physical model about laser impact on metals and alloys

L. Lazov, N. Angelov, Physical <strong>model</strong> <strong>about</strong> <strong>laser</strong> <strong>impact</strong> on metals and alloysContemporary Materials I−2 (2010) Page 124 of 128Original scientific papers UDK 535.42:528.8.04DOI: 10.5767/anurs.cmat.100102.en.114LPHYSICAL MODEL ABOUT LASER IMPACTON METALS AND ALLOYSL. Lazov * , N. AngelovTechnical University of Gabrovo, Hadzhi Dimitar 4, 5300 Gabrovo, BulgariaAbstract: In this article we present our <strong>physical</strong> <strong>model</strong> for interaction of <strong>laser</strong> radiationwith metals and alloys through structural changes, melting and vaporizing. We describethe interaction of <strong>laser</strong> radiation with materials, kinetic process of energy transmitting fromfree electrons to the crystal lattice and propagation of heat and the processing zone. Weconsider influence of optical and thermal properties over exploring process as they changewith temperature and in the presence of mixtures.Keywords: <strong>physical</strong> <strong>model</strong>, <strong>laser</strong>, metals, alloys, characteristics.INTRODUCTIONLaser marking is a technological process inwhich a number of mutual connected <strong>physical</strong> phenomenaand effects participate, and with interactionof <strong>laser</strong> radiation with material. These processes areconnected with each other in many cases, i.e. theyinteract with each other. In order to manage the qualityand the results of technology process, it is necessaryto know these processes, as well as to know theprinciples connecting them. This knowledge is alsonecessary for successful monitoring of technologicalprocess in on-line regime and for selection of appropriatedevice for creating of technological systems.Laser processing occurs in space and time andrepresents an <strong>impact</strong> of radiation on the material.Therefore, there is a need to explore the quantity ofabsorbed energy of <strong>laser</strong> radiation in substrate andits <strong>impact</strong> on the material. Figure 1 presents the principalscheme of energy balance of <strong>laser</strong> <strong>impact</strong> onmetals and alloys. This gives us a notion of complexityof interaction of <strong>laser</strong> radiation with materialand connections between these phenomena and processes[1].As a result of interaction, electromagneticenergy is transformed in thermal energy. The efficiencyof the entire process is strongly <strong>impact</strong>ed bythe losses that are a result of scattering and reflection.Only actually absorbed quantity has a direct i-mpact on the technology method and the result ofthe processing. It is clear that with regards to the technologicalmethod of melting, vaporizing, or structuralchanges in the material, only a part of thatenergy makes a real contribution, because the lossesappear as a result of convection, heat radiation andthermal conductivity.Interaction of<strong>laser</strong> radiationAtmosphereCoveringSampleLASERENERGYAbsorbed<strong>laser</strong>energyUsefulenergyFigure 1. Principal scheme of energy balance of <strong>laser</strong><strong>impact</strong> over metals and alloysPRESENTATIONDissipationReflectionLossesConvectionThermal radiationConductionFor technological processStructural changesMeltingVaporizationWe may examine the absorbed energy as a degreeof efficiency η А of total <strong>laser</strong> energy that fallsonto the material, i.e. that is a part of falling energy* Corresponding author: llazov@abv.bg

L. Lazov, N. Angelov, Physical <strong>model</strong> <strong>about</strong> <strong>laser</strong> <strong>impact</strong> on metals and alloysContemporary Materials I−2 (2010) Page 125 of 128which really participates in processing (structuralchanges, melting, vaporization in the unit volume).In certain references it is defined as a percentage ofthe total energy falling onto the material, necessaryfor concrete processing [1]. Under certain simplifications,if we ignore the conditions of working zone(convection, heat radiation and thermal conductivity)we assume that it is energy absorbed by thematerial.INTERACTION OF RADIATIONWITH A SAMPLEThe interaction of <strong>laser</strong> radiation with a sampleis connected with the level of absorption А%,which is defined as a percentage of energy absorbedby material from the total energy falling onto thematerial. Optical depth of penetration δ is definedwith absorption coefficient δ = 1/α. In this case wehave exponential decrease of