materials
Article Thermal Efficiency in Laser-Assisted Joining of Polymer–Metal Composites
Klaus Schricker * , Mohammad Alhomsi and Jean Pierre Bergmann Production Technology Group, Department of Mechanical Engineering, Technische Universität Ilmenau, Gustav-Kirchhoff-Platz 2, 98693 Ilmenau, Germany; [email protected] (M.A.); [email protected] (J.P.B.) * Correspondence: [email protected]; Tel.: +49-3677-69-3808
Received: 4 September 2020; Accepted: 27 October 2020; Published: 30 October 2020
Abstract: Heat conduction joining is mainly used in laser-based joining of metals with polymers but results in a large amount of dissipated heat. The consideration of thermal efficiency allows the determination of power actually used for creating the joint, which is highly relevant for technical and economic reasons, e.g., for calculating the carbon footprint. In order to describe the thermal efficiency universally, process parameters (focal diameter, joining speed, energy per unit length), metallic materials (AA 6082, AISI 304), geometric parameters (overlap width, material thickness) and various polymers (polypropylene, polyamide 6, polyamide 6.6) were examined experimentally. The discussion of the results is supplemented by numerical simulations of the temperature field. For a general description of the physical relationships, some dimensionless numbers based on the Buckingham π theorem were developed, applied to the experimental data. One of these numbers shows similarity to the Fourier number and provides further information on thermal efficiency and its general understanding in the context of polymer–metal joints, enabling the physical background dissipated to stored heat.
Keywords: laser; joining; welding; polymer; metal; thermal efficiency; dimensionless numbers; hybrid; composite; heat transfer
1. Introduction Polymer–metal hybrid composites are gaining importance in several fields of application and the motivation for this is manifold. On the one hand, the lightweight potential of such composites can be exploited in novel constructions, e.g., in the automotive or aviation industries. On the other hand, functional integration and cost reduction can be achieved for large series products, e.g., in household appliance technology or the electronics industry. There are different joining approaches for different material groups to realize polymer–metal composites. In addition to mechanical joining processes [1] and adhesive bonding [2], thermal direct joining has great potential for application in thermoplastic–metal hybrid joints [3]. By saving on auxiliary joining elements such as screws or rivets and on filler materials such as adhesives, a direct bond between polymer and metal can be created [4]. Numerous energy sources can be used in thermal joining [4–6]. For industrial applications, however, laser beams have great advantages over alternative processes due to the non-contact energy input and the high degree of flexibility with regard to the components to be manufactured [7]. In laser-based heat conduction joining, polymer and metal are in contact in overlap configuration (Figure1). The laser beam is focused on the metal surface, and the sheet heats up and the polymer starts melting at the interface due to the heat conduction between the two joining partners. The molten material can now wet the metal surface and penetrate surface structures already present. The geometry
Materials 2020, 13, 4875; doi:10.3390/ma13214875 www.mdpi.com/journal/materials Materials 2020, 13, 4875 2 of 16
Materials 2020, 13, x FOR PEER REVIEW 2 of 17 of the molten zone in the polymer follows the temperature distribution within the joining zone the(schematically joining zone drawn (schematically as isotherms) drawn and as is thereforeisotherms) present and is at therefore temperatures present above at temperatures the beginning above of the the beginning of the melting interval Tim [8]. With cooling and solidification, a solid composite of melting interval Tim [8]. With cooling and solidification, a solid composite of polymer and metal is polymerformed by and mechanical metal is formed interlocking by mechanical at the surface interlocking (form fit) at [the9] andsurface the physico-chemical(form fit) [9] and the interactions physico- chemical(e.g., bonds interactions between aluminium (e.g., bonds oxide between layer alumin and polyamideium oxide 6.6) layer [10]. and Due polyamide to the different 6.6) applications,[10]. Due to thenumerous different materials applications, are the numerous focus of materials interest, e.g., are high-alloythe focus of steels interest, [11] e.g., or aluminium high-alloy alloyssteels [11] [12] or as aluminiummetallic joining alloys partners [12] as metallic as well asjoining polyamides partners [13 as] orwell polypropylene as polyamides [14 [13]] as or thermoplastic polypropylene joining [14] aspartners. thermoplastic In contrast joining to laser partners. transmission In contrast joining, to the laser maximum transmission temperatures joining, in thethe polymer maximum are temperaturesreduced and joiningin the ofpolymer polymers are withreduced a high and proportion joining of of polymers aggregates with and a reinforcing high proportion materials, of aggregatese.g., talcum and or glass reinforcing fibres, ismaterials, possible. e.g., talcum or glass fibres, is possible.
1 Heating in overlap configuration 2 Formation of molten zone
laser beam laser beam
metal metal T
polymer polymer
3 Metal-polymer joint after solidification max. size of the molten zone at isotherm T = Tim metal
polymer
metal mechanical interlocking based on penetration of polymer in undercuts at the metal surface
molten zone physico-chemical interactions at boundary layer
Figure 1. Process steps of laser-based metal–polymer joining. Figure 1. Process steps of laser-based metal–polymer joining. Literature on the state of the art includes different studies of the temperature distribution based Literature on the state of the art includes different studies of the temperature distribution based on temperature measurements [11] and numerical simulation [15–17]. The complex heat conduction on temperature measurements [11] and numerical simulation [15–17]. The complex heat conduction conditions in joining technology preclude the use of analytical solutions to describe the temperature conditions in joining technology preclude the use of analytical solutions to describe the temperature field sufficiently. However, the application of dimensionless numbers for the description of heat and field sufficiently. However, the application of dimensionless numbers for the description of heat and mass transfer problems and the comparison of different process parameters is known from laser beam mass transfer problems and the comparison of different process parameters is known from laser welding [18] and additive manufacturing [19]. These dimensionless numbers can be developed by the beam welding [18] and additive manufacturing [19]. These dimensionless numbers can be developed Buckingham π theorem [20,21]; familiar parameters such as the Fourier number or the Péclet number by the Buckingham π theorem [20,21]; familiar parameters such as the Fourier number or the Péclet are typically used. number are typically used. The Fourier number (Fo, Equation (1)) expresses the relation between the heat dissipation rate The Fourier number (Fo, Equation (1)) expresses the relation between the heat dissipation rate and the heat storage rate [22], where α is the thermal diffusivity (Equation (2)), τ the characteristic and the heat storage rate [22], where α is the thermal diffusivity (Equation (2)), τ the characteristic time and L the characteristic length. The thermal diffusivity α is the thermal conductivity divided time and L the characteristic length. The thermal diffusivity α is the thermal conductivity divided by by density ρ and specific heat capacity cp. An increasing Fo indicates a higher cooling rate, a higher density ρ and specific heat capacity cp. An increasing Fo indicates a higher cooling rate, a higher temperature gradient and less heat accumulation [23]: it affects such characteristics as the melt pool temperature gradient and less heat accumulation [23]: it affects such characteristics as the melt pool shape in laser welding [24]. The characteristic length L is chosen according to the specific situation, shape in laser welding [24]. The characteristic length L is chosen according to the specific situation, e.g., the melt pool length [23] or focal diameter [25]. e.g., the melt pool length [23] or focal diameter [25]. 2 FoFo=α∙τ∙L= α τ L− (1)(1) · · 1 1 αα== λ ∙ρρ− c∙c− (2) · · p (2) InIn contrast,contrast, the the P éPécletclet number number (Pe, (Pe, Equation Equation (3)) represents (3)) represents the ratio the of heatratio transfer of heat by transfer convection by convectionto conduction to conduction [19], where [19], L is thewhere characteristic L is the characteristic length, α is thelength, thermal α is ditheffusivity thermal of diffusivity the material of andthe material and v is the characteristic velocity. In laser welding, the weld seam width [26], the focal diameter [27] and the molten bath diameter [28] are among the parameters that can be define the
Materials 2020, 13, 4875 3 of 16 v is the characteristic velocity. In laser welding, the weld seam width [26], the focal diameter [27] and the molten bath diameter [28] are among the parameters that can be define the characteristic length L. The Pe is used, among other things, to estimate the length of the molten bath in relation to its width [27] or to obtain an indication of thermal efficiency [29,30].
