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Mechanisms and processing limits in laser thermochemical machining
CIRP Annals - Manufacturing Technology 59 (2010) 251–254
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er. com/ci rp/ def a ult . asp
Mechanisms and processing limits in laser thermochemical machining A. Stephen *, F. Vollertsen (1) BIAS-Bremer Institut fuer angewandte Strahltechnik, Klagenfurter Str. 2, 28359 Bremen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Laser Etching Mechanism
Metallic microparts can be produced with high quality by laser thermochemical machining when the etching liquid is injected coaxially to the laser beam directly into the irradiated area. The basic mechanisms and limits of the process are described. It is shown that the reaction is temperature driven independent of the laser wavelength. A limiting factor is the diffusion of the anions identified by comparing experimentally determined and calculated diffusion coefficients for the reaction products. The machining quality with respect to aspect ratio, edge radius and roughness can be enhanced by increasing the velocity of the etching liquid. ß 2010 CIRP.
1. Introduction
2. Experimental
Laser machining is a flexible tool for structuring materials with high strength and hardness. In general, the domain for laser material processing techniques can be divided into three major classes involving only heating, melting and vaporising. Laser ablation mainly removes material as vapor, hence, needs delivery of a high power density within a very short interaction time. In industry lasers with nanosecond pulses are recognized as a rapid and efficient tool for machining micro-features into hard to machine materials. Laser machining using nanosecond pulses exhibits no material restrictions, if a suitable laser beam source is chosen [1]. A severe problem with laser ablation consists in the incompatibility of high ablation rates and good surface qualities [2]. High ablation rates are usually connected with strong mechanical damages of the surface and a significant heating of the material [3]. Using laser pulses in the femtosecond range melting could almost be avoided [4]. However, the process speed is low due to the low energies used [5]. If machining metals even femtosecond pulses can cause deleterious thermal effects and also melt can be observed when drilling holes [6]. Laser chemical removal, which allows surface heating without surface melting or vaporising, requires a low power density. Deleterious thermal effects, recast or redeposition of evaporated material can be significantly reduced by chemical assisted laser machining in salt solutions [7] or even avoided by a laser activation of chemical reactions [8]. Laser thermochemical etching of metals can be achieved in solutions of acids or bases using cw lasers in the VIS or NIR region. Compared to electrochemical machining, which also allows the processing of conductive materials regardless their hardness [9], the aspect ratio is much smaller [10], but better resolution [11] and surface roughness [12] can be achieved [13]. In this paper, the basic mechanisms and limits of the process, which can be used as an industrial example for the fabrication of superelastic micro-grippers made of the nickel–titanium alloy nitinol [13], are presented.
The major equipment for laser chemical machining consists of a laser, a chemical jet assembly and a positioning system, shown in Fig. 1. In brief, the beam of a continuous wave laser operating in its fundamental Gaussian mode is focused on the metal surface by a lens system with a focal length of 50 mm. As etching processes are transport limited, a fast exchange of the reaction products is an essential requirement to avoid saturation effects. Such efficient exchange is realized by the liquid jet. The liquid phase etching cell consists of two parts: a coaxial nozzle assembly and a basin. The nozzle, which injects the etching liquid coaxially to the laser beam directly into the irradiated area, can be adjusted laterally and in height with respect to the laser beam focus. Pumping the liquid through the nozzle leads to flow speeds between 2 and 20 m/s. The basin holds the workpiece and is mounted onto a computer controlled xyz-stage allowing a relative positioning resolution of 0.1 mm for the workpiece with respect to the nozzle and the incident laser beam over a distance of 100 mm. Measurements of the electrochemical potential can be performed by a usual three-electrode configuration which is integrated into the chemical cell. The working electrode is the metallic workpiece itself. The counter electrode is a circularly formed wire made of inert platinum, which is located in front of the nozzle. The reference electrode is a Saturated Calomel Electrode located inside the basin. Investigations of the laser thermochemical processing were performed using two different laser systems. The relevant specific properties of each system are listed in Table 1. Main differences which influence the surface temperature of the material are the laser power PL, laser wavelength l and the spot diameter d. Materials used for the investigations and their relevant specific properties are listed in Table 2. Relevant material parameters influencing the surface temperature are the reflectivity for a specific wavelength Ropt and the thermal conductivity K. While processing the workpieces were immersed in an etching liquid consisting of 5.6 M phosphoric acid (H3PO4) and 1.5 M sulfuric acid (H2SO4) at room temperature.
