Impact of the thermomechanical load on subsurface phase transformations during cryogenic turning of metastable austenitic steels

Hotz, Hendrik; Kirsch, Benjamin; Aurich, Jan C. Article — Published Version Impact of the thermomechanical load on subsurface phase transformations during cryogenic turning of metastable austenitic steels Journal of Intelligent Manufacturing Provided in Cooperation with: Springer Nature Suggested Citation: Hotz, Hendrik; Kirsch, Benjamin; Aurich, Jan C. (2020) : Impact of the thermomechanical load on subsurface phase transformations during cryogenic turning of metastable austenitic steels, Journal of Intelligent Manufacturing, ISSN 1572-8145, Springer US, New York, NY, Vol. 32, Iss. 3, pp. 877-894, https://doi.org/10.1007/s10845-020-01626-6 This Version is available at: https://hdl.handle.net/10419/288334 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) 1 3 Journal of Intelligent Manufacturing (2021) 32:877–894 https://doi.org/10.1007/s10845-020-01626-6 Impact ofthethermomechanical load onsubsurface phase transformations duringcryogenic turning ofmetastable austenitic steels HendrikHotz1 · BenjaminKirsch1· JanC.Aurich1 Received: 11 October 2019 / Accepted: 11 July 2020 / Published online: 22 July 2020 © The Author(s) 2020 Abstract When machining metastable austenitic stainless steel with cryogenic cooling, a deformation-induced phase transformation from γ-austenite to α′-martensite can be realized in the workpiece subsurface. This leads to a higher microhardness and thus improved fatigue and wear resistance. A parametric and a non-parametric model were developed in order to investigate the correlation between the thermomechanical load in the workpiece subsurface and the resulting α′-martensite content. It was demonstrated that increasing passive forces and cutting forces promoted the deformation-induced phase transformation, while increasing temperatures had an inhibiting effect. The feed force had no significant influence on the α′-martensite content. With the proposed models it is now possible to estimate the α′-martensite content during cryogenic turning by means of in-situ measurement of process forces and temperatures. Keywords Martensite· Cryogenic turning· Metastable austenitic steel· Deformation-induced phase transformation Introduction The surface integrity of a component significantly influences its performance in technical applications. In recent years, numerous investigations have been carried out to investigate the influence of the machining process on surface integrity. Brinksmeier etal. (2018) described a general causal sequence of correlations starting from the input parameter of the machining process to the resulting thermomechanical loads during machining, the surface integrity after machining and the resulting functional properties. An understanding of the individual correlations allows the targeted configuration of the surface integrity and thus the functional properties by specific adjustment of the input parameters, e.g. by means of variations of the cutting parameters, the cooling strategy or the tool design. There are several approaches that allow to calculate the process forces (Sharma etal. 2008; Rodic etal. 2020) and the temperatures (Komanduri & Hou 2000; Huang & Liang 2003) depending on the input parameter. Non-parametric models become increasingly established in manufacturing technology and allow to predict and improve the component properties (Choudhary etal. 2009). Xu etal. (2020) used artificial neural networks (ANN) to calculate the residual stresses and the surface roughness depending on the cutting parameter. Ji etal. (2019) reduced the thickness of the white layer in the workpiece subsurface in a big data approach. Recently, the investigation of soft-sensors in machining processes has gained importance. That is, when the correlations between the thermomechanical load and the resulting surface integrity have already been quantified, in-situ measurable values such as temperature and process forces can be used to determine the surface integrity already during the machining process. According to Uebel etal. (2019) the use of soft-sensors enables the in-situ detection of deviations in the thermomechanical load caused by disturbance variables (e.g. tool wear), which in turn would result in undesired deviations in the surface integrity. By knowing the causal correlations between input variables and the thermomechanical load, these undesired deviations can be compensated, e.g. by adjusting the cutting parameters, allowing for the manufacturing of components with uniform surface integrity. The prerequisite for the compensation of disturbance * Hendrik Hotz [email protected] https://www.fbk-kl.de 1 Institute forManufacturing Technology andProduction Systems, TU Kaiserslautern, 67663Kaiserslautern, Germany 878 Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 variables by means of a control loop is the quantification of the correlations between input parameter, thermomechanical load and surface