2004 modeling schemes, transiency, and strain …yly1/pdfs2/1-s2.0-s1526612504700705-main.pdf ·...

Journal of Manufacturing ProcessesVol. 6/No. 2

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AbstractIn this paper, a coupled modeling scheme, which consid-

ered the dynamic evolution of laser-induced plasma and thecomplete physical interaction between the plasma, confinedmedium, coating layer, and processed metal, is comparedwith two decoupled modeling schemes in which shock pres-sure was first determined and used as loading in subse-quent FEM-based stress/strain analysis. The relative meritsand limitations of these schemes are evaluated in terms oftheir ability to describe process transiency such as shockpressure, shock velocity, and dynamic deformation historyand to predict the stress/strain to be imparted into a targetmaterial. Both bulk and thin-film samples of copper were stud-ied. Model predictions were investigated together with strainmeasurements based on an X-ray microdiffraction technique.

Keywords: Laser-Induced Plasma, Shock Wave Evolution,FEM Simulation, X-Ray Microdiffraction

1. IntroductionLaser shock processing (LSP) has been studied

since the 1960s (White 1963; Clauer and Holbrook1981; Peyre et al. 1998). Laser-generated shockwaves in a confining medium have been used toimprove the mechanical properties of various met-als such as aluminum, steel, and copper. In particu-lar, LSP can induce compressive residual stresses inthe target and improve its fatigue life, which is im-portant in applications such as turbo blades of anaircraft engine. Earlier modeling work on LSP wascarried out by Clauer and Holbrook (1981). Fabbroet al. (1990) developed a model assuming that a cer-tain amount of plasma exists instantaneously oncethe laser is on and that the process is time dependentonly and not spatially dependent. The dynamic de-formation process of the target material under theaction of shock load had been simulated using thefinite element method (FEM) (Peyre et al. 1995;Berthe et al. 1998).

The expanding applications of microdevices makethe mechanical properties of such devices an increas-

ing concern. Failure and reliability problems inMEMS have attracted increasing attention recently(Miller et al. 1998; Tanner et al. 2000; Que et al.2000). In metal structures experiencing rubbing orcyclic loading (mechanical or thermal), such asmicroelectromechanical actuators, micro-gears, mi-cro-switches, and microchannels, wearing and fa-tigue performance of the metal structure should beimproved to increase the reliability of the system.

More recently, laser shock processing of alumi-num and copper using a micron-sized beam has beenstudied (Zhang and Yao 2000a, b; Zhang and Yao2001a, b). It has been shown that microscale lasershock processing can efficiently induce favorableresidual stress distributions in bulk metal targets withmicron-level spatial resolution. Modifications in themodeling of LSP were made from Fabbro’s modelto account for the microscale involved (Zhang andYao 2000a, b). A further improvement of the pres-sure model, taking into account mass, energy, andmomentum conservation, was carried out with theplasma modeled as a laser-supported combustionwave and its spatial expansion effects accounted for(Zhang and Yao 2001b). A dynamic deformation pro-cess of the target material under the action of shockload had been simulated using the finite elementmethod (FEM) for the axisymmetric case (Zhang andYao 2000a, b) where semi-infinity boundary condi-tions were implicitly assumed. The stress and strainanalysis was extended to 3-D, and finite geometrywas considered, which again is important formicroscale LSP (Zhang and Yao 2001b). The microscale poses challenges in the characterization of thestress/strain fields. Conventional X-ray diffraction doesnot provide the spatial resolution necessary to char-acterize the residual stress distribution. High-spatialresolution characterization of the stress/strain fieldsin thin films was presented in Zhang and Yao (2002).

Modeling Schemes, Transiency, andStrain Measurement for MicroscaleLaser Shock Processing

Hongqiang Chen and Y. Lawrence Yao, Dept. of Mechanical Engineering, Columbia University,New York, New York, USA

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However, there exist limitations in the work onmicroscale LSP. It was assumed that the plasma gen-erated in laser shock processing obeys ideal gas lawsand that the laser irradiation absorption is a constant.It was also assumed that density, internal energy, andpressure of the plasma are uniform within the plasmavolume and vary with time only. To simplify the cal-culation, the coating layer was considered to be thinand well coupled with the metal target; thus, the shockpressure and the particle velocities of the coatinglayer and the metal target are identical. The model-ing is decoupled in which the shock pressure wascomputed first from the pressure model and then usedas loading for the strain/stress analysis via the FEMcode, assuming that the mechanical deformation willnot affect the pressure evolution. In fact, the processis coupled. The objective of this paper is to investi-gate ways to overcome these limitations.

2. Coupled Modeling of LaserShock Processing

To overcome the limitations of the previous mod-eling work, a coupled model with a hydrodynamicapproach is presented here. The dynamic evolutionof plasma and the complete physical interaction be-tween plasma, confined medium, coating layer(ablator), and processed metal (target) are consid-ered as a whole. The shock pressure can be consid-ered very high and much larger than the yield stressof the material. So the strength effects may be ne-glected and the target material can be treated as aninviscid compressible fluid, which is known as the“hydrodynamic” approach. The dynamic materialdeformation history, shock wave evolution, andshock pressure can be obtained simultaneously com-pared to the decoupled model, which uses shockpressure as loading in FEM analysis and assumingthat the mechanical deformation will not affect thepressure evolution.

2.1 Physical Phenomena in LSP

The mechanism of forming a high-temperature,high-pressure plasma is as follows. Laser absorp-tion in the ablator occurs within a skin depth thathas a thickness measured in tens of angstroms (Guy1989). Therefore, only a very thin surface layer ofthe ablator material is heated by the laser light. Be-cause of the rapid energy deposition time, thermaldiffusion of energy away from the interaction zone

is limited to, at most, a few micrometers. The heatedmaterial vaporizes and the vapor rapidly achievestemperatures greater than several tens of thousandsof degrees; the generation of a large concentrationof electrons above the surface due to thermion emis-sion has often been considered as the cause of plasmaignition (Guy 1989). At first, electron-neutral inverseBremsstrahlung or multi-photon ionization (for shortwavelengths such as UV laser) contributes to thecreation of initial electrons. When sufficient elec-trons are generated, the dominant laser absorptionmechanism makes a transition from electron-neutralinverse Bremsstrahlung to electron-ion inverseBremsstrahlung. So the laser absorption of the va-por becomes much stronger and the vapor is rapidlytransformed into the plasma. This plasma inducesshock waves during expansion from the irradiatedsurface, and mechanical impulses are transferred tothe target. The plasma-target interaction can be mod-eled as a hydrodynamic motion under very highpressure and temperature. If the plasma is not con-fined, that is, it is in open air, the pressure can onlyreach several tenths of one GPa when the surface isirradiated by a laser pulse of, say, 1 GW/cm2. If theplasma is confined by water or other media, the shockpressure can be magnified by a factor of five or morecompared with the open-air condition (Fox 1974).At the same time, the shock pressure lasts two tothree times longer than the laser pulse duration.