* Corresponding author. 0007-8506/$ – see front matter ß 2010 CIRP. doi:10.1016/j.cirp.2010.03.069
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
252
described by the heat conduction differential equation:
DTðx; y; z; tÞ
aq ðx; y; tÞð1 Ro pt Þeaz 1 @Tðx; y; z; tÞ ¼ L0 k @t K
(1)
where k is the material diffusivity, K the thermal conductivity, a the absorption coefficient and Ropt the wavelength dependent optical reflectivity of the material. In the one-dimensional case and assuming a constant flux density the surface temperature TSC derived from this equation for a semi-infinite solid body is: T SC ¼
ð1 Ro pt ÞqL0 d þ T0 2K
(2)
or as a function of the laser power: T SC ¼ Fig. 1. Experimental setup for laser thermochemical machining.
Table 1 Laser system specifications. Laser
l (nm)
PL (W)
d (mm)
Ar-ion Nd:YAG
514 1064
2.4 16
7.8 13.0
Laser spot diameter calculated by [14].
Table 2 Material specifications. Material
Ropt (1064 nm)
Ropt (514 nm)
K (W/m K)
Ni NiTi Steel 1.4301
0.75 0.69 0.63
0.69 0.63 0.58
90.9 9.0 16.3
Reflectivity and thermal conductivity values are taken from [15].
The machining result was characterized by the geometrical parameters defined in Fig. 2. The maximum removal depth hmax and width bmax, removed area Fgeo and edge radius Rgeo can be directly measured from prepared cross-sections. Therewith, the aspect ratio AR, edge sharpness Kgeo, removal rate yV with the known feed rate y can be determined. 3. Mechanisms 3.1. Temperature The temperature distribution T(x, y, z, t) in the material as a function of the laser light flux density at the surface qL0(x, y, t) is
4ð1 Ro pt ÞPL þ T0 2pKd
(3)
where d is the laser spot diameter and T0 is the initial temperature of the body. Furthermore, in case of the used metals and cw laser systems, the penetration depth of heat was assumed to be much larger than the penetration depth of light and the laser spot diameter. The respective surface temperatures for the Ar-ion and the Nd:YAG laser systems for different applied laser powers can be calculated using Eq. (3) and the specifications of the laser systems and materials from Tables 1 and 2. The cooling effect by the etching liquid is neglected in this case as it should show no difference for the two laser systems at equal flow speeds. Fig. 3 shows a plot of the removal rates yV normalized to the laser spot area Fd against the surface temperature for both laser systems for the material nickel. According to this, equal temperatures lead to equal normalized removal rates for different laser wavelength and spot diameters. Therefore, it has been proved, that the laser thermochemical removal depends only on the material surface temperature and not on the absorbed laser wavelength. If the processing speed of laser thermochemical machining is only dependent on the material surface temperature, this must be also reflected in the respective removal rates for materials with different thermal conductivities. Fig. 4 shows a plot of the removal rates normalized to the thermal conductivity of the material against the reflectivity dependent absorbed flux density for different materials using the Nd:YAG laser system. Therefore, the main influencing factor on the removal rate of a specific material is its thermal conductivity. Indeed, this applies at least to materials differing in their thermal properties (one order of magnitude in the thermal conductivity) but chemically similar as used in the presented investigations.
Fig. 2. Characteristic geometrical parameters of the machining result.
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
Fig. 3. Dependence of the removal rates normalized on the laser spot area on the calculated surface temperature for nickel using laser systems with different wavelengths.
