key: cord-0323427-a5f3ryjc
authors: Gleason, Glenn; Sunny, Sumair; Sadeh, Sepehr; Yu, Haoliang; Malik, Arif
title: Eulerian Modeling of Plasma-Pressure Driven Laser Impact Weld Processes
date: 2020-12-31
journal: Procedia Manufacturing
DOI: 10.1016/j.promfg.2020.05.039
sha: 4ffcc7a8343c57fa150069709d7720c1bb076ef7
doc_id: 323427
cord_uid: a5f3ryjc

Abstract In this study, details of the rapidly evolving state of a laser impact welding (LIW) process are simulated by incorporating a hydrodynamic plasma pressure model into a high-fidelity thermomechanical Eulerian numerical approach. Detailed evolution of the localized velocities, shear stresses, plastic strains, and temperature state in the vicinity of the weld interface during its formation are revealed. The presented simulation technique applies a load distribution that is temporally and spatially modeled based on the plasma pressure induced during surface ablation by a nanosecond-pulsed infrared laser. Due to the Gaussian plasma-pressure loading profile, significant shear stress patterns are observed to develop in the flyer foil prior to its collision with the target foil, the character of which appears to be significant in achieving a successful impact weld. Moreover, features already known to be critical to successful impact welding of thin foils are captured by the combination of the high-fidelity Eulerian control volume and the plasma pressure model, including the requisite collision velocity and impact angle. During the impact welding, interfacial material ‘jetting’ is observed, in addition to concentrated shear stress fields along the weld front. A wavy interface arising from a regular pattern of material mixing is confirmed to occur, in addition to significant plastic strains and heat generation due to the plastic deformation, all of which indicate the formation of a collision joint due to the more realistic loading condition imposed.

Yield stress (dynamic)

Impact welding is a solid-state joining process that introduces bonds between two metal substrates that may differ substantially in their material properties, particularly melting temperature, where the use of more conventional fusion welding processes do not yield satisfactory results. Process parameters currently understood to create strong joints in impact welds include an angle between the colliding interfaces, and closing velocities that appear to span an order of magnitude below the speed of sound in the parent materials (~200-1500 m/s) [1] , though research into optimal impact weld conditions is subject to ongoing study [2, 3] .

Under proper conditions for weld formation, a small zone of rapid plastic deformation forms at the collision front, which advances rapidly along the interface of the two materials being joined. This causes ablation of the outer layers of the joining surfaces, ejecting any surface oxides and contaminants away from the weld zone in a high-speed jet. Despite significant localized heating at the interface, the collision weld process takes place in a very short time, on the order of 1 µs or less. This rapid collision process has the advantage of minimizing or eliminating adverse thermal effects found in many fusion welds between metals with extreme melting point variation, such as the formation of brittle intermetallic compounds, or compromising structural effects of the cooling process such as formation of porosities and/or microcracks. The result is a joint that is primarily mechanical in character. Reducing the size of the intermetallic zone is a common process design goal to improve the strength of resulting joints, even in fusion welding processes [4] [5] [6] .

Despite the evident advantages and unique applications of the LIW process, the mechanisms of impact weld formation are not yet well understood, though many theories have been proposed, largely making comparisons to fluid-like behavior at the collision weld front [7] [8] [9] .

In some studies, impact welds were simulated by accelerating the parent materials to the requisite velocities for collision weld formation, but without modeling flyer stresses prior to impact [2, 10] . Typical numerical approaches have modeled collision weld processes using prescribed (assumed) initial velocity boundary conditions, rather than by imposing the actual force or pressure load distributions. Raoelison et al. [11] , for example, used a linear velocity distribution in their Eulerian magnetic pulse welding model. Such simplification helps reduce computational expense, but limits accuracy when estimating internal stresses and final configuration of an impact welded foil joint [12] .

A loading model is therefore used in this study, according to the LIW process performed by Sadeh et al., in which a confined ablation process from a Q-switched Nd:YAG laser was used to create solid state spot welds between 50 µm thick foil samples [12] . The experimental setup irradiates a matte black paint layer (thickness ~25 µm) applied to an aluminum alloy 1100 flyer with a total pulse energy of 3 J, as depicted in Fig. 1 . The circular laser shot is focused down to a 3.2 mm diameter and persists for 17 ns. The paint absorbs this energy and instantly vaporizes to form an expanding plasma that accelerates the flyer to a high velocity distribution in less than 1 µs. This process is facilitated by the confinement of the plasma within the borosilicate glass overlay. Peak pressures reach around 2.7 GPa, an estimate based on Fabbro et al.'s solution of an analytical 1-D hydrodynamic plasma pressure model [13] ; the resulting collision with the stainless steel alloy 304 target results in spot welding of the two foils [12] .