radiation intensity withdepth z. For strong absorbing materials, such as metalsand alloys, the depth of penetration δ is lowerthan wavelength λ of falling radiation. Total energythat penetrates the material is absorbed and it doesnot depend on the thickness of the sample [1].The ratio of absorption according to [2] dependson: optical constants of material - coefficient of reflectionR, absorption index к / ; <strong>physical</strong> properties of <strong>laser</strong> radiation – wavelengthλ, polarization, power density q S ; chemical composition of surface – oxides, nitride,graphite layers and so far; topography of surface (roughness);as well as on the angle of radiation falling, temperatureand aggregate state of material which is under<strong>impact</strong>.The dependence of absorption ability А onwavelength λ for different materials at room temperatureand angle of falling 0 o (towards normal) to thesurface is presented in Fig. 2 [3].We can see from the graph that absorptionability (except for Аl) decreases with an increase ofwavelength. Differences in separate groups of metalwhich are under <strong>laser</strong> <strong>impact</strong> are clearly noticeable.Thus, for example, for precious metals (Ag, Cu) absorptiondecreases very fast for wavelengths fromvisible spectrum, and for transition metals (Fe, Mo)the absorption change is more smooth and expandsto the far infra-red range. Аl, which is a representativeof polyvalent metals, has specific change of absorptionwith medium maximum for wavelength λ =0,84 µm and almost for total range of wave lengthsit has low absorption [1]. We can see on the graphfor industry used <strong>laser</strong>s that there are great differencesconcerning the ratio of absorption for differentmetals. For example, iron (Fe) under <strong>impact</strong> fromCO 2 -<strong>laser</strong> and Nd:YAG <strong>laser</strong> has absorption capabilitywhich changes 4 times and for Аl this differenceis insignificant. If we compare the ratio of absorptionfor Аl under <strong>impact</strong> of diode <strong>laser</strong>s (λ = 0,808 -0,940 µm) and Nd:YAG <strong>laser</strong>s, the diode ones havepriority over others. The temperature of surfacewhich is under processing is very important for increasingabsorption of <strong>laser</strong> radiation falling on thematerial. This is easy to see in Fig. 3. If we reach themelting point then the absorption ability changes rapidly.This effect is noticed for Аl with different <strong>laser</strong>sources - CO 2 -<strong>laser</strong>, Nd:YAG <strong>laser</strong> and diode <strong>laser</strong>.For <strong>laser</strong>s with shorter wavelength that jump issignificant comparing to CO 2 -<strong>laser</strong>. Other variables,which <strong>impact</strong> absorption, are polarization and angleof falling of the <strong>laser</strong> beam. (For <strong>laser</strong> radiation <strong>impact</strong>s,we have clearly expressed maximum forBrewster’s angle, if electric vector E vibrates parallelto surface of falling. As for the <strong>impact</strong> with polarized<strong>laser</strong> radiation, if electric vector E vibratesnormally to plane of falling we observe a smooth increaseof absorption (see fig. 4). Nature of absorptionmaximum depends on wavelength λ. For λ = 10,6µm the maximum is narrow and has a value of <strong>about</strong>80%, and for visible range it is wide and <strong>about</strong> 30%.The above effects are valid at low power density thatdoes not allow creation of plasma–cloud over theprocessing surface.Figure 2. How absorption ability А depends onwavelength λ for different metals and steel at roomtemperature and angle of falling along normally to thesurface

L. Lazov, N. Angelov, Physical <strong>model</strong> <strong>about</strong> <strong>laser</strong> <strong>impact</strong> on metals and alloysContemporary Materials I−2 (2010) Page 126 of 128<strong>impact</strong>, the heat propagates to short distances indepth of the product and also on its surface. The finalresult is insignificant heat <strong>impact</strong>ed zone as wellas lack of convection losses.100%8060λ = 10,6 μmA40λ = 1,064μmFigure 3. Graphics of dependence of absorption A ontemperature T for Аl at different wavelengths of <strong>laser</strong>radiation20λ = 0,532 μmTHEORY OF THERMAL CONDUCTIVITYFOR METALSConcerning the <strong>impact</strong> with power densityover certain threshold, when absorbed energy of processingzone is bigger than that and is scattered as aresult of heat conductivity, we see that materialstarts