Measurements of the temperature dependent chemical potential show for both laser systems and the different materials a cathodic shift of the potential. Due to the chemical dissolution of the material according to Eq. (4) the activity of the educts (metal and protons) decreases, whereas the activity of the products (metal ions and hydrogen) increases. Me þ 2Hþ ! Me2þ þ H2 "
(4)
According to the Nernst equations the increase of the metal ion activity results in a positive change of the potential, while the increase of the proton activity causes a decrease of the potential. Therefore, the protons are essential for the formation of the electrochemical potential of the reaction, i.e. the proton activity is the driving force for laser thermochemical machining. 3.2. Diffusion To identify the limiting mechanism of the processing speed, the temporal evolution of the maximum removal depth hmax was investigated. Fig. 5 shows a double logarithmic plot of the temporal derivative of the removal depth (dhmax/dt) versus the removal depth itself. For small depths the differentiation causes noise around a constant value, but for larger depths a monotone decrease with a gradient of m = 1 can be observed, i.e. the reaction rate is inversely proportional to the removal depth: dhmax D ¼ f ðhmax Þ ¼ hmax dt
(5)
253
Fig. 5. Double logarithmic plot of the temporal derivative of the maximum removal depth versus the maximum removal depth itself for NiTi using an Nd:YAG laser system.
The reaction rate for a heterogeneous chemical reaction with mass transport limitation is a function of the diffusion coefficient D and the thickness of the Nernst layer d: dhmax D / dt d
(6)
Therefore, the processing speed in laser thermochemical machining is diffusion limited from a certain removal depth. Diffusion coefficients in liquids can be described by the Stokes– Einstein equation: D¼
kB T 6phR0
(7)
where kB = 1.38 J/K is the Boltzmann constant, T the absolute temperature, h the dynamic viscosity of the liquid and R0 the radius of the diffusing particles. As the dynamic viscosity is a function of the temperature the dependence of the diffusion coefficient on the temperature is nonlinear. The dynamic viscosity of liquids can be described by the Arrhenius–Andrade equation: E (8) h ¼ h0 exp A RT where R = 8.314 J/mol K is the universal gas constant, h0 a material specific constant and EA the activation energy. The material constant and the activation energy can be calculated from tabular values of the viscosity for different temperatures. The viscosity for 5 M phosphoric acid at room temperature is 2.8 mN s/m2 [16]. The calculated temperature dependent diffusion coefficients for the reaction educts and products as well as the experimental ones are shown in Fig. 6. For the calculation Eq. (7) was used with atomic respectively covalence radii of hydrogen (30 pm), Ni/Ti (135/ 140 pm), phosphate (179 pm) and oxygen (60 pm) [15]. Accordingly, the transport of the anions is the limiting reaction sub-step. 4. Processing limits For the evaluation of the processing limits with respect to the machining quality the geometrical parameters aspect ratio AR, edge sharpness Kgeo, and roughness Ra according to Fig. 2 were investigated. For a general expression of the machining quality these geometrical parameters were normalized to their highest value and the following quality number defined: quality number ¼
Fig. 4. Dependence of the removal rates normalized on the thermal conductivity on the absorbed laser flux density for different materials using an Nd:YAG laser system.
ARnorm K geo;norm Ra;norm
(9)
The dependence of this quality number on the maximum removal depth is shown in Fig. 7. In principle, the machining
254
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
quality decreases with increasing removal depth. Nevertheless, at the same removal depth a higher machining quality can be achieved if higher flow speeds of the etching liquid are applied. This is an important fact as for the specification of a machining result often the achievable quality for a given structure depth is of importance for its application. A machined cut edge in nitinol using a laser power of 5 W, a feed rate of 10 mm/s and a flow speed of 10 m/s is shown in Fig. 8. The machining results in an aspect ratio of 2, an edge radius of 9 mm and a roughness of 0.3 mm, which equals the quality number of 0.15. Therefore, even at relatively low quality numbers according to Eq. (9) a good machining result can be achieved by laser thermochemical machining. 5. Conclusions
Fig. 6. Calculated diffusion coefficients for the reaction educts/products and the experimental values in dependence on the temperature for the chemical dissolution of NiTi in phosphoric acid.