integrity, as well as the in-situ measurement of the thermomechanical load. After machining with geometrically defined cutting edges, an elongation of the grains in the cutting direction and a pronounced grain refinement can be observed below the workpiece surface for a wide range of materials, as reported by Jawahir etal. (2011) in a comprehensive keynote paper. In addition to the formation of new grain boundaries, machining also leads to a significant increase in the dislocation density below the surface. These alternations in the microstructure contribute to strain hardening and result in an increase in microhardness as demonstrated by Outeiro etal. (2015) and Zhang etal. (2018a). Jawahir etal. (2016) concluded in a more recent keynote paper that the use of cryogenic cooling leads to a more pronounced grain refinement and thus stronger strain hardening compared with dry machining or machining with conventional flood cooling lubrication, due to the lower temperatures during machining. Metastable austenitic steels are widely used in industry due to their favorable combination of strength and ductility as well as their excellent corrosion resistance. When cryogenically turning these steels, a deformation-induced phase transformation from the metastable γ-austenite into ε- and α′-martensite can occur, which was first reported by Aurich etal. (2014). As the microhardness of the martensitic phase fractions is higher than the microhardness of the initially existent γ-austenite, this deformation-induced phase transformation contributes to the hardening of the surface layer. According to Pranke etal. (2015), the microhardness increases linearly with the phase fraction of martensite. Zhang etal. (2018b) demonstrated that the increase in microhardness caused by phase transformation as well as the microhardness increase caused by strain hardening superimpose additively. Due to this superposition of different hardening mechanisms, a pronounced surface hardening can be achieved by cryogenic turning of metastable austenitic steels. Depending on the application and the required surface integrity of the component, a separate hardening process can thus be rendered obsolete, leading to a more economical and ecological process chain. Frölich etal. (2015) proved that metastable austenitic steel AISI347 showed a higher wear resistance after cryogenic turning compared to a conventional turning process in a radial shaft seal ring system. Boemke etal. (2018) showed that cryogenic turning leads to improved fatigue strength in the very high cycle fatigue regime, which was mainly contributed to the α′-martensite in the workpiece surface layer. The understanding and quantification of the causal correlations between the input parameters, the thermomechanical load and the surface integrity, especially regarding the α′-martensite content, is of high technological and economic importance in order to tailor the cryogenic turning process depending on specific application requirements. The effects of the input parameters on the thermomechanical load and the resulting surface integrity are partly well understood: Mayer etal. (2018) reported on the influence of the cutting parameters, while the research of Hotz and Kirsch (2020) addressed the impact of the tool properties on the thermomechanical load and the surface integrity. These investigations demonstrate that, due to the deformation-induced phase transformation and strain hardening, the microhardness of the workpiece subsurface can almost be doubled by cryogenic turning. However, the correlation between the thermomechanical load and the deformation-induced phase transformation are not fully understood yet. While the past research implied that increasing mechanical loads and decreasing thermal loads benefit the deformation-induced phase transformation, which matches well with literature from materials science as we will discuss later, the exact correlations are not known. The existing phenomenological cause-effect relationships already allow the targeted configuration of the α′-martensite content in the workpiece surface layer by adjusting the input parameters. However, as the correlation of thermomechanical load and α′-martensite cannot be quantified yet, it is not possible to use a soft-sensor based approach for the in-situ estimation of the α′-martensite content. Hence it is also not possible to use a control loop in order to compensate disturbance variables, which is needed for a robust manufacturing of components with specific, predefined surface integrity. In this article the impact of the thermomechanical load on deformation-induced phase transformation in the workpiece surface layer during cryogenic machining will be modeled for the first time. The parallel investigation of a parametric and a non-parametric modelling approach provides in-depth insights into the subsurface phase transformations during this machining process. The results will allow for the future implementation of a soft-sensor based process control and will also lead to