1 Pe = L v α− (3) · · The thermal efficiency is of particular interest. On the one hand, it allows the determination of the proportion of energy input used for actual material processing [31]. On the other hand, the power dissipation can be estimated, which in turn can cause adverse effects, e.g., thermal distortion during welding [22,26]. According to [29], thermal efficiency describes the ratio of process power Pp to absorbed laser beam power Pa (Equation (4)). The process power Pp is used to form the molten zone with the cross-section Ap at the joining speed v. Based on [29] and [31] and under the assumptions (a) that the volume of the molten zone is described by the temperature at the beginning of the melting interval Tim and (b) that there is no decomposition of the thermoplastic in the joining process, the process power Pp follows the representation in Equation (5). The material properties density ρ and specific heat capacity cp are assumed to be constant as mean values. The temperature difference between Tim and T0 stands for the temperature interval which must be exceeded by the power input of the process to form the molten zone. Because of the solid–liquid phase transformation in this zone, the melting enthalpy ∆Hm is taken into account. Pp thus stands for the power required to create the molten zone in the polymer in turn creates the joint with the metal. It should be noted that this does not take into account overheating of the polymer or any further thermal effects. The equation thus represents the minimum process power and the minimum thermal efficiency. This has been deliberately chosen to provide a conservative estimation of the CO2 balance of the process.
1 η = Pp P− (4) th · a h i Pp = Ap v ρ cp (T T ) + ∆Hm (5) · · · · im − 0 For laser beam welding, there are numerous studies on the factors influencing thermal efficiency, e.g., welding speed and focal diameter [32]. The thermal efficiency of laser-based polymer–metal joining has so far only been considered to a limited extent. Trials on spot joints [33], which investigated different factors that influence thermal efficiency (e.g., melting interval of the polymer, thermal diffusivity, melting enthalpy) were carried out on the basis of a simplified model material in numerical simulation. The study applied idealized conditions, e.g., by neglecting heat accumulation. The factors assumed to influence thermal efficiency were considered in particular groups, e.g., melting interval and melting enthalpy or material thickness and joining time. For composites of high-alloy steel with the model material, maximum thermal efficiencies of approximately 2 to 3% were achieved without damaging the thermoplastic. The heat conduction losses, in particular via the metallic joining partner, are decisive for the relatively low values due to indirect heating of the polymer part. A general description of the parameters affecting thermal efficiency in laser-based joining of polymers with metals has not yet been given. In this paper, systematic assessments of the thermal efficiency for laser-assisted metal–polymer joining are carried out. Different geometric arrangements (overlap width, material thickness metal), materials (high-alloy steel, aluminium, the polymers polyamide 6 (PA 6), polyamide 6.6 (PA 6.6) and polypropylene (PP)), focal diameters and energies per unit length are examined. These studies enable the individual factors to be examined individually for their effect on thermal efficiency. On this basis, the data obtained are used to determine general correlations of thermal efficiency by means of newly developed dimensionless numbers and their analogies to the Péclet and Fourier numbers. Materials 2020, 13, 4875 4 of 16
2. Materials and Methods The experiments were carried out using a three-axis processing portal (Figure2a) and a Laserline LDM 1000 diode laser (Laserline, Mülheim-Kärlich, Germany, average wavelength: 980 nm) at a constant beam power Pl of 1000 W. Three focal diameters (1.7 mm, 3.5 mm, 5.3 mm) were used and adjusted by different focusing lenses (f = 100 mm, 200 mm, 300 mm). A sample intensity distribution of theMaterials laser 2020 beam, 13, x is FOR given PEER in REVIEW Figure 2b for a focal diameter of 5.3 mm (measured with Primes4 Beamof 17 Monitor at 500 W laser beam power). A clamping device with two air-cooled clamping jaws allowed preciseMonitor adjustment at 500 W of laser the beam clamping powe forcer). A clamping due to integrated device with load two cells. air-cooled The size clamping of the specimensjaws allowed was 200precise mm in adjustment length and of 75 the mm clamping in width. force The due overlap to integrated width load was variedcells. The in size four of steps the specimens (14 mm, 24 was mm, 200 mm in length and 75 mm in width. The overlap width was varied in four steps (14 mm, 24 mm, 36 mm, 75 mm). The main trials were carried out with a complete overlap between both specimens 36 mm, 75 mm). The main trials were carried out with a complete overlap between both specimens of 75 mm, while further investigations used a smaller overlap width to examine the effect of heat of 75 mm, while further investigations used a smaller overlap width to examine the effect of heat accumulation on thermal efficiency. The joining speed in all cases was adapted to the respective accumulation on thermal efficiency. The joining speed in all cases was adapted to the respective materialmaterial combination combination and and sheet sheet thickness thickness inin stepssteps ofof atat most 0.05 m/min. m/min. At At low low joining joining speeds speeds the the metalmetal is molten, is molten, which which is is considered considered as as exclusion exclusion criterion.criterion. On the the other other hand, hand, a aminimum minimum width width of of thethe melting melting zone, zone, 3 mm, 3 mm, is is specified specified for for increasing increasing joiningjoining speeds to to ensure ensure a aload-bearing load-bearing connection connection betweenbetween the the materials. materials. Both Both conditions conditions are are considered considered due due to to the the application-oriented application-oriented character character of of the investigations.the investigations. Since Since the focus the focus of the of investigationthe investigatio isn on is on thermal thermal effi efficiency,ciency, no no surface surface structuring structuring of theof metallic the metallic samples samples is carried is carried out. Metallic out. Metallic as well as as well polymeric as polymeric samples samples are cleaned are cleaned with isopropyl with beforeisopropyl joining. before joining.
FigureFigure 2. ( 2.a) ( Experimentala) Experimental setup setup and and ( b(b)) schematic schematic viewview of the joining joining zone zone with with relevant relevant parameters parameters for thermalfor thermal effi efficiency.ciency.
TheThe polymers polymers polyamide polyamide 6 6 (PA (PA 6), 6), polyamide polyamide 6.66.6 (PA 6.6) and polypropylene polypropylene (PP) (PP) are are used used in in severalseveral applications, applications, e.g., e.g., automotive automotive and and domestic domestic applianceappliance industries, industries, and and are are therefore therefore taken taken into into account.account. A sheetA sheet thickness thickness of of 2 2 mm mm was was chosen. chosen. TheseThese also also have have different different thermophysical thermophysical properties, properties, especiallyespecially the the beginning beginning of of the the melting melting intervalinterval T Timim (Table(Table 1).1). This This temperature temperature must must be exceeded be exceeded to to startstart thethe meltingmelting ofof thethe polymer.polymer. Therefore Therefore it it is is considered considered in in the the expression expression of of thermal thermal efficiency efficiency (Equation(Equation (5)). (5)). The The isotherm isotherm of of T Timim isis decisive decisive for for the the maximum maximum expans expansionion of the of molten the molten zone zone[31]. In [31 ]. In orderorder toto adequatelyadequately calculate the thermal thermal efficiency efficiency,, the the thermophysical thermophysical properties properties of ofthe the polymers polymers were calculated as mean values of the interval from 20 °C to Tim based on previously published data were calculated as mean values of the interval from 20 ◦C to Tim based on previously published data[34–36]. [34–36 ]. On the metals side, the high alloyed steel AISI 304 (X5CrNi18-10, cold rolled, surface 2B according Table 1. Material properties [34–36]. to EN 10088-2 [37]) was used due to its importance in the household appliance industry. Therefore, material thicknessesMaterial ofProperty 0.5 mm, 1 mm Symbol and 1.5 mm Unit were AISI chosen. 304 The AA aluminium6082 PA 6 alloy PA 6.6 AA 6082PP (heat 1 −1 −1 treatment conditionthermal conductivity T6 according to ENλ 515 [W38∙])m was∙K chosen15 because 185 of its0.35 relevance 0.31 in lightweight0.24 specific heat capacity 1 cp J∙kg−1∙K−1 470 896 1700 1670 2090 applications which is why thicknesses of 1 mm, 1.5 mm and 2 mm were applied. The metallic materials density 1 ρ kg∙m−3 7900 2700 1130 1140 910 beginning of melting interval 2 Tim °C 1400 585 191 235 126 melting enthalpy 2 ∆Hm kJ∙kg−1 - 3 - 3 50 47 87 absorptivity 3,4 A 1 0.39 0.28 - 3 - 3 - 3 1 at room temperature, 2 determined by DSC analysis at 10 K∙min−1 heat rate according to [34], 3 not relevant in the context of the study, 4 at wavelength of 980 nm. On the metals side, the high alloyed steel AISI 304 (X5CrNi18-10, cold rolled, surface 2B according to EN 10088-2 [37]) was used due to its importance in the household appliance industry.