The laser thermochemical machining in a reactive fluid jet is driven by the temperature dependent proton activity of a redox reaction. Thus, the laser supports the kinematic of dissolution and has no melting effects. The radiation wavelength has an indirect influence by the differences in the absorptivity of the machined material, but no direct one. For the investigated different materials, namely metals which form a native oxide layer, the relation of their thermal conductivities is reflected in the achievable processing speeds. The processing speed is limited by the diffusion of the anions formed during the redox reaction, in this case phosphate ions, from a certain depth of removal on. The machining quality with respect to the aspect ratio, the edge sharpness and the surface roughness can be enhanced by increasing the flow speed of the etching liquid. Acknowledgements The authors thank the German Research Foundation (DFG) for funding the project Vo530/14-3 and the subproject A5 of the Collaborative Research Centre 747 (SFB 747). References
Fig. 7. Quality number in dependence on the maximum removal depth for different flow speeds of the etching liquid.
Fig. 8. Machined cut edge in a 200 mm thick nitinol foil.
[1] Herbst L, Quitter JP, Ray GM, Kuntze T, Wiessner AO, Govorkov SV, Heglin M (2003) High Peak Power Solid State Laser for Micromachining of Hard Materials. Proceedings of the SPIE 4968:134–142. [2] Stephen A, Vollertsen F (2005) 3D Microstructuring of Mold Inserts by Laserbased Removal, Microengineering of Metals and Ceramics. Wiley–VCH, Weinheim. pp. 131–160. [3] Schmidt M, Esser G (2003) Laser Micro Processing—Facts and Trends. Proceedings of the SPIE 5063:163–171. [4] Weikert M, Dausinger F (2004) Surface Structuring, Femtosecond Technology for Technical and Medical Applications. Springer, Berlin. pp. 117–129. [5] Weikert M, Fo¨hl C, Dausinger F, Abeln T (2003) Surface Structuring of Metals with Short and Ultrashort Laser Pulses. Proceedings of the SPIE 5063:208–213. [6] Dausinger F (2003) Femtosecond Technology for Precision Manufacturing: Fundamental and Technical Aspects. RIKEN Review 50:77–82. [7] Li L, Achara C (2004) Chemical Assisted Laser Machining for the Minimisation of Recast and Heat Affected Zone. Annals of the CIRP 53/1:175–178. [8] Stephen A, Lilienkamp T, Metev S, Sepold G (2002) Laser-assisted Chemical Micromachining of Metals and Alloys. RIKEN Review 43:56–62. [9] Zhu D, Qu NS, Li HS, Zeng YB, Li DL, Qian SQ (2009) Electrochemical Micromachining of Microstructures of Micro Hole and Dimple Array. Annals of the CIRP 58/1:177–180. [10] Ali S, Hinduja S, Atkinson J, Pandya M (2009) Shaped Tube Electrochemical Drilling of Good Quality Holes. Annals of the CIRP 58/1:185–188. [11] Jo CH, Kim BH, Chu CN (2009) Micro Electrochemical Machining for Complex Internal Micro Features. Annals of the CIRP 58/1:181–184. [12] Curtis DT, Soo SL, Aspinwall DK, Sage C (2009) Electrochemical Superabrasive Machining of a Nickel-based Aeroengine Alloy Using Mounted Grinding Points. Annals of the CIRP 58/1:173–176. [13] Stephen A, Sepold G, Metev S, Vollertsen F (2004) Laser-induced Liquid-phase Jet-chemical Etching of Metals. Journal of Materials Processing Technology 149:536–540. [14] Hu¨gel H (1992) Strahlwerkzeug Laser—Eine Einfu¨hrung. Teubner, Stuttgart. [15] Gray . DE (1982) American Institute of Physics Handbook. McGraw-Hill, New York [16] Safonova LP, Pryahin AA, Fadeeva JA, Shmukler LE (2008) Viscosities, Refractive Indexes, and Conductivities of Phosphoric Acid in N,N-Dimethylformamide + Water Mixtures. Journal of Chemical Engineering Data 53:1381–1386.
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er. com/ci rp/ def a ult . asp
Mechanisms and processing limits in laser thermochemical machining A. Stephen *, F. Vollertsen (1) BIAS-Bremer Institut fuer angewandte Strahltechnik, Klagenfurter Str. 2, 28359 Bremen, Germany
A R T I C L E I N F O
A B S T R A C T
Keywords: Laser Etching Mechanism
Metallic microparts can be produced with high quality by laser thermochemical machining when the etching liquid is injected coaxially to the laser beam directly into the irradiated area. The basic mechanisms and limits of the process are described. It is shown that the reaction is temperature driven independent of the laser wavelength. A limiting factor is the diffusion of the anions identified by comparing experimentally determined and calculated diffusion coefficients for the reaction products. The machining quality with respect to aspect ratio, edge radius and roughness can be enhanced by increasing the velocity of the etching liquid. ß 2010 CIRP.
