linear function for external work (
Chapter 10)
LTransformation matrixLLink intensityLcCharacteristic length based on domain sizeLfLatent heat of fusion
Laguerre polynomial of order p and index lmAtomic massmbMass of the ball (
Chapter 9)mbDeposited binder (
Chapter 6)mpParticle massmpMass of the bound powder (
Chapter 6)mfFluid mass
Mass flow rateM2Beam quality factorMaMarangoni numbernReflection's indexNMatrix of shape function for mesh elementNiNumber of atoms or electrons per unit volume in the energy levelsNLAmount of atoms per unit volume of liquidNlxNeumann functionNSAmount of atoms per unit volume of solidNuNusselt numberNthShape vector for thermal expansionOhOhnesorge number pConstant characteristic of the material (
Chapter 4)pPressurepPenalty value (
Chapter 10)pcCapillary forcePfPacking fractionPPowerPatAttenuated laser power by particlesPelPower of electrical motor in FDM systemPlNet/average laser powerPpeakPeak power per pulsePonOn the state of the laser powerPoffOff state of the laser powerPtotTotal delivered beam powerPePeclet numberPrPrandtl numberPRPacking density of the powderPWPulsed wave laserP(∞)Value of the extrudate property after an infinite healing timeqHeat fluxQPower generated per unit volume (in all chapters except Chapter 3)QBeam propagation factor (
Chapter 3)QcTotal energy absorbed by the substrateQextExtinct coefficientQlLaser energyQrsReflected energy from the substrateQLLatent energy of fusionQvVolumetric flow raterRadius of nucleus (
Chapter 8)r*Critical nucleus radiusrbBall mill radiusrfFilament radiusr0lBeam radius of the waistrjetRadius of powder spray jetrlBeam spot radius on the substratersPowder stream diameterrpPowder particle radiusRReflectivityRSolidification rate where it is referred toRcClad surface curvatureRcurRadius of curvatureReReynolds numberRe*Property‐based Reynolds numberRhHeat load by convectionRh(t)Intrinsic healing functionRLLocal growth rate RNNominal growth rateRrRadius of the actuating motorRporeEffective pore diameter in the bedRqHeat load by surface conductionRQHeat load by volume conductionsHatch spacingsSpecific surface areaSBinder saturationSijLateral distance between neuron i and j (
Chapter 11)SmaxSpreading ratioSmeasAmount of signal (
Chapter 11)SØSource term corresponding to ØS (ϕ)Shape factorSSScan speed
Strain rate deformation tensorΔ SExpansion of surface areatTime and/or laser interaction timet*Dimensionless timetc = tμViscous timetCDACorresponding penetration timetfSolidification timetIInertial‐capillary timetVViscous‐capillary timeTTemperatureTαReference temperatureTaveAverage temperatureTinFilament temperatureTgGlass transition temperatureToutOutlet temperature
Temperature of the liquefier wallTdDrying timeTeEquilibrium temperatureTlLiquidus temperatureTAmbient temperatureTmMaterials melting pointTpMaximum temperatureΔTUndercooling temperatureΔTtotTotal undercooling temperatureΔTCUndercooling temperature: solute diffusionΔTTUndercooling temperature: thermal diffusionΔTKUndercooling temperature: attachment kineticsΔTRUndercooling temperature: solid–liquid boundary curvatureTEMplGaussian–Laguerre transverse electromagnetic modesUBeam velocity
UTravel velocity vector
UGlobal displacement vector (
Chapter 10)
UpParticle velocity vectorUsRate of solidificationvScanning speedvcCollision velocityυjJet velocityvpVelocity of the particlevprintVelocity of the print headVVolume of melt pool
VDesign volume (
Chapter 10)VaAcceleration voltageVSVolume of nucleusVEDThe energy enters the substrate from the surface in LPBFwTrack or melt pool widthwNeuron weight (
Chapter 11)wiWeight factorWLaser pulse widthWeWeber numberXs + cWeight percent of element X in the total surface of the clad regionXcWeight percent of element X in the powder alloyXsWeight percent of element X in the substrateyDendrite arm spacing (
Chapter 8)zDistance from the surfacezWaist location with respect to an arbitrary coordinate along the propagation axisZPrintability of a liquidZhHeat penetration depth
Greek Symbols
αThermal diffusivityαtCoefficient of thermal expansionβAbsorption factorβAbsorption factorβpPowder particles’ absorbed coefficientβwSubstrate laser power absorptivityγSurface tensionγNet electron beam energy (Chapter 5)γESpecific surface energyγSLSolid–liquid interfacial free energyγSVSolid–vapor interfacial energyγLVLiquid–vapor interfacial energyShear rateΓTorque of electrical motors in FDMΓSurface function (Chapter 10)δSolid/liquid interface thicknessδDirac delta function (Chapter 6)εTotal strainεcCooling rateεtEmissivityεMMechanical strainsεTThermal strainsεpEquivalent plastic stressεVacuum permittivityεmMechanical strainεthThermal strain∑Covariance matrixηDynamic viscosityηPowder catchment efficiency (wherever it refers to throughout chapters)ηNumerical damping coefficient for OCM (Chapter 10)ηLearning rate (Chapter 11)ηeAbsorption efficiency for electron beamηdDynamic viscosityηpPowder catchment efficiencyθRepresenting different angles based on figuresθWetting angle (Chapter 2)θFar‐field divergence angle (Chapter 3)θDimensionless temperature in numerical models (Chapter 7)θjetAngle between powder jet and substrateθdDynamic wetting angleθeqSteady‐state angleΘDimensionless temp in analytical modelsλWavelengthλLagrange multiplier (Chapter 10)λnRoots of zero‐order Bessel function of its first kindμViscosityμMembership function (Chapter 11)υFrequency (Chapter 3)υKinematic viscosityρDensityρbDensity of binderρpbPowder bed densityρcDensity of melted powder alloyρsDensity of substrate materialρsPacking density of the pores (Chapter 6)σStefan–Boltzmann constantσCovariance (Chapter 11)σcCharge densityσijElastic stressτThermal time constantτcDimensionless capillary timeϕDifferent label for angles as indicated in the associated figures ϕPowder bed porosityϕShape factorΦInterpolation function (Chapter 10)ϕ(x, y)Level‐set equationϕtapTapped porosityϕ(t)Rate of heat liberation in a continuous point sourceØAngle of incidenceΨStrain energyωSpinning speedωRelaxation factor (Chapter 11)ωiStrength of anisotropyωrAngular velocity of the actuating motorΩSubstrate surfaces or melt pool boundary and material domain
1 Additive Manufacturing Process Classification, Applications, Trends, Opportunities, and Challenges