Materials 2020, 13, 4875 5 of 16 differ significantly in their physical properties, especially with regard to thermal conductivity and thermal diffusivity, which is why a distinct influence on the thermal efficiency can be assumed (Table1).
Table 1. Material properties [34–36].
Material Property Symbol Unit AISI 304 AA 6082 PA 6 PA 6.6 PP 1 1 1 thermal conductivity λ W m− K− 15 185 0.35 0.31 0.24 1 · 1 · 1 specific heat capacity cp J kg− K− 470 896 1700 1670 2090 Materials 2020, 13, x FOR1 PEER REVIEW · · 3 5 of 17 density ρ kg m− 7900 2700 1130 1140 910 2 · beginning of melting interval Tim ◦C 1400 585 191 235 126 2 1 3 3 Therefore,melting material enthalpy thicknesses of∆ H0.5m mm, 1kJ mmkg and 1.5 mm- were chosen.- The aluminium50 47 alloy AA 87 · − 6082 (heatabsorptivity treatment3,4 condition T6 Aaccording to 1 EN 515 [38]) 0.39 was chosen 0.28 because- 3 of its relevance- 3 - in3 1 2 1 3 lightweightat room temperature, applicationsdetermined which is bywhy DSC thicknesses analysis at 10 of K min 1 mm,− heat 1.5 rate mm according and 2 to mm [34], werenotrelevant applied. in theThe 4 · metalliccontext materials of the study, differat wavelength significantly of 980 in nm.their physical properties, especially with regard to thermal conductivity and thermal diffusivity, which is why a distinct influence on the thermal efficiency can be assumedFurthermore, (Table the 1). absorptivity A differs significantly between both metals. The reflectance was calculatedFurthermore, by reflection the absorptivity measurements A differs in an integratingsignificantly sphere between (spectrophotometer both metals. The reflectance Varian Cary was 5000 UV-VIS-NIR,calculated by Figure reflection3a, Agilent, measurements Santa Clara, in an CA,integrating USA). The sphere transmission (spectrophotometer is zero and Varian so the Cary absorptivity 5000 canUV-VIS-NIR, be calculated Figure as a 3a, function Agilent, of theSanta wavelength. Clara, CA, TheUSA). absorptivity The transmission is assumed is zero to beand constant so the for theabsorptivity wavelength can of be the calculated diode laser as (980a function nm) and of the is approximately wavelength. The 28% absorptivity for AA 6082 is assumed and 39% to for be AISI constant for the wavelength of the diode laser (980 nm) and is approximately 28% for AA 6082 and 304. Since the laser irradiates the surface at an angle of 15◦, the effect of the angle of incidence in the diode39% laserfor AISI wavelength 304. Since is the insignificant laser irradiates [39,40 the]. The surface changes at an in angle absorptivity of 15°, the of steeleffect and of the aluminium angle of are comparativelyincidence in the small diode in thelaser experimental wavelength is temperature insignificant interval [39,40]. becauseThe changes the metallicin absorptivity material of wassteel not and aluminium are comparatively small in the experimental temperature interval because the molten during the experiments [30,41]. Therefore, the absorptivity was kept constant at the measured metallic material was not molten during the experiments [30,41]. Therefore, the absorptivity was kept value for both metals. It follows that the absorbed beam power Pa, which was necessary for the constant at the measured value for both metals. It follows that the absorbed beam power Pa, which calculation of the thermal efficiency (confer Equation (5)), could be calculated by multiplying the was necessary for the calculation of the thermal efficiency (confer Equation (5)), could be calculated absorptivity A by the laser beam power Pl (Equation (6)). by multiplying the absorptivity A by the laser beam power Pl (Equation (6)).
PPa ==A∙PA P (6) (6) · l
a) b) laser beam with focal diameter df 0.4 AISI 304 and beam power Pl diode laser F F at 980 nm thermal insulation 0.3 velocity clamping v clamping AA 6082 jaw jaw 0.2 m absorptivity 1 / metal λm, ρm, cp,m, A t 0.1 molten molten zone polymer thickness dp area A λp, ρp, cp,p p molten width wp ∆Hm, Tim 0 900 940 980 1020 1060 1100 wavelength / nm overlap width w o
FigureFigure 3. 3.( a()a) Absorptivity Absorptivity andand (b) schematic view view of of the the joining joining zone zone with with relevant relevant parameters parameters for for thermalthermal e ffiefficiency.ciency.
FigureFigure3b 3b shows shows the the relevant relevant characteristics characteristics of the materials materials and and the the process process in in a cross-sectional a cross-sectional viewview through through the the clamping clamping device. device. The The thermal thermal insulation insulation was was intended intended to to prevent prevent a a large large loss loss of of heat inheat the directionin the direction of the clampingof the clamping jaws, whichjaws, which is also is typical also typical for clamping for clamping devices devices in this in joining this joining process. Regardingprocess. Regarding properties properties of importance of importance for the joining for the partners, joining thepartners, index the m indicatesindex m theindicates affiliation the of theaffiliation metal and of thep to metal the polymer and p to material. the polymer The material. area Ap ,The width area w Ap pand, width thickness wp and d thicknessp of the molten dp of the zone aremolten measured zone are in materialographicmeasured in materialographic cross-sections cros throughs-sections the through middle the of middle the specimens, of the specimens, i.e., after a seami.e., after length a seam of 100 length mm (Figureof 100 mm4). The(Figure area 4). A Thep is area included Ap is included in the calculation in the calculation of thermal of thermal efficiency (Equationefficiency (5)). (Equation As shown (5)). inAs Figure shown4 ,in any Figure bubbles 4, an thaty bubbles occur that are includedoccur are inincluded the area in as the they area have as a they have a minor effect on the resulting volume of the molten zone [34]. These three measured variables are taken into account in the development of dimensionless numbers.
Materials 2020, 13, 4875 6 of 16 minor effect on the resulting volume of the molten zone [34]. These three measured variables are taken Materialsinto account 2020, 13 in, x the FOR development PEER REVIEW of dimensionless numbers. 6 of 17
FigureFigure 4. Cross-sectionCross-section of of the the molten molten zone zone in the polymer (metal removed in cross-section).