1. Introduction
2. Experimental
Laser machining is a flexible tool for structuring materials with high strength and hardness. In general, the domain for laser material processing techniques can be divided into three major classes involving only heating, melting and vaporising. Laser ablation mainly removes material as vapor, hence, needs delivery of a high power density within a very short interaction time. In industry lasers with nanosecond pulses are recognized as a rapid and efficient tool for machining micro-features into hard to machine materials. Laser machining using nanosecond pulses exhibits no material restrictions, if a suitable laser beam source is chosen [1]. A severe problem with laser ablation consists in the incompatibility of high ablation rates and good surface qualities [2]. High ablation rates are usually connected with strong mechanical damages of the surface and a significant heating of the material [3]. Using laser pulses in the femtosecond range melting could almost be avoided [4]. However, the process speed is low due to the low energies used [5]. If machining metals even femtosecond pulses can cause deleterious thermal effects and also melt can be observed when drilling holes [6]. Laser chemical removal, which allows surface heating without surface melting or vaporising, requires a low power density. Deleterious thermal effects, recast or redeposition of evaporated material can be significantly reduced by chemical assisted laser machining in salt solutions [7] or even avoided by a laser activation of chemical reactions [8]. Laser thermochemical etching of metals can be achieved in solutions of acids or bases using cw lasers in the VIS or NIR region. Compared to electrochemical machining, which also allows the processing of conductive materials regardless their hardness [9], the aspect ratio is much smaller [10], but better resolution [11] and surface roughness [12] can be achieved [13]. In this paper, the basic mechanisms and limits of the process, which can be used as an industrial example for the fabrication of superelastic micro-grippers made of the nickel–titanium alloy nitinol [13], are presented.
The major equipment for laser chemical machining consists of a laser, a chemical jet assembly and a positioning system, shown in Fig. 1. In brief, the beam of a continuous wave laser operating in its fundamental Gaussian mode is focused on the metal surface by a lens system with a focal length of 50 mm. As etching processes are transport limited, a fast exchange of the reaction products is an essential requirement to avoid saturation effects. Such efficient exchange is realized by the liquid jet. The liquid phase etching cell consists of two parts: a coaxial nozzle assembly and a basin. The nozzle, which injects the etching liquid coaxially to the laser beam directly into the irradiated area, can be adjusted laterally and in height with respect to the laser beam focus. Pumping the liquid through the nozzle leads to flow speeds between 2 and 20 m/s. The basin holds the workpiece and is mounted onto a computer controlled xyz-stage allowing a relative positioning resolution of 0.1 mm for the workpiece with respect to the nozzle and the incident laser beam over a distance of 100 mm. Measurements of the electrochemical potential can be performed by a usual three-electrode configuration which is integrated into the chemical cell. The working electrode is the metallic workpiece itself. The counter electrode is a circularly formed wire made of inert platinum, which is located in front of the nozzle. The reference electrode is a Saturated Calomel Electrode located inside the basin. Investigations of the laser thermochemical processing were performed using two different laser systems. The relevant specific properties of each system are listed in Table 1. Main differences which influence the surface temperature of the material are the laser power PL, laser wavelength l and the spot diameter d. Materials used for the investigations and their relevant specific properties are listed in Table 2. Relevant material parameters influencing the surface temperature are the reflectivity for a specific wavelength Ropt and the thermal conductivity K. While processing the workpieces were immersed in an etching liquid consisting of 5.6 M phosphoric acid (H3PO4) and 1.5 M sulfuric acid (H2SO4) at room temperature.