By making use of confined irradiated plasma on a relatively thin foil workpiece during the acceleration phase, laser impact welding produces internal shock and stress effects that are likely to strongly influence the dynamics of the collision weld front. Laser pulses of similar power density are used for laser shock peening processes that induce residual stresses greater than 1 mm below the surface of relatively large metallic parts [14] . Based on this observation, substituting a rapidly pulsed loading condition for a velocity on the flyer in an impact weld simulation is hypothesized to improve the quality of the predictions the simulation offers.

This paper seeks to numerically predict the in-situ evolution of the localized velocities, shear stresses, plastic strains, and temperature state along the weld interface during the LIW process, with incorporation of the plasma pressure load condition. In a previous study [12] , the displacement-only Eulerian formulation was compared with the experimentally validated ALE formulation. Satisfactory agreement was observed between the two formulations. The analysis in this work not only uses a much more refined Eulerian grid, together with the plasma pressure load condition, but it adds thermomechanical coupling to capture the rapidly evolving state of a LIW process. More importantly, the weld structure observed (at the timescales specific to weld formation) in this work still matches that observed experimentally and numerically in [12] . While this work pioneered implementing the laser-induced plasma pressure loading condition in LIW simulations to capture the detailed velocity distribution of the flyer foil, its relatively low fidelity ALE formulation was not able to reveal the detailed evolution of the localized velocities, shear stresses, plastic strains, and temperature state in the vicinity of the weld interface. Therefore, the model proposed in this work combines a thermomechanical (vs. displacement only), high-fidelity Eulerian formulation with the same plasma pressure loading condition to predict details of the rapidly evolving state of a LIW process. This is motivated by the fact that such detail cannot currently be characterized by experimental means. Note that consideration of the thermal effects due to laser-actuated impact in a model that incorporates measured temporal and spatial beam energy profiles has not previously been reported in literature.

The background for this model begins in the next section, with the Eulerian framework discussed in Section 2.2. Section 2.3 provides explanations for the material constitutive modeling and the layout of the simulation, which is followed by a description of the laser-induced plasma load model in Section 2.4. Observations discussed in Section 3 illustrate and describe the predictions of the proposed numerical model, with conclusions discussed in Section 4.

A wide variety of numerical approaches have been employed to model impact welding processes, including Arbitrary Lagrangian-Eulerian (ALE) [12, 15, 16] , Eulerian [11] , Lagrangian [10] and Smoothed Particle Hydrodynamics (SPH) [13, [15] [16] [17] . Meshed Lagrangian methods are more efficient for tracking free material surfaces, using fewer computational resources and data storage when compared to Eulerian methods. However, meshed Lagrangian methods typically lack the ability to accurately model the distinctive wavy interface geometry; output data instead reveals excessive mesh distortion. Purely Lagrangian approaches thus generally suffer from inaccuracy due to extreme mesh distortion at the simulated weld interface [15] . The remeshing procedure in ALE can mitigate mesh distortion inaccuracies, but there is still the disadvantage that ALE does not directly model the material jetting phenomenon [12, 15] . Sapanathan et al. [18] noted failure of their ALE model due to excessive mesh degradation when a critical impact velocity was reached that was beyond the remeshing procedure's capability to correct; there was, however, good agreement between their ALE model and experimental weld morphology at lower velocities.

Beginning in 2012, the meshless Lagrangian SPH method was employed [15] [16] [17] 19 ] to better depict the jetting phenomenon, as well as the periodic, unstable motions of the traveling weld interface that lead to distinctive wavy interfacial patterns found in many collision-welded joints. While pure Eulerian and SPH numerical models each have advantages when modeling collision welding processes, the Eulerian formulation was chosen because of the shared material volume fraction capability offered by the fixed Eulerian grid, and because of the relative simplicity in applying the plasma pressure loading condition for this particular study compared to SPH.