2.2 Governing Relations in LSP

Laser absorption in LSP: As for the plasma ab-sorption, the so-called inverse Bremsstrahlungmechanism of the ionization is dominant, and onepart of the laser energy is used to increase the ther-mal internal energy of the plasma (increase theplasma pressure). The other part of the laser energyis used for plasma ionization. The absorption coeffi-cient, �p, changes with the temperature, and a dif-ferent equation, (1) or (2), should be used accordingto different temperature.

At temperatures less than 10,000 K, only a fewelectrons are present and electron-neutral inverseBremsstrahlung dominates. The effective absorptioncoefficient is given by (Robert 1989):

1 exp( )p j e jj

hcQ n n

kT⎡ ⎤α = − −⎢ ⎥λ⎣ ⎦

∑ (1)


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where ne and nj are the number density of the elec-tron and the jth neutral atomic species, respectively,Qj is the average cross section for absorption of aphoto of wavelength � by an electron during a colli-sion with species j, k is Boltzmann’s constant, h isPlanck’s constant, c is velocity of light, and T is tem-perature. When temperature gets higher and the moreelectrons are generated, electron-ion inverseBresstrahlung dominates. The effective absorptioncoefficient is:

16 322

4

4 21 exp( ) ( )

3 3p e i i ije e

hc en z n g

cT hc m m kT

λ π⎡ ⎤α = − −⎢ ⎥λ⎣ ⎦∑ (2)

where zi and ni are the charge and number densityof the ith ionic species, respectively, gi is the appro-priate Gaunt factor that corrects the semi-classicalexpression for quantum effects, and me is the massof the electron.

Ionization model: Because the laser pulse widthin LSP is 50 ns in this study, which is much largerthan the electron-ion collision time, �ei, the ion for-mation can be treated within the framework of thelocal thermal equilibrium theory (LTE) and it is pos-sible to employ the Saha relations (Mitchner andKruger 1973).

/3/ 212

22 ( ) k kTe l e

k k

n n g m kTe

n g hλ

+ +−επ= (3)

where ne is the free electron number density, 1n+ isthe number density of single ionized positive ions inthe ground level, and nk is the number density ofneutral particles in the kth level. Here is assumed anequilibrium between electrons, ions, and neutrals,and the electron and ion density are always equal.The Saha-Eggert equation was used and the degreeof ionization was given by:

23/ 2

2 2

2( ) exp( )

1ekTmm U

h kT

πη = −− η ρ (4)

where me is the mass of the electron, m denotes themass of the particles, k is the Boltzmann constant,and U is the ionization potential of the target mate-rial (U = 5.989 eV for the Al coating layer). Thedegree of ionization, i

total

n

nη = , is expressed by the

number density ratio of ions and all particles. Someother ion models, such as the Thomas-Fermi model,

which is based on Fermi-Dirac statistics and is par-ticularly good for metals, or the average-atom model,which is relevant to dense plasmas, have also beenused in LSP modeling depending on the materialsinvolved and process conditions used.

Hydrodynamics: After the creation of the plasma,the expansion of the high-pressure plasma drives ashock wave into the target and the confining me-dium in two opposite directions. The interface move-ment between plasma and the target and confiningmedium can be treated as the hydrodynamic motionbehind the two shock waves that are propagatinginside the target and confining medium. For theplasma itself, it is also possible and advantageous toview the plasma as a continuum, or fluid. A suffi-cient condition for the applicability of such a de-scription is that the plasma be collision dominated(Mitchner and Kruger 1973). By this it is meant thatthe mean free paths for particle collisions for all spe-cies be much smaller than the characteristic lengthscale for macroscopic change, and that the particlecollision intervals be much smaller than the charac-teristic time scale for macroscopic change. So, onecan adopt a primarily macroscopic approach here andthe hydrodynamic motions are redescribed by the con-servation of mass, momentum, and energy. For simpli-fication, only the one-dimensional hydrodynamicgoverning equation is shown (Vertes et al. 1989):

( )v

t x

∂ρ ∂ ρ= −∂ ∂ (5)

2( ) ( )v p v

t x

∂ ρ ∂ + ρ= −∂ ∂

(6)

2 2[ ( / 2)] [ ( / / 2)]e v v e p v

t x

∂ ρ + ∂ ρ + ρ += − + αΦ∂ ∂

(7)

where � is density, v is velocity, e is internal energy,p is pressure, and � is input laser intensity. From theideal gas law, there is the well-known form:

(1 )pkT

pm

= + η (8)

where � is the degree of ionization.The conservation equations of mass, momentum,

and energy can be closed by a constitute equation,which relates the physical parameters of the mate-


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rial. The simplest equation of state is governed bythe ideal gas law (Vertes et al. 1989):

3[ (1 ) ]2

e kT Um

ρρ = + η + η (9)

where e is the internal energy and m is the mass ofthe particles. More reliable equations of state for dif-ferent materials can be based on the tabulated formsuch as the Los Alamos Sesame Library. In such atable, plasma pressure p and internal energy e canbe obtained as the dependent of temperature T andplasma density �. Because an equilibrium is assumedbetween electrons, ions, and neutrals and only onetype of neutral atomic species is considered, in Eq.(1), j = 1, the electron number density ne = ntotal �,and the number density of neutral is nn = ntotal (1 –�). Similarly, in Eq. (2), i = 1 and the charge densityzi = ne = ni = ntotal � = ��/m. Thus, there are sevenunknowns, �, v, p, e, T, �, and �p in seven equations,(1) or (2) and (4)–(9). The finite-difference methodis used to solve those unknowns through those equa-tions. Numerical values for all parameters used inequations have been given in a table in the Appendix.

3. Simulation and Experiment ConditionThe coupled analysis of shock pressure genera-

tion and dynamic deformation process of the targetmaterial subjected to LSP was carried out. The simu-lation results were compared with that from twodecoupled analysis schemes, in which shock pres-sure generated either based on the above model orthe model (Zhang and Yao 2001b) is used as load-ing in a subsequent FEM deformation analysis. Thecoupled analysis was implemented using a commer-cial radiation hydrodynamics simulation code, HY-ADES (Hyades 2001). HYADES is a one-dimensional,Lagrangian hydrodynamics and energy transportcode, designed for high temperature applications suchas that in the laser-material interaction, where mate-rials are significantly ionized. The temporal and spa-tial change of pressure, density of different meshzones in the depth direction can be tracked. Differ-ent materials in different regions can be defined andso it is convenient to solve multiplayer LSP prob-lems such as thin-film/substrate targets. Moreover,the hydrodynamic code incorporates deformationanalysis so the dynamic deformation result can be

obtained together with other physical parameterssuch as pressure, temperature and density. Thomas-Fermi model was used for ionization in copper andaluminum regions because it is more appropriate formetals. As for the confinement medium, water, Sahamodel was used. Models for equation of state of Cu,Al and water are selected from material tables fromthe Los Alamos Sesame Library. Room temperatureis selected for the floor temperature of electron andion in sample material.