an in-depth understanding of the cryogenic turning process. Fundamentals Metastability fromathermodynamic point ofview Metastable austenitic steels are characterized by the fact that compared to the initial γ-austenite microstructure a more energetically favorable state can be achieved by providing a critical amount of free energy ∆Gmin. When cooling the material down to the martensite start temperature Ms, the martensitic phase transformation occurs. For this thermallyinduced phase transformation, the critical amount of free energy is solely provided by the temperature decrease. Patel 879Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 and Cohen (1953) investigated the influence of applied stress on the martensitic phase transformation. With increasing stress, the mechanically induced free energy ∆Gmech also increases, so that less thermal free energy ∆Gtherm has to be induced in order to reach the critical amount of free energy ∆Gmin. Hence, the phase transformation can occur at higher temperatures. This is illustrated schematically in Fig.1a, based on a diagram by Vöhringer and Macherauch (1977). In Fig.1b, which goes back to Olson and Cohen (1972), several cases of martensitic transformation in metastable austenitic steels can be differentiated depending on the temperature. As already mentioned, below the Ms-temperature, a solely thermally-induced phase transformation occurs. In the temperature range Ms ≤ T ≤ Md a distinction can be made between stress-induced and deformation-induced martensite formation. In stress-induced martensite formation, an applied stress below the yield strength is sufficient to achieve ∆Gmech at a given temperature. The temperature up to which stress-induced martensite formation occurs due to purely elastic deformation is referred to as Ms,σ, which was introduced by Bolling and Richman (1970). Above Ms,σ the applied stress must surpass the yield strength to trigger the phase transformation. The deformation-induced martensite formation is characterized by plastic deformation. The martensite deformation temperature Md is the highest temperature at which the martensitic phase transformation can take place. Between Md and T0 the free energy of the α′-martensite is still below that of the γ-austenite, so that the phase transformation would still be possible from purely thermodynamic points of view (see Fig.1a). However, the required critical free energy ∆Gmin can no longer be applied, since the stress required to reach ∆Gmech increases exponentially (see Fig.1b). The susceptibility of a metastable austenitic steel regarding martensitic phase transformation is not only determined by the applied thermomechanical load, but also by materialspecific properties, especially the chemical composition, which also highly influence the stacking fault energy, as discussed by Rhodes and Thompson (1977). The Ms- and Md-temperature can therefore be used as parameters for characterizing the material-specific austenite stability (see Fig.1a). The first investigations in this regard go back to Eichelmann and Hull (1953), who empirically determined Eq.1 in order to calculate the Ms-temperature of a steel as a function of its chemical composition. As it is hardly possible to experimentally determine the Md-temperature, Angel (1954) introduced the Md30-temperature (see Eq.2), at which 50% α’ martensite is formed at 30% plastic deformation. The Ms-temperature can hence be used to evaluate the susceptibility regarding thermally-induced phase transformation (see Fig.1a) and the Md30-temperature regarding deformation-induced phase transformation. In both cases, a higher temperature goes along with a higher susceptibility to phase transformation, or in other words, a lower austenite stability. Nucleation andkinetics ofdeformation‑induced phase transformation Herper (2000) summarized the characteristics of the martensitic transformation as a diffusion-free change of the lattice structure from face centered cubic (fcc) to body centered cubic (bcc), which is dominated by shearing, while the habitus plane remains unaffected. The nucleation of an α′-martensite embryo inside the fcc-lattice usually takes place at sites with high local distortion. Venables (1962) reported on the nucleation at the intersection of two plates of ε-martensite. Lagneborg (1964) stated that nucleation can also take place at intersections of active slip systems with (1) Ms=1350 −1665(C+N)−28Si −33Mn −42Cr −61Ni (2) Md30 =413−462(C+N)−9.2Si−8.1Mn−13.7Cr−9.5Ni−18.5Mo (a) (b) Fig. 1 a Schematic illustration of the free energy required for phase transformation depending on the temperature according to Vöhringer and Macherauch (1977), b applied stress necessary for martensitic phase transformation depending on the temperature according to Olson and Cohen (1972) 880 Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 ε-martensite plates. Furthermore, nucleation can also occur at the intersection of ε-martensite and a twin or grain boundary of the γ-austenite, as investigated by Mangonon and