- Email: [email protected]
Modeling and Simulation of the Microstructure Evolution of 42CrMo4 Steel During Electrochemical Machining
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 68 (2018) 505 – 510
19th CIRP Conference on Electro Physical and Chemical Machining, 23-27 April 2018, Bilbao, Spain
Modeling and Simulation of the Microstructure Evolution of 42CrMo4 Steel during Electrochemical Machining Klocke, F.a,b; Harst, S.a*; Zeis, M.b; Klink, A.a a
Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Steinbachstraße 19, 52074 Aachen, Germany b Fraunhofer-Institute for Production Technology IPT, Steinbachstraße 17, 52074 Aachen, Germany
* Corresponding author. Tel.: +49-241-80-28038; fax: +49-241-80-22293. E-mail address: [email protected]
Abstract Machining independently of mechanical material properties like hardness or high temperature strength is one mayor advantage of the electrochemical machining process (ECM). Additionally, high material removal rates can be achieved in combination with best surface integrities. Nevertheless, one limiting factor in the resulting surface integrity can be a significantly varying dissolution rate of material phases in a multi phase material during ECM. These differences in the dissolution rates determine the surface topography as well as the achievable surface roughness. However, this behavior cannot be forecasted up to now. For that reason, this paper presents a model for the prediction of the microstructure evolution as well as simulation results regarding the influence of the electrochemical machining process on resulting surface topography for the ferritic perlitic steel 42CrMo4 in a passivating electrolyte system. With the help of the model, the evolution of surface topography can be predicted and will be analyzed for different process parameters and various initial microstructures. 2018The The Authors. Published by Elsevier ©©2018 Authors. Published by Elsevier B.V. ThisB.V. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining. Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining
Keywords: ECM, Microstructure, Process Signature, 42CrMo4, Process Simulation
1. Introduction Setting up the surface integrity and targeted rim zone properties of components during machining processes a priori is one mayor challenge in manufacturing technology nowadays. Due to the chemical based material removal in electrochemical machining (ECM), the development of some undesirable rim zone changes, like white layers or heat affected zones, can be avoided, as one mayor advantage of this manufacturing technology [1, 2]. Besides this, process induced modifications in the workpiece rim zone during electrochemical machining are mainly caused due to differences in dissolution behavior of the individual material phases within the machined alloy [3]. Consequently, the machining process as well as the initial microstructure determine the resulting properties of the rim zone like surface topography, roughness and residual stress on grain scale [4, 5]. These changes in rim zone characteristics of manufactured parts influence decisively the functional properties of these
components for example the hardness or the residual stresses in application. Increasing loads on manufactured components during application require improved and especially targeted rim zone properties from the manufacturing process. However, this inverse problem of the manufacturing technology – to calculate necessary process parameters from the desired rim zone specifications – is not solved yet for ECM and most other manufacturing technologies. For this reason, most of the time these manufacturing processes have to be set up in time and cost intensive iteration cycles. This inverse problem is investigated by means of an approach called process signatures. These signatures allow the defined setup of rim zone properties in advance and thus ensuring components functionality during its lifetime [6]. While the macroscopic electrochemical shaping process can be forecasted within industrial manufacturing tolerances by numerical simulation nowadays [7, 8], there are hardly any studies describing the local evolution of surface topography
2212-8271 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining doi:10.1016/j.procir.2017.12.082
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neither analytically nor empirically. However, forecasting this evolution of topography and consequently surface roughness is decisive for reaching the required surface integrity in ECM and thus, of high value [9, 10]. For this reason, the results of a simulation model for rim zone changes in ECM based on the concept of process signatures are introduced in this paper. Nomenclature α ε μ ϕ κ E J s S T t U vA vf w z
angle of the grain / ° electrode potential / V chemical potential / (J/mol) electrical potential / V electrolyte conductivity / (mS/cm) electrical field strength / (V/m) current density / (A/mm²) working gap / µm entropy / (J/K) temperature / K time / s applied working potential / V dissolution rate / (mm/min) feed rate / (mm/min) width of material lamellae / electrochemical valence / -
Thus, the spatial gradient of the chemical potential μj and the spatial gradient of the electric potential ϕj scaled by the chemical valence zj and Faraday´s constant F are the two mayor driving forces in ECM [12], whereby, the spatial gradient of the electrical potential is equal to local electrical field strength E. For that reason, the chemical potential μ and its spatial gradient as well as the local field strength E will be used to forecast material modifications for ECM-processes in this work. To show the applicability of this concept, a process signature component for the ferrite depletion during the machining of steel will be calculated with an extended numerical model of the ECM-process. 3. Simulation model
2. Concept of process signature The concept of process signatures shall overcome the lack of knowledge to set up rim zone properties a priori. To achieve this aim the changes of rim zone properties are described based on local material loadings, which cause these changes (e. g. Fig. 1).
It was shown that classical models of the ECM process – using only linear electrical element – are unable to predict the inhomogeneous dissolution behavior of a multi-phase materials [13–15]. For that reason, an extended model using semiconductor elements was build up to simulate resulting surface topographies of multi-phase materials. Due to the arrangement of schottky contact, semiconductor and ohmic contact at the anode, the system is capable to model the several potential drops due to the chemical reactions themselves, the oxide layer and the vicious sublayer (e. g. Fig. 2). Those three effects dominate the overall potential drop at the anode and distribute finally the local material dissolution rate [16]. Cathode
Machining Process
Electrolyte Initial state
Energy input
Energy dissipation
Material loading
Material modification
Output state
Process signature
Schottky contact Semiconductor Anode
Ohmic contact
Fig. 1. Schematic structure of the model including the semiconductor layer.