For the decoupled analysis, the model (Zhang andYao 2001b) assumed that density, internal energy andpressure of the plasma are uniform within the plasmavolume and the plasma’s absorption of laser energyis a constant. The time history of the shock pressurewas then used as loading in a subsequent stress/strainanalysis. The deformation analysis was carried outusing ABAQUS. Axisymmetric models with semi-in-finite geometry were created for bulk targets (Zhangand Yao 2001a), and 3-D models with finite geom-etry were created for targets made of copper thin filmson silicon substrate (Zhang and Yao 2002). A secondtype of comparison was also carried out, in whichHYADES generated shock pressure was used as load-ing in a subsequent FEM stress/strain analysis. In theFEM simulation, nonlinear constitutive equations in-cluding work hardening, strain rate and pressure ef-fects on yield strength of copper target are considered(Zhang and Yao 2000a) assuming room temperaturebecause most heat generated by coating layer abla-tion is shielded from the target by the layer.

Both bulk and thin-film samples of copper werestudied. Copper foils of 90 micron thickness wereused as bulk samples. Thin-film samples are pre-pared by physical vapor deposition (PVD) for 1 µmthick copper film and electrochemical plating (ECP)for 3 µm thick copper film on 0.5 mm thick single-crystal (004) silicon substrate. A 16 micron thick alu-minum foil was used as the ablative coating layerfor both bulk and thin-film cases and foil was firmlyattached to targets using vacuum grease. As seen inFigure 1, a sample was placed in a shallow containerfilled with distilled water around 3 mm above thesample’s top surface. A frequency tripled Q-switchedNd:YAG laser (wavelength 355 nm) in TEM modewas used, the pulse duration was 50 ns, and pulserepetition rate could vary between 1 KHz to 20 KHz.Laser beam diameter is 12 microns and laser inten-sity was varied from 2 to 6 GW/cm2.


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As mentioned above, the plasma temperature andpressure in simulation is time and spatially resolved(one dimensional). The plasma temperature can beobtained by spectroscopic measurements but the resultis not spatially resolved, especially for the 12 µm laserspot size in microscale laser shock processing. Alsothe response of spectroscopic measurement may beinadequate for the short laser pulse duration (50 ns).The plasma pressure can be measured with syntheticX-cut quartz crystals and its response is adequate fornanosecond laser pulse. Typically, the quartz crystal isattached firmly to the backside of shocked sample, andthe sample should be a foil and can not be too thick (<10 µm) to affect the response. Thus, we need to use athin-foil like sample and change the sample thicknessthat we would like to investigate (90 µm for bulksample). For the thin-film sample, the thickness of thesilicon substrate is 0.5 mm and it cannot be made as avery thin foil. Due to those limitations, we did not chooseto measure the plasma temperature and pressure di-rectly and the model can be validated by X-ray diffrac-tion measurement for the LSP-induced strain in thesample predicted by simulation. Traditional X-ray dif-fraction is limited by its spatial resolution (in the orderof millimeters) and cannot be applied to measure themicroscale strain distributions generated by microscaleLSP. Recent developments in X-ray microdiffractionprovide the possibility of measuring the stress/strainfields with micron-level spatial resolution. The X-raymicrobeam system in the National Synchrotron LightSource was used in this study and more details will beprovided in Section 5.

4. Results and Discussion4.1 Shock Pressure Comparison from DifferentModeling Schemes

To facilitate discussions, the model (Zhang andYao 2001b) used in the decoupled analysis is de-noted as Model 1, while the coupled modeling asModel 2. Figure 2 compares the shock pressuresbetween these two models under the same laser in-tensity (I = 4 GW/cm2). In Model 2, both bulk andthin-film targets were considered and for the thin-film target two different tabular equations of statewere used for the film and substrate, respectively.As seen in Figure 2, the shock pressure is higher andlasts longer as predicted by Model 2 than that byModel 1. Model 1 assumes that part of the laser en-ergy is used for the breakdown of water and targetbesides the expansion of plasma. So the more massflows from water and target into plasma due to break-down, the less laser energy converts into the internalenergy in the plasma. As a result, the pressure ofplasma is lower and reduces to the atmosphere valuefaster. In Figure 3, the density of different regions ofwater and Al coating layer are compared and it showsthat the top layer of Al (zone 0) is changed into theplasma as evidenced by the fast density decrease,while the region 1 µm below the top layer (zone –1)can be regarded as the molten layer and the zone –2(2 µm below the top layer) is still in solid state. Forthe water, the region near the top Al layer (zone 0 ofwater, 2 µm thick) can still be regard as liquid thatdid not change into the plasma. Thus, the plasmagenerated in Model 2 is mainly from the breakdownof the Al coating layer and not from water. How-

Figure 2Pressure of Plasma in LSP from Different Models and Samples

(Laser intensity I = 4 GW/cm2)

Pre

ssur

e (G

Pa)

5

4

3

2

1

0

Bulk, Model 2Thin film (3ωm ), Model 2Bulk, Model 1

0 20 40 60 80 100

Time (ns)

Figure 1LSP Experiment Setup

PrecisionX-Y-Z stage

Samplesubmerged inliquid

Laserfocus lens


160

ever, in Model 1, the mass flow from the water isone magnitude higher than from the metal target(Zhang and Yao 2001b) so that much more laserenergy was used to breakdown the water to gener-ate the plasma, so the shock pressure is lower thanthat in Model 2 and it decreases much faster as well.

The pressure difference between these two mod-els can be better explained considering the physicalphenomena discussed in Section 2. At short laserwavelengths such as 355 nm used in this study, multi-photon-ionization (MPI) is dominant in the laser waterinteraction (Berthe et al. 1999). This means the wa-ter can be ionized by a sufficient number (m) of pho-tons as

M mhv e M+ ++ → + (10)

where M is an atom or molecule. At � = 355 nm, onlyfour photons are required to ionize single water mol-ecules, which have an ionization energy of 12.6 eV.Thus, the energy needed for directly ionizing the wa-ter and converting it into the existing plasma is around67,500 kJ/kg. However, in Model 1, the energy usedto convert water to plasma was simply considered asthe liquid to vapor (which is not quite the plasma yet)phase change energy, that is around 2,212 kJ/kg(Zhang and Yao 2001b) and much lower than that inthe direct ionization case. For the metal target, Model1 also considers the mass flow as the phase changeenergy from the liquid (molten metal) to vapor and itsvalue is around 6,418 kJ/kg, not much lower than theionization energy of Al (11,872 kJ/kg) used in Model2. So the water is more likely to convert into the plasma

in Model 1 and generates a higher mass flow fromwater to the “plasma,” which is not realistic.

In Model 1, only one type of target material canbe considered, and it cannot be used to model thecomplex multilayer thin-film sample, which is verycommon in the MEMS field and also important inmicroscale LSP. However, in Model 2, thin-filmsamples can be readily modeled by defining differ-ent meshes and regions for different material layers.From Figure 2, it shows that the peak pressure isslightly lower than that in the bulk sample case, bothobtained from Model 2. That is because the single-crystal silicon substrate has lower shock impedancethan copper so the plasma and shock wave will ex-pand faster, and there is a material discontinuity be-tween the 3 µm copper thin film and the siliconsubstrate, which will cost some plasma energy whenthe shock wave passes through it. Thus, the shockpressure is slightly lower in the thin-film sample thanin the bulk sample.