Thomas (1970). Besides the consecutive transformation of γ-austenite into ε-martensite and finally into α′-martensite, it is possible that α′-martensite is formed directly from γ-austenite, e.g. at the intersection of stacking faults, which was observed by Schumann (1975) and Staudhammer etal. (1983). Olson and Cohen (1975) summarized ε-martensite plates, twins and bundles of stacking faults with the term “shear bands”, because their intersections all serve as nucleation sites for α′-martensite embryos and they are furthermore difficult to distinguish microscopically. Pati and Cohen (1969) state that after nucleation of the first α′-martensite embryo an autocatalytic transformation occurs in the adjacent lattice, as the lattice structure is already disturbed and less free energy is needed for the phase transformation. This means that after nucleation the phase transformation rapidly spreads until the transformation front encounters an obstacle. Grain boundaries, for example, represent such obstacles, which is why increasing grain sizes favor the deformation-induced formation of α′-martensite, as elaborated by Nohara etal. (1977). The kinetics of the deformation-induced phase transformation from γ-austenite to α′-martensite were firstly modeled by Olson and Cohen (1975). They found that the α′-martensite contents determined experimentally by Angel (1954) at constant temperature resulted in a sigmoidal function depending on the plastic strain. In their model, they regarded shear band intersections as the dominant nucleation sites, which increase with increasing plastic strain. The volume fraction of shear bands fsb increases with rising plastic strain ε according to Eq.3, while α is a strain-independent parameter representing the rate of shear band formation, which is sensitive to stacking fault energy and strain rate. They assumed that a single shear band has a constant volume of vsb, hence the number of shear bands per austenite volume Nsb v can be calculated with Eq.4. The number of shear band intersections per austenite volume NI v was then related to the number of shear bands with Eq.5 with a constant K and an exponent n. As not every shear band intersection leads to α′-martensite nucleation, they correlated the number of α′-martensite embryos N α � v to the number of shear band intersections NI v , whereby p was the probability for nucleation: (3) fsb =1−e−α ⋅ ε (4) N sb v= f sb v sb (5) N I v =K⋅ ( Nsb v)n The probability of nucleation p was expressed as a gaussian distribution function relative to the temperature. When using Eqs.3–6, Eq.7 can be derived to calculate the phase fraction of α′-martensite fα′ depending of the strain ε, the exponent n and two parameters α and β, which are sensitive to temperature, as α depends on the stacking fault energy and β is proportional to the probability p of nucleation at a shear band intersection (see Eq.8). When setting the exponent to n = 4.5, Olson and Cohen (1975) were able to fit the experimental data of Angel (1954) very well for a wide range of temperatures and plastic strains. The model attracted considerable attention in the scientific community and is still frequently used for calculations regarding the deformation-induced formation of α′- martensite. Hecker etal. (1982) extended the model of Olson and Cohen (1975) for biaxial loading by substituting the uniaxial strain with the vonMises effective strain. They proved validity to the Olson-Cohen model. However, they needed to adapt the temperature sensitive parameters α and β. This is probably due to the fact that a different batch of metastable austenitic steel was used and the different chemical composition and thus different austenitic stability led to the deviations in metastability. Huang etal. (1989) provided an overview of the effect of plastic strain and temperature. Figure2 shows the results of Angel (1954) in solid lines, the dotted lines represent extrapolation of Angels data by the model of Olson and Cohen (1975) and the dashed lines show the results obtained by Hecker etal. (1982). With increasing (6) d N α� v =p⋅dN I v (7) fα�=1−e−β ⋅ (1−e−α ⋅ ε)n (8) β= v α� ⋅K v sbn ⋅ p Fig. 2 Content of α′-martensite in metastable austenitic steel AISI 304 as a function of plastic strain at different temperatures according to Huang etal. (1989): solid lines by Angel (1954), dotted lines by Olson and Cohen (1975), dashed lines by Hecker etal. (1982) 881Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 plastic strain, the sigmoid shaped functions lead to a saturation, at which further increasing the strain does not increase the α′-martensite content. The plateau depends on the temperature sensitive parameter β. Inspired by the model of Olson and Cohen (1975), further approaches for modeling the deformation-induced α′-martensite formation by means of sigmoidal functions were developed by several researchers. Stringfellow etal. (1992) take the changes in the mechanical properties during phase transformation into account. Based on this, Zaera etal. (2012) developed