Transferring this concept to the process of electrochemical machining to describe occurring rim zone modifications, the first mayor task is to identify the process induced material loadings. One way to identify these loadings is to analyse physical parameters, which cause changes in the system thermodynamically. From this thermodynamic point of view every irreversible change in the system causes a production of entropy [11]. The entropy balance for an isothermal system results in the following terms of entropy S [12]: ݀ܵ ܶ ڄ ൌ ܬ ܺ ڄ Ǥ (1) ݀ݐ
In equation (1) Jj are the several fluxes in the system and Xj the corresponding driving forces. Analyzing this production term for an ECM system, the driving force follows as [12]: ݀ߤ ݀ߤ ݀Ԅ (2) ܺ ൌ െ െ ݖ ڄ ܨ ڄ ൌെ െ ݖ ܧ ڄ ܨ ڄǤ ݀ݔ ݀ݔ
Fig. 2. Schematic structure of the model including the semiconductor layer [13].
The size of the semiconductor layer is in the order of some ten nanometers and moves in the direction of dissolution during the ECM-process [17]. For this reason, effects of the several phases can be computed spatially resolved on the grain scale. The numerical system was solved using the extended simulation model implanted in COMSOL Multiphysics, due to the opportunity to compute the electrochemical system with most relevant physical effects [13, 18] (e. g. Figure 3). To ensure the independency of the computed solution from the chosen numerical grid, the grid convergence index was used [19]. For this purpose, the maximum failure due to the grid is less than two percent. Referencing to the results later on, this
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Ferrite
wFe
wFe3 C
J / (A/mm²) 3 2 1
0 Δh
r
8
Fig. 3. Distribution of current density at the beginning of the machining process (upper part) and at equal dissolution rates (lower part) [13].
Figure 3 shows that the electrical streamlines (black) are curved near the cementite lamellae due to the higher nobility of this material phase. Due to this fact, the more ignoble ferrite phase is dissolved faster and depleted until the electrical resistance of the electrolyte balances this fact. Thus, along the ECM process the differences in the dissolution rate between the two material phases decrease until a nearly stationary level Δh is reached. From this stationary level, the depletion of the more ignoble phase and resulting surface roughness can be calculated for example. The set-up of the model is nearly independent of chosen material and electrolyte system. To discuss and to proof the functionality of the developed model, it is applied to the following system (Table 1). Most of the other influencing properties are varied in the results chapter. Table 1. Boundary conditions for the simulation. Property
Unit
Value
Workpiece material
-
42CrMo4 / AISI 4140 in a ferrite / pearlite structure
Simulated grain
-
Pearlite consisting of ferrite (Fe) and cementite Fe3C
Cathode material
-
Brass
Electrolyte salt
-
NaNO3
Salt concentration
wt. %
21
Temperature
°C
36
4. Results The classical DC-ECM process has two mayor process parameters – influencing the material removal – feed rate vf and applied external voltage U. Effects of both parameters to
U = 18 V κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm wFe3 C = 2 µm
6 4 2
0 5E+06 1E+07 1.5E+07 2E+07 2.5E+07 Maximum electric field strength E / (V/m)
t1 > 0 s
3 μm
Fig. 4. Height difference between ferrite and cementite lamellae as a function of the occurring electrical field strength
From Figure 4 it is recognizable that with increasing maximum field strength the height difference between the two material phases lowers. Interpreting this fact from the process parameters point of view, the maximum field strength increases with an increasing feed rate vf. This electrochemical behavior corresponds qualitively very good to experimental examinations of this material [4, 20]. To analyze the qualitive accordance of these simulation results, the height difference can also be plotted as a function of the local current density J. But, as the current density is normally used with the unit A/mm² and the simulated area is much less than one square millimeter, this seems to be not the most useful notation for further examinations (Figure 5). 8 Height difference Δh / µm
3 μm
Cementite
t0 = 0 s
working gap size and surface roughness are well known and allow a discussion of the applicability of this model. Thus first of all the feed rate is varied and the resulting height differences between cementite and ferrite lamellae is analyzed as a function of the occurring maximum electrical field strength E (Figure 4). For this part of the work, the size of the grain was kept constant with a width of five micrometer for the ferrite lamellae and two micrometer for the cementite lamellae. Height difference Δh / µm
is a variance in height less than ten nanometers and thus, sufficient to discuss only the physical relevant effects.
U = 18 V κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm wFe3 C = 2 µm
6 4 2
0 0
0.5 1 1.5 2 Current density J / (A/mm²)
2.5
Fig. 5 Height difference between ferrite and cementite lamellae as a function of resulting current density
Klocke F. et al. / Procedia CIRP 68 (2018) 505 – 510
From Figure 5 it is recognizable, that both approaches – the classical representation with help of the current density J and the signature approach with the electric field strength E – lead to quite similar graphs for the height difference, which is also in accordance with the Maxwell equations [21]. As they are equal, the approach of the process signature seems to be good to calculate material modifications more casual as a function of the local material loading. Nevertheless, the quantative agreement between the computed height differences does not fit to the classical mean roughness Ra. Instead of this, the numerical value corresponds much better to the roughness depth Rz and the difference between experiment and simulation is less than 10 percent [4]. This fact is not a shortcoming of the physical model itself, but due to the fact that only one grain is simulated in this numerical model. The carbon content – which is responsible for the cementite evolution – is only 0.42 per cent for 42CrMo4, leading to a cementite content of about 7 percent cementite accumulated in several pearlite grains. Consequently, there are areas with almost pure ferrite dissolving much more homogeneous and thus, lowering the value of the mean surface roughness. Hence, the simulation results correspond quite well to roughness depth Rz of this material and the numerical simulation has to be extended to several grains to reproduce also mean surface roughness values Ra. Another limiting fact of this simulation model is the region of very low field strength. The effect of electrochemical polishing and its electrochemical mechanisms is not integrated yet to this model, but also of minor relevance for the simulation of the sinking ECM-process [1]. Nevertheless, it is possible to calculate the change of ferrite and cementite content for every variation of feed rate or applied voltage in one grain with help of this model (Fig. 6). This allows forecasting changes in downstream hardening processes due to the ECM process for example.