In Figure 4, the peak pressure values under dif-ferent laser intensity obtained using Model 1 arecompared with those obtained using Model 2. Asdiscussed earlier, the peak value from Model 2 ishigher than that from Model 1. However, such dis-crepancy decreased from 110% to 25% when laserintensity increased from 2 to 6 GW/cm2. This is be-cause, when the laser intensity increases, the ioniza-tion level of water becomes higher (Figure 5) andsome water near the plasma can be broken down,thus generating a mass flow into the plasma as as-sumed in Model 1. So the pressure predicted by thetwo models gets closer as laser intensity increases.

Figure 4Peak Pressure Comparison of Bulk Material from

Model 1 and Model 2

Figure 3Density at Different Depths of Coating Layer and Confined

Medium (zone –2 of coating: 2 µm below the coating surface;zone –1 of coating: 1 µm below the coating surface; zone 0 of

coating: coating-water interface, in coating; and zone 0 ofwater: coating-water interface, in water)

zone - 2 of coatingzone - 1 of coatingzone - 0 of coatingzone - 0 of water

0 20 40 60 80 100

Time (ns)

Des

ity o

f di

ffer

ent

regi

on (

g/cm

3 )

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Pressure discrepancy in %Peak pressure, Model 1Peak pressure, Model 2

Peak

Pre

ssur

e (G

Pa)

Laser Intensity (GW/cm2)2 4 6

8

6

4

2

Peak Pressure (GPa)

120

100

80

60

40

20


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4.2 Transient Processes and DeformationHistory in Target

The transient processes in laser shock processingare important in order to study the laser-induced shockwave and the dynamic deformation in the target ma-terial. From the particle velocity and density changeof different zones in the target depth direction, thedynamic evolution of the shock wave can be studied.

Pressure attenuation through the coating layer:In Model 1, the pressure of plasma is considered asthe pressure directly applied onto the target. How-ever, when the plasma-induced laser shock wavepasses through the Al coating layer, the pressure willbe slightly attenuated. In Model 2, the pressure dis-tribution in the depth direction can be obtained di-rectly so that the attenuated shock pressure at theinterface of coating layer and the copper target canbe determined and continuously used either in thecoupled analysis or as loading in a subsequent FEMstress/strain analysis.

Figure 6 shows the pressure attenuation in Model2 after the plasma-induced shock wave passesthrough the Al coating layer. The laser intensity is 4GW/cm2 and the thickness of the coating layer is 16µm. The pressure attenuation is about 0.2 GPa forthe bulk samples. In Table 1, shock pressure attenu-ation under different laser intensities (I = 2, 4, and 6GW/cm2) are compared. As seen, pressure attenua-tion decreases from 0.25 to 0.1 GPa when the laserintensity increases. According to the analysis ofBoslough and Asay (1992), the shock impedanceincreases with initial shock pressure. Thus, under ahigh laser intensity, the shock impedance of the coat-ing layer is higher so that the pressure attenuation

across it is larger. For thin-film samples, the attenua-tion values are nearly the same as the bulk samplesdue to the same coating layer used.

Deformation history analysis: to study the dynamicdeformation history in the target material (copper),as mentioned in Section 3, both coupled anddecoupled methods are applied here. The coupledmethod determines the history of deformation, den-sity, and pressure directly from Model 2. In thedecoupled method, shock pressure is calculated ei-ther from both Model 1 and Model 2 and then usedas loading in a subsequent FEM simulation. FromModel 1, the pressure is from the plasma and targetinterface, while in Model 2 the pressure at the coat-ing target is used. Figures 7 and 8 show typical FEM-predicted deformation results in the depth directionfor copper bulk and thin-film samples with pressureloading from Model 1. Axisymmetric modeling iscarried out, also assuming semi-infinity in the radialdirection. For the thin-film samples, both displace-ment and normal stress are considered continuousacross the copper-silicon interface. As seen from Fig-ure 7, the vertical deformation reaches about 30 mi-crons into the bulk sample and the maximumdeformation is around 1.8 µm at the top surface. Suchdeformation also covers a region around 15 µm inradius. For the thin-film sample in Figure 8, the ver-

Table 1Shock Pressure Attenuation Across 16 µm Al Coating Layer

Under Different Laser Intensity in Bulk and Thin-Film Sample

Laser Intensity (GW/cm2)Bulk 2 0.12 0.13

Samples (GPa) 4 0.19 0.2

Thin-Film Samples (GPa) 6 0.24 0.26

Figure 5Ionization Level of Water at Coating-Water Interface Under

Different Laser Intensity (I = 2, 4, and 6 GW/cm2)

1=6GW/cm2

1=4GW/cm2

1=2GW/cm2

0 20 40 60 80 100 Time (ns)

Ion

izat

ion

leve

l of

wat

er (

x10-3

)3

3

2

2

1

1

0

Figure 6Shock Pressure Attenuation Predicted by Model 2 Across 16 µm

Al Coating Layer (bulk copper sample, I = 4 GW/cm2)

0 20 40 60 80 100

Time (ns)

Pre

ssur

e (G

Pa)

5

4

3

2

1

0

Pressure at the plasma-coating interfacePressure at the coating-target interface


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tical deformation is primarily confined in the 3 µmcopper thin film. Very little deformation is seen inthe silicon substrate due to its higher Young’s modu-lus than copper. The maximum deformation in cop-per thin film is around 1.25 µm at the top surface, andthe radius of deformation region is also about 15 µm.

Figure 9 shows the transient deformation of thetop surface of a copper sample under LSP predictedby different modeling schemes. The results directlyfrom Model 2 is compared with the top surface dis-placement from the result of FEM simulation withthe shock pressure of Models 1 and 2. It shows thatthe deformation history from FEM simulation usingModel 1 and 2 is in the same order and the value ofModel 2 is slightly larger due to its higher shockpressure than that of Model 1 (Figure 2). When com-paring the FEM simulation result with that directly

from Model 2, a major discrepancy is evident. Asseen, during the initial stage of LSP (t < 10 ns, andpressure < 2 GPa), the deformation directly fromModel 2 is consistent with the FEM simulation re-sults. However, when time goes on, the deformationdetermined directly from Model 2 increases muchmore than FEM simulation results predicted and thenrebounds. This can be explained by the differentconsiderations about the material response to shockwave adopted in these two models.

According to Chou (1972), the material responseto intensive impulsive loading (such as shock waveinduced in LSP) may be described in one of threepossibilities, depending on the shock pressure in-volved: hydrodynamic, finite-plastic, and linear elas-tic. In Model 2, the shock pressure (2 to 6 GPa) isconsidered so high that strength effects can be ne-glected and the target can be treated as a compress-ible fluid, which is known as the hydrodynamicapproach. While in Model 1, shock pressure is usedas a loading in FEM simulation, which is based onthe finite-plastic approach. Strength effects such aswork hardening, strain rate, and pressure effects onyield strength are considered in the FEM simulation(Zhang and Yao 2001b).

