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 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].