle Hydrodynamics (SPH): SPH is a meshless method where collection of particles are used to represent a continuum body. The ability of SPH to model the jetting process is advantageous to accurately representing the process.

Fig.7. SPH simulation (Nassiri and Kinsey 2016, Journal of Manufacturing Processes)

Experimental Tests 

Experimental tests were conducted to validate and inform both the mathematical and finite element modeling efforts. The main goal of the experimental tests was to determine a range (i.e., for impact velocity and impact angle) in which the wavy morphology at the interface emerges. The workpiece velocity was measured with Photon Doppler Velocimetry, which provides a robust method for measuring velocities with submicron displacement resolution and temporal resolution in the nanosecond range. Microstructural analyses were performed in order to assess and investigate the wavy morphology at the interface. Optical microscopy was used as this provided an overall picture of the structure obtained and guided further analyses. To observe the possible molten zone at the weld interface, Scanning Electron Microscopy was used.

  • Magnetic Pulsed Welding (MPW): In MPW, a capacitor bank is charged with energy that is quickly dissipated into a specially designed coil. A magnetic field is generated which repels the flier workpiece away from the coil at a high velocity and creates a large impact pressure when it collides with a base (or stationary) workpiece.


Fig.8. Al-Al experiment with MPW process, a) before test, b) after test, c) during cutting with diamond saw d) cold mounted sample, and e) optical micrograph (Nassiri A., Ph.D dissertation)

  • Vaporizing Foil Actuator Welding (VFAW): In VFAW, the flier is launched toward the base plate by the pressure created from the electrically driven rapid vaporization of a thin metallic conductor.



Fig.9. Experimental test using VFAW, a) experimental setup, b) welded sample, and c) stitched optical micrograph (Nassiri et al., 2015, Materials & Design)

Analytical Modeling 

While some Finite Element software packages exist that are capable of modelling the electromagnetic forming process and estimating the corresponding process parameters (e.g., magnetic pressure and workpiece velocity), there is a lack of simplified and accuracy analytical modelling tools for this purpose. In this study, a coupled analytical model was created to predict the magnetic pressure generated by a multi-turn, axisymmetric coil and the corresponding tube radial displacement and velocity. In the proposed model at each time increment the magnetic field geometry is updated in response to the tube deformation.

Fig.10. Left) Procedure of the analytical model, Right) predicted pressure distribution along the tube (Nassiri et al. 2016, 7th International Conference in High-speed Forming)

To validate the analytical model, experimental tests with Photon Doppler Velocimetry (PDV) were conducted. Due to the shape of the coil and difficulty to measure the velocity during the process from the outside, a device was designed and fabricated to measure the velocity on the inside of the surface of the tube. In this setup, an angled optical path was created by a laser mirror and tube velocity was measured by PDV.

Fig.11. Left) Experimental setup, Right) Comparison of velocity between the experimental, analytical, and numerical simulations (Nassiri and Kinsey 2017, CIRP Annals-Manufacturing Technology)

Project: Fundamental Studies and Modeling of High Impact Pressure, Supersonic Water Droplets for Material Deformation and Removal (Funded by NSF)

The goal of this research was to create a fundamental understanding of the mechanism of material deformation and removal during the high impact pressure, supersonic water droplets impact. The ability of a continuous high-velocity focused water jet to generate extreme impact pressures and forces is well known. Processes for deforming/cutting soft materials (e.g., food processing) to brittle materials (e.g., ceramics) to high strength metals (e.g., hardened steel) are currently in use. For hard materials, the addition of abrasives is required, which is undesirable from environmental and machine maintenance perspectives. In addition, a continuous jet is not the optimal delivery mechanism for hard surfaces, as much of its momentum is expended on inertial penetration of the liquid accumulated on the surface. To partially address these continuous water jet deficiencies, approaches, e.g., pulsed-flow water jets, are used. While an improvement to machining with abrasives, these are still not the optimal means of utilizing water alone for materials processing. Alternatively, a high velocity stream of discrete water droplets would allow for a significantly more efficient transfer of momentum to the metal surface. A high-velocity train of discrete water droplets has been shown to produce a significantly more efficient transfer of momentum to a surface than a continuous jet alone. If the ability of water droplets to produce extremely large pressures when impacting surfaces at high velocities can be understood and controlled, environmentally friendly applications for a wide range of technologies, from peening to coating removal to machining, will be achieved.

Fig.12. Left) Schematic of a high-velocity water droplet stream impacting a surface (US Patent No. 7,380,918 B2), Right)  Schematic of high-speed droplet impact: (a) geometry of the initial impact; (b) shock propagation and radial jetting phenomenon (Haller et al. 2003, Journal of Fluid Mechanics)

In this research, we were promoted an environmentally friendly and cost-effective alternative to the currently in-use waterjet technology.

Fig.13. Numerical simulations of drop impact inside a vacuum channel

I assisted in designing, building, and implementing a new prototype to study high-velocity impact of water droplets in a vacuum condition for material deformation and removal. I also implemented Coupled Eulerian-Lagrangian (CEL) and Smoothed Particle Hydrodynamics (SPH) Finite Element Analyses to simulate Water Droplet Impact.


Fig.14. Water droplet impact, left) numerical simulations, right) Scanning Electron Microscope (SEM) image of removed paint and deformed metals caused by high-velocity (~600m/s) water droplets from a focused jet (a) & (b) Al6061-T6 (c) steel

Project: Fundamental Studies on Interface Structures and Properties of Impact Welding across Varying Length Scales (Collaborative Research- Funded by NSF)

The objectives of this Grant Opportunity for Academic Liaison with Industry (GOALI) research project are to:

(i) create a fundamental understanding of the mechanisms which promote a strong and tough joint during impact welding

(ii) bring together and validate a suite of predictive finite element design tools

(iii) provide the scientific basis by which these impact welding processes can be related and effectively implemented across various length scales.

If the mechanism whereby metals colliding at high impact velocities (between 300-1000 m/s) are successfully welded together can be fundamentally understood, then the ability to weld dissimilar metals can be achieved which will promote lightweighting for various structures, e.g., in the automotive industry.

Project: Multi-Materials Support (Funded by HONDA R&D Americas, Inc)

We are developing and documenting test procedures for structural joint testing which achieve the deliverables required by the Honda R&D Americas (HRA). We are also leading and performing tasks in the areas of joining, mechanical design, simulation, experimental test, and advanced characterization for HRA.

Fig.15. TKD analysis results, high-strength steel (JSC980)/aluminum alloy (Al6111-T4) joined by solid-state welding (Nassiri et al., in preparation)