In the hydrodynamic approach, the equation ofstate that relates pressure, density, and energy is usedto replace the complicated nonlinear constitutiveequations in the FEM simulation. Also, a shockHugoniot curve can be obtained, in which one prop-erty versus others (such as P vs. V) behind the shockis depicted. When the shock pressure is low (i.e., t <10 ns), the Hugoniot curve is very close to an isotro-

Figure 8Typical FEM Simulation Result for Vertical (the 2-direction)

Deformation in 3 µm Copper Thin-Film Sample(Laser intensity I = 4 GW/cm2, laser beam diameter = 12 µm.

Computation domain is 50 µm by 200 µm assumingaxisymmetry. The region shown is 5 µm by 15 µm.)

+9.429e—04–1.006e—01–2.021e—01–3.037e—01–4.052e—01–5.067e—01–6.083e—01–7.098e—01–8.113e—01–9.129e—01–1.014e—00–1.116e—00–1.217e—00

U, U2

2

3 1

Figure 9Displacement History of Surface of Copper Target

in Bulk Samples(Model 1, decoupled: pressure from Model 1 as loading in FEM;

Model 2, decoupled: pressure from Model 2 as loading in FEM; andModel 2, coupled: displacement history directly from Model 2)

0 20 40 60 80 100

Time (ns)

Dis

plac

emen

t of

top

cop

per(

um)

0

-4

-8

-12

-16

Model 1 + FEMModel 2 + FEMModel 2, coupled

Figure 7Typical FEM Simulation Result of Vertical Displacement

(the 2-direction) in Copper Bulk Sample(Laser intensity I = 4 GW/cm2, laser beam diameter = 12 µm.

Computation domain is 100 µm by 1000 µm assumingaxisymmetry. The region shown is 15 µm by 20 µm.)

+4.818e—08–1.063e—07–2.608e—07–4.153e—07–5.698e—07–7.243e—07–8.788e—07–1.033e—06–1.188e—06–1.342e—06–1.497e—06–1.651e—06–1.806e—06

ν, ν2

2

3 1


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5

0

-5

-10

-15

pic path, which is usually the case for a solid underimpact if the solid is only compressed slightly. Thus,the result from the hydrodynamic approach is con-sistent with the result from FEM simulation. Whentime goes on and pressure goes up, the target is com-pressed more such that both hydrodynamic andstrength effect should be considered. The Hugoniotstate (P vs. V) will be offset above the hydrostaticHugoniot (which assumes hydrodynamic approach)due to strength effect (Fowles 1960). Thus, in Model2, which adopted the hydrodynamic approach, alower pressure is needed to achieve the same den-sity, so that for the same pressure the material is easierto deform and the top surface displacement will belarger than the FEM simulation result. Moreover, asseen from Figure 10, the deformation will becomelarger when the loading shock pressure goes higher(from 2 to 4 GW/cm2). This is consistent with thefact that the Hugoniot state will be offset much moreunder higher pressure loading so that the material iseasier to deform (Figure 11).

Figure 12 shows the deformation history for the 1µm and 3 µm copper thin film predicted by the samesimulation methods mentioned above. The deforma-tion determined by the Model 2-based coupledmethod is again much larger than the decoupled re-sults due to the same reason mentioned above. Thedeformation in the 3 µm sample is slightly largerthan in the 1 µm sample from the decoupled simula-tion results. This is because a thicker film has a longertime to absorb the shock energy than a thinner film.Moreover, the slope of the deformation history, whichequals the particle velocity under shock (480 m/s),is about twice as large as that of the bulk samples

(Figure 13). In thin-film samples, the substrate is 200µm single-crystal silicon as compared to 90 µm cop-per total thickness in bulk samples. The impedanceof single-crystal silicon is about 1.97 × 107 kg/m2s,smaller than that of copper (4.18 × 107 kg/m2s). Ac-cording to the wave-surface interaction analysis(Boslough and Asay 1992), when shock wave propa-gates from the high-impedance material (copper thinfilm here) to the low-impedance material (siliconsubstrate here), the interaction will result in a re-flected release wave back in copper and a transmit-ted shock in silicon, which has a higher particlevelocity due to its lower impedance. Thus, the shockwave can pass through the copper-silicon interfaceand propagate much easier and the hydrodynamic de-formation will be larger than that in the bulk samples.

Laser shock wave propagation: Consider a shockwave passing through the target, the states are un-disturbed ahead of the shock front and the target iscompressed behind the shock, so shock front posi-

Figure 11Hugoniot Offset Under Different Pressure:

Pressure-Specific Volume Curve

0.096 0.098 0.100 0.102 0.104

Time (ns)

Pre

ssur

e(G

Pa)

5

0

-5

-10

-15

1=2GW/cm2

1=3GW/cm2

1=4GW/cm2

Figure 12Displacement History at Top Surface of Copper Thin Film

for Thin-Film Samples (Laser intensity I = 4 GW/cm2)

0 50 100 150 200

Time (ns)

Dis

plac

emen

t, M

odel

+FE

(µm

)

0.0

-0.5

-1.0

-1.5

-2.0

-2.5

Model 1 + FEM(3µm)Model 2 + FEM(1µm)Model 2 + FEM(3µm)Model 2 + FEM(1µm)

Model 2, coupled(3µm)Model 2, coupled(1µm)

Dis

plac

emen

t, M

odel

2 c

oupl

ed(µ

m)0

-10

-20

-30

-40

-50

Figure 10Displacement History of Copper Target Surface of Bulk Samplefrom Model 2-Based Coupled Analysis Under Different Pressures

0 20 40 60 80 100

Time (ns)

Dis

plac

emen

t of

top

cop

per(

µm)

1=2GW/cm2

1=3GW/cm2

1=4GW/cm2


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tion and shock velocity can be determined if defor-mation history in the depth direction is known. InFigure 13, the deformation history at different depthlevels in the copper target is shown, from which theshock wave velocity can be seen so that the lasershock wave propagation history can be studied.From the Model 2-based coupled analysis, the par-ticle velocity, that is, the slope of the deformationhistory curve, is about 240 m/s, and the shock ve-locity, that is, the slope of the straight line that con-nects the shock front at different times, is about 2km/s. From the decoupled results, the particle veloc-ity is 120–160 m/s, while the shock velocity is about4.14 km/s. The discrepancy is explained as follows.

Examining the material response parameters un-der shock impact, the shock velocity of copper isU = C0 + Su, where C0 (3.94 km/s) is the soundvelocity in copper, S = 1.489 (Asay and Shahinpoor1992), and particle velocity u = 135 m/s under 5GPa shock pressure as determined above. This givesU = 4.17 km/s, which is very close to that deter-mined by the decoupled analysis shown in Figure13. This is because in the FEM portion of thedecoupled analysis, nonlinear constitutive equationsincluding work hardening, strain rate, and pressureeffects on yield strength of the copper target areconsidered and they are comparable with theHugoniot data obtained from material experiments.In the Model 2-based coupled analysis, the shockvelocity (2 km/s) is close to that of water, which isaround 2.1 km/s for the same particle velocity. Thisis because, under the hydrodynamic approach em-ployed by the coupled analysis, the target materialis considered as a compressible fluid.