Further variables variables were were also also considered considered in inthe the development development of new of new dimensionless dimensionless numbers. numbers. The The energy per unit length E was defined as laser beam power P divided by joining velocity v energy per unit length E was defined as laser beam power Pl dividedl by joining velocity v (Equation (7)).(Equation E is (7)).a widely E is a widelyused parameter used parameter in joining in joining technology: technology: it establishes it establishes an an application-oriented application-oriented relationship between laser beam power and joinin joiningg speed and enables a direct comparison between the two metals used. 1 E = Pl v− (7) · E=P ∙ v (7) The interaction time of the laser beam τl at the surface (Equation (8)) was defined as focal diameter The interaction time of the laser beam τl at the surface (Equation (8)) was defined as focal df divided by joining velocity v. This allowed the introduction of a time-dependent parameter for the diameterdimensionless df divided numbers. by joining velocity v. This allowed the introduction of a time-dependent parameter for the dimensionless numbers. 1 τ = d v− (8) l f· A sample size of one (n = 1) was chosenτ for=d the ∙ v experiments to determine the effect of sheet(8) thicknessA sample tm, focalsize of diameter one (n = d f1), energywas chosen per unit for the length experiment E, polymers to determine type and overlapthe effect width of sheet wo. thicknessThis decision tm, focal waspossible diameter because df, energy in materialography per unit length the E, processpolymer has type a very andsmall overlap standard widthdeviation wo. This decisionfor the evaluation was possible quantities because considered; in materialography at the same th timee process more stepshas a invery the small experimental standard parameters deviation forcould the be evaluation considered quantities [33]. considered; at the same time more steps in the experimental parameters couldThe be dimensionlessconsidered [33]. numbers were calculated by applying the Buckingham π theorem following [21]. The identifiedThe dimensionless influencing numbers variables were (see calculated Figure3b) by are applying summarized the Buckingham in Table2 with π theirtheorem SI base following units [21].(M: mass,The identified L: length, influencing T: time, θ: variables temperature) (see Figure and subdivided 3b) are summarized into categories in Table for 2 awith better their overview. SI base unitsFrom (M: this mass, parameter L: length, pool, nineT: time, dimensionless θ: temperature) numbers andwere subdivided derived into as discussed categories in for Section a better 3.4. overview.The application From ofthis the parameter Buckingham pool,π theorem nine dimensionless offers the advantage numbers that were the characteristicderived as discussed lengths arein Sectionautomatically 3.4. The determined application if of analogies the Buckingham to known π dimensionless theorem offers numbers the advantage like Fourier that number the characteristic are found. lengthsThese characteristic are automatically lengths determi can deviatened fromif analogies those of to previous known investigations dimensionless (see numbers Section 1like) due Fourier to the numberindirect joiningare found. process, These i.e., characteristic the laser beam lengths is absorbed can deviate at the from metal those surface of previous and the investigations polymer is heated (see Sectiononly by 1) heat due conduction. to the indirect joining process, i.e., the laser beam is absorbed at the metal surface and the polymerDue to is the heated wide only range by heat of conduction. parameters and material properties that were investigated, double-logarithmic graphs are used in order to be able to present the results of the dimensionless numbers in a compact way.Table When2. Relevant regression parameters curves for dimensionless are given, the numbers. coefficient of determination R2 is specified. Category Variable Symbol Unit SI Base Unit 1 Numerical simulations of the process were performed based on a thermal model to provide absorbed laser beam power Pa W M∙L2∙T−3 process parameters further information about the temperatureinteraction distribution time during joiningτl and tos support discussion T of the results. In order to reduce the calculationoverlap times, width consideration w ofo a transientm thermal model L was joint configuration omitted. Due to the sample length of 200thickness mm, itof was metal assumed sheet that a tm steady statem was reached L from a particular seam length on. Therefore, a stationarythermal conductivity model was assumedλm to provideW∙m−1 su∙Kffi−1 cientM information∙L∙T−3∙θ−1 on thematerial temperature properties field. of the metal specific heat capacity cp,m J∙kg−1∙K−1 L2∙T−2∙θ−1 density ρm kg∙m−3 M∙L−3 thermal diffusivity αp m2∙s−1 L2∙T−1 material properties of the polymer beginning of melting interval Tim °C θ melting enthalpy ∆Hm kJ∙kg−1 L2∙T−2 resulting molten zone molten zone area Ap m2 L2
Materials 2020, 13, 4875 7 of 16
Table 2. Relevant parameters for dimensionless numbers.
Category Variable Symbol Unit SI Base Unit 1 2 3 absorbed laser beam power Pa W M L T process parameters · · − interaction time τl s T overlap width w m L joint configuration o thickness of metal sheet tm m L 1 1 3 1 thermal conductivity λm W m− K− M L T− θ− material properties of · 1 · 1 ·2 · 2 · 1 specific heat capacity cp,m J kg− K− L T− θ− the metal · · 3 · · 3 density ρm kg m M L · − · − 2 1 2 1 thermal diffusivity αp m s L T material properties of · − · − beginning of melting interval Tim ◦C θ the polymer 1 2 2 melting enthalpy ∆Hm kJ kg L T · − · − 2 2 molten zone area Ap m L resulting molten zone molten zone width wp m L molten zone thickness dp m L 1 SI base units: M–mass, L–length, T–time, θ–temperature.
The specimens as well as the clamping device were considered simplified as depicted in Figure3. Both the basic physics and the initial and boundary conditions were based on the model of [15]. The temperature distribution was calculated from the heat equation assuming an ideal heat transfer between metal and polymer. An ideal heat transfer was also used in [16,42] and showed good agreement with experimental investigations. Further dissipated heat flows were considered by convection and thermal radiation. Density, thermal conductivity and specific heat capacity were considered to be dependent on temperature for both metals and polymers. This allowed the solid-liquid phase transition due to the melting enthalpy to be taken into account. The laser beam absorbed at the metal surface was modelled as a heat flux density of constant intensity over focal diameter. The absorption coefficient of the laser beam power at the metal surface was kept constant at the levels as described above.
3. Results and Discussion
3.1. Effect of Sheet Thickness, Focal Diameter and Energy per Unit Length on Thermal Efficiency The following experiments are focused directly on thermal efficiency based on 60 experiments with a sample size of 1. General information on the effect of different material properties on the growth and geometry of the molten zone are provided in [33]. In the first step, the effect of sheet thickness and focal diameter on energy per unit length are discussed. The overlap was kept constant at 75 mm, which meant that the joining partners overlapped completely. The process windows can be easily distinguished by the data series which are connected by a dashed line. The different sheet thicknesses tm are subdivided by colour with the focal diameter df represented by different symbols (: df = 5.3 mm, : df = 3.5 mm). It should be noted that no process window was reached for a focal diameter of 1.7 mm# in these tests. This can be explained using aluminium at 2 mm sheet thickness as an example: at 0.35 m min 1, deep penetration welding occurs after a certain seam length; at 0.40 m min 1, · − · − heat conduction welding occurs, and at 0.45 m min 1, an insufficient molten zone width below 3 mm · − is reached. Therefore, the focal diameter of 1.7 mm is not considered in further investigations. In general, the thermal efficiency ηth increased with rising energy per unit length, but decreased width rising sheet thickness. AA 6082 (Figure5a) reached a maximum of approximately 3% at a sheet thickness of 1.0 mm. A maximum of approximately 2.1% and 1.4% was obtained at 1.5 mm and 2.0 mm respectively. This behaviour can be explained by the heat that was dissipated in the metal sheet. Increasing thickness led to the input of higher energies per unit length to compensate for the heat loss. For example, the creation of a molten zone with an area of 1.5 mm2 required an energy per unit length of 100 kJ m 1 at 1.0 mm while 218 kJ m 1 was necessary at 2.0 mm sheet thickness. A thicker sheet · − · − basically led to an increase in molten zone width due to the higher progression of isotherms [33] and an increase in the width of the process window. It should be noted that thermal distortion at 1.0 mm Materials 2020, 13, 4875 8 of 16 induced deviations in the results and limited the process window due to a change in heat conduction Materials 2020, 13, x FOR PEER REVIEW 8 of 17 between the materials. On the one hand, higher thermal efficiencies were reached. Constant steps of 0.05 m min 1 in joining velocity led to different maximum thermal efficiencies. Smaller gradations of Smaller· gradations− of the joining speeds could provide further information about the maximum thethermal joining speedsefficiency could achievable provide furtherin practice, information but within about the the scope maximum of the thermal observations efficiency the achievable basic inrelationships practice, but are within recognised. the scope of the observations the basic relationships are recognised.
a) AA 6082: thermal efficiency b) temperature profile at interface (numerical simulation)
df = 5.3 mm df = 3.5 mm 4 500 AA 6082 AA 6082 v wo = 75 mm ∆T wo = 75 mm tm = 1.0 mm n = 1 400 tm = 1.0 mm -1 x / % 3 df =5.3 mm E = 66.7 kJ∙m
th d df = 3.5 mm z = interface f tm = 1.5 mm 300
2 x t = 2.0 mm m 200 0 Tim = 191 °C
1 temperature / at surface°C thermal efficiencythermal η 100
0 0 0 100 200 300 400 -20 -10 0 10 20 energy per unit length / kJ∙m-1 x-coordinate / mm FigureFigure 5. 5.( a(a)) TheThe dependencedependence of thermal efficiency efficiency on on energy energy per per unit unit length length for for various various sheet sheet thicknessesthicknesses and and focal focal diameters diameters forfor thethe aluminium alloy alloy AA AA 6082 6082 and and (b ()b temperature) temperature distribution distribution in in thethe interface interface for for di differentfferent focal focal diameters diameters basedbased on numerical simulation. simulation.