* Corresponding author. 0007-8506/$ – see front matter ß 2010 CIRP. doi:10.1016/j.cirp.2010.03.069
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
252
described by the heat conduction differential equation:
DTðx; y; z; tÞ
aq ðx; y; tÞð1 Ro pt Þeaz 1 @Tðx; y; z; tÞ ¼ L0 k @t K
(1)
where k is the material diffusivity, K the thermal conductivity, a the absorption coefficient and Ropt the wavelength dependent optical reflectivity of the material. In the one-dimensional case and assuming a constant flux density the surface temperature TSC derived from this equation for a semi-infinite solid body is: T SC ¼
ð1 Ro pt ÞqL0 d þ T0 2K
(2)
or as a function of the laser power: T SC ¼ Fig. 1. Experimental setup for laser thermochemical machining.
Table 1 Laser system specifications. Laser
l (nm)
PL (W)
d (mm)
Ar-ion Nd:YAG
514 1064
2.4 16
7.8 13.0
Laser spot diameter calculated by [14].
Table 2 Material specifications. Material
Ropt (1064 nm)
Ropt (514 nm)
K (W/m K)
Ni NiTi Steel 1.4301
0.75 0.69 0.63
0.69 0.63 0.58
90.9 9.0 16.3
Reflectivity and thermal conductivity values are taken from [15].
The machining result was characterized by the geometrical parameters defined in Fig. 2. The maximum removal depth hmax and width bmax, removed area Fgeo and edge radius Rgeo can be directly measured from prepared cross-sections. Therewith, the aspect ratio AR, edge sharpness Kgeo, removal rate yV with the known feed rate y can be determined. 3. Mechanisms 3.1. Temperature The temperature distribution T(x, y, z, t) in the material as a function of the laser light flux density at the surface qL0(x, y, t) is
4ð1 Ro pt ÞPL þ T0 2pKd
(3)
where d is the laser spot diameter and T0 is the initial temperature of the body. Furthermore, in case of the used metals and cw laser systems, the penetration depth of heat was assumed to be much larger than the penetration depth of light and the laser spot diameter. The respective surface temperatures for the Ar-ion and the Nd:YAG laser systems for different applied laser powers can be calculated using Eq. (3) and the specifications of the laser systems and materials from Tables 1 and 2. The cooling effect by the etching liquid is neglected in this case as it should show no difference for the two laser systems at equal flow speeds. Fig. 3 shows a plot of the removal rates yV normalized to the laser spot area Fd against the surface temperature for both laser systems for the material nickel. According to this, equal temperatures lead to equal normalized removal rates for different laser wavelength and spot diameters. Therefore, it has been proved, that the laser thermochemical removal depends only on the material surface temperature and not on the absorbed laser wavelength. If the processing speed of laser thermochemical machining is only dependent on the material surface temperature, this must be also reflected in the respective removal rates for materials with different thermal conductivities. Fig. 4 shows a plot of the removal rates normalized to the thermal conductivity of the material against the reflectivity dependent absorbed flux density for different materials using the Nd:YAG laser system. Therefore, the main influencing factor on the removal rate of a specific material is its thermal conductivity. Indeed, this applies at least to materials differing in their thermal properties (one order of magnitude in the thermal conductivity) but chemically similar as used in the presented investigations.
Fig. 2. Characteristic geometrical parameters of the machining result.
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
Fig. 3. Dependence of the removal rates normalized on the laser spot area on the calculated surface temperature for nickel using laser systems with different wavelengths.
Measurements of the temperature dependent chemical potential show for both laser systems and the different materials a cathodic shift of the potential. Due to the chemical dissolution of the material according to Eq. (4) the activity of the educts (metal and protons) decreases, whereas the activity of the products (metal ions and hydrogen) increases. Me þ 2Hþ ! Me2þ þ H2 "
(4)
According to the Nernst equations the increase of the metal ion activity results in a positive change of the potential, while the increase of the proton activity causes a decrease of the potential. Therefore, the protons are essential for the formation of the electrochemical potential of the reaction, i.e. the proton activity is the driving force for laser thermochemical machining. 3.2. Diffusion To identify the limiting mechanism of the processing speed, the temporal evolution of the maximum removal depth hmax was investigated. Fig. 5 shows a double logarithmic plot of the temporal derivative of the removal depth (dhmax/dt) versus the removal depth itself. For small depths the differentiation causes noise around a constant value, but for larger depths a monotone decrease with a gradient of m = 1 can be observed, i.e. the reaction rate is inversely proportional to the removal depth: dhmax D ¼ f ðhmax Þ ¼ hmax dt
(5)
253
Fig. 5. Double logarithmic plot of the temporal derivative of the maximum removal depth versus the maximum removal depth itself for NiTi using an Nd:YAG laser system.