a constitutive model for calculating the α′-martensite content at very high strain rates. Ahmedabadi etal. (2016) modeled the sigmoidal curve by means of a logistic function and found a good agreement with the model by Olson and Cohen (1975). Smaga etal. (2008) used a sigmoid function in order to calculate the amount of deformation induced α′-martensite in fatigue experiments. In their model, they used the cumulative plastic strain, which results from the number of cycles and the plastic strain of the individual cycles. Das etal. (2011a) used ANN to investigate various impact factors on the deformation-induced formation of α′-martensite. They compared the influence of materialspecific properties such as chemical composition and grain size with the influence of thermomechanical load on the α′-martensite content. According to this study, the temperature has the greatest influence, closely followed by the applied stress. Interestingly, stress had a much greater effect on the phase transformation than strain. The strain rate had only a marginal influence. While using the experimental data of 26 publications in their ANN, Das etal. (2011b) proved that a large amount of published data regarding the α′-martensite content depending on the plastic strain can actually be described with the effect of stress. This conclusion matches well with the thermodynamic aspects of deformation induced phase transformation, as the stress contributes to the mechanically induced free energy ∆Gmech (see Fig.1). Das etal. (2011a,b) show that the α′-martensite content increases in a sigmoidal function depending on the stress, whereby a critical minimum stress must be applied to overcome the yield stress and to realize plastic deformation. Similar correlations between the stress and the α′-martensite content were more recently obtained by Ishimaru etal. (2015) in cyclic tension–compression tests and also after draw bending of metastable austenitic steel. Methodology andexperimental procedure Modelling approach Compared to material science investigations regarding the influence of thermomechanical load on the deformation-induced formation of α′-martensite, several particularities have to be taken into account for cryogenic turning which make the modelling more difficult. First, stress, strain and temperature are not the adjustment parameters of the experiment, but result depending on the choice of the cutting parameters, the cooling strategy and the tool properties, which represent the input parameters during cryogenic turning. Therefore, in the experiments, the thermomechanical load must be modified by a variation of these input parameters, which requires a priori knowledge. Second, during the experiments, the stress, strain and temperature are not homogeneously distributed inside the workpiece material and therefore the resulting α′-martensite content is not homogeneously distributed either, unlike for instance in unidirectional tensile or fatigue tests. The α′-martensite is locally generated when the tool causes a mechanical load in the subsurface at a temperature given at that point in time. Depending on the distance from the surface, there are steep gradients in stress, strain, temperature and α′-martensite content. Third, the characterization of thermomechanical loads in the workpiece subsurface during the cryogenic turning is rather difficult. The equivalent stress within the subsurface can be calculated e.g. according to a model developed by Garbrecht (2006). However, the equivalent stress depends not only on the forces but also directly on the contact conditions, which means on the tool design. The plastic strain in the subsurface caused by turning can be examined ex-situ by analyzing the microstructure by means of electron back scatter diffraction or metallographic examinations. Furthermore, the elastic and plastic strain can also be modeled as a function of the equivalent stress if a material model is used in which the stress strain response takes the deformationinduced martensite formation and the associated changes in mechanical behavior into account. The temperature in the area of the inaccessible contact zone can hardly be measured. Becker etal. (2018) developed a model which allows for the calculation of the temperature distribution inside the workpiece during cryogenic turning. However, numerical errors occur in an area up to approx. 