ItIt is is noticeable noticeable that that the the process process windowswindows also shifted shifted depending depending on on the the focal focal diameter. diameter. While While considerablyconsiderably lower lower energies energies perper unitunit length were applied applied with with a asmaller smaller focal focal diameter diameter for for sheet sheet thicknessesthicknesses of of 1.0 1.0 and and 1.5 1.5 mm, mm, comparablecomparable energies per per unit unit length length for for both both spot spot sizes sizes could could be beused used atat 2.0 2.0 mm. mm. The The reason reason for for this this behaviourbehaviour can be found in in the the resulting resulting temperature temperature field. field. A smaller A smaller focalfocal diameter diameter led led to to higher higher maximummaximum temperatures at at the the surface surface and and therefore therefore the the melting melting of the of the metalmetal was was reached reached at at lower lower energies energies perper unitunit length for for 3.5 3.5 mm mm compared compared to to 5.3 5.3 mm. mm. The The behaviour behaviour continuescontinues to to the the interface, interface, where where lowerlower maximummaximum temp temperatureseratures were were reached reached at at larger larger spots. spots. This This is is −1 shownshown for for example example as as∆T ∆ inT in Figure Figure5b for5b for a constant a constant energy energy per per unit unit length length of 66.7 of 66.7 kJ m kJ1∙m. On. On the the other · − hand,other the hand, effect the of effect heat sinkof heat increased sink increased with sheet with thickness. sheet thickness. This led This to a led reduction to a reduction of the maximum of the maximum temperatures and a comparable process window for both focal diameters was achieved at temperatures and a comparable process window for both focal diameters was achieved at 2 mm 2 mm thickness. However the temperature distribution for a larger focal diameter led to a slightly thickness. However the temperature distribution for a larger focal diameter led to a slightly wider wider temperature distribution of 7% for Tim at the interface between the materials where the molten temperature distribution of 7% for T at the interface between the materials where the molten zone zone formed. This is also illustrated imfor both focal diameters in Figure 5b by half of the molten zone formed. This is also illustrated for both focal diameters in Figure5b by half of the molten zone width width (wp/2). This resulted in an overall larger molten zone and explains the slightly higher thermal (wefficiencyp/2). This in resulted case of inthe an larger overall focal larger diameter. molten zone and explains the slightly higher thermal efficiency in caseA of comparison the larger focal with diameter.the steel illustrates the effect of the metallic material on thermal efficiency (FigureA comparison 6a). Although with AISI the 304 steel has illustrates an 39% higher the e absorptivityffect of the metalliccompared material to AA 6082, on thermal just 10% e ffiofciency the (Figureenergy6a). per Although unit length AISI compared 304 has to an aluminium 39% higher was absorptivity required. At compared the same time, to AA the 6082, thermal just efficiency 10% of the energyincreases per unitsignificantly length compared and reaches to a aluminium maximum of was 12%. required. The changes At the in same the thermophysical time, the thermal properties efficiency increasesand in particular significantly the and major reaches reduction a maximum of 92% ofin 12%.thermal The conductivity changes in the compared thermophysical to AA 6082 properties are anddecisive in particular for this the behaviour. major reduction Thus, the of dissipated 92% in thermal heat is conductivity reduced significantly, compared and to AA a higher 6082 are amount decisive forof this power behaviour. is used for Thus, molten the dissipatedzone formation. heat is reduced significantly, and a higher amount of power is used for molten zone formation.
Materials 2020, 13, 4875 9 of 16 Materials 2020, 13, x FOR PEER REVIEW 9 of 17
a) AISI 304: thermal efficiency
15 AISI 304 wo = 75 mm n = 1 tm = 0.5 mm
/ % / df =5.3 mm th d = 3.5 mm η f 10
efficiency tm = 1.0 mm
5 thermal
tm = 1.5 mm
0 0 10 20 30 40 energy per unit length / kJ∙m-1
b) AISI 304: temperature at surface and interface (numerical simulation)
temperature at surface - d = 3.5 mm AISI 304 v f 25 T / C 900 tm = 1 mm E = 16 kJ∙m-1
= = mm5.3 PA 6
f 191 C d
191 C z: surface
= = mm3.5 v f temperature at surface d = 5.3 mm 5 mm df
d f
500 temperature at interface z: interface
C y
400 v df
300 d f = 3.5 mm y d = 5.3 mm 0 200 f Tim = 191 C
100 temperature at surface / / surface at temperature
0 0 50 100 150 y-coordinate / mm FigureFigure 6. ( a6.) ( Thermala) Thermal effi efficiencyciency depending depending on energy per per unit unit length length under under varying varying sheet sheet thickness thickness andand focal focal diameter diameter for for the the high high alloyed alloyed steelsteel AISI 304 and and (b (b) )temperature temperature distribution distribution at the at thesurface surface andand in the in the interface interface for for di differentfferent focal focal diameters diameters basedbased on numercial numercial simulations. simulations.