The reaction rate for a heterogeneous chemical reaction with mass transport limitation is a function of the diffusion coefficient D and the thickness of the Nernst layer d: dhmax D / dt d
(6)
Therefore, the processing speed in laser thermochemical machining is diffusion limited from a certain removal depth. Diffusion coefficients in liquids can be described by the Stokes– Einstein equation: D¼
kB T 6phR0
(7)
where kB = 1.38 J/K is the Boltzmann constant, T the absolute temperature, h the dynamic viscosity of the liquid and R0 the radius of the diffusing particles. As the dynamic viscosity is a function of the temperature the dependence of the diffusion coefficient on the temperature is nonlinear. The dynamic viscosity of liquids can be described by the Arrhenius–Andrade equation: E (8) h ¼ h0 exp A RT where R = 8.314 J/mol K is the universal gas constant, h0 a material specific constant and EA the activation energy. The material constant and the activation energy can be calculated from tabular values of the viscosity for different temperatures. The viscosity for 5 M phosphoric acid at room temperature is 2.8 mN s/m2 [16]. The calculated temperature dependent diffusion coefficients for the reaction educts and products as well as the experimental ones are shown in Fig. 6. For the calculation Eq. (7) was used with atomic respectively covalence radii of hydrogen (30 pm), Ni/Ti (135/ 140 pm), phosphate (179 pm) and oxygen (60 pm) [15]. Accordingly, the transport of the anions is the limiting reaction sub-step. 4. Processing limits For the evaluation of the processing limits with respect to the machining quality the geometrical parameters aspect ratio AR, edge sharpness Kgeo, and roughness Ra according to Fig. 2 were investigated. For a general expression of the machining quality these geometrical parameters were normalized to their highest value and the following quality number defined: quality number ¼
Fig. 4. Dependence of the removal rates normalized on the thermal conductivity on the absorbed laser flux density for different materials using an Nd:YAG laser system.
ARnorm K geo;norm Ra;norm
(9)
The dependence of this quality number on the maximum removal depth is shown in Fig. 7. In principle, the machining
254
A. Stephen, F. Vollertsen / CIRP Annals - Manufacturing Technology 59 (2010) 251–254
quality decreases with increasing removal depth. Nevertheless, at the same removal depth a higher machining quality can be achieved if higher flow speeds of the etching liquid are applied. This is an important fact as for the specification of a machining result often the achievable quality for a given structure depth is of importance for its application. A machined cut edge in nitinol using a laser power of 5 W, a feed rate of 10 mm/s and a flow speed of 10 m/s is shown in Fig. 8. The machining results in an aspect ratio of 2, an edge radius of 9 mm and a roughness of 0.3 mm, which equals the quality number of 0.15. Therefore, even at relatively low quality numbers according to Eq. (9) a good machining result can be achieved by laser thermochemical machining. 5. Conclusions
Fig. 6. Calculated diffusion coefficients for the reaction educts/products and the experimental values in dependence on the temperature for the chemical dissolution of NiTi in phosphoric acid.
The laser thermochemical machining in a reactive fluid jet is driven by the temperature dependent proton activity of a redox reaction. Thus, the laser supports the kinematic of dissolution and has no melting effects. The radiation wavelength has an indirect influence by the differences in the absorptivity of the machined material, but no direct one. For the investigated different materials, namely metals which form a native oxide layer, the relation of their thermal conductivities is reflected in the achievable processing speeds. The processing speed is limited by the diffusion of the anions formed during the redox reaction, in this case phosphate ions, from a certain depth of removal on. The machining quality with respect to the aspect ratio, the edge sharpness and the surface roughness can be enhanced by increasing the flow speed of the etching liquid. Acknowledgements The authors thank the German Research Foundation (DFG) for funding the project Vo530/14-3 and the subproject A5 of the Collaborative Research Centre 747 (SFB 747). References
Fig. 7. Quality number in dependence on the maximum removal depth for different flow speeds of the etching liquid.
Fig. 8. Machined cut edge in a 200 mm thick nitinol foil.
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