200μm below the surface. This leads to unreliable predictions for the temperature in the area in which the deformation-induced phase transformation occurs. Due to the difficulties in determining the thermomechanical load as a function of the distance to the surface, it is advisable to model the mean α′-martensite content in the workpiece subsurface which requires input variables that are not location-dependent and therefore easier to determine. As mentioned, according to Das etal. (2011a,b), the stress has a significantly higher impact on deformation-induced α′-martensite formation than the strain. Thus, when considering the mechanical load, the process forces, which are very easy to measure, were used as input variables. As the input variable regarding the thermal load the temperature, 882 Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 measured inside the workpiece near the surface, was used, which will be described later in greater detail. The α′-martensite content was measured ex-situ with a magnetic sensor. The integral value determined in this way represents the target variable according to which the models were fitted to. As schematically illustrated in Fig.3, two different models have been developed to calculate the α′-martensite content in the workpiece subsurface as a function of the process forces and the temperature. On the one hand, a parametric model was developed based on the fundamentals of deformation-induced phase transformation (see Sect.2). On the other hand, a non-parametric model was developed using ANN. The same 51 data sets (process forces, temperature, α′-martensite content) were used for the development of both models. Data sets of four experiments which were not included in the development of the models were then used for testing. Workpiece material Metastable austenitic stainless steel AISI347 was used for the investigations. Because varying chemical composition and thus varying austenite stability have an influence on the deformation-induced phase transformation during cryogenic turning, as discussed by Kirsch etal. (2019), the same batch was used for all experiments. Based on the chemical composition (see Table1) the Ms-temperature can be calculated to −87°C, according to Eq.1. The Md30-temperature amounts to 46°C, according to Eq.2. The average grain diameter of the initial austenitic microstructure was 17μm and the initial microhardness was 187HV0.01. Machining setup The longitudinal turning experiments were carried out on a CNC lathe (see Fig.4). The feed travel was 18mm at a final workpiece diameter of 14mm. A bi-phase CO2 solid–gas mixture was used for cooling. The CO2 was supplied via two nozzles with a constant mass flow rate of 1.75kg/ min per nozzle. A depth of cut of ap = 0.2mm and a cutting speed of vc = 30m/min were used. The feed rate was varied in a wide range in order to cause variations in the thermomechanical load during turning. Furthermore, the tool properties were varied: 5 different coatings as well as uncoated inserts were used. The cutting edge radius rβ, the form factor K of the cutting edge and the chamfer angle γβ were varied as well. At several experiments, a precooling was applied in order to manipulate the thermal load. During Fig. 3 Schematic illustration of the modelling approach Table 1 Chemical composition of metastable austenitic steel AISI 347 in wt% C Cr Ni N Nb Mn Mo Si Cu Fe 0.021 17.19 9.44 0.022 0.38 1.55 0.23 0.59 0.11 Rest Fig. 4 Experimental setup 883Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 precooling, the tool moved slightly above the workpiece with activated cooling without removing a chip. While the CO2-mass flow was constant, the feed rate during precooling (fpc) was varied in order to adjust the workpiece temperature immediately before machining. All these variations of the input parameter aimed at varying the thermomechanical load during cryogenic turning in order to analyze and model the influence between thermomechanical load and the extent of deformation-induced α′-martensite formation. An overview of the used parameters, the measured process forces and temperatures, the resulting α′-martensite contents as well as the modeled α′-martensite contents is given in the “Appendix”. Measurement technology During the cryogenic turning, a three-component peizoelectric dynomometer was used to measure the cutting force Fc, the passive force Fp and the feed force Ff. In order to measure the temperature within the workpiece subsurface, type K thermocouples (NiCr–Ni) with a diameter of 1mm were used. They were positioned in eroded holes with a diameter of 1.2mm. Before insertion, the holes were filled with a heat transfer compound to ensure good heat transfer between the thermocouples and the borehole wall. The distance between the centre of the the thermocouple and the workpiece surface after machining (diameter 14mm) was 1mm. The thermocouples were connected to a radio unit positioned between the clamping chucks (see Fig.4). This enabled to transmit the measuring signals to a receiver outside the CNC lathe. The time synchronous recording of the process forces and the temperatures made it possible to evaluate the temperatures as a function of the cutting time. In axial direction, the tool surpassed the thermocouples after machining a feed travel of 10mm. The heat generated by machining conducted into the workpiece subsurface and resulted in a temperature increase. The temperature T of the local maximum was dependent on the input parameters. This maximum temperature was used as the input variable for model development, as it represents the temperature within the workpiece subsurface during machining. The