TheThe process process windows windows of of lower lower sheet sheet thicknessesthicknesses shifted shifted to to lower lower energies energies per per unit unit length length as with as with AAAA 6082 6082 (Figure (Figure6a). 6a). However, However, the the influence influence ofof thethe focal diameter diameter is is different di fferent compared compared to AA to AA6082, 6082, i.e., with a smaller focal diameter, comparable thermal efficiencies were achieved at lower energies i.e., with a smaller focal diameter, comparable thermal efficiencies were achieved at lower energies per per unit length. The reason for this behaviour is based on the different characteristics of the unit length. The reason for this behaviour is based on the different characteristics of the temperature temperature field compared to AA6082. Figure 6b shows an overhead view of the simulated field compared to AA6082. Figure6b shows an overhead view of the simulated temperature field on temperature field on the metal surface. The temperature field is represented by the isotherm Tim at the metal191 °C surface.as the polymer The temperature begins to melt field above is represented this temperature. by the The isotherm width of Tim theat temperature 191 ◦C as the field polymer is beginscomparable to melt abovefor both this spot temperature. sizes despite The a significantly width of the higher temperature maximum field temperature is comparable of the for smaller both spot sizesfocal despite diameter a significantly due to the low higher thermal maximum diffusivity temperature and thermal ofconductivity the smaller of AISI focal 304. diameter The increased due to the lowmaximum thermal di temperatureffusivity and led thermal to an extended conductivity length of of AISI the characteristic 304. The increased isotherm maximum in the direct temperatureion of ledmovement to an extended. From length this effect, of the the characteristic temperature distributionisotherm in of the the direction interface of in movement. this direction From was this effect,considered. the temperature The low thermal distribution conductivity of the interface led to a significant in this direction reduction was of the considered. maximum The temperature low thermal conductivitycompared led to the to asurface, significant while reduction it even exceed of theed maximum the decomposition temperature temperature compared of 400 to the °C surface,for a focal while diameter of 3.5 mm. On the other hand, it can be seen that the characteristic temperature Tim was it even exceeded the decomposition temperature of 400 ◦C for a focal diameter of 3.5 mm. On the other hand, it can be seen that the characteristic temperature Tim was exceeded for a longer time and at higher temperatures. This led to a larger melt pool depth in which the melt pool width remained Materials 2020, 13, 4875 10 of 16 Materials 2020, 13, x FOR PEER REVIEW 10 of 17 constantexceeded for for both a longer focal time diameters. and at higher These temperatur mechanismses. This explain led to the a larger increased melt pool efficiency depth atin which smaller focal diameterthe melt pool for AISI width 304 remained and are constant consistent for with both the focal experimental diameters. These results. mechanisms It should explain be noted the that the increaseincreased of efficiency the melting at smaller zone depth focal diameter was of minor for AISI importance 304 and are for consistent the application, with the sinceexperimental the connected arearesults. was It not should increased be noted at thisthat point;the increase this is of however the melting decisive zone depth for composite was of minor production. importance for the application, since the connected area was not increased at this point; this is however decisive for 3.2.composite Effect of production. Polymer on Thermal Efficiency
3.2. EffectThe eofff Polymect ofer di onff erentThermal polymers Efficiency on thermal efficiency was investigated on a sample basis of 18 experiments with a sample size of 1. Figure7a shows the thermal e fficiency for AA 6082 joints with The effect of different polymers on thermal efficiency was investigated on a sample basis of 18 PP, PA 6 and PA 6.6. It can be seen that a rising energy per unit length led to an increase in thermal experiments with a sample size of 1. Figure 7a shows the thermal efficiency for AA 6082 joints with ePP,fficiency. PA 6 and At thePA same6.6. It time,can be the seen thermal that a erisingfficiency energy was per aff unitected length by the led thermophysical to an increase in properties thermal of the polymer,efficiency. especially At the same the time, melting the thermal interval. efficiency The beginning was affected of the by melting the thermophysical interval Tim propertiesis the temperature of whichthe polymer, must be especially exceeded forthe themelting formation interval. of the The molten beginning zone. Therefore,of the melting thermal interval efficiency Tim is is the higher for lowertemperature Tim. PP which correspondingly must be exceeded showed for the the lowest formation value of (T imthe= molten126 K), zone. followed Therefore, by PA 6thermal(Tim = 191 K) andefficiency PA 6.6 is (Thigherim = 235for lower K). The Tim.relationship PP correspondingly applied showed equally the to lowest AISI value 304 (Figure (Tim = 1267b), K), although followed higher thermalby PA 6 e(Tffiimciencies = 191 K)were and PA achieved 6.6 (Tim due= 235 to K). a The reduction relationship in heat applied dissipation equally into theAISI high 304 (Figure alloyed steel. It7b), follows although that higher higher thermal joining effici speedsencies can were be addressed achieved due by joiningto a reduction polymers in heat with dissipation a low Tim inand the metals withhigh aalloyed low thermal steel. It conductivity,follows that higher producing joining a speeds comparable can be moltenaddressed zone by area.joining polymers with a low Tim and metals with a low thermal conductivity, producing a comparable molten zone area.
a) AA 6082 b) AISI 304 2.5 10 AA 6082 AISI 304
tm = 2 mm tm = 1.5 mm w = 75 mm w = 75 mm PP 2 o 8 o df = 5.3 mm df = 5.3 mm / % / % / n = 1 n = 1 PA 6 th th 1.5 6 PA 6.6
PP 1 4 PA 6 thermal efficiency thermal η thermal efficiencythermal η 0.5 PA 6.6 2
0 0 0 100 200 300 0 204060 energy per unit length / kJ∙m-1 energy per unit length / kJ∙m-1
Figure 7. (a)Effect of polymer material on thermal efficiency for AA 6082 and (b) AISI 304. Figure 7. (a) Effect of polymer material on thermal efficiency for AA 6082 and (b) AISI 304. 7 2 1 The thermal diffusivity of the polymers also differed (a−7 =2 −11.15 10− m −7s− 2,−1 a = The thermal diffusivity of the polymers also differed (aPP = 1.15∙10PP m ∙s , aPA 6 = 1.39∙10 m ∙s PA 6 7 2 1 7 2 1 × · 1.39 10 m s −and7 2 a−1 = 1.23 10 m s ), however, no systematic pattern to the results and× aPA 6.6− = 1.23· −∙10 m ∙sPA), 6.6however, no× systematic− · − pattern to the results could be discerned. The couldsame applied be discerned. to the melting The same enthalpy; applied however, to the this melting parameter enthalpy; is of minor however, importance this parameter for the size is of minor importancethe molten forzone the according size of the to molten[33]. Further zone accordinginformation to is [ 33provided]. Further by informationthe consideration is provided of the by the considerationcalculated dimensionless of the calculated numbers dimensionless in Section 3.4. numbers in Section 3.4.
3.3.3.3. EEffectffect of Overlap Width Width on on Thermal Thermal Efficiency Efficiency TheThe overlap width width along along with with the the specimen specimen length length determines determines the contact the contact surface surface of the joining of the joining partners.partners. TheThe test series consists of of 24 24 experiments experiments with with a asample sample size size of of1. 1.A Areduced reduced overlap overlap joint joint can generatecan generate heat heat accumulation accumulation at theat the sheet sheet edge. edge. The The laser laser beam beam was was always always positioned positioned ininthe themiddle ofmiddle the overlap. of the overlap. The heat The dissipated heat dissipated from from thejoining the joining zone zone thus thus reached reached the the metal metal edge, edge, whichwhich was in was in contact with the polymer, before it reached the free edge. Both factors affect the temperature contact with the polymer, before it reached the free edge. Both factors affect the temperature field and field and the dissipated heat. The overlap width was therefore varied for each material thickness. The the dissipated heat. The overlap width was therefore varied for each material thickness. The energy energy per unit length for the respective metallic joining partner was kept constant for better percomparability unit length and for to the isolate respective the influence metallic of joining the overlap partner width. was keptThis constantresulted in for a betterrelatively comparability low and to isolate the influence of the overlap width. This resulted in a relatively low thermal efficiency for thicker sheets at an overlap width of 75 mm. However, the overall process remained comparable and melting of the metal sheet for decreased overlap widths was avoided. Materials 2020, 13, x FOR PEER REVIEW 11 of 17 Materials 2020, 13, 4875 11 of 16 thermal efficiency for thicker sheets at an overlap width of 75 mm. However, the overall process remained comparable and melting of the metal sheet for decreased overlap widths was avoided. FigureFigure8 illustrates 8 illustrates this this based based on on the the temperature temperature fieldfield at at the the interface interface for for an an AA AA 6082-PA 6082-PA 6 joint 6 joint withwith an overlapan overlap of 14of 14 and and 75 75 mm. mm. At At constant constant joiningjoining parameters, parameters, the the heat heat accumulation accumulation at the at thesheet sheet edgeedge with with reduced reduced overlap overlap is is clearly clearly observed, observed, comparedcompared to to the the symmetrically symmetrically formed formed temperature temperature distributiondistribution of theof the large large overlap. overlap. At At the the samesame time, the the propagation propagation ofof the the molten molten area area at the at interface, the interface, characterizedcharacterized by by the the 191 191◦C °C isotherm, isotherm, increases increases significantly.significantly. Therefore, Therefore, a great a great impact impact on the on thethermal thermal efficiencyefficiency is expected. is expected.
FigureFigure 8. ( a8.) ( Temperaturea) Temperature distribution distribution in in the the interfaceinterface for for an an AA AA 6082–PA 6082–PA 6 joint 6 joint width width overlap overlap widths widths of 14of and 14 and (b) ( 75b) mm75 mm based based on on numerical numerical simulations. simulations.