Change of phase concentration Δc / %
40 30 20
21 wt. % NaNO3 κ = 160 mS/cm Cementite (Fe3 C) Ferrite (Fe) Averaging depth 20 µm
From Figure 6 it is recognizable, that ferrite is depleted in the pearlite grain, while the ratio of cementite and thus carbon increases. The depletion of ferrite is less compared to the accumulation of cementite due to the higher initial content of ferrite (c0,Fe) compared to cementite (c0,Fe3C) in this grain. Nevertheless, the overall value of depletion and accumulation depends on the volume of averaging and thus on a statistical method. Besides the influences of the process on one special grain, it is necessary to discuss, if the chosen spatial grain dimensions are representable for the alloy 42CrMo4 in a normalized heat treatment. For this reason, the surface of a raw material specimen is analyzed experimentally by SEM regarding the surface ratio of the grain size distribution (Figure 7). Thereby, the surface ratio a of one grain diameter d is the part of the surface with grains of this special size. Cementite Grain diameter d
Ferrite
Pearlite
50 µm
Ferrite
8 Surface ratio a / %
508
6 4 2
42CrMo4 normalized
0 0
10 20 30 Grain diameter d / µm
40
Fig. 7 SEM-image of normalized 42CrMo4 steel (upper part) and Surface ratio of the different grain sizes (lower part)
10 0 -10
co,Fe = 78.95 % c0,Fe3C = 21.05 %
-20 5E+06 1E+07 1.5E+07 2E+07 2.5E+07 Maximum Electric field strength E / (V/m) Fig. 6 Change of phase concentration as a function of the maximum electrical field strength in one pearlite grain
The distribution of grain sizes within the alloy is not homogeneous, but a classical Gaussian distribution with a maximum for grains with a diameter about twenty microns. Thus, the assumed size of the grain in the simulation above – the sum of the width of the several lamellae – was within this range und following eligible for the analysis of the model. As the grains are distributed over this huge range, it is necessary to examine the influence of the grain size on the roughness. Within one pearlite grain, the ratio of cementite and ferrite can differ. Therefore, first of all the influence of varying width of ferrite lamellae wFe at constant width of the cementite lamellae wFe3C is analyzed with help of the simulation model (Fig. 8).
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1.7 U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe3 C = 2 µm
1.6 1.5 1.4 0
5 10 15 20 Width of the ferrite lamellae wFe / µm
Fig. 8. Influence of the width of ferrite lamellae in the pearlite grain on resulting surface roughness
Figure 8 shows that the height difference and thus, the resulting surface roughness varies with the change of the ferrite lamellae width. Nevertheless, within the examined range the influence of the size is much smaller compared to the influence of the electric field strength (Fig. 4 and Fig. 8). For a range between 2 µm and 17 µm, the correlation of ferrite width and height difference follows quite well a linear trend. For grains smaller than two micrometer, the height difference decreases stronger compared to linear. In this area, the electric field lines at the cementite lamellae repress the field lines to the ferrite, due to which the ferrite is dissolved less (Figure 3). Within a pearlite grain, also the width of the cementite lamellae wFe3C can differ. For that reason, the influence of that width at a constant ferrite width wFe is examined within the spatial dimension distribution of the 42CrMo4 (Fig. 9 and Fig. 7). Height difference Δh / µm
1.9
1.76 Height difference Δh / µm
1.8
Due to this, the significance of the simulation model in the region is limited and not necessarily valid for very small grains. Analogue to the variation of one lamellae size, the overall grain size varies in an alloy. To examine this effect, the overall ratio of the width of the two lamellae is kept constant, while simulating a variation of both sizes (Fig. 10). U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe / w Fe3 C = 2.5
1.74 1.72
1.7
1.68 2
3 4 5 Width of the ferrite lamellae wFe / µm
6
Fig. 10. Influence of the grain size on resulting roughness
Like in both former variations, the examination in Figure 10 shows that the roughness increases with increasing grain size. Thus, the conclusion from these three series is that, the influence of the grain size is smaller than the influence of the machining parameters. Nevertheless, the maximum grain size determines the achievable surface topography at fixed machining parameters. Finally, not all grains are orientated parallel to the machining direction. For this reason, the influence of an angle α between machining direction and grain is examined. Whereby at α = 0° the grain is orientated in the machining direction (Figure 11). 1.75
1.8
1.7 1.6 1.5
U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm
1.4 0 2 4 6 8 Width of the cementite lamellae wFe3 C / µm Fig. 9. Influence of the width of cementite lamellae in the pearlite grain on resulting surface roughness
From Figure 9 it can be seen, that the influence of cementite lamellae width on resulting surface roughness is also nearly linear in the observed range. For smaller cementite lamellae, the influence of the initial assumed radius at the edge of the lamellae becomes very strong, because the grains are dissolved from the side more than from the top (Fig. 3).