As seen from Figures 9 and 12, the deformationcurves determined by the Model 2-based coupledanalysis reverse their direction at a certain time. Thiscan be explained by the shock velocity analysisabove. When a shock front propagates to reach thebottom surface of the target, the rarefaction wave(release wave) is reflected back and this reflectedwave generally cancels part of the original incom-ing shock wave so that the total pressure decreases.In the hydrodynamic approach employed by theModel 2-based coupled analysis, the target materialwill expand when the pressure decreases by behav-ing like a compressible fluid or gas. Thus, the defor-mation reverses its direction at that time. The shockvelocity here is about 2 km/s (see analysis above). Ittakes about 80 ns for the shock wave to propagateto the bottom surface and then reflect back to thetop surface of the 90 µm thick bulk copper target.That corresponds to the time when deformation re-verses its direction (Figure 9). For the thin-film sampleshown in Figure 12, the direction of deformation reversesat about 115 ns due to the thicker silicon substrate (200µm) than the bulk sample (90 µm) and larger shock ve-locity in the silicon substrate (around 3 km/s).

Pressure/stress analysis in the depth direction:Figure 14 shows the history of the stress normal tothe sample top surface at different depths of a bulkcopper sample obtained from the decoupled analy-sis with Model 2-determined pressure as loading ina subsequent FEM analysis. Figure 15 shows thesame result determined using the Model 2-basedcoupled analysis. As seen, stress peak value decaysmuch faster in Figure 14 than in Figure 15. This isbecause, in the FEM simulation of the decoupled

Figure 13Displacement History in Different Depths of Bulk Copper Target

(0, 10, and 20 µm below the top surface,laser intensity I = 4 GW/cm2)

0 10 20 30 40 50 60 Time (ns)

Pre

ssur

e(µm

)

0

7

-5

-15

-20

-25

Model 2, coupled (Depth=0,10,20µm)Model 2+FEM (Depth=0,10,20µm)

slope=shock velocity

Figure 14Stress Normal to Top Surface at Different Depths for Bulk

Samples Determined by FEM Simulation Using Pressure Loadingfrom Model 2 (laser intensity I = 4 GW/cm2)

Time (ns)

Pre

ssur

e(G

Pa)

Depth=0Depth=10µmDepth=30µm

0 20 40 60 80


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analysis, plastic deformation and strength effect areconsidered so that more work is dissipated on thedeformation of the target when the shock wavepropagates into the target. While under the hydro-dynamic approach employed in the coupled analy-sis, pressure is determined by the equation of stateof the target and the target is considered as an elasti-cally compressible fluid. So no extra work is dissi-pated on the irreversible plastic deformation and thepressure decay is slower.

Another phenomenon observed in Figure 14 isthe asymmetrical profile of pressure at differentdepths. When the depth changes from 0 to 30 µm,the steep rising edge, which corresponds to the shockfront in the target, shifts from left to right, makes thepressure profile nearly symmetric, and thus no sig-nificant shock front can be observed any more. Thatis because, in the FEM simulation, dissipative mecha-nisms such as plastic deformation and dynamic yieldstrength increase prevent the shock from becominga true, infinitesimally thin discontinuity. So the shockfront is hard to observe here. In comparison, the pres-sure profiles’ becoming symmetric is less pronouncedin Figure 15, where the Model 2-based coupledanalysis assumed no such dissipative mechanisms.

5. Strain Measurement via X-RayMicrodiffraction5.1 Measurement Setup and Principle

LSP-induced strains were measured to comparewith that predicted by simulation. Recent develop-ments in X-ray microdiffraction provide the possi-bility of measuring the stress/strain fields with

micron-level spatial resolution. Figure 16 shows thesetup of the X-ray microdiffraction experiment. Ex-periments were conducted at the X20A beamline ofthe National Synchrotron Light Source atBrookhaven National Laboratory. The incident X-ray was focused using a tapered glass capillary toform a 10 × 10 µm spot on the sample surface. Thin-film samples after LSP were measured using the dif-fraction intensity contrast method (Noyan et al. 1998).The samples are either 1 or 3 µm thick polycrystal-line copper thin films on single-crystal silicon sub-strate with (004) orientation. Samples werevacuum-held onto a motorized, high-precision XYZstage. By scanning the sample relative to the beamin 2-micron step size across the shocked region, Si(004) diffraction from the silicon substrate was col-lected using a scintillation detector and the distribu-tion of the Si (004) intensity across the shockedregion was recorded.

In the diffraction intensity contrast method (Noyan1998), the X-ray microbeam is so chosen that it pen-etrates the thin-film polycrystalline copper to reachthe silicon substrate and the diffraction intensity ofthe single-crystal substrate is recorded. The stress/strain in the substrate was coupled to by [delete by?]the LSP-deformed thin film. The increase of diffrac-tion intensity comes from the increased mosaic struc-ture in the substrate under the influence by the stress/strain field in the thin film at the interface (Cullity1978). An index to evaluate this combined effect isstrain energy density D, defined as follows (Ventseland Krauthammer 2001):

11 11 22 22 33 33 12 12 13 13 23 23

1 1( )

2 2ij ijD = ε σ = ε σ + ε σ + ε σ + ε σ + ε σ + ε σ (11)

Figure 15Shock Pressure History at Different Depths of Bulk Samples

from Model 2 (laser intensity I = 4 GW/cm2)

Time (ns)

Pre

ssur

e(G

Pa)

4.0

3.2

2.4

1.6

0.8

0.0

Depth=0Depth=10µmDepth=30µm

0 20 40 60 80

Figure 16X-Ray Microdiffraction Experiment Setup


166

where �ij is the total strain tensor and sij is the re-sidual stress tensor at the thin-film/substrate inter-face. The unit of D is J/m3. Strain energy density isdifficult to measure experimentally, but its value canbe extracted from simulation.

5.2 Measurement Results and Comparison withFEM Simulation

The measured diffraction intensity contrast curvesare compared with the FEM-determined strain en-ergy density. The plasma pressure determined fromthe simulation result is used as the loading in theFEM simulation. So the X-ray measurements pro-vide comparisons between simulation and experi-ment results.

Figure 17 shows the profiles of diffraction inten-sity contrast measured across the shocked region ofthe samples. Each sample was shocked along itscenterline by a series of laser pulses, with spacingbetween consecutive pulses being 25 µm. As notedearlier, the laser beam diameter is about 12 microns.The diffraction intensity is normalized to the back-ground diffraction intensity. All the measurementswere taken at 2-micron spacing. As seen from Fig-ure 17a, a contrast peak stands out at the centerlineunder both laser energy levels, 280 and 350 µJ, whichcorrespond to 3.89 and 4.86 GW/cm2, respectively.The contract peak for 350 µJ is higher than that of280 µJ due to the stronger shock effect. The widthof the peaks is around 75 µm. This clearly showsthat LSP has imparted significant strain in the samples.Figure 17b superimposes the diffraction intensitycontrast curve measured from a sample, which was

shocked along three parallel lines, onto the curvefrom a sample that was shocked along only one line.The three parallel shock lines have 50-µm spacingbetween them with the midline right on the samplecenterline. As seen, the peak at the center remains,while two secondary peaks appear in both sides ofthe main peak at about ±50 µm from the center. Thisis consistent with the line spacing used in the shock-ing experiments. The center peak is higher than thesecondary peaks due to a level of superposition.