FigureFigure9a provides9a provides the the results results for AA AA 6082. 6082. The The high high thermal thermal conductivity conductivity of aluminium of aluminium led to leda to strong a strong effect e ffofect overlap of overlap width widthon thermal on thermalefficiency. effi Forciency. 1.0 mm, For the 1.0 thermal mm, theefficiency thermal increased efficiency increasedfrom 2% from up to 2% 5.8%. up toThe 5.8%. characteristic The characteristic curve progression curve progressionwas comparable was for comparable all the sheet for thicknesses all the sheet thicknessesinvestigated, investigated, i.e., the thermal i.e., the efficiency thermal e ffiincreaseciencyd increasedwith smaller with overlap smaller width overlap due width to the due heat to the heataccumulation accumulation from from the the reduced reduced heat heat loss. loss. In Incomparison, comparison, AISI AISI 304 304showed showed a different a different behaviour behaviour (Figure(Figure9b). 9b). A decrease A decrease of theof the overlap overla widthp width showed showed just just a a slight slight eeffectffect on thermal efficiency efficiency because because of of the significantly lower thermal conductivity. For the same reason, higher maximum values of ηth the significantly lower thermal conductivity. For the same reason, higher maximum values of ηth were were reached for the high alloyed steel. The thermal efficiency was nearly constant for changing reached for the high alloyed steel. The thermal efficiency was nearly constant for changing overlap. overlap. Even for a sheet thickness of 0.5 mm, the increase in thermal efficiency was 0.8% between 14 Even for a sheet thickness of 0.5 mm, the increase in thermal efficiency was 0.8% between 14 mm and mm and 75 mm overlap width. 75 mmMaterials overlap 2020, width.13, x FOR PEER REVIEW 12 of 17
a) AA 6082 b) AISI 304 AA 6082 AISI 304 PA 6 PA 6 -1 tm = 1.0 mm E = 100 kJ∙m E = 20 kJ∙m-1 6 d = 5.3 mm f 15 t = 0.5 mm df = 5.3 mm / %
/ % / m n = 1 n = 1 th th
tm = 1.5 mm 4 10
tm = 1.0 mm 2 t = 2.0 mm
thermal efficiencythermal η 5
thermal efficiency thermal η m
tm = 1.5 mm
0 0 0 204060800 20406080
overlap width wo / mm overlap width wo / mm
Figure 9. (a) The dependence of thermal efficiency on overlap width with constant energy per unit Figure 9. (a) The dependence of thermal efficiency on overlap width with constant energy per unit length for AA 6082 and (b) AISI 304. length for AA 6082 and (b) AISI 304.
3.4. General Description of Thermal Efficiency by Dimensionless Numbers Based on the experimental results, the parameters investigated were qualitatively pooled in Figure 10 regarding their effect on thermal efficiency. In general, a minimum energy per unit length was required before the polymer melted. The thermal efficiency then increased approximately linearly in the field under consideration. An increase in the absorbed laser beam power Pa thus shifted the curve to the left. Both a reduction of the metal sheet thickness tm and a lowering of the melting interval of the polymer, characterized by the beginning of the melting interval Tim, contributed to an increase of thermal efficiency. In contrast, an increase in the overlap width wo led to a reduction in thermal efficiency; this effect was closely related to the thermal diffusivity of the metal material as discussed in Section 3.3. In contrast, an increase in thermal diffusivity led to a reduction in thermal efficiency due to the enhanced heat conduction loss. The influence of the focal diameter was ambivalent for different thermal diffusivities due to the temperature field formed and could lead to either an increase or a decrease of thermal efficiency (see Section 3.1). th
tm ↓ Tim ↓
Pa ↑ wo ↑ αm ↑ hra fiinyη efficiency thermal df ↓
energy per unitlength E
Figure 10. Qualitative illustration of the influencing parameters on thermal efficiency.
Figure 10 does not show quantification across different materials, parameters and ambivalent effects. To provide a quantified and generally valid description of the thermal efficiency in laser- based joining of polymers and metals, dimensionless numbers were calculated by means of Buckingham π theorem (see Section 2). The Buckingham π theorem provides a method for calculating dimensionless numbers based on given variables with known dimensions, even if the form of the equation is unknown. The theorem states, among other things, that any physical law can be expressed by dimensionless indices or their combination, on the condition that the physical problem is modelled
Materials 2020, 13, x FOR PEER REVIEW 12 of 17
a) AA 6082 b) AISI 304 AA 6082 AISI 304 PA 6 PA 6 -1 tm = 1.0 mm E = 100 kJ∙m E = 20 kJ∙m-1 6 d = 5.3 mm f 15 t = 0.5 mm df = 5.3 mm / %
/ % / m n = 1 n = 1 th th
tm = 1.5 mm 4 10
tm = 1.0 mm 2 t = 2.0 mm
thermal efficiencythermal η 5
thermal efficiency thermal η m
tm = 1.5 mm
0 0 0 204060800 20406080 overlap width w / mm overlap width w / mm o o
Figure 9. (a) The dependence of thermal efficiency on overlap width with constant energy per unit Materialslength2020 ,for13 ,AA 4875 6082 and (b) AISI 304. 12 of 16
3.4. General Description of Thermal Efficiency by Dimensionless Numbers 3.4. General Description of Thermal Efficiency by Dimensionless Numbers Based on the experimental results, the parameters investigated were qualitatively pooled in Based on the experimental results, the parameters investigated were qualitatively pooled in Figure 10 regarding their effect on thermal efficiency. In general, a minimum energy per unit length Figure 10 regarding their effect on thermal efficiency. In general, a minimum energy per unit length was required before the polymer melted. The thermal efficiency then increased approximately was required before the polymer melted. The thermal efficiency then increased approximately linearly linearly in the field under consideration. An increase in the absorbed laser beam power Pa thus shifted in the field under consideration. An increase in the absorbed laser beam power Pa thus shifted the the curve to the left. Both a reduction of the metal sheet thickness tm and a lowering of the melting curve to the left. Both a reduction of the metal sheet thickness tm and a lowering of the melting interval interval of the polymer, characterized by the beginning of the melting interval Tim, contributed to an of the polymer, characterized by the beginning of the melting interval Tim, contributed to an increase increase of thermal efficiency. In contrast, an increase in the overlap width wo led to a reduction in of thermal efficiency. In contrast, an increase in the overlap width wo led to a reduction in thermal thermal efficiency; this effect was closely related to the thermal diffusivity of the metal material as efficiency; this effect was closely related to the thermal diffusivity of the metal material as discussed in discussed in Section 3.3. In contrast, an increase in thermal diffusivity led to a reduction in thermal Section 3.3. In contrast, an increase in thermal diffusivity led to a reduction in thermal efficiency due to efficiency due to the enhanced heat conduction loss. The influence of the focal diameter was the enhanced heat conduction loss. The influence of the focal diameter was ambivalent for different ambivalent for different thermal diffusivities due to the temperature field formed and could lead to thermal diffusivities due to the temperature field formed and could lead to either an increase or a either an increase or a decrease of thermal efficiency (see Section 3.1). decrease of thermal efficiency (see Section 3.1). th
tm ↓ Tim ↓
Pa ↑ wo ↑ αm ↑ hra fiinyη efficiency thermal df ↓
energy per unitlength E
Figure 10. Qualitative illustration of the influencing parameters on thermal efficiency. Figure 10. Qualitative illustration of the influencing parameters on thermal efficiency. Figure 10 does not show quantification across different materials, parameters and ambivalent Figure 10 does not show quantification across different materials, parameters and ambivalent effects. To provide a quantified and generally valid description of the thermal efficiency in laser-based effects. To provide a quantified and generally valid description of the thermal efficiency in laser- joining of polymers and metals, dimensionless numbers were calculated by means of Buckingham π based joining of polymers and metals, dimensionless numbers were calculated by means of theorem (see Section2). The Buckingham π theorem provides a method for calculating dimensionless Buckingham π theorem (see Section 2). The Buckingham π theorem provides a method for calculating numbers based on given variables with known dimensions, even if the form of the equation is unknown. dimensionless numbers based on given variables with known dimensions, even if the form of the The theorem states, among other things, that any physical law can be expressed by dimensionless equation is unknown. The theorem states, among other things, that any physical law can be expressed indices or their combination, on the condition that the physical problem is modelled considering the by dimensionless indices or their combination, on the condition that the physical problem is modelled correct parameters. This provides a simple way of doing dimensional analysis, but does not provide a direct description of the physical relationship or of the importance of the dimensionless numbers. In order to determine specific relationships, all dimensionless numbers were calculated using the parameters of each experiment and compared to the thermal efficiency. Therefore, the dimensionless numbers were applied to the complete data set consisting of all test series from Sections 3.1–3.3, in order to check the general validity regarding all different parameters considered. It should be noted that the aggregated results also contain data sets that have not previously been presented and which were created by increasing the sample size for individual experiments. This results in a total of 276 experiments, which were accordingly materialographically evaluated. The aim was to provide a broader database for the validation of the dimensionless numbers. The derived numbers are given in Table3. The evaluation showed that π1 to π8 did not provide a generally valid relationship with thermal efficiency. In contrast, π9 provided interesting results regarding thermal efficiency as shown in Figure 11. To show the results most clearly, the upper diagram has linear axes while the lower has logarithmic axes, and different colours highlight various material combinations. The dimensionless number π9 allows a correlation of the metals used, aluminium and steel, even though they have different material properties. Due to the higher thermal efficiencies, steel is mainly located on the left of the diagram, with aluminium on the right. Nevertheless, there Materials 2020, 13, 4875 13 of 16 is a considerable transition area in the range of approximately 0.03–0.06 10 6 of the dimensionless × − number π9. In the logarithmic representation, it is evident that the correlation is equally valid for different material combinations. However the coefficient of determination of 0.92 should not hide the fact that the vast majority of experiments were carried out on two combinations of materials (AISI 304 with PA 6, EN AW 6082 with PA 6), which favoured the high value. Nevertheless, all test series–overall and in detail–followed an exponential function.