A pure Eulerian model of the LIW process, despite the computational disadvantage compared to a meshed Lagrangian method, offers a useful framework for a numerical study based on an estimated plasma pressure loading condition and is therefore employed in this study, together with a hydrodynamic plasma pressure loading model. An Eulerian frame allows for a relatively simple nodal load application condition as well (see end of Section 2.4), and, in its discretized form, the Eulerian model avoids mesh interference problems by allowing more than one material to occupy each fixed element, including void material. Tables 1-2 summarize previously used numerical techniques in simulation of impact welding, along with their advantages and disadvantages.

The finite element Eulerian approach is based on the application of conservation of mass, momentum, and energy to finite elements in a fixed grid (control volume) of the process. This method is well suited for modeling the extreme strain rates and deformations encountered in impact welding processes that can cause inaccuracies in Lagrangian procedures due to mesh distortion. Abrahamson [7] , Hunt [8] , and Cowan [9] make analogies of the extreme plastic deformation of material at the weld interface to fluid flow, for which Eulerian frames are well suited for analysis. Equations 1-3 provide the governing equations for the Eulerian formulation, describing the conservation of mass, momentum, and energy, respectively.

The term on the right in Eq. 3 accounts for the dissipative heating effects of plastic work, which is significant over the duration of the impact weld process near the weld zone. 

The strain rate-and temperature-dependent isotropic Johnson-Cook empirical model (numerical values listed in Table 3 ) is used to compute dynamic yield stresses in the simulation. Regions of extreme plastic deformation form very quickly in impact welds, with significant associated dissipative heating from plastic work, making the temperature-dependent model applicable. The Johnson-Cook model is defined by the following expression:

where the nondimensional temperature * is given by A Mie-Grüneisen equation of state (EoS) is used to thermodynamically model changes in pressure and volume associated with the impact process, which includes volumetric stress effects in the solid material. This numerical study employs a linearized Hugoniot relationship of shock velocity to particle velocity, which is then utilized in the Hugoniot form of the EoS. Parameters for the EoS are included in Table 4 . The laser parameters for the LIW process in this work, as discussed later in Table 5 , are as given in experimental studies of Sadeh et al. [12] . Since SEM and optical images from their experiments revealed no signs of flyer or target foil rupture, damage (fracture) modeling is not included in the proposed model. Figure 2 depicts the geometric layout of the plane strain Eulerian impact weld simulation in this study. Strictly speaking, the simulation is coupled Eulerian-Lagrangian, as there are two discretely meshed Lagrangian rigid bodies bounding the process domain at the upper and lower limits of the Z-ordinate. However, an Eulerian grid encompasses the active volume in which the LIW process takes place. In addition, the impact occurs between two Eulerian-modeled materials. A 50 µm thick flyer foil is instanced as an active material volume fraction in the Eulerian grid, adjacent to the upper rigid body. This upper Lagrangian rigid body is representative of the transparent overlay, borosilicate glass in this case. Similarly, a target foil of the same thickness is modeled across a 400 µm standoff distance on top of the lower rigid body, representative of a fixed specimen base. The remainder of the initial volume of the grid is modeled as a void (vacuum). Contact behavior with no permitted slip or postcontact separation is automatically applied between the Eulerianmodeled materials in the analysis.

LIW involves the creation of a joint between two metals due to significant thermally dissipative plastic work near the collision interface. This results in a thermal coupling between the dynamic yield strengths of the flyer and target, as indicated earlier in Eq. 4. Accordingly, the numerical approach simultaneously computes the thermal and mechanical solutions. The software utilized offers a coupled temperature-displacement element formulation that is used for the Eulerian volumetric grid, to which material volume fractions are assigned based on the positions of the flyer and target foils. The materials are assumed to be isotropic, with aluminum 1100 properties implemented for the flyer, and stainless steel 304 for the target foil [20] . Elements are 8-node, thermally-coupled linear displacement Eulerian bricks with reduced integration (EC3D8RT). A linear elasticity model for the flyer and target materials is employed with a von Mises yield criterion. As the volumetric stress-strain relationship is already modeled via the EoS, the solid elastic properties are described with the use of shear moduli. An adiabatic assumption is made for the boundaries of the solid parts, which is reasonable for the limited timescale (1 µs) of the process.