to melt. The size of melting zone depends onparameters of processing, absorbed energy per unitlength, but also on geometry and properties of thesample. For the purpose of marking, we need absorbedenergy to generate such structural or phasechanges in surface layer to obtain the quality of markingwe need. Optimization of processing consists ofselection of such parameters of processing (functionof <strong>physical</strong> processes) which should cause appropriatetemperature fields in material, ensuring desiredgeometry and quality of marking zone. By performingpreliminary numeric calculation for temperaturefields at <strong>laser</strong> <strong>impact</strong> over certain materials, whenwe notice the factors which influence processing, wemay predict and optimize the final results. In therange of optical absorption of <strong>laser</strong> radiation in themetal, photon-electron interaction occurs, which resultsin absorption of electromagnetic energy, whichis transformed into heat energy. Propagation of heatin the material is described by phenomenon of thermalconductivity.Laser marking is known by its specific verysmall range of <strong>impact</strong> (several by ten µm), big powerdensity and short duration of <strong>impact</strong>. High temperaturegradients for warming and cooling of theworking zone are observed. Concerning duration of00 20 40θ, oFigure 4. Graphs of the dependence of absorbance A ofthe angle of incidence θ of <strong>laser</strong> radiation for Al atdifferent wavelengthsPenetrated in metal, <strong>laser</strong> radiation is completelyabsorbed by free electrons in thin layer underthe surface with depth 0,1 1,0 m. That is the reasonfor their energy to increase and intensity of hitsbetween them to grow. For the duration (time11t ~ 10 s ) from the beginning of the <strong>impact</strong>, theyhave delivered a very small part of that energy tocrystal lattice. During that time strong overheatingof electronic gas occurs ( Te Ti, where Teis thetemperature of electronic gas and T iis the temperatureof crystal lattice). During that time, intensity ofhits between free electrons and ions of crystal latticeincreases as well as a stream of energy from electron9gas to the lattice. For time t rel~ 10 s from the beginningof the <strong>impact</strong>, the temperature difference T T e T ibecomes minimum and the state inworking volume has a characterization of sharedtemperature of metal T . The time t relis defined asthe time of relaxation.As explained already, the main part of transmissionof heat in the metal at the <strong>laser</strong> <strong>impact</strong> occursfrom electron conductivity. This means that heatprocesses of processing with <strong>laser</strong> radiation havethe same <strong>physical</strong> nature as with the <strong>impact</strong> with traditionalsources of heat. That gives the basis to de-6080

L. Lazov, N. Angelov, Physical <strong>model</strong> <strong>about</strong> <strong>laser</strong> <strong>impact</strong> on metals and alloysContemporary Materials I−2 (2010) Page 127 of 128scribe the heat propagation in the metal caused by<strong>laser</strong> radiation with classic theory of thermal conductivity.As it was realized, optical depth of penetrationof <strong>laser</strong> radiation in the metal is in the range of 10 -7- 10 -8 m and it is considerably less than the length ofheat diffusion ( 4а). That is why in this casethe <strong>laser</strong> radiation is considered as surface <strong>impact</strong>ingheat source. Differential equation of heat conductivityisTc div( k grad T ) qS (1 R), (1)twhereby T is temperature; c - specific heat capacity;ρ – density of material; k – coefficient of heat conductivity;q S – surface power density of <strong>laser</strong> radiation;R – coefficient of reflection; α – coefficient ofabsorption.Equation (1) describes heat transfer through h-eat conductivity in the most general form. One initialand two limiting conditions are necessary for itsapplication.Initial condition – temperature of samples atthe moment t = 0 is assumed to be equal to theambient temperatureT o = const. (2)For <strong>laser</strong> processing, the following applies:Condition of restriction of I stockIt defines distribution of temperature at thesample surface at every moment of the timeT o = const or T o = T o (t). (3)Condition of restriction of II stockIt is given surface density of heat stream q S atevery point of the surface of the sample at everymoment of time. It is assumed that surface density q Sin every point