Table 3. Calculated dimensionless numbers πi.
Number πi Formula 1 π1 tm wo− 5 · 3 π2 wo ρm Pa τl− 2 · · · 3 1 π3 Pa τl cp,m wo− λm− · · · 1 · π4 wp wo− 2 · 2 π5 τl ∆H wo− · · 1 π6 wo λm Tim Pa− · 2· · 1 π7 wo Ap− · 1 π8 dp wo− · 1 Materials 2020, 13, x FOR PEER REVIEW π9 τ αp Ap 14 of 17 l· · −
20 AISI 304+PA6
AISI 304+PP / % 15 th AISI 304+PA6.6
EN AW 6082+PA6
10 EN AW 6082+PP
EN AW 6082+PA6.6 5 thermal efficiency η efficiency thermal
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.4 0.9 1.4 -6 π9 / 1×10 100 AISI 304+PA6
AISI 304+PP
/ % / AISI 304+PA6.6 th 10 EN AW 6082+PA6
EN AW 6082+PP
EN AW 6082+PA6.6 1 R² = 0.92 thermal efficiency η efficiency thermal
0.1 0.001 0.01 0.1 1 10 π / 1×10-6 9 Figure 11. The dependence of thermal efficiency on π in linear (top) and logarithmic Figure 11. The dependence of thermal efficiency on π9 in linear9 (top) and logarithmic (bottom) (bottom) representations. representations.
A more detailed examination of π9 reveals a similarity to the Fourier number (Fo, Equation (1)) A more detailed examination of π9 reveals a similarity to the Fourier number (Fo, Equation (1)) which describes the ratio of dissipated to stored heat (see Section1) as shown in Figure 11 (top). which describes the ratio of dissipated to stored heat (see Section 1) as shown in Figure 11 (top). Compared to the characteristic length L, which enters the Fo quadratically, the Buckingham π theorem Compared to the characteristic length L, which enters the Fo quadratically, the Buckingham π led to the molten zone area Ap taken into account. This area was melted by the energy input in the theorem led to the molten zone area Ap taken into account. This area was melted by the energy input in the indirect joining process, i.e., the heat was conducted through the metal into the polymer, which is why it can also be seen as a characteristic quantity of the process. The calculation of the thermal efficiency is also based on it (Equations (4) and (5)). For small values of π9, the ratio of stored to dissipated heat results in a higher thermal efficiency; for larger values of π9, the opposite applies. In addition to the interaction time of the laser beam, the thermal diffusivity of the polymer was also taken into account. It can be assumed that propagation of the temperature field was also reflected in the molten zone area, since it directly causes its width [33]. The dimensionless number thus provides a description of thermal efficiency across different material combinations, material properties, joining parameters and geometric variables. Alternative trials with other model approaches, e.g., considering the joining velocity, could also establish dimensionless numbers similar to the Péclet number (Pe, Equation (2)). However, a general validity for both metallic materials was not reached. It should be noted that dimensionless numbers can combine various factors and even boundary conditions. This is noticeable in that the trials on overlap width are integrated into the characteristic number π9 without major deviations. An extension of the thermal analysis to thermal-mechanical questions, e.g., the influence of boundary conditions on hot cracking as shown in [43], is conceivable in principle. However, the modelling of such questions is more difficult due to the fact that decisive factors on the mechanical processes, e.g., the material history, cannot be determined directly.
Materials 2020, 13, 4875 14 of 16 indirect joining process, i.e., the heat was conducted through the metal into the polymer, which is why it can also be seen as a characteristic quantity of the process. The calculation of the thermal efficiency is also based on it (Equations (4) and (5)). For small values of π9, the ratio of stored to dissipated heat results in a higher thermal efficiency; for larger values of π9, the opposite applies. In addition to the interaction time of the laser beam, the thermal diffusivity of the polymer was also taken into account. It can be assumed that propagation of the temperature field was also reflected in the molten zone area, since it directly causes its width [33]. The dimensionless number thus provides a description of thermal efficiency across different material combinations, material properties, joining parameters and geometric variables. Alternative trials with other model approaches, e.g., considering the joining velocity, could also establish dimensionless numbers similar to the Péclet number (Pe, Equation (2)). However, a general validity for both metallic materials was not reached. It should be noted that dimensionless numbers can combine various factors and even boundary conditions. This is noticeable in that the trials on overlap width are integrated into the characteristic number π9 without major deviations. An extension of the thermal analysis to thermal-mechanical questions, e.g., the influence of boundary conditions on hot cracking as shown in [43], is conceivable in principle. However, the modelling of such questions is more difficult due to the fact that decisive factors on the mechanical processes, e.g., the material history, cannot be determined directly.
4. Conclusions In this paper, the thermal efficiency of laser-based joining of polymers with metals was investigated. Based on individual test series on the influence of sheet thickness, focal diameter and energy per unit length, different polymers as well as various overlap conditions were considered. The partially opposing effects on thermal efficiency were clarified by numerical simulation of the temperature distribution. The methodology that was developed allowed the comparison of strongly differing material properties, e.g., the absorbed laser beam power for the comparison of aluminium and steel materials. Factors that had a decisive effect on the thermal efficiency were identified and a qualitative model was developed. In addition, a quantitative description of thermal efficiency was achieved by applying the Buckingham π theorem. The development of a dimensionless number enabled all test series to be incorporated. This characteristic number shows similarity to the Fourier number, enabling the physical background of dissipated to stored heat. This model enables the thermal efficiency of the process to be described in general, but also allows measures for increasing the thermal efficiency and to be derived and used for the evaluation of the joining process, e.g., for calculation of the carbon footprint.
Author Contributions: Conceptualization, K.S.; methodology, K.S. and M.A.; formal analysis, K.S. and M.A.; investigation, M.A. and K.S.; data curation, K.S. and M.A.; writing—original draft preparation, K.S.; writing—review and editing, J.P.B. and K.S.; visualization, K.S.; supervision, J.P.B. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors would like to thank Andrea Knauer and the Institute of Micro- and Nanotechnologies MacroNano® at the Technische Universität Ilmenau for performing the reflection measurements in the integrating sphere and James Andrew Lenard for proof-reading the paper. We acknowledge support for the Article Processing Charge by the Open Access Publication Fund of the Technische Universität Ilmenau. Conflicts of Interest: The authors declare no conflict of interest. Materials 2020, 13, 4875 15 of 16
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