Height difference Δh / µm
Height difference Δh / µm
1.9
U = 18 V v F = 1 mm/min κ = 160 mS/cm
1.7 1.65
1.6 21 wt. % NaNO3 wFe / w Fe3 C = 2.5 wFe = 5 µm
1.55 1.5 0
5 10 15 Angle of the grain α / °
20
Fig. 11 Influence of the grain angle on resulting roughness
Figure 11 shows that with an increasing angle between the grain orientation and the machining direction the height difference decreases. These results correspond as well to the expectations, as with an increasing angle, the electric
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streamlines have to be bend more at the cementite lamellae and thus the dissolution of ferrite is inhibited. The results of the examinations showed that the electrochemical process and the achievable surface roughness strongly depend on the microstructure. For a given limiting surface roughness of a workpiece, it is a prerequisite to analyze the grain size to set up the corresponding maximum field strength to achieve this roughness. 4. Summary and Outlook Within this paper, the electrical field strength as mayor material loading in ECM processes was deduced thermodynamically. It was shown, that with the help of this field strength, material modifications – like surface roughness – can be plotted physical valid. Based on this fact and an advanced simulation model, changes in a pearlite grain of the normalized steel 42CrMo4 were simulated and it was shown, that the results correspond to previous experimental examinations. Finally, the influence of varying grain size on resulting surface topography was simulated and analyzed. The model will be extended in future to simulate the electrochemical material dissolution of several grains to forecast a representative material surface. With help of this numerical model, also conclusions regarding the average surface roughness should be possible. Furthermore, the influence of the chemical potential as the secondary main material loading will be transferred into the model. Due to this, several electrolyte systems can be analyzed numerically, to obtain the optimum combination of electrolyte and workpiece material. Acknowledgements The authors wish to thank the German Research Foundation (DFG) for funding the Collaborative Research Center SFB/ TRR 136 “Function Oriented Manufacturing Based on Characteristic Process Signatures” (Bremen, Aachen, Oklahoma), subproject F03. References [1] Klocke, F., König, W. Fertigungsverfahren: Abtragen, Generieren und Lasermaterialbearbeitung, 4th ed. VDIVerl. [et al.], Düsseldorf [and others], 2007. [2] McGeough, J.A. Principles of electrochemical machining. Chapman and Hall; Halsted Press Division, Wiley, London, New York, 1974. [3] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Influence of Material Microstructure on the Electrochemical Machinability of Steel 42CrMo4. Proceedings INSECT, 2015, 43–50. [4] Baehre, D., Ernst, A., Weißhaar, K., Natter, H., Stolpe, M., Busch, R. Electrochemical Dissolution Behavior of Titanium and Titanium-based Alloys in Different Electrolytes. Procedia CIRP 42, 2016, 137–142. [5] Speidel, A., Mitchell-Smith, J., Walsh, D.A., Hirsch, M., Clare, A. Electrolyte Jet Machining of Titanium Alloys
Using Novel Electrolyte Solutions. Procedia CIRP 42, 2016, 367–372. [6] Brinksmeier, E., Klocke, F., Lucca, D.A., Sölter, J., Meyer, D. Process Signatures – a new approach to solve the inverse surface integrity problem in machining processes. Procedia CIRP 13, 2014, 429–434. [7] Hinduja, S., Kunieda, M. Modelling of ECM and EDM processes. CIRP Annals - Manufacturing Technology 62 (2), 2013, 775–797. [8] Klocke, F., Zeis, M., Klink, A. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology, 2015. [9] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Surface integrity in electrochemical machining processes: An analysis on material modifications occurring during electrochemical machining. Proceedings of the IMechE 45, 2017. [10] Rajurkar, K.P., Hewidy, M.S. Effect of grain size on ECM performance. Journal of Mechanical Working Technology 17, 1988, 315–324. [11] Lucas, K. Thermodynamik: Die Grundgesetze der Energie- und Stoffumwandlungen, 3rd ed., Springer, Berlin, 2001. [12] Nagy, Z. Applications of non-equilibrium thermodynamics to the theory of overvoltage. Electrochimica Acta 22 (2), 1977, 191–195. [13] Klocke, F., Harst, S., Karges, F., Zeis, M., Klink, A. Modeling of the Electrochemical Dissolution Process for a Two-phase Material in a Passivating Electrolyte System. Procedia CIRP 58, 2017, 169–174. [14] Kozak, J., Zybura-Skrabalak, M. Some Problems of Surface Roughness in Electrochemical Machining (ECM). Procedia CIRP 42, 2016, 101–106. [15] Lohrengel, M.M., Schultze, J.W., Speckmann, H.D. The equivalent circuit diagram of oxide films with a limited potential drop. Electrochimica – Acta 31 (1), 1986, 123– 126. [16] Hamann, C.H., Vielstich, W. Elektrochemie, 4th completely revised and updated ed. Wiley-VCH, Weinheim, 2005. [17] Lohrengel, M.M., Rataj, K.P., Münninghoff, T. Electrochemical Machining - mechanisms of anodic dissolution. Electrochimica Acta 201, 2016, 348–353. [18] Zeis, M. Modellierung des Abtragprozesses der elektrochemischen Senkbearbeitung von Triebwerksschaufeln. Apprimus, Aachen, 2015. [19] Wilcox, D.C. Formulation of the k-w Turbulence Model Revisited. AIAA Journal 46 (11), 2008, 2823–2838. [20] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Material Loadings during Electrochemical Machining (ECM) - a First Step for Process Signatures. Key Engineering Materials, 2015. [21] Klocke, F., Zeis, M., Harst, S., Klink, A., Veselovac, D., Baumgärtner, M. Modeling and Simulation of the Electrochemical Machining (ECM) Material Removal Process for the Manufacture of Aero Engine Components. Procedia CIRP 8, 2013, 265–270.