Numerical solutions are obtained using the explicit solver of Abaqus v6.14, run with double precision. The discretized Eulerian grid uses elements 2.5 µm square in the XZ-plane, which is the plane of interest in the model. The deformable parts in the simulation have Y-direction thickness of 10 µm; however, motion in this direction is constrained with a prescribed boundary condition of zero displacement along the Y-axis. Approximately 1.25 million elements comprise the process space in which active material volumes can interact, with additional layers of elements on either side in the out-of-plane direction acting as "buffers" to prevent material interaction with the boundary faces of the grid. (This results in an "enforced" plane-strain analysis, as the software used does not allow for a strictly two-dimensional Eulerian calculation.) Table 5 lists the laser parameters on which solution to the 1D hydrodynamic plasma pressure model [13] described in Section 2.4.2 is based, according to the laser energy spatial profile discussed next in Section 2.4.1. 

A pressure load is applied as a distribution of concentrated forces in the Eulerian grid at the beginning of the process time step, occupying a region of nodes coincident with the portion of the flyer actuated by the laser-induced plasma. Moving in the Xdirection (representative of the radial direction), away from the center of the shot target location, the load magnitude decays according to an approximated Gaussian function. When normalized, the applied pressure load is represented as unity at the center, and decays to zero at the edge of the circular spot (diameter 3.2 mm).

While the magnitude of the load can vary based on experimentally controlled settings, the spatial distribution is modeled by the Gaussian expression:

≥ 0 (6) where the standard deviation and mean µ of the distributed load ( ) are approximately 0.65 mm and 0 mm, respectively, when predicted to within 95% confidence bounds, and with being the radial distance from the LSP shot center. The statistical model described by Eq. 6 was calibrated as follows: A fast photodetector (Ophir FPS-1) converted optical signals intercepted by a beam splitter into electrical signals. These were measured using an oscilloscope (LeCroy Waverunner 204Xi DSO), which provided the temporal profile of the laser pulse. Concurrently, the laser pulse's spatial profile was identified using a high resolution beam profiling camera (Ophir SP928), equipped with a silicon CCD sensor. A Gaussian spatial distribution of plasma pressure is modeled with direct proportion to the laser intensity profile, experimentally found to be approximately Gaussian [23] . As a result, the Gaussian fit in Fig. 3 , which approximates the laser intensity profile, is the same function used for the spatial distribution of the load condition.

The temporal plasma pressure profile, as well as the normalized peak value of the pressure for the model as seen in Fig. 4 , is calculated via a one-dimensional hydrodynamic confined ablation model by Fabbro et al. [13] . During the heating phase (0 < < ), Eq. 7 relates the laser intensity , pressure at the confined interface , plasma internal energy , and displacement (between the flyer surface and the transparent overlay) , all of which are functions of time. However, an approximate solution can be reached by assuming a constant intensity 0 for the incident laser for the duration of the pulse width, coincident with the heating phase.

The internal energy affected by the laser fluence of intensity has both a thermal component = and an ionization component (1 − ) . Assuming an ideal gas relation for a monatomic gas gives

which, combined with Eq. 7, results in

The borosilicate glass transparent overlay and the aluminum flyer have shock impedances and respectively, which combine according to

This quantity completes the pressure and plasma layer thickness relationship via the linear differential equation

To provide an initial condition, the pressure at = 0 is calculated via the expression

Solving the coupled Eqs. 7-12 via numerical approximation yields the heating phase portion of Fig. 4 in the domain 0 < < , with the peak pressure at 2.7 GPa. The heating phase and adiabatic cooling phase ( > ) are governed by Eqs. 13a and 13b, respectively:

Equations 13a-b yield the temporal plasma pressure profile in Fig. 4 . With the pressure values during the heating and cooling Pressure is modeled as zero at = 300 ns [21] . phase thus determined, the resulting curve in Fig. 4 provides a suitable temporal model for the initial loading condition.

With the temporally and spatially normalized amplitude and analytical fields imposed, the pressure load ( ) is then set to a peak value of 2.7 GPa. The Eulerian analysis requires loading at nodes rather than element faces, requiring the pressure loading to be converted to concentrated forces located within the active volume fraction inside the laser spot's radius.

Equation 14 results in a peak discretized nodal force magnitude of 1.6×10 -3 N in the loading condition, considering a square element edge length ( ) in the X and Z-directions of 2.5 µm, and a thickness in the constrained Y-direction ( 0 ) of 5 µm per element. To maintain stability in the loading phase, the load was divided among all the layers of nodes throughout the 50 µm thickness of the flyer in the Z-direction ( ).