Figure 18 correlates the diffraction intensity con-trast curves with the FEM-determined strain energydensity [Eq. (11)]. Decoupled FEM analysis is usedhere and the shock pressure is determined from thecoupled model. Figure 18a shows that they matchvery well for the single-line shock case, and Figure18b shows they exhibit a similar pattern for the three-line shock case. The agreement is expected, but tofurther understand the correlation it is important andinteresting to explore the strain coupling status atthe thin film and substrate interface. Figure 19 illus-trates the variation of individual strain componentsin (a) the 1 µm thin-film copper and (b) the siliconsubstrate at their interface determined by the FEMsimulation. In copper, the normal strains E11, E22,and E33 are dominant as compared with the shearstresses. In-plane strains E11 and E22 are both com-pressive and have a similar magnitude to each other,which indicates an equibiaxial plane-strain distribu-tion. The depth-direction strain, E33, is tensile ac-cording to the volume conservation throughPoisson’s ratio and consistent with the maximumprincipal elastic strain. Across the interface, a corre-

Figure 17Diffraction Intensity Contrast Across Shocked Region on 1 µm Thick Thin-Film Sample Measured in 2 µm Step Size. (a)

280 and 350 µJ, single-line LSP and (b) comparison of single line and three-line results, 280 µJ.Diffraction intensity is normalized to average background intensity (18,000 counts).

280µJ350µJ

-200 -150 -100 -50 0 50 100 150 200 Distance from center(µm)

Dif

frat

ion

Inte

nsity

Con

tras

t

1.5

1.4

1.3

1.2

1.1

1.0

(a)

3 line shock1 line shock

-200 -150 -100 -50 0 50 100 150 200

Distance from center(µm)

Dif

frat

ion

Inte

nsity

Con

tras

t

1.4

1.3

1.2

1.1

1.0

(b)


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sponding strain field balancing the residual stress inthe copper layer exists in the silicon layer. From Fig-ure 19b, it is clear that in silicon the normal strainsare smaller compared with the shear strains. As men-tioned before, the shear stress or shear strain in sili-con is due to the nonuniformity of stress/strain inthe copper layer at the interface. Silicon has a higherYoung’s modulus than copper so that the strain val-ues in the silicon are smaller than that in the copperunder the same level of stress.

From the analysis above, it is clear that elasticstrain concentration exists in the silicon substratethrough the strain coupling across the interface andit causes the silicon deform in the shock-affectedregion. This deformation will change the initiallyperfect single crystal to an imperfect single crystalso that X-ray diffraction intensity increases in this

shock-affected region. The width of the maximumprincipal elastic strain, which is consistent with thedistribution of the elastic strain concentration in thesilicon, is around ±50 µm, the same as the widthfrom the X-ray diffraction intensity result.

6. ConclusionsThree modeling schemes were considered: (1)

coupled analysis based on Model 2, (2) decoupledanalysis based on Model 1 and FEM, and (3)decoupled analysis based on Model 2-determinedshock pressure as loading in FEM. Due to the limita-tion of the measurement method and the sample ge-ometry, the plasma temperature and pressure werenot measured directly by spectroscopic measure-ments and a quartz crystal sensor, and the residualstrain measurement through X-ray microdiffraction

Figure 18Comparison of Simulated Strain Energy Density and X-Ray Diffraction Intensity Contrast Measurement. (a) Shocked

along a single line and (b) shocked along three parallel lines with 50 µm spacing (1 µm thick thin-film sampleand 280 µJ laser pulse energy).

Simulated starin energy densityMeasured contrast

-200 -150 -100 -50 0 50 100 150 200


Str

ain

ener

gy d

ensi

ty (

KJ/

m3 )

8

6

4

2

0

X-r

ay d

iffr

actio

n in

tens

ity c

ontr

ast

1.5

1.4

1.3

1.2

1.1

1.0

Simulated starin energy densityMeasured contrast

-200 -150 -100 -50 0 50 100 150 200


Str

ain

ener

gy d

ensi

ty (

KJ/

m3 )

1.4

1.3

1.2

1.1

1.0 Dif

frac

tion

inte

nsity

con

tras

t

(a) (b)

8

6

4

2

0

Figure 19Strain Coupling at Copper-Silicon Interface, 1 µm Thin-Film Sample Shocked at 350 µJ. (a) Variations of elastic straincomponents in copper across shock region and (b) variations of elastic strain components in silicon across shock region.

EE max, principalEE11EE12EE13EE22(along the shocked line)EE23EE33(normal to sample surface)

0 50 100 150 200


Ela

stic

str

ain

0.004

0.003

0.002

0.001

0.000

-0.001

-0.002

-0.003

-0.004

(a)

EE max, principalEE11EE12EE13EE22(along the shocked line)EE23EE33(normal to sample surface)

0 50 100 150 200


Ela

stic

str

ain

0.001 2

0.000 8

0.000 4

0.000 0

-0.0004

-0.0008

-0.0012

(b)


168

was used to verify the model. Strain measurementsbased on the diffraction intensity contrast methodagreed with the strain energy density determined bymodeling scheme 3, indicating the scheme may rep-resent a good compromise in capturing the physicsof microscale LSP. Shock pressure obtained fromscheme 1, which considered the dynamic evolutionof plasma and the complete physical interaction inlaser shock process, has a higher amplitude and lastslonger as compared with that from scheme 2. This islikely to be correct because scheme 2 assumed thatpart of the laser energy was used to break downwater, while this is true only when the laser intensityis very high. An advantage of scheme 1 is that manytransient quantities, such as shock and particle ve-locity, can be directly obtained. Results show thedynamic deformation is much larger if obtained un-der scheme 1, which assumed that the target defor-mation under shock is hydrodynamic; under the othertwo schemes, the FEM simulation considered thetarget response as a finite-plastic process, and thematerial strength effect was included. This is likelyto be incorrect because the particle and shock ve-locity of the target material (copper) determinedthrough the FEM in schemes 2 and 3 are consistentwith the tabulated Hugoniot data. Shock-pressureattenuation along the target depth direction deter-mined by scheme 1 is smaller than the normal stress(in depth direction) attenuation predicted by the FEMsimulation under the other two schemes. As a result,more clear shock fronts were found under scheme 1.

Acknowledgment

This work is partially supported by the NationalScience Foundation under grant DMI-02-00334.Support by Columbia University is gratefully ac-knowledged. Valuable discussions with Dr. W. Zhangof GE Global Research Center are also greatly ap-preciated. HYADES code was made availablethrough Cascade Applied Sciences, Inc. Dr. I. CevNoyan of IBM Watson Research Center provided guid-ance and permission to access X-ray microdiffractionapparatus at the National Synchrotron Light Sourceat Brookhaven National Laboratory.