ScienceDirect Procedia CIRP 68 (2018) 505 – 510
19th CIRP Conference on Electro Physical and Chemical Machining, 23-27 April 2018, Bilbao, Spain
Modeling and Simulation of the Microstructure Evolution of 42CrMo4 Steel during Electrochemical Machining Klocke, F.a,b; Harst, S.a*; Zeis, M.b; Klink, A.a a
Laboratory for Machine Tools and Production Engineering (WZL) of RWTH Aachen University, Steinbachstraße 19, 52074 Aachen, Germany b Fraunhofer-Institute for Production Technology IPT, Steinbachstraße 17, 52074 Aachen, Germany
* Corresponding author. Tel.: +49-241-80-28038; fax: +49-241-80-22293. E-mail address: [email protected]
Abstract Machining independently of mechanical material properties like hardness or high temperature strength is one mayor advantage of the electrochemical machining process (ECM). Additionally, high material removal rates can be achieved in combination with best surface integrities. Nevertheless, one limiting factor in the resulting surface integrity can be a significantly varying dissolution rate of material phases in a multi phase material during ECM. These differences in the dissolution rates determine the surface topography as well as the achievable surface roughness. However, this behavior cannot be forecasted up to now. For that reason, this paper presents a model for the prediction of the microstructure evolution as well as simulation results regarding the influence of the electrochemical machining process on resulting surface topography for the ferritic perlitic steel 42CrMo4 in a passivating electrolyte system. With the help of the model, the evolution of surface topography can be predicted and will be analyzed for different process parameters and various initial microstructures. 2018The The Authors. Published by Elsevier ©©2018 Authors. Published by Elsevier B.V. ThisB.V. is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining. Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining
Keywords: ECM, Microstructure, Process Signature, 42CrMo4, Process Simulation
1. Introduction Setting up the surface integrity and targeted rim zone properties of components during machining processes a priori is one mayor challenge in manufacturing technology nowadays. Due to the chemical based material removal in electrochemical machining (ECM), the development of some undesirable rim zone changes, like white layers or heat affected zones, can be avoided, as one mayor advantage of this manufacturing technology [1, 2]. Besides this, process induced modifications in the workpiece rim zone during electrochemical machining are mainly caused due to differences in dissolution behavior of the individual material phases within the machined alloy [3]. Consequently, the machining process as well as the initial microstructure determine the resulting properties of the rim zone like surface topography, roughness and residual stress on grain scale [4, 5]. These changes in rim zone characteristics of manufactured parts influence decisively the functional properties of these
components for example the hardness or the residual stresses in application. Increasing loads on manufactured components during application require improved and especially targeted rim zone properties from the manufacturing process. However, this inverse problem of the manufacturing technology – to calculate necessary process parameters from the desired rim zone specifications – is not solved yet for ECM and most other manufacturing technologies. For this reason, most of the time these manufacturing processes have to be set up in time and cost intensive iteration cycles. This inverse problem is investigated by means of an approach called process signatures. These signatures allow the defined setup of rim zone properties in advance and thus ensuring components functionality during its lifetime [6]. While the macroscopic electrochemical shaping process can be forecasted within industrial manufacturing tolerances by numerical simulation nowadays [7, 8], there are hardly any studies describing the local evolution of surface topography
2212-8271 © 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the scientific committee of the 19th CIRP Conference on Electro Physical and Chemical Machining doi:10.1016/j.procir.2017.12.082
506
Klocke F. et al. / Procedia CIRP 68 (2018) 505 – 510
neither analytically nor empirically. However, forecasting this evolution of topography and consequently surface roughness is decisive for reaching the required surface integrity in ECM and thus, of high value [9, 10]. For this reason, the results of a simulation model for rim zone changes in ECM based on the concept of process signatures are introduced in this paper. Nomenclature α ε μ ϕ κ E J s S T t U vA vf w z
angle of the grain / ° electrode potential / V chemical potential / (J/mol) electrical potential / V electrolyte conductivity / (mS/cm) electrical field strength / (V/m) current density / (A/mm²) working gap / µm entropy / (J/K) temperature / K time / s applied working potential / V dissolution rate / (mm/min) feed rate / (mm/min) width of material lamellae / electrochemical valence / -
Thus, the spatial gradient of the chemical potential μj and the spatial gradient of the electric potential ϕj scaled by the chemical valence zj and Faraday´s constant F are the two mayor driving forces in ECM [12], whereby, the spatial gradient of the electrical potential is equal to local electrical field strength E. For that reason, the chemical potential μ and its spatial gradient as well as the local field strength E will be used to forecast material modifications for ECM-processes in this work. To show the applicability of this concept, a process signature component for the ferrite depletion during the machining of steel will be calculated with an extended numerical model of the ECM-process. 3. Simulation model
2. Concept of process signature The concept of process signatures shall overcome the lack of knowledge to set up rim zone properties a priori. To achieve this aim the changes of rim zone properties are described based on local material loadings, which cause these changes (e. g. Fig. 1).
It was shown that classical models of the ECM process – using only linear electrical element – are unable to predict the inhomogeneous dissolution behavior of a multi-phase materials [13–15]. For that reason, an extended model using semiconductor elements was build up to simulate resulting surface topographies of multi-phase materials. Due to the arrangement of schottky contact, semiconductor and ohmic contact at the anode, the system is capable to model the several potential drops due to the chemical reactions themselves, the oxide layer and the vicious sublayer (e. g. Fig. 2). Those three effects dominate the overall potential drop at the anode and distribute finally the local material dissolution rate [16]. Cathode
Machining Process
Electrolyte Initial state
Energy input
Energy dissipation
Material loading
Material modification
Output state
Process signature
Schottky contact Semiconductor Anode
Ohmic contact
Fig. 1. Schematic structure of the model including the semiconductor layer.