of head stream across the surface q S =const or q S = q S (t) i.e. it is constant or is a function oftime.Since the surface density is proportional totemperature’s gradient we may write:T k ) q(S qxS = const or q S = q S (t). (4)SSolution of the differential equation of heatconductivity at assigned initial (2) and limiting conditions(3) and (4) allow us to determine the temperaturefield of the sample in the given moment of time,as it is defined as function T T ( x,y,z,t).For analytic solution of differential equationwe assume the following simplifications:− Heat losses as result of radiation and convectionare ignored (that is based at pulse <strong>laser</strong> processing);− Dependence of temperature on optical and thermo-<strong>physical</strong>characteristics of materials is ignored.With these limitations, the heat source in metalmay be considered as moving surface’s heat sourcewith defined geometry of working zone. In thiscase analytic solution for equation of heat-conductivityis obtained.The heat conductivity equation is not ananalytic solution of a general case and that is whynumerical methods are used for its resolution. Ofmany well known methods for exploration of temperaturefields for <strong>laser</strong> <strong>impact</strong> on materials, the methodof limited elements (4) is accepted as universaland well applied.We have made certain theoretical calculationsfor the evaluation of described <strong>physical</strong> <strong>model</strong>,which we compared with concrete experimental results.A concrete technological process was examined– <strong>laser</strong> marking of products of carbon tool steelsУ7, У12 and alloyed tool steel Р6М5. Initial parametersfor numeric calculations were:- diameter of working spot d = 30 μm;- speed of marking v = 50 mm/s;- frequency of pulse repetition ν = 19 kHz.The trends of theoretical research are directedtowards:− Calculation of critical pulse energy for structuralchanges E imp(sc) and critical power density q S(sc)for structural changes (sc);− Calculation of critical pulse energy for meltingE imp(m) and critical power density at melting q S(m) ;− Calculation of critical pulse energy for vaporizationE imp(t) and critical power density q S(t) for vaporization.The results of calculations are presented in table1.Table 1: Calculations of critical pulse energy and criticalpower densityMaterialVariableУ7 У12 Р6М5E imp(sc) , mJ 10,2 11,3 13,8q s(sc) , W/m 2 2,84.10 9 3,12.10 9 3,83.10 9E imp(m) , mJ 19.9 21,9 26,8q s(m) , W/m 2 5,51.10 9 6,09.10 9 7,43.10 9E imp(t) , mJ 31,0 34,1 41,8q s(t) , W/m 2 8,60.10 9 9,49.10 9 1,16.10 10Indicative results of calculations very wellcorrelate with experimental data, obtained by markingof tool steels with this type of <strong>laser</strong> [5].

L. Lazov, N. Angelov, Physical <strong>model</strong> <strong>about</strong> <strong>laser</strong> <strong>impact</strong> on metals and alloysContemporary Materials I−2 (2010) Page 128 of 128CONCLUSIONThe considered <strong>model</strong> is applied for receivingpreliminary engineering evaluations and prognosisof results of <strong>laser</strong> processing of metals and alloyswith different <strong>laser</strong> sources. It helps selecting a <strong>laser</strong>source during construction of a technologicalsystem. Specific technological processes are beingoptimized by a mathematical <strong>model</strong> which was createdon a <strong>physical</strong> basis.REFERENCES[1] F. Dausinger, Strahlwerkzeug Laser:Energieeinkopplung und Prozeßeffektivität, UniversitätStuttgart, Habilitation 1995.[2] Bergmann Ludwig, Schaefer Clemens Lehrbuchder Experimentalphysik, Band 3 Optik, Berlin:den Gruyter-Verlag 1987.[3] Landolt, Bornstein Daten- und Funktionssammlungin Wissenschaft und Technik, Berlin,Springer-Verlag 1990.[4] J. Xie, A. Kar, Mathematical <strong>model</strong>ing ofmelting during <strong>laser</strong> materials processing. Journalof Applied Physics, Nr. 81 (7), (1997) S.3015.[5] www.pulslight.comФИЗИЧКИ МОДЕЛ ЗА ЛАСЕРСКО МАРКИРАЊЕ МЕТАЛА И ЛЕГУРАСажетак: У раду је представљен наш физички модел за интеракцију ласерскогзрачења са металном легуром кроз структурне промјене, топљење и испаривање. Објашњенаје интеракција ласерског зрачења са материјалима, кинетички процес преносаенергије слободних електрона у кристалну решетку и ширење топлоте у проводнојзони. Разматран је утицај оптичких и термалних особина преко испитиваних процесакао што су промјене температуре и присуство смјесе.Кључне ријечи: физички модел, ласер, метали, легуре, обиљежја.