Appendix

Numerical values of parameters:

h = 6.626 × 10–34 J secPlanck’s constant

k = 1.381 × 10–23 J /° KBoltzmann’s constant

c = 2.998 × 108 m sec–1

Velocity of light� = 355 nm

Laser wavelengthQ

1 = 1 × 10–36 cm5

Cross section of electron-neutral collisiong1 = 1

Gaunt factor that corrects the semiclassicalexpresion for quantum effects

U = 5.989 eV (Al)Ionization potential of the target material (Alcoating)

me = 9.110 × 10–31 kgMass of the electron

m = 26.981539 amu (Al)Mass of the target particle

1 amu � 1.6605402 × 10–27 kg

ReferencesAsay, J.R. and Shahinpoor, M. (1992). High-pressure Shock Com-

pression of Solids. New York: Springer-Verlag, p379.Berthe, L.; Fabbro, R.; Peyre, P.; and Bartnicki, E. (1998). “Experi-

mental study of the transmission of breakdown plasma generatedduring laser shock processing.” The European Physical Journalof Applied Physics (v3), pp215-218.

Berthe, L.; Fabbro, R.; Peyre, P.; and Bartnicki, E. (1999). “Wave-length dependent of laser shock-wave generation in the water-confinement regime.” Journal of Applied Physics (v85, n11),pp7552-7555.

Boslough, M.B. and Asay, J.R. (1992). “Basic principles of shockcompression.” High-pressure Shock Compression of Solids. NewYork: Springer-Verlag, pp20-25.

Chou, P.C. (1972). Dynamic Response of Materials to Intense Impul-sive Loading. published, pp2-5.

Clauer, A.H. and Holbrook, J.H. (1981). “Effects of laser inducedshock waves on metals.” Shock Waves and High Strain Phenom-ena in Metals – Concepts and Applications. New York: Plenum,pp675-702.

Cullity, B.D. (1978). Elements of X-ray Diffraction, 2nd ed. London:Addison-Wesley Publishing Co., pp103, 268-270.

Fabbro, R.; Fournier, J.; Ballard, P.; Devaux, D.; and Virmont, J.(1990). “Physical study of laser-produced plasma in confinedgeometry.” Journal of Applied Physics (v68, n2), pp775-784.


2004

169

Fowles, G.R. (1960). “Attenuation of the shock wave produced in asolid by a flying plate.” Journal of Applied Physics (v31), pp655-661.

Fox, J.A. (1974). “Effect of water and paint coatings on laser-irradi-ated targets.” Applied Physics Letters (v24, n10), pp461-464.

Guy, M.W. (1989). “Physics of laser-induced breakdown: an update.”Laser-induced Plasmas and Applications. New York: MarcelDekker, pp48-49.

Hyades (2001). HYADES Professional and HYADES ProfessionalPlus. Cascade Applied Sciences, Inc.

Miller, S.L.; Rodgers, M.S.; LaVigine, G.; Sniegowski, J.J.; Clews, P.;Tanner, D.M.; and Peterson, K.A. (1998). “Failure modes in sur-face micromachined micro-electro-mechanical actuators.” IEEE98 CH36173. 36th Annual Int’l Reliability Physics Symp., pp17-25.

Mitchner, M. and Kruger, Charles H. (1973). “Collisional and radia-tive process.” Partially Ionized Gases. New York: John Wiley &Sons, pp75-79.

Noyan, I.C.; Jordan-sweet, J.L.; Liniger, E.G.; and Kaldor, S.K. (1998).“Characterization of substrate/thin-film interfaces with X-raymicrodiffraction.” Applied Physics Letters (v72, n25), pp3338-3340.

Peyre, P.; Scherpereel, X.; Berthe, L.; and Fabbro, R. (1998). “Cur-rent trends in laser shock processing.” Surface Engg. (v14, n5),pp377-380.

Peyre, P.; Merrien, P.; Lieurade, H.P.; and Fabbro, R. (1995). “Laserinduced shock waves as surface treatment for 7075-T7351 alumi-num alloy.” Surface Engg. (v11), pp47-52.

Que, L.; Park, J.S.; Li, M.H.; and Gianchandani (2000). “Reliabilitystudies of bent-beam electrical-thermal actuators.” IEEE 00 CH37059.38th Annual Int’l Reliability Physics Symp., pp118-122.

Robert, G.R. (1989). “Modeling of post-breakdown phenomena.”Laser-induced Plasmas and Applications. New York: MarcelDekker, pp72-75.

Tanner, D.M.; Walraven, J.A.; Helgesen, K.S.; Irwin, L.W.; Gregory,D.L.; Stake, J.R.; and Smith, N.F. (2000). “MEMS reliability in avibration environment.” IEEE 00 CH37059. 38th Annual Int’lReliability Physics Symp., pp139-145.

Ventsel, E. and Krauthammer, T. (2001). Thin Plates and Shells:Theory, Analysis and Applications. New York: Marcel Dekker, p37.

Vertes, A.; Juhasz, P.; Dewolf, M.; and Gijbels, R. (1989). “Hydrody-namic modeling of laser plasma ionization processes.” Int’l Jour-nal of Mass Spectrometry and Ion Processes, pp63-85.

White, R.M. (1963). “Elastic wave generation by electron bombard-ment or electromagnetic wave absorption.” Journal Applied Phys-ics (v34), pp2123-2124.

Zhang, W. and Yao, Y.L. (2000a). “Improvement of laser inducedresidual stress distributions via shock waves.” Proc. of ICALEO’00,Laser Materials Processing (v89), ppE183-192.

Zhang, W. and Yao, Y.L. (2000b). “Micro scale laser shock process-ing of metallic components.” ASME Journal of Mfg. Science andEngg. (v124, n2), pp369-378.

Zhang, W. and Yao, Y.L. (2001a). “Feasibility study of inducingdesirable residual stress distribution in laser micromachining.”Trans. of the North American Manufacturing Research Institutionof SME (v29), pp413-420.

Zhang, W. and Yao, Y.L. (2001b). “Modeling and simulation im-provement in laser shock processing.” Proc. of ICALEO’01, Sec-tion A.

Zhang, W. and Yao, Y.L. (2002). “Micro scale laser shock penning ofmetal thin film.” ASME Journal of Mfg. Science and Engg., to besummated.

Authors’ Biographies

Hongqiang Chen is a PhD candidate in the mechanical engineer-ing department at Columbia University. He received a BS in 1997 andan MS in 2000 in mechanical and electrical engineering from theUniversity of Science and Technology of China (USTC), P.R. China.His research interests are laser materials processing and laser manu-facturing. He is a student member of ASME.

Y. Lawrence Yao is a professor in the Dept. of Mechanical Engi-neering at Columbia University. He received his PhD from the Uni-versity of Wisconsin-Madison in 1988. He currently serves on theboard of directors of the Laser Institute of America and on the boardof directors of the North American Manufacturing Research Instituteof the Society of Manufacturing Engineers. He and his team in theManufacturing Research Laboratory (MRL) are interested inmultidisciplinary research in manufacturing and design, nontradi-tional manufacturing processes, laser materials processing, industrialmanipulators in manufacturing, and monitoring and fault diagnosisof manufacturing processes and machinery.

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