Transferring this concept to the process of electrochemical machining to describe occurring rim zone modifications, the first mayor task is to identify the process induced material loadings. One way to identify these loadings is to analyse physical parameters, which cause changes in the system thermodynamically. From this thermodynamic point of view every irreversible change in the system causes a production of entropy [11]. The entropy balance for an isothermal system results in the following terms of entropy S [12]: ݀ܵ ܶ ڄ ൌ ܬ ܺ ڄ Ǥ (1) ݀ݐ
In equation (1) Jj are the several fluxes in the system and Xj the corresponding driving forces. Analyzing this production term for an ECM system, the driving force follows as [12]: ݀ߤ ݀ߤ ݀Ԅ (2) ܺ ൌ െ െ ݖ ڄ ܨ ڄ ൌെ െ ݖ ܧ ڄ ܨ ڄǤ ݀ݔ ݀ݔ
Fig. 2. Schematic structure of the model including the semiconductor layer [13].
The size of the semiconductor layer is in the order of some ten nanometers and moves in the direction of dissolution during the ECM-process [17]. For this reason, effects of the several phases can be computed spatially resolved on the grain scale. The numerical system was solved using the extended simulation model implanted in COMSOL Multiphysics, due to the opportunity to compute the electrochemical system with most relevant physical effects [13, 18] (e. g. Figure 3). To ensure the independency of the computed solution from the chosen numerical grid, the grid convergence index was used [19]. For this purpose, the maximum failure due to the grid is less than two percent. Referencing to the results later on, this
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Ferrite
wFe
wFe3 C
J / (A/mm²) 3 2 1
0 Δh
r
8
Fig. 3. Distribution of current density at the beginning of the machining process (upper part) and at equal dissolution rates (lower part) [13].
Figure 3 shows that the electrical streamlines (black) are curved near the cementite lamellae due to the higher nobility of this material phase. Due to this fact, the more ignoble ferrite phase is dissolved faster and depleted until the electrical resistance of the electrolyte balances this fact. Thus, along the ECM process the differences in the dissolution rate between the two material phases decrease until a nearly stationary level Δh is reached. From this stationary level, the depletion of the more ignoble phase and resulting surface roughness can be calculated for example. The set-up of the model is nearly independent of chosen material and electrolyte system. To discuss and to proof the functionality of the developed model, it is applied to the following system (Table 1). Most of the other influencing properties are varied in the results chapter. Table 1. Boundary conditions for the simulation. Property
Unit
Value
Workpiece material
-
42CrMo4 / AISI 4140 in a ferrite / pearlite structure
Simulated grain
-
Pearlite consisting of ferrite (Fe) and cementite Fe3C
Cathode material
-
Brass
Electrolyte salt
-
NaNO3
Salt concentration
wt. %
21
Temperature
°C
36
4. Results The classical DC-ECM process has two mayor process parameters – influencing the material removal – feed rate vf and applied external voltage U. Effects of both parameters to
U = 18 V κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm wFe3 C = 2 µm
6 4 2
0 5E+06 1E+07 1.5E+07 2E+07 2.5E+07 Maximum electric field strength E / (V/m)
t1 > 0 s
3 μm
Fig. 4. Height difference between ferrite and cementite lamellae as a function of the occurring electrical field strength
From Figure 4 it is recognizable that with increasing maximum field strength the height difference between the two material phases lowers. Interpreting this fact from the process parameters point of view, the maximum field strength increases with an increasing feed rate vf. This electrochemical behavior corresponds qualitively very good to experimental examinations of this material [4, 20]. To analyze the qualitive accordance of these simulation results, the height difference can also be plotted as a function of the local current density J. But, as the current density is normally used with the unit A/mm² and the simulated area is much less than one square millimeter, this seems to be not the most useful notation for further examinations (Figure 5). 8 Height difference Δh / µm
3 μm
Cementite
t0 = 0 s
working gap size and surface roughness are well known and allow a discussion of the applicability of this model. Thus first of all the feed rate is varied and the resulting height differences between cementite and ferrite lamellae is analyzed as a function of the occurring maximum electrical field strength E (Figure 4). For this part of the work, the size of the grain was kept constant with a width of five micrometer for the ferrite lamellae and two micrometer for the cementite lamellae. Height difference Δh / µm
is a variance in height less than ten nanometers and thus, sufficient to discuss only the physical relevant effects.
U = 18 V κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm wFe3 C = 2 µm
6 4 2
0 0
0.5 1 1.5 2 Current density J / (A/mm²)
2.5
Fig. 5 Height difference between ferrite and cementite lamellae as a function of resulting current density
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From Figure 5 it is recognizable, that both approaches – the classical representation with help of the current density J and the signature approach with the electric field strength E – lead to quite similar graphs for the height difference, which is also in accordance with the Maxwell equations [21]. As they are equal, the approach of the process signature seems to be good to calculate material modifications more casual as a function of the local material loading. Nevertheless, the quantative agreement between the computed height differences does not fit to the classical mean roughness Ra. Instead of this, the numerical value corresponds much better to the roughness depth Rz and the difference between experiment and simulation is less than 10 percent [4]. This fact is not a shortcoming of the physical model itself, but due to the fact that only one grain is simulated in this numerical model. The carbon content – which is responsible for the cementite evolution – is only 0.42 per cent for 42CrMo4, leading to a cementite content of about 7 percent cementite accumulated in several pearlite grains. Consequently, there are areas with almost pure ferrite dissolving much more homogeneous and thus, lowering the value of the mean surface roughness. Hence, the simulation results correspond quite well to roughness depth Rz of this material and the numerical simulation has to be extended to several grains to reproduce also mean surface roughness values Ra. Another limiting fact of this simulation model is the region of very low field strength. The effect of electrochemical polishing and its electrochemical mechanisms is not integrated yet to this model, but also of minor relevance for the simulation of the sinking ECM-process [1]. Nevertheless, it is possible to calculate the change of ferrite and cementite content for every variation of feed rate or applied voltage in one grain with help of this model (Fig. 6). This allows forecasting changes in downstream hardening processes due to the ECM process for example.