deformation-induced phase transformation occuring during cryogenic turning led to changes in permeability, which were measured by means of the magnetic sensor Feritscope FMP301 subsequent to the turning experiments. While this does not allow to measure the content of the paramagnetic ε-martensite and also does not yield any information regarding the α′-martensite, this is still a reliable method to determine the α′-martensite content of a workpiece fast and non-destructively immediately after cryogenic turning. For each workpiece, the α′-martensite content was measured at eight equidistant points in circumferential direction and five points in axial direction, so that the measurement grid covered the whole area of the machined workpiece surface. The mean value of the total 40 measurement points was calculated in order to give a representative α′-martensite content of a single workpiece. While the field lines of the magnetic sensor flow through the component up to a depth of approx. 3–4mm, the α′-martensite content after the cryogenic turning is usually located within the first 200μm below the surface. Therefore the measurement signals determined by the magnetic sensor were always significantly lower than the actual α′-martensite content in the near surface layer. For calibration, cross sections of the cryogenically turned workpieces were treated with Beraha II etching agent in order contrast the α′-martensite needles. In addition to workpieces that were cryogenically turned within the framework of this study, workpieces with exceptionally high and low α′-martensite content from earlier studies by Mayer etal. (2018) and Hotz etal. (2018) were also used for calibration. After capturing images with an optical microscope, an image processing method according to Mayer etal. (2018) was used in order to quantify the α′-martensite content in the surface layer and give insights into the α′-martensite distribution. The α′-martensite content ξm deterimed with the magnetic sensor was then compared to the mean α′-martensite phase fraction fα′ within the workpiece subsurface. The resulting calibration curve given in Fig.5 is a superposition of a root function and a linear function (see Eq.9) and is qualitatively in good agreement with an overview given by Talonen etal. (2004), who compared the Feritscope1 calibration curves when measuring the α′-martensite content of different researchers including Hecker etal. (1982). (9) f α �=5.86 ⋅ √ξm+1.17 ⋅ ξm Fig. 5 Calibration curve of magnetic sensor 884 Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 Results Experimental results The wide range of varied input parameters in cryogenic turning led to a great data range of process forces, temperatures and consequently the resulting α′-martensite content. Figure6 provides an overview on the influence of thermomechanical load on the α′-martensite content ξm measured with the magnetic sensor, each accompanied by the trend line, the 95%confidence interval and the correlation coefficient r. It can be seen, that the α′-martensite content increased with higher cutting force Fc and passive force Fp. The similar influence of cutting force and passive force can be explained by the fact that these themselves correlate strongly with each other (r = 0.89). The feed force did not have a significant influence on the deformation-induced phase transformation. As expected, rising temperatures inhibited the phase transformation. Due to the conversion of mechanical energy into heat in the nearly adiabatic primary shear zone, a high negative correlation between cutting force and temperature could be expected, which would make it difficult to separate the individual influences on α′-martensite formation. However, due to the modification of the temperature by means of varying precooling, the correlation between the process forces and the temperatures is very low (see Table2). Although trends can be seen regarding the influence of cutting force, passive force and temperature on deformation-induced phase transformation, the overall scatter is very high. This is because the deformation-induced formation of α′-martensite cannot be explained solely by the mechanical or thermal load, but only by their superposition. (a) (b) (c) (d) Fig. 6 α′-martensite content depending on a the cutting force, b the passive force, c the feed force and d the temperature Table 2 Correlation coefficients between the different measured values – FcFpFfT ξm Fc1 0.89 0.618 −0.173 0.68 Fp0.89 1 0.382 −0.058 0.727 Ff0.618 0.382 1 0.193 0.108 T −0.173 −0.058 0.193 1 −0.628 ξm0.68 0.727 0.108 −0.628 1 891Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 Appendix Data set Input variables Thermomechanical load α′-martensite content Coating f K rβγβfpc FpFcFfT ξmξc,p ξc,np Train – 0.35 0.5 30 0 – 269 238 60 −1.1 3.35 2.44 3.37 Train – 0.35 0.5 90 0 – 426 314 86 11.9 3.73 1.44 3.62 Train – 0.35 1 30 0 – 257 235 55 −0.6 3.18 2.33 3.09 Train – 0.35 1 60 0 – 285 242 61 0.0 3.14 2.36 3.54 Train – 0.35 1 90 0 – 291 248 64 0.5 3.55 2.39 3.66 Train – 0.35 2 30 0 – 240 224 51 −1.4 3.14 2.26 2.74 Train – 0.35 2 60 0 – 283 239 63 −1.6 3.91 2.53 3.62 Train – 0.35 2 90 0 – 291 244 63 2.1 4.07 2.11 3.45 Train – 0.35 1 4 20 – 284 240 58 −0.6 3.54 2.41 3.56 Train AlTiN 0.15 1 8 20 – 171 124 50 −34.2 2.63 1.87 2.83 Train Multilayer 0.15 1 27 20 – 177 135 50 −31.4 3.02 2.35 2.85 Train TiAlSiN 0.15 1 11 20 – 191 144 48 −25.5 2.78 2.39 2.89 Val TiB20.15 1 5 20 – 182 129 49 −29.9 2.81 1.88 2.89 Train – 0.15 1 4 20 – 186 144 49 −32.0 2.91 2.87 3.15 Train – 0.35 1 32 0 – 246 232 53 −0.4 2.97 2.26 2.83 Val – 0.35 1 32 0 – 241 230 55 −17.5 3.81 4.51 4.05 Train – 0.35 1 32 0 – 241 232 54 −10.3 3.35 3.59 3.45 Train – 0.35 1 32 0 – 246 235 56 −3.1 3.06 2.66 3.03 Train – 0.35 1 32 0 – 251 232 56 −1.2 2.10 2.36 2.99 Train – 0.15 1 4 30 – 195 128 51 −18.9 3.26 1.24 2.58 Train – 0.15 1 4 50 – 346 188 73 −21.2 4.61 3.71 4.68 Train – 0.35 1 4 0 0.274 215 196 47 −30.4 4.07 5.02 4.04 Val – 0.35 1 4 30 0.274 453 355 51 −41.3 10.42 10.88 10.71 Train – 0.65 1 4 30 0.203 721 433 57 −44.7 10.03 12.70 10.12 Train – 0.65 1 4 50 0.203 511 279 84 −36.0 8.49 8.37 7.35 Train – 0.65 1 4 0 0.203 520 425 48 −40.7 11.82 12.06 11.90 Train – 0.95 1 4 30 0.186 291 220 51 −41.4 7.40 7.17 7.30 Val – 0.95 1 4 50 0.186 304 307 47 −42.7 7.65 9.97 8.35 Train – 0.95 1 4 0 0.186 369 385 42 −43.0 10.19 11.67 10.48 Val – 0.65 1 4 0 0.4 302 311 47 −19.1 6.91 6.65 6.39 Train – 0.65 1 4 50 0.4 644 384 78 −27.5 8.07 9.43 7.66 Train – 0.65 1 4 30 0.4 435 344 56 −12.3 7.73 6.12 7.22 Val – 0.45 1 4 30 0.8 349 269 26 −6.2 5.63 3.73 5.03 Train – 0.85 1 4 30 0.8 507 411 55 −4.6 6.62 5.60 7.34 Train – 0.65 1 4 50 0.4 626 382 88 −22.3 7.47 8.54 7.15 Train – 0.65 1 4 50 0.8 616 389 87 −8.3 5.28 6.06 5.63 Val – 0.45 1 4 50 0.8 524 316 90 −7.0 5.35 4.68 4.79 Train – 0.85 1 4 50 0.8 700 445 69 −7.9 5.71 6.74 5.86 Train – 0.35 1 4 50 0.15 482 265 75 −54.8 8.18 10.21 9.34 Train – 0.35 1 4 50 0.8 485 283 83 −14.1 4.41 5.26 5.21 Train – 0.65 1 4 50 0.15 636 367 75 −49.1 9.95 12.08 9.89 Train – 0.85 1 4 50 0.15 686 420 62 −41.6 9.94 12.10 9.82 Train – 0.45 1 4 50 0.15 543 302 78 −50.0 8.55 10.73 9.24 Train – 0.35 1 4 30 0.15 300 232 59 −4.0 2.78 2.72 3.88 Train – 0.35 1 4 30 0.15 290 216 51 −52.5 8.63 8.26 8.25 Train – 0.35 1 4 30 0.8 295 223 56 −25.3 6.40 5.33 5.83 Train – 0.65 1 4 30 0.15 415 326 51 −46.0 11.23 10.83 10.61 892 Journal of Intelligent Manufacturing (2021) 32:877–894 1 3 Data set Input variables Thermomechanical load α′-martensite content Coating f K rβγβfpc FpFcFfT ξmξc,p ξc,np Train – 0.85 1 4 30 0.15 477 398 48 −46.0 12.38 12.29 12.09 Train – 0.45 1 4 30 0.15 340 261 54 −48.8 9.77 9.42 9.29 Train – 0.15 1 4 0 0.15 134 106 35 −62.6 2.47 1.49 2.95 Train – 0.45 1 4 0 0.15 245 239 46 −51.1 6.72 8.96 6.67 Test TiN 0.15 1 3 20 – 151 122 40 −34.4 2.68 1.72 2.19 Test – 0.35 0.5 60 – – 289 254 62 1.4 3.38 2.34 3.65 Test – 0.65 1 4 30 0.8 438 349 57 −12.0 6.46 6.14 7.34 Test – 0.35 1 4 50 0.274 638 376 76 −45.3 10.26 11.79 9.71 Nomenclature: feed rate f in mm/rev, cutting edge radius rβ in μm, formfactor K of the cutting edge, feed rate during precooling fpc in mm/rev, passive force Fp in N, cutting force Fc in N, Feed force Ff in N, Temperature T in °C, measured α′-martensite content ξm in vol%, α′-martensite content calculated with parametric model ξc,p in vol%, α′-martensite content calculated with non-parametric model ξc,np in vol% ANN 12345678910 Epoch 29 111 48 33 61 107 191 85 186 37 Function hidden layer exp tanh tanh tanh tanh exp exp exp log tanh Function output layer tanh log id id id exp id id exp id Weights hidden layer wi1,h1 −0.19 7.13 −0.75 0.45 0.70 1.21 0.31 0.00 −1.32 −0.32 wi1,h2 −6.97 −7.16 3.02 −0.66 −1.73 −10.65 −3.63 1.03 1.48 −2.94 wi1,h3 3.28 −10.18 −1.01 0.20 1.06 2.54 2.07 −0.40 −1.97 0.82 wi1,h4 −0.28 6.23 0.61 −0.55 0.26 0.92 −0.41 0.20 1.76 −0.48 wi2,h1 1.04 −2.38 0.67 0.46 −2.16 −1.30 −1.33 −1.20 −8.87 0.55 wi2,h2 0.32 0.89 −0.71 −0.14 0.70 0.78 0.08 0.53 4.86 0.07 wi2,h3 −0.41 −4.55 −0.24 0.20 0.65 1.20 −2.39 0.77 −19.37 −0.01 wi2,h4 0.89 −6.33 0.68 0.17 1.92 −3.13 7.44 −0.14 7.08 −0.02 wi3,h1 0.99 0.31 −0.74 −0.09 −7.17 1.21 −3.05 1.39 −5.75 −0.73 wi3,h2 0.54 −0.38 0.25 1.38 3.33 −0.16 1.79 −0.45 −9.22 1.01 wi3,h3 1.08 0.32 0.44 −0.30 −0.26 3.98 −0.37 0.17 2.09 −0.58 wi3,h4 1.19 5.50 −1.60 −3.34 2.75 −1.12 2.31 2.37 −11.77 0.42 Weights output layer wh1,o1 −0.25 −14.04 0.33 0.78 −0.99 −0.95 3.94 −1.14 21.18 1.59 wh2,o1 0.03 9.92 0.77 −0.76 −1.07 2.33 1.92 1.00 −1.42 −1.00 wh3,o1 2.10 4.73 1.16 −0.34 0.52 −1.97 0.00 3.74 −1.93 0.26 wh4,o1 −0.55 −0.75 1.23 1.24 −1.24 −0.56 −0.70 1.93 −28.89 −1.34 Bias hidden layer bh1 −0.43 0.20 0.39 −1.49 −0.42 −4.04 2.05 1.55 −17.71 −0.14 bh2 −0.46 0.77 0.50 0.12 −0.15 −0.36 −0.49 −1.01 1.94 0.09 bh3 −0.10 −4.31 −0.24 0.55 0.48 −0.14 −0.35 0.79 0.41 −0.10 bh4 0.26 0.61 −0.11 0.87 0.78 1.48 3.64 −0.36 −3.79 −0.06 Bias output layer bo1 −1.01 −1.69 0.01 0.21 0.06 0.07 −5.21 −4.40 0.39 0.35 Nomenclature: exponential function (exp), hyperbolic tangent (tanh), 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