Analysis was performed in 8 hours and 37 minutes running on 8 CPUs on a cluster that was equipped with Intel Xeon E5-2667 processors having clock speed of 2.9 GHz, and 48 GB of RAM. Figure 5a outlines the shape of the flyer foil just prior to impact, with velocity magnitudes plotted (maximum 932 m/s in the vacuum). The spatial loading pattern has a noticeable effect on the geometry of the flyer, causing variation of impact angles for the pending collision as seen in Fig. 6 . Up to 480 ns, the time interval just after collision (Fig. 5b) , no jet is observed in the model, which suggests an impact angle at the weld center that is insufficient to form a joint. The next frame of the simulation shown (Fig. 5c) indicates the requisite jetting for a collision weld. The multiple material volume fractions that the discretized Eulerian model allows in each element provide a distinct advantage at this point in the analysis, as the allowance of a partial void fraction in each element enables minute jetting phenomena to be mapped in the stationary mesh. The model thus far agrees with the laser impact weld experiments by Wang et al. [20, 24] , which show that the impact weld region is annular when actuated by plasma energized by a circular pulsed laser spot, with no bonding occurring in the central region.

The curvature in the flyer foil results in a variation in impact angle at the weld front. Figure 6 plots estimates of collision angle based on an analysis of each frame of the simulation at = 480 ns ( = 19.2º), the first frame after the collision, to 1000 ns ( = 43.0º).

Predicted values of velocity in the weld jet range widely in magnitude from 5,400 m/s, a value that is reached at the initial formation of the weld jet ( = 520 ns), to 750 m/s at the end of the simulation ( = 1 µs) . These values are found by probing elements containing jetted material nearest to the weld zone in the velocity output plots, some frames of which are shown in Fig.  5 . The numerical model considers a vacuum condition around the setup, and hence inclusion of air resistance in the Eulerian domain is neglected.

A contour plot of equivalent plastic strain at 680 ns is shown in Fig. 7 . Peak plastic strain reaches approximately 6.21 within the jetted material and the weld front throughout the jetting phase, consistent with the ablation mechanisms generally present in impact welding. Equivalent plastic strain values within the weld domain are lower, but still range from 2.8 to 3 between the flyer and target after impact, which are similar to the plastic strains that Sapanathan et al. numerically modeled and found experimentally at impact-welded interfaces [18] . This shear stress field's oscillatory pattern typically causes excessive mesh distortion in Lagrangian models, causing an attendant loss of accuracy. Alternatively, the Eulerian model presented in this work maps the interface using volume fractions for each material within each grid element containing a nonzero solid fraction, with void filling the remainder. As the mesh of the Eulerian grid is stationary, mesh distortion issues are thus avoided, though interfacial location detail is compromised as a result of the material volume fraction interpolation algorithm.

The numerical model presented assumes plane strain conditions, thereby approximating the axisymmetric geometry. The plane strain assumption results in calculated stress effects in the out-of-plane Y-direction that are not of particular interest to the planar analysis. Experimentally, LIW processes typically result in an annular-shaped weld between two foils, with the process driven by expanding plasma pressure from a focused, pulsed laser spot. As impact weld interfaces develop via shear instability [25] , the stress component of primary interest thus becomes the in-plane shear. Figure 8 illustrates shear stresses in the flyer in the XZ-plane, which shows values between 60 and 90 MPa for much of the flyer foil prior to impact. These stresses result from the uneven loading conditions, and may play a role of some significance in the impact process, and resulting weld. Figure 9 shows the shear stresses in the XZ-plane in the flyer and target foils during the weld phase. Very high shear stress concentrations near the weld (within a 10 µm radius) are evident, resulting in thermally dissipative plastic work and the ejection of material at high speed. Larger opposing shear regions throughout the foil thicknesses in the surrounding portions of the flyer and target quickly form, with the positive shear region in the flyer reversing direction in reaction to the impact. These regions of high shear stress magnitude, with opposing directions in the flyer versus the target, are mirrored across the front. Additionally, a wake of positive shear stress is predicted that trails approximately 120 µm behind the weld front, which crosses the newly created weld interface. A waveform of small amplitude appears in the interface between the two foils as a result of these shear oscillations. Figure 10 shows the temperature field of the foils while the impact weld process is underway (approximately 200 ns after impact). Maximum temperatures briefly reach 1,460 K at impact, prior to the start of the weld; these modeled temperatures quickly decline to under 900 K during the jetting phase where the weld takes place. These jetting temperatures are lower than the melting point of both the aluminum flyer and target, further confirming that a solid-state weld that is primarily or entirely mechanical in nature, is achievable through the laser-plasma actuation technique with minimal to no melting required between the parent materials. Figure 11 shows the shear stresses after the completion of the weld phase. Jetting terminates at approximately 1000 ns, and the shear wake begins to dissipate. High magnitude stress regions remain near the weld and along the flyer's leading edge, and the Nodal Temperature positive shear stress region in the target ahead of the weld front is notably smaller compared to that in Fig. 9 .