Change of phase concentration Δc / %
40 30 20
21 wt. % NaNO3 κ = 160 mS/cm Cementite (Fe3 C) Ferrite (Fe) Averaging depth 20 µm
From Figure 6 it is recognizable, that ferrite is depleted in the pearlite grain, while the ratio of cementite and thus carbon increases. The depletion of ferrite is less compared to the accumulation of cementite due to the higher initial content of ferrite (c0,Fe) compared to cementite (c0,Fe3C) in this grain. Nevertheless, the overall value of depletion and accumulation depends on the volume of averaging and thus on a statistical method. Besides the influences of the process on one special grain, it is necessary to discuss, if the chosen spatial grain dimensions are representable for the alloy 42CrMo4 in a normalized heat treatment. For this reason, the surface of a raw material specimen is analyzed experimentally by SEM regarding the surface ratio of the grain size distribution (Figure 7). Thereby, the surface ratio a of one grain diameter d is the part of the surface with grains of this special size. Cementite Grain diameter d
Ferrite
Pearlite
50 µm
Ferrite
8 Surface ratio a / %
508
6 4 2
42CrMo4 normalized
0 0
10 20 30 Grain diameter d / µm
40
Fig. 7 SEM-image of normalized 42CrMo4 steel (upper part) and Surface ratio of the different grain sizes (lower part)
10 0 -10
co,Fe = 78.95 % c0,Fe3C = 21.05 %
-20 5E+06 1E+07 1.5E+07 2E+07 2.5E+07 Maximum Electric field strength E / (V/m) Fig. 6 Change of phase concentration as a function of the maximum electrical field strength in one pearlite grain
The distribution of grain sizes within the alloy is not homogeneous, but a classical Gaussian distribution with a maximum for grains with a diameter about twenty microns. Thus, the assumed size of the grain in the simulation above – the sum of the width of the several lamellae – was within this range und following eligible for the analysis of the model. As the grains are distributed over this huge range, it is necessary to examine the influence of the grain size on the roughness. Within one pearlite grain, the ratio of cementite and ferrite can differ. Therefore, first of all the influence of varying width of ferrite lamellae wFe at constant width of the cementite lamellae wFe3C is analyzed with help of the simulation model (Fig. 8).
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1.7 U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe3 C = 2 µm
1.6 1.5 1.4 0
5 10 15 20 Width of the ferrite lamellae wFe / µm
Fig. 8. Influence of the width of ferrite lamellae in the pearlite grain on resulting surface roughness
Figure 8 shows that the height difference and thus, the resulting surface roughness varies with the change of the ferrite lamellae width. Nevertheless, within the examined range the influence of the size is much smaller compared to the influence of the electric field strength (Fig. 4 and Fig. 8). For a range between 2 µm and 17 µm, the correlation of ferrite width and height difference follows quite well a linear trend. For grains smaller than two micrometer, the height difference decreases stronger compared to linear. In this area, the electric field lines at the cementite lamellae repress the field lines to the ferrite, due to which the ferrite is dissolved less (Figure 3). Within a pearlite grain, also the width of the cementite lamellae wFe3C can differ. For that reason, the influence of that width at a constant ferrite width wFe is examined within the spatial dimension distribution of the 42CrMo4 (Fig. 9 and Fig. 7). Height difference Δh / µm
1.9
1.76 Height difference Δh / µm
1.8
Due to this, the significance of the simulation model in the region is limited and not necessarily valid for very small grains. Analogue to the variation of one lamellae size, the overall grain size varies in an alloy. To examine this effect, the overall ratio of the width of the two lamellae is kept constant, while simulating a variation of both sizes (Fig. 10). U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe / w Fe3 C = 2.5
1.74 1.72
1.7
1.68 2
3 4 5 Width of the ferrite lamellae wFe / µm
6
Fig. 10. Influence of the grain size on resulting roughness
Like in both former variations, the examination in Figure 10 shows that the roughness increases with increasing grain size. Thus, the conclusion from these three series is that, the influence of the grain size is smaller than the influence of the machining parameters. Nevertheless, the maximum grain size determines the achievable surface topography at fixed machining parameters. Finally, not all grains are orientated parallel to the machining direction. For this reason, the influence of an angle α between machining direction and grain is examined. Whereby at α = 0° the grain is orientated in the machining direction (Figure 11). 1.75
1.8
1.7 1.6 1.5
U = 18 V v F = 1 mm/min κ = 160 mS/cm 21 wt. % NaNO3 wFe = 5 µm
1.4 0 2 4 6 8 Width of the cementite lamellae wFe3 C / µm Fig. 9. Influence of the width of cementite lamellae in the pearlite grain on resulting surface roughness
From Figure 9 it can be seen, that the influence of cementite lamellae width on resulting surface roughness is also nearly linear in the observed range. For smaller cementite lamellae, the influence of the initial assumed radius at the edge of the lamellae becomes very strong, because the grains are dissolved from the side more than from the top (Fig. 3).
Height difference Δh / µm
Height difference Δh / µm
1.9
U = 18 V v F = 1 mm/min κ = 160 mS/cm
1.7 1.65
1.6 21 wt. % NaNO3 wFe / w Fe3 C = 2.5 wFe = 5 µm
1.55 1.5 0
5 10 15 Angle of the grain α / °
20
Fig. 11 Influence of the grain angle on resulting roughness
Figure 11 shows that with an increasing angle between the grain orientation and the machining direction the height difference decreases. These results correspond as well to the expectations, as with an increasing angle, the electric
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streamlines have to be bend more at the cementite lamellae and thus the dissolution of ferrite is inhibited. The results of the examinations showed that the electrochemical process and the achievable surface roughness strongly depend on the microstructure. For a given limiting surface roughness of a workpiece, it is a prerequisite to analyze the grain size to set up the corresponding maximum field strength to achieve this roughness. 4. Summary and Outlook Within this paper, the electrical field strength as mayor material loading in ECM processes was deduced thermodynamically. It was shown, that with the help of this field strength, material modifications – like surface roughness – can be plotted physical valid. Based on this fact and an advanced simulation model, changes in a pearlite grain of the normalized steel 42CrMo4 were simulated and it was shown, that the results correspond to previous experimental examinations. Finally, the influence of varying grain size on resulting surface topography was simulated and analyzed. The model will be extended in future to simulate the electrochemical material dissolution of several grains to forecast a representative material surface. With help of this numerical model, also conclusions regarding the average surface roughness should be possible. Furthermore, the influence of the chemical potential as the secondary main material loading will be transferred into the model. Due to this, several electrolyte systems can be analyzed numerically, to obtain the optimum combination of electrolyte and workpiece material. Acknowledgements The authors wish to thank the German Research Foundation (DFG) for funding the Collaborative Research Center SFB/ TRR 136 “Function Oriented Manufacturing Based on Characteristic Process Signatures” (Bremen, Aachen, Oklahoma), subproject F03. References [1] Klocke, F., König, W. Fertigungsverfahren: Abtragen, Generieren und Lasermaterialbearbeitung, 4th ed. VDIVerl. [et al.], Düsseldorf [and others], 2007. [2] McGeough, J.A. Principles of electrochemical machining. Chapman and Hall; Halsted Press Division, Wiley, London, New York, 1974. [3] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Influence of Material Microstructure on the Electrochemical Machinability of Steel 42CrMo4. Proceedings INSECT, 2015, 43–50. [4] Baehre, D., Ernst, A., Weißhaar, K., Natter, H., Stolpe, M., Busch, R. Electrochemical Dissolution Behavior of Titanium and Titanium-based Alloys in Different Electrolytes. Procedia CIRP 42, 2016, 137–142. [5] Speidel, A., Mitchell-Smith, J., Walsh, D.A., Hirsch, M., Clare, A. Electrolyte Jet Machining of Titanium Alloys
Using Novel Electrolyte Solutions. Procedia CIRP 42, 2016, 367–372. [6] Brinksmeier, E., Klocke, F., Lucca, D.A., Sölter, J., Meyer, D. Process Signatures – a new approach to solve the inverse surface integrity problem in machining processes. Procedia CIRP 13, 2014, 429–434. [7] Hinduja, S., Kunieda, M. Modelling of ECM and EDM processes. CIRP Annals - Manufacturing Technology 62 (2), 2013, 775–797. [8] Klocke, F., Zeis, M., Klink, A. Interdisciplinary modelling of the electrochemical machining process for engine blades. CIRP Annals - Manufacturing Technology, 2015. [9] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Surface integrity in electrochemical machining processes: An analysis on material modifications occurring during electrochemical machining. Proceedings of the IMechE 45, 2017. [10] Rajurkar, K.P., Hewidy, M.S. Effect of grain size on ECM performance. Journal of Mechanical Working Technology 17, 1988, 315–324. [11] Lucas, K. Thermodynamik: Die Grundgesetze der Energie- und Stoffumwandlungen, 3rd ed., Springer, Berlin, 2001. [12] Nagy, Z. Applications of non-equilibrium thermodynamics to the theory of overvoltage. Electrochimica Acta 22 (2), 1977, 191–195. [13] Klocke, F., Harst, S., Karges, F., Zeis, M., Klink, A. Modeling of the Electrochemical Dissolution Process for a Two-phase Material in a Passivating Electrolyte System. Procedia CIRP 58, 2017, 169–174. [14] Kozak, J., Zybura-Skrabalak, M. Some Problems of Surface Roughness in Electrochemical Machining (ECM). Procedia CIRP 42, 2016, 101–106. [15] Lohrengel, M.M., Schultze, J.W., Speckmann, H.D. The equivalent circuit diagram of oxide films with a limited potential drop. Electrochimica – Acta 31 (1), 1986, 123– 126. [16] Hamann, C.H., Vielstich, W. Elektrochemie, 4th completely revised and updated ed. Wiley-VCH, Weinheim, 2005. [17] Lohrengel, M.M., Rataj, K.P., Münninghoff, T. Electrochemical Machining - mechanisms of anodic dissolution. Electrochimica Acta 201, 2016, 348–353. [18] Zeis, M. Modellierung des Abtragprozesses der elektrochemischen Senkbearbeitung von Triebwerksschaufeln. Apprimus, Aachen, 2015. [19] Wilcox, D.C. Formulation of the k-w Turbulence Model Revisited. AIAA Journal 46 (11), 2008, 2823–2838. [20] Klocke, F., Harst, S., Ehle, L., Zeis, M., Klink, A. Material Loadings during Electrochemical Machining (ECM) - a First Step for Process Signatures. Key Engineering Materials, 2015. [21] Klocke, F., Zeis, M., Harst, S., Klink, A., Veselovac, D., Baumgärtner, M. Modeling and Simulation of the Electrochemical Machining (ECM) Material Removal Process for the Manufacture of Aero Engine Components. Procedia CIRP 8, 2013, 265–270.