The joint interface that results from stabilizations of the shear oscillations in the model is shown in Fig. 12 , which has an amplitude of approximately 2.5 µm. This is the same size as the mesh, limiting the accuracy of the estimate, but there is still a distinct wavy interface shape, indicating the presence of a collision joint resulting from the shear instability driving the weld process.

A plane strain, thermomechanical Eulerian numerical model that implements a Gaussian plasma pressure loading condition in a LIW process is developed and demonstrated in this work. This model can predict the rapidly evolving velocities, shear stresses, plastic strains, and temperatures during the dynamic process.

• The model reveals jet velocities throughout the weld phase reaching a peak of 5,400 m/s at 520 ns, declining to 750 m/s after the termination of the weld at 1 µs. • The predicted velocity of the flyer reaches a magnitude of 932 m/s prior to collision at 440 ns, in the central region near the center of the plasma pressure load, coincident with the axis of symmetry. • Shear stresses are shown to have opposite sign in the flyer and target in regions across the weld interface during the weld phase. At = 700 ns, in-plane shear stress magnitudes are at a peak, with variation from 232 MPa to -231 MPa. • Significant shear stresses of 60-90 MPa are predicted in the flyer prior to impact. • During the jetting phase, maximum equivalent plastic strains reach values of 6.21 at 680 ns. • Temperatures peak briefly at 1,460 K at impact prior to weld, but decline in subsequent frames of the simulation to under 900 K, indicating no melting effect during the weld process. 

A robust process-structure model for predicting the joint interface structure in impact welding

Process window acquisition for impact welding processes

Flyer thickness effect in the impact welding of aluminum to steel

Suppression of intermetallic reaction layer formation by controlling heat flow in dissimilar joining of steel and aluminum alloy

Effect of input current modes on intermetallic layer and mechanical property of aluminum-steel lap joint obtained by gas metal arc welding

Intermetallic Fe x Al y-phases in a steel/Al-alloy fusion weld

Permanent periodic surface deformations due to a traveling jet

Wave formation in explosive welding. The Philosophical Magazine: A

Mechanism of bond zone wave formation in explosion-clad metals

Single and double plate impact welding: Experimental and numerical simulation

Interfacial kinematics and governing mechanisms under the influence of high strain rate impact conditions: Numerical computations of experimental observations

Simulation and Experimental Comparison of Laser Impact Welding with a

Physical study of laser-produced plasma in confined geometry

Laser shock peening: performance and process simulation

Numerical studies on high-velocity impact welding: smoothed particle hydrodynamics (SPH) and arbitrary Lagrangian-Eulerian (ALE)

Numerical investigation of CP-Ti & Cu110 impact welding using smoothed particle hydrodynamics and arbitrary Lagrangian-Eulerian methods

Numerical study of the mechanism of explosive/impact welding using smoothed particle hydrodynamics method

Depiction of interfacial characteristic changes during impact welding using computational methods: Comparison between Arbitrary Lagrangian-Eulerian and Eulerian simulations

Numerical simulation of laser impact spot welding

Experimental and Numerical Study on the Laser Shock Welding of Aluminum to Stainless Steel

Investigation of Aluminum Equation of State Generation

Radioss Theory Manual, 14.0 version, Appendices

Prediction of Residual Stress Random Fields for Selective Laser Melted A357 Aluminum Alloy Subjected to Laser Shock Peening

An experimental and numerical study of laser impact spot welding

Shear instability of plasticallydeforming metals in high-velocity impact welding